# I want to learn non tonal theory?



## Manok

I have a project that I think it would be best suited not to be tonal but I don't know anything other than 12 tone theory as far as modern music theory goes, can anyone help me out?


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## Mahlerian

There is no real comprehensive study, but there are books out there that deal specifically with post-tonal techniques such as those used by Debussy, Stravinsky, Bartok, Schoenberg, and others. The problem is that none of this has come close to being systematized, and I'm not sure that we have a real working theory of how post-tonal music functions yet.


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## millionrainbows

Manok said:


> I have a project that I think it would be best suited not to be tonal but I don't know anything other than 12 tone theory as far as modern music theory goes, can anyone help me out?


The music of Debussy, Stravinsky, Bartok, early Schoenberg, and others, are varieties of tonality, and show how tonality can be a matter of degree, and not an absolute term. Thus, *tonality* *is an inclusive term*, general, and does not have to describe music specifically, since the term is by nature general. If one must have specifics, then we can say that all tonal music has reference to a center, or centers, regardless of how tenuous or fleeting.

If you want your project to be "not tonal," then you must use set theory, or ordered rows to achieve this, since *"not tonal" or* *"atonal" are terms which are exclusive*: they refer to any music in which a reference to a tonal center (or centers) is not used in its construction. Also, atonal music does not use tonal devices, such as scales.


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## Mahlerian

millionrainbows said:


> If you want your project to be "not tonal," then you must use set theory, or ordered rows to achieve this, since *"not tonal" or* *"atonal" are terms which are exclusive*: they refer to any music in which a reference to a tonal center (or centers) is not used in its construction. Also, atonal music does not use tonal devices, such as scales.


There's no such thing as music that doesn't use scales. The chromatic scale, microtonal collections, modes of limited transposition, all of these are scales.

Also, the majority, if not all, of the music usually called atonal has very clear tonal centers.

Post-tonal as a general term means post-common practice, and this is the accepted definition. It's unhelpful for you to jump in and start confusing someone who's trying to learn more.


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## EdwardBast

Mahlerian said:


> *There's no such thing as music that doesn't use scales. The chromatic scale*, microtonal collections, modes of limited transposition, all of these are scales.
> 
> Also, the majority, if not all, of the music usually called atonal has very clear tonal centers.
> 
> Post-tonal as a general term means post-common practice, and this is the accepted definition. It's unhelpful for you to jump in and start confusing someone who's trying to learn more.


The "chromatic scale," being an undifferentiated collection of all pitch classes, is not a scale in any meaningful sense, and statements like: "twelve tone music is like other music in that it too uses a scale, the chromatic scale," is just empty nonsense and obfuscation.


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## Mahlerian

EdwardBast said:


> The "chromatic scale," being an undifferentiated collection of all pitch classes, is not a scale in any meaningful sense, and statements like: "twelve tone music is like other music in that it too uses a scale, the chromatic scale," is just empty nonsense and obfuscation.


It's not all possible pitch classes, it's _a particular set of pitch classes_, just like any other scale. There are infinitely many pitches it does not include.

I'm not trying to obfuscate, I'm trying to clarify. If you can come up with a definition of scale that doesn't include the chromatic scale, I'll be waiting.


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## SeptimalTritone

Edward, what privileges the completely equally spaced whole tone scale, or the transpositionally invariant octatonic scale, over the 12 tone chromatic scale? And who says that there cannot be more than 12 pitch classes regularly used, as in Harry Partch or Ben Johnston, or certain 19TET 16th century music, or Ives's 24TET piano duets, or a non-equally spaced 12 tone scale, as in La Monte Young, or just overtone chords as in Stockhausen or Georg Haas, or various other microtonal scales like Javanese Gamelan?

What in the world makes the 12 tone chromatic scale non-specific, as if it doesn't have any particularities on its own? And why cannot there cannot be scales with more notes, or other notes? What makes the 12 tone chromatic scale a collection of "all" pitch classes, or all relative pitch classes? Why cannot there be more pitches, or other pitches?


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## Dim7

Mahlerian said:


> There's no such thing as music that doesn't use scales.


Well, to be fair some microtonal music that does not deliberately restrict itself to any partiular set of notes could be said to "not use scales".


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## Mahlerian

Dim7 said:


> Well, to be fair some microtonal music that does not deliberately restrict itself to any partiular set of notes could be said to "not use scales".


Yeah, and things like music for non-pitched percussion and such couldn't be meaningfully tied to a scale, like some electroacoustic music.


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## millionrainbows

Mahlerian said:


> There's no such thing as music that doesn't use scales.


A tone row is not a scale. A scale is, by definition, an "index" of unordered notes.



> The chromatic scale, microtonal collections, modes of limited transposition, all of these are scales.
> Also, the majority, if not all, of the music usually called atonal has very clear tonal centers.


Whatever. If you hear tonal centers in atonal music, good for you.



> Post-tonal as a general term means post-common practice, and this is the accepted definition.


No, post-tonal is not a chronological term. It refers to new practices, such as set theory, interval projection, interval vectors, etc.



> It's unhelpful for you to jump in and start confusing someone who's trying to learn more.


Irrelevant ad-hominem statement.


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## millionrainbows

From WIK: In music theory, a *scale* is any set of musical notes ordered by fundamental frequency or pitch. A scale ordered by increasing pitch is an ascending scale, and a scale ordered by decreasing pitch is a descending scale.

Due to the principle of octave equivalence, scales are generally considered to span a single octave, with higher or lower octaves simply repeating the pattern. A musical scale represents a division of the octave space into a certain number of scale steps, a scale step being the recognizable distance (or interval) between two successive notes of the scale. [SUP][2][/SUP] However, there is no need for scale steps to be equal within any scale and, particularly as demonstrated by microtonal music, there is no limit to how many notes can be injected within any given musical interval.

A specific scale is defined by its characteristic interval pattern and by a special note, known as its first degree (or tonic). The tonic of a scale is the note selected as the beginning of the octave, and therefore as the beginning of the adopted interval pattern. Typically, the name of the scale specifies both its tonic and its interval pattern. For example, C major indicates a major scale with a C tonic. (end quote)

So, as you can see from that last passage, a scale is an inherently tonal device, as its first degree implies a tonic.


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## millionrainbows

EdwardBast said:


> The "chromatic scale," being an undifferentiated collection of all pitch classes, is not a scale in any meaningful sense, and statements like: "twelve tone music is like other music in that it too uses a scale, the chromatic scale," is just empty nonsense and obfuscation.


That depends on context. If a drone bass note is placed under a 12-note collection, it begins to sound tonal, since every note is referenced to that bass drone. This is easily heard in later Miles Davis (Cellar Door Sessions, etc.) where the drummer and bass player establish a drone "groove" and whatever the soloists play on top of it, no matter how far "out," sounds rooted.

I agree with what you said::_ "...Statements like: "twelve tone music is like other music in that it too uses a scale, the chromatic scale," is just empty nonsense and obfuscation." _since tone-rows differ from scales in significant ways.


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## millionrainbows

Mahlerian said:


> Yeah, and things like music for non-pitched percussion and such couldn't be meaningfully tied to a scale, like some electroacoustic music.


True, but even in the context of the 12-note scale of specific pitches, music can be composed which does not use scales.



> If you can come up with a definition of scale that doesn't include the chromatic scale, I'll be waiting.


This is putting the cart before the horse. A collection of notes must first meet certain criteria in order to be called a scale. A chromatic collection could meet these criteria of being a scale if:

It is listed with a starting note.

It covers an octave.

It divides the octave into a certain number of steps, namely, 12.

It is an "index" of unordered notes which one can select from at random, to create melodies and such.

The "chromatic collection" could also be a* set,* which can be ordered. In this case, it is not a scale.


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## Mahlerian

millionrainbows said:


> A tone row is not a scale. A scale is, by definition, an "index" of unordered notes.


Sure. But it's not an either/or proposition. A piece can use tone rows and the diatonic scale, tone rows and the whole tone scale, or tone rows and the chromatic scale, as is most common. There's no contradiction between the two, and although you keep asserting that there is, that's the whole extent of your argument, just "I said so."



> Whatever. If you hear tonal centers in atonal music, good for you.


I've never heard any atonal music, so how could I hear tonal centers in it? Tonal centers in the extremely generalized sense you keep referring to are simply a product of any kind of relationship between notes. Why should it be surprising that something that is tightly organized in regards to pitch, as you yourself would acknowledge, produces audible pitch relationships?



> No, post-tonal is not a chronological term. It refers to new practices, such as set theory, interval projection, interval vectors, etc.


Set theory is not a compositional practice, but a tool which was developed in order to analyze music that responded poorly to traditional methods. I didn't say that post-tonal was chronological, merely that it describes any post-common practice music, from Debussy on, where functional tonality is either rejected or ameliorated to the point of meaninglessness. Naturally, there was some common practice music written into the 20th century, but the vast majority was not.



> Irrelevant ad-hominem statement.


This is a misunderstanding of what an ad-hominem statement is.


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## Barbebleu

Reading through this thread, which I actually find both interesting and fascinating, I am reminded of a quote attributed to Benjamin Franklin, which I have slightly altered. "Three people can discuss music theory, if two of them are dead!"

Carry on chaps, I'm keen to see who caves first.


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## Mahlerian

Barbebleu said:


> Reading through this thread, which I actually find both interesting and fascinating, I am reminded of a quote attributed to Benjamin Franklin, which I have slightly altered. "Three people can discuss music theory, if two of them are dead!"
> 
> Carry on chaps, I'm keen to see who caves first.


In my view, the idea that tonality is universal is based in either:

1 - A belief that western music, and specifically the common practice era, is the most natural of all musics, which others aspire to be

2 - A definition of tonality that covers everything except certain specific music in the 20th century, which definition, if examined, is inherently contradictory and nonsensical (because it requires music that's not tonal to also be tonal, unless you add in ad hoc arguments like Millionrainbows' stuff about ordered sets)

The idea that Schoenberg came along and wrote the first music that was ever in the history of humanity not tonal is historically short-sighted (tonality was, after all, only 300 or so years old) and Eurocentric (no other group of people ever developed tonality).

The third option, of course, is the very common dislike of Schoenberg and the belief, based simply in that dislike, that there's something inherently wrong (sometimes voiced as a claim that it's unnatural) with the music (and some or all of the rest of modernist music) because the person dislikes it.


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## Reichstag aus LICHT

Barbebleu said:


> I am reminded of a quote attributed to Benjamin Franklin, which I have slightly altered. "Three people can discuss music theory, if two of them are dead!"


Spookily, that quote - or, rather, its original - featured in a question on "The Chase" earlier today.

(The Chase = British TV quiz/game show on ITV)


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## Barbebleu

Mahlerian said:


> In my view, the idea that tonality is universal is based in either:
> 
> 1 - A belief that western music, and specifically the common practice era, is the most natural of all musics, which others aspire to be
> 
> 2 - A definition of tonality that covers everything except certain specific music in the 20th century, which definition, if examined, is inherently contradictory and nonsensical (because it requires music that's not tonal to also be tonal, unless you add in ad hoc arguments like Millionrainbows' stuff about ordered sets)
> 
> The idea that Schoenberg came along and wrote the first music that was ever in the history of humanity not tonal is historically short-sighted (tonality was, after all, only 300 or so years old) and Eurocentric (no other group of people ever developed tonality).
> 
> The third option, of course, is the very common dislike of Schoenberg and the belief, based simply in that dislike, that there's something inherently wrong (sometimes voiced as a claim that it's unnatural) with the music (and some or all of the rest of modernist music) because the person dislikes it.


I concur Mahlerian. I don't subscribe to any of those thoughts. A lot of Indian classical, Japanese classical and other Middle and Far Eastern musical forms don't depend on western practice, far from it. In another thread I may have inadvertently suggested that I actively dislike Schoenberg. Not so. There is a lot of his music that appeals to me as does the music of Haydn. But there are aspects of his work that doesn't resonate with me just as Haydns choral output, e.g. The Creation doesn't either. I fear the last word on the subject of "tonality" has still to be said!


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## Barbebleu

Reichstag aus LICHT said:


> Spookily, that quote - or, rather, its original - featured in a question on "The Chase" earlier today.
> 
> (The Chase = British TV quiz/game show on ITV)


The original quote is one I have used on numerous occasions when people have told me things that they probably shouldn't have!


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## Mahlerian

Barbebleu said:


> I concur Mahlerian. I don't subscribe to any of those thoughts. A lot of Indian classical, Japanese classical and other Far Eastern musical forms don't depend on western practice, far from it. In another thread I may have inadvertently suggested that I actively dislike Schoenberg. Not so. There is a lot of his music that appeals to me as does the music of Haydn. But there are aspects of his work that doesn't resonate with me just as Haydns choral output, e.g. The Creation doesn't either. I fear the last word on the subject of "tonality" has still to be said!


No worries, I didn't actually have any idea what your opinion of Schoenberg was. Millionrainbows says he likes his music, but his ideas about tonality and harmony seem very strange and contradictory to me (and they also aren't in line with any academic view I've encountered).

I don't listen to a lot of non-Western music, but I've looked into a good number of traditions, including gamelan and gagaku, and have some cursory familiarity with Indian and Chinese music. One must learn to cast aside preconceptions when encountering unfamiliar culture.

In my experience, a lot of people who have strong negative opinions of Schoenberg couldn't recognize any of the melodies he wrote and yet they still have the idea that he was a poor melodist. They don't know any of his later pieces well yet they believe fervently that they're deficient in some way. It's frustrating to see so much ignorance and hostility about one of the greatest composers of the era.


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## Woodduck

Mahlerian said:


> In my view, the idea that tonality is universal is based in either:
> 
> 1 - A belief that western music, and specifically the common practice era, is the most natural of all musics, which others aspire to be
> 
> 2 - A definition of tonality that covers everything except certain specific music in the 20th century, which definition, if examined, is inherently contradictory and nonsensical (because it requires music that's not tonal to also be tonal, unless you add in ad hoc arguments like Millionrainbows' stuff about ordered sets)
> 
> The idea that Schoenberg came along and wrote the first music that was ever in the history of humanity not tonal is historically short-sighted (tonality was, after all, only 300 or so years old) and Eurocentric (no other group of people ever developed tonality).
> 
> The third option, of course, is the very common dislike of Schoenberg and the belief, based simply in that dislike, that there's something inherently wrong (sometimes voiced as a claim that it's unnatural) with the music (and some or all of the rest of modernist music) because the person dislikes it.


I thought this subject was pretty well exhausted and had devolved into a permanent standoff, but I have to say how surprised I am by this post.

When people (including people in various sciences that study music as a phenomenon) say that tonality seems to be a "universal" phenomenon, they mean simply that certain kinds of musical systems - systems in which the notes of a certain scale or set are organized so as to relate in specific ways around specific tones felt as points of gravitation and resolution within the system - have arisen in the majority of mankind's musics around the world. Such a common human phenomenon is what is called a "statistical universal," as opposed to an "absolute universal," and does not imply that all music must be tonal, merely that there is a strong, widespread, innate, cross-cultural human tendency to feel and structure music in this way. The scientific approach is to try to account for a phenomenon of such enormous prevalence and significance in terms of human nature and culture.

Your explanations of the use of the term "universal" miss the point.

1 - Belief in the (statistical) universality of tonality is _not_ based in any belief that common practice Western music is the most natural music or that all music aspires to be that kind of music. I have never heard anyone express either view, although some may hold them.

2 - I know of no definition of tonality which must cover all music except certain specific musics of the 20th century. The definition I give above (which is not my invention, but the common definition used by ethnomusicogists, evolutionary biologists, neurologists, and others who study music as a human phenomenon) does appear to apply to most of the world's music. There are probably exceptions.

The actual (correct) idea people have about Schoenberg is that he is the first composer who, appearing in the context of a musical culture rooted in a tonal tradition, set out to eliminate systemic tonality as an underlying, assumed basis for musical structure and perception. Although it's true that the sensation of tonal centricity is attenuated or suspended in some music written before Schoenberg's innovation, it is rarely absent for long and, more importantly, the presumption of its existence as a norm against which the music in question is to be heard is rarely if ever called into question. This is as true for the floating triads (with their inherent tonal suggestiveness) of Debussy as for the tonally ambiguous chromatic excursions of Wagner (which can only be ambiguous because they are fundamentally tonal). It's no secret that Schoenberg contrived specific procedures and proscribed certain constructions in order to prevent a sense or expectation of tonal centricity from arising in the listener. This is deliberately non-tonal composition, and plenty of listeners recognize it when they hear it.

It's true that some listeners feel that such music is "unnatural," and that's because they share the statistically universal instinct which tells them that tonality is a natural phenomenon - which it is - and therefore they find that music which uses the familiar materials of tonal music - the notes of the chromatic scale, in this case - but frustrates their expectations by not organizing these notes tonally, sounds "wrong" to them. This doesn't mean that such music is "wrong" in an absolute sense, any more than tonality is an "absolute universal" to which all music must conform.

You cannot rationalize away what people perceive and what they feel by obfuscating the real, empirically verifiable phenomena which give rise to their perceptions and feelings. Tonal centricity is not just another way of constructing music, much less is it just the singular way Western music was constructed for 300 years. It is at root a cognitive phenomenon of enormous significance, overwhelming prevalence, and great power in the music of mankind, rooted in human nature (as well as the perception of tone, but I'll leave that to millionrainbows) and employed because it satisfies felt human needs for intellectual and emotional coherence and satisfaction. A composer's departure from it should be noted as the departure from statistical universality which it plainly is, regardless of how we judge the product.


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## millionrainbows

Mahlerian said:


> Sure. But it's not an either/or proposition. A piece can use tone rows and the diatonic scale, tone rows and the whole tone scale, or tone rows and the chromatic scale, as is most common. There's no contradiction between the two, and although you keep asserting that there is, that's the whole extent of your argument, just "I said so."


But tonality is more than just scales; functional harmony is directed motion towards specific harmonic goals. It does this by establishing different tonal harmonies as different locations in musical space, and channels the direction of harmonic motion between these locations.

If an atonal piece such as Schoenberg's seems to be headed for a goal such as A to Eb, and even sounds to resolve, it is still atonal because its goals are not harmonically derived in terms of consonance/dissonance/resolution, but are based on row considerations.



> I've never heard any atonal music, so how could I hear tonal centers in it?


Schoenberg's Klavierstucke Op. 33a is atonal; compare it to a Bach prelude, such as No.1 in C major from WTC. Although both use motives, and invert them, and retrograde them, the Bach is clearly tonal, and the Schoenberg is not. The Bach prelude is full of voice-leading and harmonies characteristic of all tonal music, but the Schoenberg piece has none of the harmonic or voice-leading implications that they might have in a tonal composition. Woodduck has agreed with me on this point in earlier threads.



> Tonal centers in the extremely generalized sense you keep referring to are simply a product of any kind of relationship between notes. Why should it be surprising that something that is tightly organized in regards to pitch, as you yourself would acknowledge, produces audible pitch relationships?


Like I said, tonality is more than pitch-centers; its whole syntax suggests tonality, over time.



> Set theory is not a compositional practice, but a tool which was developed in order to analyze music that responded poorly to traditional methods.


That's somewhat of a tricky non-statement, since there is no common language shared by non-tonal music as there is in tonality, which has a shared language which developed over years.



> I didn't say that post-tonal was chronological, merely that it describes any post-common practice music, from Debussy on, where functional tonality is either rejected or ameliorated to the point of meaninglessness.


I don't think tonality dissolved all at once, as you imply.


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## SeptimalTritone

"When people (including people in various sciences that study music as a phenomenon) say that tonality seems to be a "universal" phenomenon, they mean simply that certain kinds of musical systems - systems in which the notes of a certain scale or set are organized so as to relate in specific ways around specific tones felt as points of gravitation and resolution within the system - have arisen in the majority of mankind's musics around the world."

Good. Schoenberg does this, and not only that, the feeling of gravitation and resolution is stronger than Debussy.

The 12 tones in Schoenberg, and a restricted set of inversions and retrogrades, definitely establish one pitch as the strongest, and other pitches as secondary, or tertiary, in different sorts of ways depending on the piece.

Any description of a Schoenberg piece, even a 12-tone one, that goes in detail through the decisions made for each measure and section, would tell you this. There are mountains of resources. 

I would say that the feeling of centricity and gravitation is also felt, even stronger than the late romantics, and especially stronger than the impressionists. But you'll just dismiss that by arguing for "statistical universality", which is merely a way of appealing to populism: if most people don't hear tonality in Schoenberg, it must not exist. I then wonder whether Bach and Mozart are relaxing, since most people (not on TC, but most people who listen to classical on a semi-regular basis) find that the case. Then, statistically universally, Bach and Mozart are merely relaxing, not dramatic and full of dissonant contrapuntal tension.

I also say right back to you: "You cannot rationalize away what people perceive and what they feel by obfuscating the real, empirically verifiable phenomena which give rise to their perceptions and feelings." You still need to explain why authors who have gone through Schoenberg measure-by-measure (the empirically verifiable part), and conclude that there's tone centricity that provides for the feeling, and listeners who follow the score and author explanations agree with the feeling provided, it's usually simple and clear the tensional contour of a piece or phrase. Are they conveniently non-existent?


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## millionrainbows

SeptimalTritone said:


> Good. Schoenberg does this, and not only that, the feeling of gravitation and resolution is stronger than Debussy.
> 
> The 12 tones in Schoenberg, and a restricted set of inversions and retrogrades, definitely establish one pitch as the strongest, and other pitches as secondary, or tertiary,* in different sorts of ways* depending on the piece.


I don't hear it that way at all, and Debussy is definitely 'more tonal' than late Schoenberg. The phrase "in different kinds of ways" is revealing. Tonality has a pervasive sense of centricity, harmonic goals, and voice-leading to accomplish its goals; Schoenberg had to invent new ones in each composition. This doesn't make them 'tonal' because a cadential device leads to a certain note.



> Any description of a Schoenberg piece, even a 12-tone one, that goes in detail through the decisions made for each measure and section, would tell you this. There are mountains of resources.


Still, the goal of 12-tone music is not to establish tonality. Whatever 'one pitch' that Schoenberg leads us to, by way of voice-leading, rhythm, or other means, is arbitrary, and is based on row considerations or other consideration, but not by tonality.



> I would say that the feeling of centricity and gravitation is also felt, even stronger than the late romantics, and especially stronger than the impressionists.


That sounds outlandish, and flies in the face of the structure of the 12-tone system, as well as the established practices of tonality. If you are basing this argument on subjective perception, then there is no answer, and I'll not argue that point. But there are, as Woodduck and I have pointed out, good empirical reasons which can be used to further the case that tonality is tonality for specific reasons, and atonal music is not.



> But you'll just dismiss that by arguing for "statistical universality", which is merely a way of appealing to populism: if most people don't hear tonality in Schoenberg, it must not exist. I then wonder whether Bach and Mozart are relaxing, since most people (not on TC, but most people who listen to classical on a semi-regular basis) find that the case. Then, statistically universally, Bach and Mozart are merely relaxing, not dramatic and full of dissonant contrapuntal tension.


No, I'll not go there.



> I also say right back to you: "You cannot rationalize away what people perceive and what they feel by obfuscating the real, empirically verifiable phenomena which give rise to their perceptions and feelings." You still need to explain why authors who have gone through Schoenberg measure-by-measure (the empirically verifiable part), and conclude that there's tone centricity that provides for the feeling, and listeners who follow the score and author explanations agree with the feeling provided, it's usually simple and clear the tensional contour of a piece or phrase. Are they conveniently non-existent?


No; not if, in those cases, Schoenberg invented them, and it was his intent to do that; but just because he, in one case, created an A-Eb relationship which mimicked the I-V of tonality, does not mean that the music is 'tonal.'

And this is said in light of the kinder, gentler Schoenberg, who wished to give the listener some slack; the harsher Schoenberg of The String Trio gave us no such quarter.


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## Woodduck

SeptimalTritone said:


> "When people (including people in various sciences that study music as a phenomenon) say that tonality seems to be a "universal" phenomenon, they mean simply that certain kinds of musical systems - systems in which the notes of a certain scale or set are organized so as to relate in specific ways around specific tones felt as points of gravitation and resolution within the system - have arisen in the majority of mankind's musics around the world."
> 
> Good. Schoenberg does this, and not only that, the feeling of gravitation and resolution is stronger than Debussy.
> 
> The 12 tones in Schoenberg, and a restricted set of inversions and retrogrades, definitely establish one pitch as the strongest, and other pitches as secondary, or tertiary, in different sorts of ways depending on the piece.
> 
> Any description of a Schoenberg piece, even a 12-tone one, that goes in detail through the decisions made for each measure and section, would tell you this. There are mountains of resources.
> 
> I would say that the feeling of centricity and gravitation is also felt, even stronger than the late romantics, and especially stronger than the impressionists. But you'll just dismiss that by arguing for "statistical universality", which is merely a way of appealing to populism: if most people don't hear tonality in Schoenberg, it must not exist. I then wonder whether Bach and Mozart are relaxing, since most people (not on TC, but most people who listen to classical on a semi-regular basis) find that the case. Then, statistically universally, Bach and Mozart are merely relaxing, not dramatic and full of dissonant contrapuntal tension.
> 
> I also say right back to you: "You cannot rationalize away what people perceive and what they feel by obfuscating the real, empirically verifiable phenomena which give rise to their perceptions and feelings." You still need to explain why authors who have gone through Schoenberg measure-by-measure (the empirically verifiable part), and conclude that there's tone centricity that provides for the feeling, and listeners who follow the score and author explanations agree with the feeling provided, it's usually simple and clear the tensional contour of a piece or phrase. Are they conveniently non-existent?


If music is tonal to a significant degree, it isn't necessary to "go through it measure by measure" to detect the presence of a tonic or a systematic hierarchy of melodic or harmonic tones which relate to that tonic. Music is not, fundamentally, written to be analyzed, but to be heard and felt. I think it says something that the people who want to argue that music generally considered non-tonal is actually tonal are people who obviously spend time doing such "measure by measure" analyses. Of course, there are people who are quite capable of such analysis who still dare to use the dreaded word "atonal."

That said, if you want us to consider this music tonal,






you are going to have to say what scale (set of pitches or mode) it uses, what note in that scale is the tonic of that scale, and what are the relationships of the various notes of that scale to the tonic and to each other, as they are employed within the tonal system you are claiming the piece represents. Or, from the perspective of the listener (which is the only perspective that really matters), what is the system of tonal relations which creates certain defined expectations in the listener, expectations which determine how the work is heard and understood?

It's quite possible for a composer to choose a set of tones and give to them different degrees of prominence, and even to use them repeatedly in specific ways, without creating a sense of systematic tonality and its attendant tonal expectations. Tonality is not an ad hoc phenomenon, and it isn't a thing that can have meaning or value solely on paper. Tonal systems differ, but unless a composer's chosen system of relationships is established in a listener's mind as a norm against which melodic or harmonic movement is measured, it is not meaningful to speak of the presence of tonality. There may be a sense of coherence in non-tonal music, but tonality is not synonymous with coherence; it is a particular means of achieving coherence.

To the matter of "statistical universals": it seems as if you think that your assertions that Schoenberg's music is tonal have some kind of credibility, while the concept of a statistical universal does not. Statistical universals are not "appeals to populism." They are observed phenomena. If it is indeed a correct observation that virtually all known cultures in the world have had music based on defined scales or modes with identifiable tonal centers and habitually employed relationships of the other notes of those scales to those tonal centers and to each other, and that these tonal systems have functioned as ingrained sets of expectations which make music comprehensible and meaningful to the listeners of those cultures, it is not an appeal to populism to point that out. Neither is it an appeal to populism to point out that people who think that tonality in this sense is present in Schoenberg's _Piano Suite_ need to make their case.

Is it an appeal to populism to suggest that the _Piano Suite_ doesn't make that case very well for itself?


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## SeptimalTritone

What is the tonic of a whole tone scale in Debussy's Violes? Or an octatonic scale? You do realize these are equally spaced in the first case, and transpositionally invariant at the minor third in the second case... what is the tonic of these scales? They are invariant under transposition, precisely to avoid any inherent suggestion of tonic through merely the scale. Expectations have to be created in their own ways if one uses scales with transpositional invariance, whether it be whole tonic, octatonic, or chromatic.

What is the tonic of a Javanese Gamelan scale? In particular, play the audio on wikipedia here: https://en.wikipedia.org/wiki/Slendro
Where's the gravitation towards C? How does the scale's notes make C the tonic? Wheres the leading, the gravitation, towards C? If the scale was played with a different beginning and ending, say D (+) or F, would you still realize that C is the tonic?

The suite op 25, I've written many posts about this piece. I have answered that question about its tonic _many_ times. Once again, the tonic note (not the triadic tonic note, but still the tonic note) is G. The secondary note is C #, which functions as a dominant analogue. Either E or B flat are in cadential chords, they are analogues to thirds. The Vienese trichord 016 is always present twice in every tone row variant. The first of these accounts for the G-C# dyad. The second of these is used to voice lead into the G-C# dyad.

The cadential endings at the many sections of Schoenberg op 25 are very strong. In Debussy's voiles, only rhythm and stepwise pattern gives the C-E dyad as the ending, and even then, it emerges out of a C-E-F# trichord: no heirarchy is resolved, no gravitation happens. The F # in the bass's and alto's strong beat disappears to end the piece. On the other hand, Schoenberg op 25 cadences through heirarchy through that path of Vienese trichords.

I don't understand this strange distrust of analysis. People make measure by measure analyses and reductions of Chopin preludes all the time to clarify the tonality established, and how the tonality is established. I've learned so much from detailed analysis of Haydn, Mozart, and Beethoven. Why the distrust of Schoenberg analysis?


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## isorhythm

SeptimalTritone said:


> The 12 tones in Schoenberg, and a restricted set of inversions and retrogrades, definitely establish one pitch as the strongest, and other pitches as secondary, or tertiary, in different sorts of ways depending on the piece.
> 
> Any description of a Schoenberg piece, even a 12-tone one, that goes in detail through the decisions made for each measure and section, would tell you this. There are mountains of resources.


I would actually be satisfied if someone could point me to just one such resource. Anyone?


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## Mahlerian

isorhythm said:


> I would actually be satisfied if someone could point me to just one such resource. Anyone?


http://symposium.music.org/index.ph...imary-musical-language-of-tonality&Itemid=124

"The specific twelve-tone row and the _method_ of its employment serve to assure that _E_-flat and _B_-flat are significant absolute tonal reference points in the [Wind Quintet]. "

There ya go. It's _really_ easy to find similar papers.


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## Woodduck

SeptimalTritone said:


> *What is the tonic of a whole tone scale in Debussy's Violes? *Or an octatonic scale? You do realize these are equally spaced in the first case, and transpositionally invariant at the minor third in the second case... what is the tonic of these scales? They are invariant under transposition, *precisely to avoid any inherent suggestion of tonic *through merely the scale. Expectations have to be created in their own ways if one uses scales with transpositional invariance, whether it be whole tonic, octatonic, or chromatic.
> 
> What is the tonic of a Javanese Gamelan scale? In particular, play the audio on wikipedia here: https://en.wikipedia.org/wiki/Slendro
> Where's the gravitation towards C? How does the scale's notes make C the tonic? Wheres the leading, the gravitation, towards C? If the scale was played with a different beginning and ending, say D (+) or F, would you still realize that C is the tonic?
> 
> *The suite op 25*, I've written many posts about this piece. I have answered that question about its tonic _many_ times. Once again, *the tonic note (not the triadic tonic note, but still the tonic note) is G.* The secondary note is C #, which functions as *a dominant analogue.* Either E or B flat are in cadential chords, they are *analogues to thirds.* The Vienese trichord 016 is always present twice in every tone row variant. The first of these accounts for the G-C# dyad. The second of these is used to voice lead into the G-C# dyad.
> 
> The cadential endings at the many sections of Schoenberg op 25 are very strong. In Debussy's voiles, only rhythm and stepwise pattern gives the C-E dyad as the ending, and even then, it emerges out of a C-E-F# trichord: no heirarchy is resolved, no gravitation happens. The F # in the bass's and alto's strong beat disappears to end the piece. On the other hand, *Schoenberg op 25 cadences through heirarchy through that path of Vienese trichords.*
> 
> *I don't understand this strange distrust of analysis.* People make measure by measure analyses and reductions of Chopin preludes all the time to clarify the tonality established, and how the tonality is established. I've learned so much from detailed analysis of Haydn, Mozart, and Beethoven. Why the distrust of Schoenberg analysis?


I don't distrust analysis. I simply contend that the map is not the territory, and that it's the territory that matters, with or without a map. Score analysis can be used to demonstrate tonality only if the idiom in which a piece is composed is already accepted as tonal. Based on a conception of tonality, one may then identify, in the score, the manifestations of, or references to, the relevant tonal system, and the particular ways in which they are used.

Schoenberg wrote clearly of his intention of thwarting tonal expectations, and devoted much mental energy to finding procedures by which to accomplish that, both in the musical moment and in larger structural terms. It's true that he didn't adhere consistently to his own severe initial strictures. But I hear few compromises with tonality in his _Piano Suite_, and I don't see anything in your descriptions of his "analogues" to tonality which demonstrates that the music is intended to invoke tonal expectations. What makes G the "tonic"? What makes C# "analogous" to the dominant? Is any interval less likely to create a sense of tonal relatedness than the one between G and C# - the tritone? "Tones "analogous" to thirds are _not_ thirds, they don't sound or feel like thirds, they have not the same physiological effect or affective value as thirds, and they do not function as thirds do in a tonal idiom in which thirds function in specific ways. Tones or sequences recurring at cadences do not necessarily have tonal meaning solely because they are made to recur at cadences. Recurrence is one way in which tonal significance is established, but it need not be a sufficient way. Emphasis, repetition, relative frequency of occurrence - all are properties of tonal music, but they may characterize any sort of music, including music which doesn't even consist of tones, music to which the concept of tonality is simply irrelevant. And in music which does consist of tones, they are not necessarily going to create a perception of tonality. I hear all sorts of relationships of those kinds in the _Piano Suite_. What I don't hear, more than fleetingly here and there, is the employment of an idiom in which a perception of tonality is not purposefully undermined.

If you want to say, with support from your score, that Schoenberg has created a system of relationships _for this particular piece_ which is somehow "analogous" to a tonal system _in certain defined respects_, I won't argue with you. But the important phrases are "for this particular piece" and "in certain definite respects." Whether these particular respects amount to tonality will still be open to question, as will the idea that a composer's personal system of relationships between tones, devised for a particular work, represent a tonal system and make that work a tonal work.

Yes, Debussy occasionally writes harmonies that avoid the suggestion of tonal centers. "Voiles," as an essay in the whole-tone scale, has very little suggestion of tonality. So what? Not even Debussy wrote much music as determined as this to avoid tonal gravity, and I'm sure that's because he perceived the limited expressive possibilities of the whole-tone scale. When he needed to go beyond "impressions" and "atmospheres" and say anything profound and human, he resorted to the language of tonality, with its enormous fund of harmonies spanning the full range of consonance and dissonance, and centuries of ever-more-complex meaning carried in its rich vocabulary and syntax. See _Pelleas et Melisande_.


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## SeptimalTritone

isorhythm said:


> I would actually be satisfied if someone could point me to just one such resource. Anyone?


You can also find a source here. This only talks about the beginning of the gavotte, which is a good start because it's sparser.

[http://www.musictheory21.com/documents/straus-introduction-to-post-pp167-178.pdf_green]
www.musictheory21.com/documents/straus-introduction-to-post-pp167-178.pdf

You may want to, using that knowledge, look at the final cadence of the final movement, the gigue (check imslp). In the last triplet in the fourth to last measure, a Vienese trichord voice leads into a strong bass chord in the third to last measure, the tonic tetrachord 0236 with the G in the lowest bass.


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## isorhythm

Thanks for these, Mahlerian and Septimal. They're interesting, but I remain unconvinced.

First, I'm not sure either analyst is actually arguing as strongly as either of you for the idea that Schoenberg's practice is "tonal" in any sense.

The Wind Quintet analysis depends heavily on identifying some fifth relationships. First, the writer doesn't demonstrate that these relationships are particularly significant in the piece or that they organize it in any important way. He only notes that some phrases start a fifth apart. Second, if the point is that the presence of these phrases starting a fifth apart is important to Schoenberg's practice in general, we have a problem because this is only one piece!

The Op. 25 analyst doesn't really seem to be arguing Schoenberg can be understood tonally at all, unless I'm missing something.

I'm getting the idea from a few posts that any perceptible relationship between pitches is "tonal." By this definition of course all music that uses pitches is "tonal," but such a definition renders the term useless.


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## millionrainbows

SeptimalTritone said:


> What is the tonic of a whole tone scale in Debussy's Violes?


The tonic can be any note, but that's not how Schoenberg or Debussy used the WT scale.

Here's an old post of mine from the "Schoenberg's Op. 26 Wind Quintet" thread.

[The row is (first hexad) Eb-G-A-B-C#-C, which gives an augmented/whole-tone scale feel, with a "resolution" to C at the end, then (second hexad) Bb-D-E-F#-G#-F, which is very similar in its augmented/whole-tone scale structure, which only makes sense: there are only two whole-tone scales in the chromatic collection, each a chromatic half-step away from the other.

I've heard Debussy use the two whole-tone scales in this manner, moving down a half-step to gain entry to the new key area. This is why Schoenberg used a "C" in the first hexad, and the "F" in the second; these are "gateways" into the chromatically adjacent scale area. Chromatic half-step relations like these can also be seen as "V-I" relations, when used as dual-identity "tri-tone substitutions" as explained following.

Another characteristic of whole-tone scales is their use (as in Thelonious Monk's idiosyncratic whole-tone run) as an altered dominant, or V chord. There is a tritone present, which creates a b7/3-3/b7 ambiguity, exploited by jazz players as "tri-tone substitution". The tritone (if viewed as b7-3 rather than I-b5) creates a constant harmonic movement, which is what chromatic jazzers, as well as German expressionists, are after.]

Still, the music under discussion is not tonal; it has allusions to tonality, but that is a special case which must be specified. It can't be off-handedly called 'tonal.'


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## millionrainbows

Mahlerian said:


> http://symposium.music.org/index.ph...imary-musical-language-of-tonality&Itemid=124
> 
> "The specific twelve-tone row and the _method_ of its employment serve to assure that _E_-flat and _B_-flat are significant absolute tonal reference points in the [Wind Quintet]. "
> 
> There ya go. It's _really_ easy to find similar papers.


That still doesn't prove that "12-tone is tonality;" only that Schoenberg's use of it involves relationships _similar_ to tonality. If I inverted some phases from Bach's Prelude 1 from WTC book one, I would have to invert them tonally for it to work. If I simply inverted them as I would an ordered tone row, it would not work, as I explain below.

If one wishes to conclude that these similarities make 12-tone practice an "extension" of tonality, and not a separate language, this reduces the argument to being a mere matter of conservative vs. radical, in order to lend Schoenberg an air of conservative normality. If one wishes to see similarities, one is conservative; if one wishes to see differences, one is being objective, and is spoiling the game of making Schoenberg a non-radical who was really very conservative. This is the agenda.

G-C# is quite a different experience to the ear than G-D. If one wishes to emphasize the similarity, it is only structural and cerebral, not based on harmonic sensation. This makes 12-tone a cerebral language of relationships, just as tonality has relationships,* but with a crucial difference:*

12-tone music does not base its relationships, however similar in structure they may be to tonality, on harmonically perceived sensations or hierarchies.

This is easily demonstrated by the idea of 'inversion,' used as structures in both 12-tone and tonality.

If we invert (spelled clockwise) a C-E-G (C major chord), in tonal inversion, it must conform to the diatonic scale it was derived from, and becomes E-G-C (spelled counter-clockwise).

In serial terms, the inversion is literal, based on interval-distances, not pitch identities, and C-E-G becomes C-Ab-F, a minor chord.

*What Mahlerian and others seem to fail to recognize is that "order" in an ordered 12-tone row is not just a linear progression of order, as in a melodic sense (although it is this when used as motivic material), but the "ordering" of the row "fixes" the intervallic distances between notes.

These fixed-distance intervallic distances become the true significance of the ordered row, unlike a scale, which is a collection of pitch-identity relationships.*

A scale is unordered, so all its member notes have a "pitch identity" which is fixed in relation to the tonic note. That's why, when we tonally invert it, G is still G, and E is still E.

Not so in an ordered row; the intervallic distances are fixed quantities, not ratios to a tonic, so C-E (clockwise, a major third up) must become C-Ab (counter-clockwise, a major third down).


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## millionrainbows

Mahlerian said:


> In my view, the idea that tonality is universal is based in either:
> 
> 1 - A belief that western music, and specifically the common practice era, is the most natural of all musics, which others aspire to be
> 
> 2 - A definition of tonality that covers everything except certain specific music in the 20th century, which definition, if examined, is inherently contradictory and nonsensical (because it requires music that's not tonal to also be tonal, unless you add in ad hoc arguments like Millionrainbows' stuff about ordered sets)
> 
> The third option, of course, is the very common dislike of Schoenberg and the belief, based simply in that dislike, that there's something inherently wrong (sometimes voiced as a claim that it's unnatural) with the music (and some or all of the rest of modernist music) because the person dislikes it.


In my view, the idea that tonality is universal is based on:

1 - The physical model of a fundamental note and its subservient harmonics, which is the way all human ears ears hear it, with the fundamental on bottom and harmonics rising in pitch above

2 - The countless examples of folk and ethnic musics which embody this harmonic principle



> The idea that Schoenberg came along and wrote the first music that was ever in the history of humanity not tonal is historically short-sighted.


That's simplistic and condescending. "Tonal/atonal" is only relevant in the context of modern dialectic, when pitch relationships became the prime concern.



> ...tonality was, after all, only 300 or so years old...


This is an improper use of the term 'tonality' if you wish to use it to make such broad statements.

Tonality must be understood in the general sense (see Harvard Dictionary of Music), not as CP tonality in an academic, chronological sense.


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## SeptimalTritone

From wikipedia: "Tonality is a musical system that arranges pitches or chords to induce a hierarchy of perceived relations, stabilities, and attractions."

If you can come up with a definition of tonality that includes Debussy's Violes or other preludes and etudes and including Bartok, while excluding Schoenberg... then you've won. And I would wonder why one would need to make this point, given that the Schoenberg gives a much stronger sense of gravitation and stability/instability, especially towards G/C#, and the supporting 0236 tetrachord (read the op 25 analysis).

The scalar definition of tonality with preferred tones of scales doesn't work because, again, whole tone, octatonic, and chromatic scales have no preferred tone. Then Debussy's Violes would have to be atonal. The same is true for the diatonic definition of tonality (heirarchy around a diatonic scale) because this is missed, again, in whole tone and octatonic music.

The tertian definition of tonality (music based on thirds/triads/seventh chords and their resolutions) doesn't work because Debussy planes dissonant chords regularly, or ends phrases or pieces on disappearance of dissonance. That's not resolution.

If your definition of tonality is music that largely uses triads and sevenths or even ninths (regardless of resolution), then look at the secundal clusters, say, in the exceprt here https://en.wikipedia.org/wiki/Secundal Is this atonal? Is Bartok's first piano sonata atonal? look at the huge amounts of clusters, including the final chord.

If you are so convinced that Debussy, Bartok, and others are not atonal, and that Schoenberg is, come up with a definition of tonality.


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## isorhythm

SeptimalTritone said:


> If you can come up with a definition of tonality that includes Debussy's Violes or other preludes and etudes and including Bartok, while excluding Schoenberg... then you've won.


I'm not interested in doing this - I don't think any sharp definition is possible.


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## SeptimalTritone

isorhythm said:


> I'm not interested in doing this - I don't think any sharp definition is possible.


If you don't want to define tonality...

and yet you still want to call Schoenberg atonal, while Debussy and Bartok not...

then I don't know what to say. You claim Schoenberg is not X without even "being interested in" defining X.

If you refuse to be interested to define X, and yet still want to declare something not X, then I am completely lost. And not only this, you are precise and sharp about Schoenberg after op 10 being atonal (except for works like Chamber Symphony 2), and yet you are imprecise and non-sharp about defining tonality, even going as far as not even trying to make a non-sharp definition. This is not reasonable in any kind of discourse.


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## Woodduck

SeptimalTritone said:


> If you don't want to define tonality...
> 
> and yet you still want to call Schoenberg atonal, while Debussy and Bartok not...
> 
> then I don't know what to say. You claim Schoenberg is not X without even "being interested in" defining X.
> 
> If you refuse to be interested to define X, and yet still want to declare something not X, then I am completely lost.


What I think isorhythm means by no "sharp definition" being possible is that individual works of music cannot always be sharply classifed as exclusively tonal or non-tonal, and that no definition will enable us all to agree on how tonal a given work is, and on what terminology is best attached to it. If that's what he's saying, I agree with him. But I don't view this as a metaphysical crisis.

Millionrainbows has made the point - as have I in different words - that tonality is a phenomenon of perception, and that the perception of it will differ in degree with different styles and works of music. In this sense it's proper to speak of music as being "more tonal" or "less tonal," with the implication that when we say a piece is "tonal," "non-tonal" or "atonal" we are not referring to an absolutely distinct category of being but to a continuum of perception. Like any aspect of musical perception, the perception of tonality will vary not only with the music heard but with the hearer.

Annoyingly imprecise as this situation may be, we should remember it when we argue about whether a given style or work of music should best be called tonal or not tonal. And we have no choice but to invoke the concept of universality, and the distinction - recognized by disciplines which study human beings, their consciousness and behavior - between "absolute universals" and "statistical universals." In the factors which result in the perception of tonality, absolute universals may reside in acoustical phenomena, in the structure of the human ear and brain (barring congenital defects and injuries), and in the processes of perception and concept-formation. But the ways in which these factors interact with the world, and the variety of forms which music takes as a result of those interactions, will be merely constrained by these universals, and far from fully determined by them.

I'm led to reflect on this by the example cited of Debussy's "Voiles," which may plausibly be cited as a specimen of musical "atonality," based on the fact that it's written in the whole-tone scale, which scale has, in and of itself, no "tonic" or other tones which suggest particular functions in relation to a tonic. The Wikipedia definition of tonality - "a musical system that arranges pitches or chords to induce a hierarchy of perceived relations, stabilities, and attractions" - is incomplete, even evasive, in that it doesn't specify even the most basic means by which that "hierarchy of perceived relations, stabilities, and attractions" is to be induced. But if we accept "stabilities and attractions" as important markers of tonality, then it would be difficult for any sensitive hearer not to perceive tonality in Debussy's piece, which features a pedal point in the bass throughout virtually its entire length and is harmonized mostly in thirds and augmented triads. No, we don't hear "functional" tonal progression as defined in the common practice subspecies of tonality. Yet augmented triads are ordinary fare in common practice music, and variously functional depending on the context in which they're used. And, in "Voiles," a context is provided by the pedal point, a standard device in music all over the world for establishing a stable foundation in relation to which other tones are heard. The fact that the pedal point is deep in the bass, where it creates the richest and most perceptible overtones, only intensifies the sense that it defines an underlying tonality. The result, for our perception of the work, is that the absence of tonality inherent in the whole-tone scale is counteracted by devices conducive to a sense of tonal grounding and progression, however ambiguous the tonal implications may be. As I pointed out with regard to chromaticism, ambiguity is a meaningful concept only in relation to alternatives which are unambiguous, and both Wagner's chromatic ambiguity and Debussy's whole-tone ambiguity assume, and even invoke, the listener's experience and sense of tonality.

Schoenberg is careful to avoid devices such as triads and pedal points which would invoke a sense of tonality. That's why "voiles" can plausibly be called tonal while Schoenberg's _Piano Suite_ can't.

Different listeners with different experience will, of course hear the music differently.


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## Mahlerian

isorhythm said:


> First, I'm not sure either analyst is actually arguing as strongly as either of you for the idea that Schoenberg's practice is "tonal" in any sense.


That's the *ENTIRE POINT* of the first paper. The title is _Comprehending Twelve-Tone Music as an Extension of the Primary Musical Language of Tonality_, and he concludes "it is important for the theorist to explain twelve-tone music as a logical extension of the primary language of tonality."


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## isorhythm

I don't care whether you want to call Schoenberg atonal or not either.

My concern here is practical: if I want to understand how Schoenberg's Op. 25 works, will trying to conceive of it as tonal help me, or will it lead to confusion and error? I think the latter is the case.

The essay you posted, rightly in my view, doesn't use the language of tonal analysis, because it is not useful.


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## Mahlerian

isorhythm said:


> I don't care whether you want to call Schoenberg atonal or not either.
> 
> My concern here is practical: if I want to understand how Schoenberg's Op. 25 works, will trying to conceive of it as tonal help me, or will it lead to confusion and error? I think the latter is the case.
> 
> The essay you posted, rightly in my view, doesn't use the language of tonal analysis, because it is not useful.


Will saying it's atonal give anyone any understanding of it? No. It just perpetuates misconceptions and misunderstandings of what the music is and what to listen for. One listens to "atonal" music the same way one listens to any other music, and there are no qualities that separate it from other music which justify a separate category, much less the completely misleading appellation "atonal."

Will keeping the term atonal lead to confusion and error? Clearly it does.

You say the essay doesn't use "the language of tonal analysis," but you are equivocating on tonal here, if you mean anything other than common practice music. The type of analysis you are referring to is for common practice music only.


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## isorhythm

This keeps coming up over and over and I still can't figure out why. Who thinks that calling something "atonal" constitutes an analysis of it or helps us understand it? Who ever said that? Worrying about the word "atonal" is just a non sequitur in this thread.


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## Mahlerian

isorhythm said:


> This keeps coming up over and over and I still can't figure out why. Who thinks that calling something "atonal" constitutes an analysis of it or helps us understand it? Who ever said that? Worrying about the word "atonal" is just a non sequitur in this thread.


But the word is nonsense and people use it as the sole crux of an argument, as if it told us something about the music.

The argument goes:

X piece is atonal.

Atonal music is unnatural/ugly/repels audiences/equal to a kid banging on a piano.

Therefore X piece is unnatural/ugly/repels audiences/equal to a kid banging on a piano.

But "Atonal" doesn't tell us anything about X piece at all, so this argument is completely vacuous. It's pretending to be a descriptive term, but it says nothing, and describes nothing. If you don't think it's pertinent, why have you been arguing to preserve it as meaningful?

At any rate, you said your concern was practical, and said that you thought calling Schoenberg's Suite for Piano tonal was misleading and confusing. Sure, it's not common practice, and doesn't respond to the analysis designed specifically for common practice, so it may indeed be confusing. But I think that calling it atonal is far, far worse, and I explained why. How could it be a non-sequitur to bring it up?


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## SeptimalTritone

"Schoenberg is careful to avoid devices such as triads and *pedal points* which would invoke a sense of tonality."

Does your computer magically shut off when the Musette movement starts? Or does your pianist play the Musette with his or her left hand chopped off? If those were the case, then even then you wouldn't be right, because there are held pedals in the intermezzo and other movements as well.

And no, triads aren't "avoided". They are no longer the final cadential chord, but their use isn't avoided.

...

"My concern here is practical: if I want to understand how Schoenberg's Op. 25 works, will trying to conceive of it as tonal help me, or will it lead to confusion and error? I think the latter is the case."

Schoenberg's op 25 isn't common practice tonal with I's and V's and IV's acting functionally, but neither is the entirety of Debussy's and Bartok's mature piano pieces and chamber and orchestral works.

If you mean "common practice tonal", of course you are right, but then the same would be with Debussy and Bartok.

If you mean "tonal" in the general gravitational/heirarchical term, then one needs to understand the centricity of G, the G-C# dyad, and the 0236 tetrachord in order to understand the Schoenberg.

Once again, your delineation cannot possibly include Debussy and Bartok but exclude Schoenberg.


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## isorhythm

I have nothing to say that I haven't said before, I'm afraid.

I made a thread a few months ago where I tried set out my thoughts on this. Late in the thread, after it had mostly died down, Woodduck wrote a post that explained what I was getting at perhaps more clearly than I did. It's worth reading: http://www.talkclassical.com/41950-i-resolve-tonality-debate-11.html#post1018415


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## SeptimalTritone

That post you quote fails to acknowledge that the (non-common practice) tonality of Schoenberg _is_ a perceptual phenomenon: rest, repose, finality onto a tonic bass and a central chord. One also hears it and feels it. Mahlerian and I have said this many, many times. Why do you keep insisting it is not perceptual, while of course refusing to define what "it" is?

It is the "theory" of atonality that obscures this perception. And when one looks at the note mechanics of the perception of gravitation in Schoenberg, Woodduck will only declare it as an ivory tower theory, as he also did in that post you quoted.


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## Woodduck

SeptimalTritone said:


> "Schoenberg is careful to avoid devices such as triads and *pedal points* which would invoke a sense of tonality."
> 
> Does your computer magically shut off when the Musette movement starts? Or does your pianist play the Musette with his or her left hand chopped off? If those were the case, then even then you wouldn't be right, because there are held pedals in the intermezzo and other movements as well.
> 
> And no, triads aren't "avoided". They are no longer the final cadential chord, but their use isn't avoided.


Now don't be sarcastic, Septimal, and read me carefully. There is a difference between a pedal point that "evokes a sense of tonality" and a pedal point which merely hangs on against a lot of non-tonal goings on. The deep pedal in the Debussy, besides being resonant with overtones as bass piano strings are, lends tonal suggestiveness to the harmonies above it, as I'm sure you can hear. I've played around with this myself, playing augmented triads and putting different bass notes beneath them, listening to the changing tonalities being evoked. Lovely iridescent effect.

The obsessive G in Schoenberg's "Musette" doesn't come across as the "tonic" you claim it is. The stuff that's going on around it doesn't suggest that it plays a role as a tonal foundation. Insistent repetition just isn't enough. I might be able to believe that the idea behind it was something like, "This is a pedal point - which in tonal music has some harmonic function, such as keeping an underlying tonality in view during various harmonic excursions - but here I'm going to do a sly take-off on that concept by not having an underlying tonality for my pedal point to represent." It's quite clever.

Same principle for triads.


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## isorhythm

SeptimalTritone said:


> That post you quote fails to acknowledge that the (non-common practice) tonality of Schoenberg _is_ a perceptual phenomenon: rest, repose, finality onto a tonic bass and a central chord.


This is just at odds with all mainstream writing about Schoenberg's music, including the two articles posted in this thread and all of Schoenberg's own writing about his music.

It's actually an extremely eccentric position, which you and Mahlerian are of course free to hold and defend. But I've never seen it expressed outside this forum, including in any of the many articles that have been posted by you and Mahlerian over the last year, and I get frustrated when it's presented to newcomers seeking information as a matter-of-fact description.

Also frustrating is my feeling that what I'm saying is being interpreted as an attack on or criticism of Schoenberg's music, which it isn't. But maybe I'm imagining that.


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## Mahlerian

isorhythm said:


> This is just at odds with all mainstream writing about Schoenberg's music, including the two articles posted in this thread and all of Schoenberg's own writing about his music.
> 
> It's actually an extremely eccentric position, which you and Mahlerian are of course free to hold and defend. But I've never seen it expressed outside this forum, including in any of the many articles that have been posted by you and Mahlerian over the last year, and I get frustrated when it's presented to newcomers seeking information as a matter-of-fact description.
> 
> Also frustrating is my feeling that what I'm saying is being interpreted as an attack on or criticism of Schoenberg's music, which it isn't. But maybe I'm imagining that.


My position is that any definition of tonality which attempts to include the modernist music you call tonal and modal music but exclude Schoenberg is incoherent, which is not at all an eccentric position. Neither is the idea that Schoenberg's music contains tonal centers eccentric, being attested in many places throughout the literature. Also, you keep painting this as an issue of theory, but you forget that both Septimal and I are speaking of our perceptual experience. We hear tonality, resolution, and harmonic progression in this music, period. One time you said that the problem lay with my concepts, but I am only trying to create concepts that are coherent with the facts of the matter and with my perception.

I don't think that what you're expressing is an attack on Schoenberg's music, though you have said in the past that you consider his dodecophonic music deficient in some way compared to Berg's and Webern's. I do think that one of the reasons that the word atonal should not be used is that it gives justification to those who do wish to use it as an attack, and as I expressed earlier, it is unhelpful to any discussion.

If you think you're frustrated, think about my position as someone who actually enjoys the music and sees people turned away from it and dismissing it out of hand on the mistaken belief that it's something completely different from anything else and needs to be listened to differently.


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## isorhythm

The claim you've made is quite a bit stronger - that Schoenberg's music is "just as tonal" as, say Brahms - that's the position I was calling eccentric (indeed, unique to this forum, as far as I know).

Your perceptions are your own, but when we try to understand how music works we have to look at how music is perceived by many people and look for commonalities.



Mahlerian said:


> I don't think that what you're expressing is an attack on Schoenberg's music, though you have said in the past that you consider his dodecophonic music deficient in some way compared to Berg's and Webern's. I do think that one of the reasons that the word atonal should not be used is that it gives justification to those who do wish to use it as an attack, and as I expressed earlier, it is unhelpful to any discussion.


I wouldn't say deficient. I don't like it as much. I also like Schoenberg's free atonal works a lot more than his 12-tone works, in general. In fact I think all the Schoenberg pieces I truly love are from his free atonal period, though I do enjoy a fair amount of his 12-tone music.

I don't agree with the idea that I or anyone else here is supposed to avoid certain language because it might "give justification" to someone or other - I actually feel quite strongly about this and will never agree with it.


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## Mahlerian

isorhythm said:


> The claim you've made is quite a bit stronger - that Schoenberg's music is "just as tonal" as, say Brahms - that's the position I was calling eccentric (indeed, unique to this forum, as far as I know).


That was Septimal, but in the general way the word tonal is used, it's not a spectrum. Mozart's music is tonal because it's organized tonally, as are Bach's and Brahms's. It doesn't make sense to say that Mozart is less tonal than folk songs, but this would have to be true in your and Millionrainbows' model. So if all things that are tonal are equally tonal, and mature Debussy is tonal, then yes, Schoenberg and Brahms are equally tonal. You'll note that this is in fact the thesis of the paper I cited earlier. Naturally, if tonal is defined in terms of common practice, Brahms is tonal and Schoenberg is not.

You can see this follows directly from what I said above:

Taking for granted that tonality encompasses modal and post-common practice music,

Tonality must also encompass "atonal" music to avoid inconsistencies of definition.

All things that are tonal are equally tonal.

Therefore atonal music is equally as tonal as common practice and pre-common practice music.

Since it follows directly given my premises, it cannot possibly be a stronger claim. It is a necessary claim.

What seems completely unique to this forum to me are the many bizarre definitions of things like "tonal function" and "harmony" on which there is a definite and resolute consensus the way there isn't for "tonality."



isorhythm said:


> Your perceptions are your own, but when we try to understand how music works we have to look at how music is perceived by many people and look for commonalities.


Yes, the majority of people think classical music is boring and incoherent. It has no beat and no hooks to remember.

I don't think the views of people who are unable to perceive the salient facets of a piece of music are qualified to make any statement about that music. That may sound snobbish or like a cop-out, but I don't see why people who think Schoenberg's music is unmelodic should be treated any differently from flat earthers or people who believe that every mass shooting is part of a government plot to take guns from the American people. It's based in absolutely nothing and there's no reason to take what anyone who misses the relevant information to that extent says seriously.

What matters to me is that these views, while uncommon among the general population, are in fact very common among composers of fully chromatic music as well as musicologists who study them. The people who know the most about the subject seem to agree with Schoenberg that atonal is a poor term for what he did.



isorhythm said:


> I wouldn't say deficient. I don't like it as much. I also like Schoenberg's free atonal works a lot more than his 12-tone works, in general. In fact I think all the Schoenberg pieces I truly love are from his free atonal period, though I do enjoy a fair amount of his 12-tone music.
> 
> I don't agree with the idea that I or anyone else here is supposed to avoid certain language because it might "give justification" to someone or other - I actually feel quite strongly about this and will never agree with it.


Well, that's not the main reason. The main reason is because it's meaningless and harmful.


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## isorhythm

Mahlerian said:


> Tonality must also encompass "atonal" music to avoid inconsistencies of definition.
> 
> All things that are tonal are equally tonal.


I neither agree that it is possible or desirable to have an airtight definition of tonality, nor that all things that are tonal are equally tonal, so I don't accept this conclusion. I thought I made that clear a long time ago.


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## Mahlerian

isorhythm said:


> I neither agree that it is possible or desirable to have an airtight definition of tonality, nor that all things that are tonal are equally tonal, so I don't accept this conclusion. I thought I made that clear a long time ago.


So you agree that Beethoven is less tonal than Mozart, or perhaps the other way around? Who is more tonal, Bach or Palestrina? Who is less tonal, Rachmaninoff or Bruckner? Can you begin to formulate an answer, even a hypothetical one, to these questions?

Which of the following chord progressions is more tonal?

I-IV-I

I-V-vi-IV-I

For my part, I see all of these questions as completely empty and self-contradictory. To say that one tonal thing is more tonal than another tonal thing lacks in any kind of reference, and makes no sense to me.


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## isorhythm

Mahlerian said:


> So you agree that Beethoven is less tonal than Mozart, or perhaps the other way around? Who is more tonal, Bach or Palestrina? Who is less tonal, Rachmaninoff or Bruckner? Can you begin to formulate an answer, even a hypothetical one, to these questions?


No, I think tonality is a phenomenon of perception, not something that inheres in the music, so I couldn't tell you a priori what's more or less tonal. Given some information about how listeners tend to perceive this music, I might be able to say something about why by analyzing it.

One obvious example is that virtually all listeners are more likely to perceive music that can be described by Roman numeral progressions like your examples - or any Roman numeral progressions for that matter - as tonal than they are to perceive highly chromatic music that cannot be described by such progressions as tonal.

But I certainly wouldn't posit that as a litmus test for tonality.


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## Mahlerian

isorhythm said:


> No, I think tonality is a phenomenon of perception, not something that inheres in the music, so I couldn't tell you a priori what's more or less tonal. Given some information about how listeners tend to perceive this music, I might be able to say something about why by analyzing it.
> 
> One obvious example is that virtually all listeners are more likely to perceive music that can be described by Roman numeral progressions like your examples - or any Roman numeral progressions for that matter - as tonal than they are to perceive highly chromatic music that cannot be described by such progressions as tonal.
> 
> But I certainly wouldn't posit that as a litmus test for tonality.


But are we talking about tonality as spectrum or tonality as perceptual fact? I gave you some very simple and specific examples, and I wanted you to argue for one being more tonal than the other. If tonality is entirely a matter of degrees, like a spectrum, then clearly one of those two chord progressions has to be less tonal, as they are not identical to each other.

What does it mean for someone to "perceive something as tonal," in your spectrum view? Does that mean that it's far along to the tonal side? It can't mean that it's tonal as an absolute, because tonality, you say, is a matter of degrees.

These aren't trick questions. You have to be able to answer in what way two things we both agree are tonal can be related to each other in terms of how tonal they are in order to posit that they are along a spectrum at all. Otherwise we're simply discussing in terms of a binary.


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## isorhythm

Mahlerian said:


> If tonality is entirely a matter of degrees, like a spectrum, then clearly one of those two chord progressions has to be less tonal, as they are not identical to each other.


This is not even logically true - two different things can be on the same point on a spectrum.

Of course I'm not proposing anything like a precise spectrum, because the individual perceptions I'm talking about are variable and not quantifiable.


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## Mahlerian

isorhythm said:


> This is not even logically true - two different things can be on the same point on a spectrum.


If they are different in non-relevant aspects, sure. But we're talking about a difference in the harmonic relations themselves. I don't need any kind of definitive answer, I just need you to give a case and argue why one could potentially be more tonal than the other so that we have an understanding about how the spectrum works and what it is measuring.



isorhythm said:


> Of course I'm not proposing anything like a precise spectrum, because the individual perceptions I'm talking about are variable and not quantifiable.


Okay, your answers may be vague. I already said that you don't have to answer definitively. Just make the case. I'm also interested in whether Beethoven's music is less tonal than Mozart's.


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## isorhythm

There's no "measuring" happening at all - that is the basic problem we are having. I don't want to measure anything.

I want to talk about listeners' perceptions. It won't do any good to look at the music first. Look at how the music is perceived and then look at the music to try to figure out why.

If in fact people tend to perceive _Voiles_ as more tonal than Schoenberg's suite (though I doubt they do, myself), then it would be useful to try to figure out why. Theory follows observation, not the other way around.


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## Mahlerian

Do listeners perceive tonality on a spectrum? I don't. In my experience, and in this thread, they don't talk about tonality as if it were a spectrum either. In most discussions and all textbooks, all of the things we've discussed _are_ tonal, period. Music can be tonal even if no one's ever listened to it, too, so I really don't think it depends on the listener.

You haven't given any credence to Septimal's and my perceptions (or those of the composers, etc.), you've asked us to prove them by theory, and derisively belittled our perceptions for differing from yours. Well, I'm sorry, but I don't perceive music in terms of theory, and I can't explain everything I can perceive. Schoenberg's music is perceived as having clear tonal centricity to me.


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## isorhythm

Mahlerian said:


> You haven't given any credence to Septimal's and my perceptions (or those of the composers, etc.), you've asked us to prove them by theory, and *derisively belittled our perceptions for differing from yours.*


I've never done any such thing, but I think this is my cue to drop the subject.


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## Mahlerian

isorhythm said:


> I've never done any such thing, but I think this is my cue to drop the subject.


Then what do you call it when you dismiss our perceptions as unique or as idiosyncratic? In terms of argument you're attempting to silence us by telling us that there are many who disagree.

We're on a classical music forum. *Everyone* here has minority tastes, and it's horribly condescending, as well as irrelevant to the substance of our arguments, to tell us, as a way of shouting us down, that we are a minority.

Focus on what we're saying, argue the questions at hand. It doesn't matter if only one person in the world believes something if that person is correct, because everyone else would be wrong. If we're wrong, we're wrong, but we want people to show us why.

You have said that you think our saying Schoenberg's music is fundamentally as tonal as any other non-common practice music is confusing for newcomers (without yourself being able to compare any two tonal things in terms of their tonality, even hypothetically). Can you justify this?


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## SeptimalTritone

Again, being intentionally vague about what tonality and atonality is, while being very clear about Schoenberg's 12 tone music being decisively atonal, is not how discourse works. Not only is it not how academic discourse works, it is not how informal discourse works. Calling a precise category X while being imprecise about what X is... that's a sure way to never be wrong.

As far as whether the Schoenberg is "just" as tonal, it is not common-practice tonal, but it has a clear note centricity and heirarchy.

As far as the Musette goes, even here, the G is functional (functional in the post-common practice sense) through its opposition with C # through and throughout. If that relation were avoided, Wooduck would be right in saying that the G is a non-functional bass, but the relation is in fact emphasized. The C # is a secondary pedal tone note. And tertiarily, the other tritone oppositions defined through the tone rows, that is, D - A flat, and C - F #, act on top of the pedal group's main tritone G - C#. And of course, in the final cadence in the gigue, D - A flat voice leads up into the central tetrachord, defined through G - C#. All function, albeit post-common practice function.


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## Rosie

People all the time used to tell me that atonal music is the worst thing ever, then when I listened to it, it just sounded like music?? Why do people hate it? Schoenberg seems a pleasant man, his music is alright. Why the hate?


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## EdwardBast

SeptimalTritone said:


> Edward, what privileges the completely equally spaced whole tone scale, or the transpositionally invariant octatonic scale, over the 12 tone chromatic scale? And who says that there cannot be more than 12 pitch classes regularly used, as in Harry Partch or Ben Johnston, or certain 19TET 16th century music, or Ives's 24TET piano duets, or a non-equally spaced 12 tone scale, as in La Monte Young, or just overtone chords as in Stockhausen or Georg Haas, or various other microtonal scales like Javanese Gamelan?
> 
> What in the world makes the 12 tone chromatic scale non-specific, as if it doesn't have any particularities on its own? And why cannot there cannot be scales with more notes, or other notes? What makes the 12 tone chromatic scale a collection of "all" pitch classes, or all relative pitch classes? Why cannot there be more pitches, or other pitches?


There can be more pitches and other pitches but generally there aren't. My statements only apply to the 99% of classical music using 12 pitch classes. The difference between other scales and the chromatic scale is that in all of the others the structure of the scale determines the choice of pitches by excluding some and specifying others. The chromatic scale, obviously, does not do that; it does not select some and exclude others. It does, however, have meaning when one considers the category "things a pianist or violinist might practice."


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## Nereffid

isorhythm said:


> There's no "measuring" happening at all - that is the basic problem we are having. I don't want to measure anything.
> 
> I want to talk about listeners' perceptions. It won't do any good to look at the music first. Look at how the music is perceived and then look at the music to try to figure out why.
> 
> If in fact people tend to perceive _Voiles_ as more tonal than Schoenberg's suite (though I doubt they do, myself), then it would be useful to try to figure out why. Theory follows observation, not the other way around.


If I didn't already know that this was a trap and someone was waiting to pounce on me, I'd say my gut response to the two would be that _Voiles_ *feels* considerably more tonal (or less atonal, for that matter) than the Schoenberg suite. I imagine a lot of that perception has to do with tempo and rhythm.


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## EdwardBast

Mahlerian said:


> It's not all possible pitch classes, it's _a particular set of pitch classes_, just like any other scale. There are infinitely many pitches it does not include.
> 
> I'm not trying to obfuscate, I'm trying to clarify. If you can come up with a definition of scale that doesn't include the chromatic scale, I'll be waiting.


Obviously, this discussion is in the context of a twelve-pitch system, the one in which the term "chromatic scale" is used.

I am not claiming that one cannot include the chromatic scale under some definitions of the term scale, only that the set of pitches it specifies lacks a crucial characteristic of all other scales: All other scales include some pitch classes and exclude others.

If a style of music uses all pitches more or less equally and never uses them in a sequential ascending or descending pattern, then saying the music is in a chromatic scale adds no useful information to the equation. It specifies nothing about the structure of the music that is not contained in the words by which the style is referenced: Twelve-tone music. Therefore, this application of the term chromatic scale is empty and meaningless. The word does no work - except to suggest an illusory common ground with music that uses scales in a structurally significant sense, hence obfuscation.


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## Mahlerian

EdwardBast said:


> If a style of music uses all pitches more or less equally and never uses them in a sequential ascending or descending pattern, then saying the music is in a chromatic scale adds no useful information to the equation. It specifies nothing about the structure of the music that is not contained in the words by which the style is referenced: Twelve-tone music. Therefore, this application of the term chromatic scale is empty and meaningless. The word does no work - except to suggest an illusory common ground with music that uses scales in a structurally significant sense, hence obfuscation.


Well, in the context of my reply, Millonrainbows was claiming that fully chromatic music uses scales (the chromatic scale specifically) and 12-tone music does not, for the reason that the latter uses ordered sets. This property is irrelevant to whether or not the music uses a scale, which in much if not most 20th century does not imply any particular structural significance, unlike a key in common practice music.


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## Woodduck

SeptimalTritone said:


> Again, being intentionally vague about what tonality and atonality is, while being very clear about Schoenberg's 12 tone music being decisively atonal, is not how discourse works. Not only is it not how academic discourse works, it is not how informal discourse works. Calling a precise category X while being imprecise about what X is... that's a sure way to never be wrong.
> 
> As far as whether the Schoenberg is "just" as tonal, it is not common-practice tonal, but it has a clear note centricity and heirarchy.
> 
> As far as the Musette goes, even here, the G is functional (functional in the post-common practice sense) through its opposition with C # through and throughout. If that relation were avoided, Wooduck would be right in saying that the G is a non-functional bass, but the relation is in fact emphasized. The C # is a secondary pedal tone note. And tertiarily, the other tritone oppositions defined through the tone rows, that is, D - A flat, and C - F #, act on top of the pedal group's main tritone G - C#. And of course, in the final cadence in the gigue, D - A flat voice leads up into the central tetrachord, defined through G - C#. All function, albeit post-common practice function.


A serviceable definition of tonality is a good thing to have, but it isn't adequate equipment for being able to say whether a given piece of music is tonal, or why and in what manner it's tonal. Similarly, we don't need to be able to define tonality in order to recognize it. That said, a number of people here, quite accomplished in discourse, have defined tonality over and over, up, down, and sideways. Where have you been?

It's true that the word "tonality" is used in several senses, and I think a lot of words are wasted here by confusing those senses. You appear to believe that tonality, in its most basic sense, is something located in musical scores, and that its existence can be demonstrated through analysis of those scores - that it's something fundamentally mechanical or technical, and that if music can be shown to exhibit certain structures defined (by someone) as tonal, the music will be tonal music, regardless of how people hear it. In this way of thinking, music which is constructed in some manner "analogous" to music generally considered tonal might be shown to be tonal by pointing out its "analogous" features and calling them by the same names - names like "function," "relation," "opposition" - normally used to describe tonal music.

I don't think that's what tonality is, or how it's recognized.

I believe that tonality, though it may be encoded in certain compositional techniques or arrangements of tones, should not be thought of as a product or property of them, and cannot be created ad hoc by abstractly conceived systems of musical organization. I believe that tonality is a perceptual phenomenon which arises from a number of causes, essentially from the interaction of acoustical phenomena, the brain's ways of processing these, and other functions (some constant or universal, some variable) of the human psyche, its sensations, concepts, and emotions - all subject to a process of learning. Tonality is a perceived system of dynamic relationships between musical tones, entailing mutual influence and attraction between tones in more or less hierarchical relation to a central tone and to each other. These dynamic relationships are not inherent in sounds, yet - and this is crucial - _they are perceived as if they were._ And, just as crucially, _that perception cannot be created by design, but must evolve through experience._

Tonality, as a perceptual phenomenon and as a corresponding musical language, evolves in a social or cultural context. Though no single tonal system is inevitable or "right," musical systems, as they evolve, will come to be felt as right, as compelling, as "natural," by listeners over a certain period of time. Because a tonal system exists on a subconscious level as a set of expectations according to which a piece of music can be felt as "logical," it exists prior to any compositional use of it: it is felt as fundamental, natural, and compelling, and a composer may use it, guided by the tonal sense in his subconscious mind, as the basis for creating the specific ordering of notes in a particular work, consciously adhering to or departing from tonal expectations as he wishes. He cannot create a new way of ordering tones - and especially not one, such as a typical tone row, in which the tonal sense is purposefully thwarted - and claim that the resulting music must be considered "tonal," or "just as tonal" as music in which evolved and widely understood relationships are perceived to operate, either explicitly or beneath the surface. It is theoretically possible that some system of organizing pitches created out of whole cloth by a composer and unrelated to known tonal systems might eventually be perceivable as tonal with sufficient exposure and use. But it isn't inevitable based merely on the application of organizational concepts such as "hierarchy" or "opposition" or "cadencing" - and, speaking realistically, it probably hasn't happened and isn't likely to happen. If a composer is going to claim that a C# can be felt to relate to a G in any way "analogous" to the relationship of the fifth degree of a major or minor scale to its first degree, he may have to find some device more compelling than constant repetition and proximity to make his case. He may create something "analogous" to the structures in tonal music, but nothing guarantees that that will give rise to the perception of the kinds of dynamic forces - or affective value - which characterize a tonal system. An "analogous dominant" a tritone away from a so-called tonic is not a dominant and is not felt to relate to its "tonic" as a dominant does. An "analogous leading tone" may be placed at cadences and evince no inherent tendency to lead.

Your description of Schoenberg's "Musette," with its structural terminology - "function," "opposition," "relation" - is inherently incapable of telling us whether it is tonal or not. It tells us only that the music utilizes constructions and devices which are in some way similar to those used in tonal music. "Tonality" on paper may not be tonality at all. Only the ear can decide.


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## SeptimalTritone

"A serviceable definition of tonality is a good thing to have, but it isn't adequate equipment for being able to say whether a given piece of music is tonal, or why and in what manner it's tonal. Similarly, we don't need to be able to define tonality in order to recognize it. That said, a number of people here, quite accomplished in discourse, have defined tonality over and over, up, down, and sideways. Where have you been?"

"If I didn't already know that this was a trap and someone was waiting to pounce on me, I'd say my gut response to the two would be that Voiles *feels* considerably more tonal (or less atonal, for that matter) than the Schoenberg suite. I imagine a lot of that perception has to do with tempo and rhythm."

I have went through all potential definitions that might exclude Schoenberg but include Debussy and Bartok on a post here. They either include Debussy + Bartok + Schoenberg together, or exclude all of them. Using your words: Where have you been? http://www.talkclassical.com/44227-i-want-learn-non-3.html#post1087923

If one refuses to take any of these definitions, then one's position is unfalsifiable, which I suppose is one way of never being wrong. I can not argue against your argument that Debussy, Bartok are tonal and Schoenberg are atonal because I have no category to base it on. The Schoenberg is atonal claim is not even wrong, it is vacuous.

As far as tempo and rhythm goes, Schoenberg has explicit cadences, especially at endings of movements. The whole point of the Debussy anyway is that it invalidates the scalar identity theory of tonality, but regardless, the Schoenberg movements have final cadential resolutions.

As far as "Only the ear can decide", I've been saying that it is audible, over and over again. In fact, not only is it audible, it is very strongly felt. Nothing in the Debussy example is remotely as strong as the final cadential resolution in Schoenberg's gigue. In the Debussy, the pedal B flat becomes a pedal F #, and rhythmically that's a final cadence, a repose. But compare that to the strength final cadence in the Schoenberg gigue. The gravitation felt is much stronger, and it's both a note phenomenon and a rhythm phenomenon. Or take the ending of the prelude 



 with the end on G / C# on the bass.


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## Woodduck

SeptimalTritone said:


> "A serviceable definition of tonality is a good thing to have, but it isn't adequate equipment for being able to say whether a given piece of music is tonal, or why and in what manner it's tonal. Similarly, we don't need to be able to define tonality in order to recognize it. That said, a number of people here, quite accomplished in discourse, have defined tonality over and over, up, down, and sideways. Where have you been?"
> 
> "If I didn't already know that this was a trap and someone was waiting to pounce on me, I'd say my gut response to the two would be that Voiles *feels* considerably more tonal (or less atonal, for that matter) than the Schoenberg suite. I imagine a lot of that perception has to do with tempo and rhythm."
> 
> I have went through all potential definitions that might exclude Schoenberg but include Debussy and Bartok on a post here. They either include Debussy + Bartok + Schoenberg together, or exclude all of them. Using your words: Where have you been? http://www.talkclassical.com/44227-i-want-learn-non-3.html#post1087923
> 
> If one refuses to take any of these definitions, then one's position is unfalsifiable, which I suppose is one way of never being wrong. I can not argue against your argument that Debussy, Bartok are tonal and Schoenberg are atonal because I have no category to base it on. The Schoenberg is atonal claim is not even wrong, it is vacuous.
> 
> As far as tempo and rhythm goes, Schoenberg has explicit cadences, especially at endings of movements. The whole point of the Debussy anyway is that it invalidates the scalar identity theory of tonality, but regardless, the Schoenberg movements have final cadential resolutions.
> 
> As far as "Only the ear can decide", I've been saying that it is audible, over and over again. In fact, not only is it audible, it is very strongly felt. Nothing in the Debussy example is remotely as strong as the final cadential resolution in Schoenberg's gigue. In the Debussy, the pedal B flat becomes a pedal F #, and rhythmically that's a final cadence, a repose. But compare that to the strength final cadence in the Schoenberg gigue. The gravitation felt is much stronger, and it's both a note phenomenon and a rhythm phenomenon. Or take the ending of the prelude
> 
> 
> 
> with the end on G / C# on the bass.


I don't really care whether someone hears this or that music as tonal or atonal or more tonal or less tonal. My ears are the only ones I can use. But it's puzzling to have someone point to certain technical features in a piece of music that doesn't sound tonal as if those features were supposed to demonstrate the presence of tonality. As far as I can tell, none of the specific features you've mentioned about the Schoenberg _Piano Suite_ are things that will necessarily evoke a sense of tonality in a listener, or are things that non-tonal music can't have (unless of course you believe that non-tonal music doesn't exist). Even you have called some of them "analogous" to tonal music's attributes. What does "analogous" mean? I thought it implied "not the same as." For all its descriptive detail, the following does nothing to indicate to me that tonality will be the audible concommitant:

_As far as the Musette goes, even here, the G is *functional (functional in the post-common practice sense)** through its opposition with C # through and throughout.* If that relation were avoided, Wooduck would be right in saying that the G is a non-functional bass, but the relation is in fact emphasized. The C # is a secondary pedal tone note. And tertiarily, the other tritone *oppositions* defined through the tone rows, that is, D - A flat, and C - F #, act on top of the pedal group's main tritone G - C#. And of course, in the final cadence in the gigue, D - A flat voice leads up into the central tetrachord, defined through G - C#.* All function,* *albeit post-common practice function. *_

What is "function" supposed to mean in a "post-common practice sense" (or in any sense where no tonality has been established)? Does it mean anything more than "similar use in different contexts?" What do you mean by "opposition?" Does it mean something other than "simultaneous but contrasting"? How is either of these things indicative of tonality?

Maybe, if you think the music is actually tonal and not just analogous to tonal, you should be the one to propose a definition of tonality that applies to Schoenberg's suite. What system of tonality are we supposed to be hearing? What are its principles? Are listeners supposed to bring a certain set of tonal expectations to the music which will enable them to make sense of it, such as listeners have brought to music since time immemorial? What are those expectations? Will they help? Are these fair questions?


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## Mahlerian

SeptimalTritone said:


> If one refuses to take any of these definitions, then one's position is unfalsifiable, which I suppose is one way of never being wrong. I can not argue against your argument that Debussy, Bartok are tonal and Schoenberg are atonal because I have no category to base it on. The Schoenberg is atonal claim is not even wrong, it is vacuous.


Yeah, we have people asking what definitions of tonality include Schoenberg's late works, but they don't seem to understand that it's _their own definitions_ that we're talking about. I actually prefer to speak of tonality in terms of common practice only, as that's the most useful and relevant way to use the term, but if you want to expand it out to include all kinds of other music (for what reason?), you have to make sure you're using it consistently.

For my part, I can imagine in the abstract what people mean by "atonal," but I don't hear music in a way that justifies such a term. Schoenberg's music is too rooted in tonality, even in common practice, for me to consider saying that it contradicts or is in opposition to either.


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## TwoPhotons

This thread has made me think a lot about what music I consider to be tonal, and what musical elements contribute to me recognizing the presence of 'tonality'...

To me, tonality represents something akin to the pivot of a pendulum. When a pendulum is displaced from its central position (i.e. the tonal center), it feels a force towards that central position. Without a pivot, this force does not exist.

In the same way, a piece of tonal music must to me evoke that sense of 'restoration' back to the tonal centre. Something like I - V - I is probably the simplest form of this kind of displacement -> restoration pattern, whereas I - IV - V - I is a bit more excited, let's say.

But of course, as in musical analysis, the pendulum model is a simplification of something much subtler than that. If you have something like a C major chord to an F major chord, and the piece stays in F major for a long time, I would perceive that as a modulation; a new tonal centre, or a shifting of the pivot. This might then suggest that the piece becomes less tonal, because the pivot is in motion. However, the main requirement for me to hear 'tonality' is that I hear a _discernible restoration_ to _some_ sort of tonal center. And sometimes, modulations can evoke a _stronger_ sense of tonality to me because of how it emphasises the different tonal centres. It's a bit like how you can make the argument that minimalist music can make the audience perceive more harmonic motion than, say, in a Chopin ballade, because the infrequency of the harmonic changes emphasises said changes to the listener.

As an example, Ligeti's "Musica Ricercata, No.1" sounds considerably less tonal to me than J.S.Bach's "Brandenburg Concerto No.3", despite the latter having far more 'harmonic motion' than the former. This is because in the first piece, I feel nothing pulling me in any direction. OK, the final D basically suggests that the entire piece is a really long perfect cadence, but that's what I mean - it's so long that to me I can rule out tonality after a few seconds. On the other hand, the Bach piece continuously makes me feel like there's something 'harmonically pulling' the piece, albeit in all sorts of different directions.

Schoenberg's so-called 'atonal' music to me represents the opposite end of the scale from Musica Ricercata in why I perceive virtually no tonality in it. When I listen to the Op.25, I'm being pulled in _so_ many different directions at once that I lose all sense of direction! It's very much 'here-and-now' music. A music analyst might point out that there are some notes which return more often than others in some of Schoenberg's music (the G in "Musette" is an obvious one which is being discussed here), but this does not evoke any kind of tonality in my ears because that G is not drawing me anywhere. It's being played repeatedly, I can hear it being played repeatedly against the rest of the musical layers, and that's about as much as I gather from it. It's an interesting effect but not one which emphasises any sort of pivot...more like a nail in the wall with nothing hanging on to it!

Some of Debussy's pieces have been mentioned as apparently sounding more tonal than Schoenberg. This to me is mainly because Debussy uses common harmonies which appear in pieces associated with tonality (in addition to tempo and rhythm as Nereffid said), but in the end Debussy will often avoid function in the traditional sense. So to me it's a sort of deceptive or 'phantom tonality' which some of his pieces (such as Voiles) employ.

Anyway, that's just my approach to tonality. I admit I didn't give any sort of objective, rigorous definition of what tonality is, but only how I perceive it. I think it's impossible to give a rigorous definition really because everybody perceives music differently, and I think that tonality _is_ to do with perception to some degree.


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## Barbebleu

Could it be that what is sometimes perceived as atonality is just dissonance? Or is that just plain wrong?


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## millionrainbows

Here's my short version: It is somewhat misleading to say that Schoenberg's 12-tone compositions are 'tonal.'

First, to clear this up: 
The whole tone scale was mentioned earlier in reference to Debussy, as 'not having a tonic.' That is a flawed statement.

The whole-tone scale IS a scale, and it is a tonal device, and here's why: the WT scale is _flexible_ in that it can have _any member note as its tonic,_ or _as a starting point for a triad or scale passage, depending on context. _This changes everything. 
Thelonious Monk used the, example, WT scale starting on G (key of C), to build augmented seventh chords and runs. There are many other examples.
In other words, whether the WT scale has a tonic, or other function, _depends on the context in which it is used.

_That is true of all tonality.It is a system whose devices (scales, triads, phrases, inversions) have a contextually-pervasive presence and effect. It produces a sense of tonality by a combination of all its elements, not just one element in isolation.

Schoenberg considered himself as a product of the CP Tonal tradition, and saw his music, and even the 12-tone system (as he used it) as an extension of the CP Tonal tradition. I agree.

But I disagree that Schoenberg's 12-tone music, or the system itself, is a tonal device or system, even though Schoenberg used it in ways that evoked tonal associations. I have good, valid, objective, structural, detailed reasons for this; this is not merely a subjective perception, although it contains an element of that, as all 'tonal' music should.

Before I list these general considerations, I'd like to say how much I dislike the argumentative use of terminology to obfuscate the issue of Tonality (as an era, and a collection of practices) vs. 'tonality', a general term meaning tone-centricity in both perception and structural features (heirarchy of notes, use of scales, harmonic devices). This is especially repelling when it produces off-the -wall statements such as "Schoenberg's music is tonal" without any explanation or definition of precise meanings of the term 'tonal'.

Plus, this argument that "Schoenberg is tonal" has a political/academic dimension. There is a school of thought, as exemplified by the article Mahlerian linked (Collegiate Music Forum or something like that), as well as Silvina Milstein's book which I own, that emphasizes the tonal devices and tonal intentions in said music.

This "Schoenberg is tonal" school is in direct opposition to the Post-war composers (Boulez, even Webern), Milton Babbitt, and George Perle, who are more interested in using tha 12-tone idea in ways suited to its true structural nature, not a tonal logic which directs its use.

What makes Schoenberg's 12-tone music 'tonal' is the _way_ he used it, not the structural features of the system itself. Schoenberg used a tonal logic in making his music, and these elements can all be listed, and can all be used to bolster the tonality side, or to disprove it. Take your pick.

Is Schoenberg's music tonal or not-tonal? It's your preference. Who will you vote for?

Still, I am a pragmatist, and I side with logic and structural features, not preferences or camps of thought. For me, the fact that ordered rows are used is the crux of the structural proof that the 12-tone method is NOT tonal, and essentially a non-harmonic, linear, melodic method, with no overriding hierarchy of notes which relate to a single tonic.


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## millionrainbows

Excerpts from Silvina Milstein's book_ Arnold Schoenberg: Notes, Sets, Forms_

_"Schoenberg developed his 12-tone method of 'self-defined' musical relations which, in a constructional sense, could replace those formerly given by tonality. Yet unlike tonality, the 12-tone method has no recourse to generalized functionality, in the sense that it does not prescribe functional relations which are constant for all compositions, such as the heirarchy of tonal distance provided by the circle of fifths in tonal music. But progression is 'associative' and 'non-functional' since no tonal motivation, hence no tonal function, can be inferred without recourse to the connotations of a generalized system of functions, such as tonality. On the contrary, in 12-tone composition 'the normative factor is determined without any reference to means of its being so recognized other than by internal structure, which is not true in tonal music..."

"Schoenberg's 12-tone works generally show that he was unwilling to relinquish completely the functional relations of tonality and often concentrated implications formerly pertaining to a tonal region or key on _*single pitch-classes or pitch-levels."

*So, he could not use harmonic means, like triads: he had to use single notes, because 12-tone is melodic, not harmonic. That's a compromise, one of many.

_"Is it legitimate to read hierarchies in a context where not all elements comply with such hierarchical structuring? Can single pitch-classes or pitch-levels placed at boundaries of groupings, supported by tonal idiomatic gestures, conceivably represent tonal centres? Is it pertinent to discuss tonal functionality when dealing with triadic material which does not unfold according to the traditional rules of harmony? Is it possible to regard such relations as crucial to the aural and aesthetic understanding of the music?"

"The revolutionary force of Schoenberg's music lies in the fact that its classicism is neither a matter of style nor of compositional technique, *but derives from its adherence to a particular type of musical logic,* while its modernism is fundamentally a matter of content."

_I can agree with all that; but I still maintain that it is rather misleading and incomplete to say that "Schoenberg's music is tonal" without first defining that term, and then elaborating on just how that is achieved.


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## Mahlerian

I'm not in disagreement with any of the quotes in your post. I don't disagree that Schoenberg's music is not common practice, which is all the first person means by tonal.

As for the idea that my descriptions of the music are "political/academic," that seems absurd. I didn't _choose_ to hear the music as having centricity. I simply listened to the music and realized that that's what I was hearing. My understanding of the term atonal as essentially meaningless and harmful developed in response primarily to the music itself, and only secondarily to arguments I read from people such as Babbitt and Schoenberg who dismissed the idea of atonality.


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## Woodduck

TwoPhotons said:


> This thread has made me think a lot about what music I consider to be tonal, and what musical elements contribute to me recognizing the presence of 'tonality'...
> 
> To me, tonality represents something akin to the pivot of a pendulum. When a pendulum is displaced from its central position (i.e. the tonal center), it feels a force towards that central position. Without a pivot, this force does not exist.
> 
> In the same way, a piece of tonal music must to me evoke that sense of 'restoration' back to the tonal centre. Something like I - V - I is probably the simplest form of this kind of displacement -> restoration pattern, whereas I - IV - V - I is a bit more excited, let's say.
> 
> But of course, as in musical analysis, the pendulum model is a simplification of something much subtler than that. If you have something like a C major chord to an F major chord, and the piece stays in F major for a long time, I would perceive that as a modulation; a new tonal centre, or a shifting of the pivot. This might then suggest that the piece becomes less tonal, because the pivot is in motion. However, the main requirement for me to hear 'tonality' is that I hear a _discernible restoration_ to _some_ sort of tonal center. And sometimes, modulations can evoke a _stronger_ sense of tonality to me because of how it emphasises the different tonal centres. It's a bit like how you can make the argument that minimalist music can make the audience perceive more harmonic motion than, say, in a Chopin ballade, because the infrequency of the harmonic changes emphasises said changes to the listener.
> 
> As an example, Ligeti's "Musica Ricercata, No.1" sounds considerably less tonal to me than J.S.Bach's "Brandenburg Concerto No.3", despite the latter having far more 'harmonic motion' than the former. This is because in the first piece, I feel nothing pulling me in any direction. OK, the final D basically suggests that the entire piece is a really long perfect cadence, but that's what I mean - it's so long that to me I can rule out tonality after a few seconds. On the other hand, the Bach piece continuously makes me feel like there's something 'harmonically pulling' the piece, albeit in all sorts of different directions.
> 
> Schoenberg's so-called 'atonal' music to me represents the opposite end of the scale from Musica Ricercata in why I perceive virtually no tonality in it. When I listen to the Op.25, I'm being pulled in _so_ many different directions at once that I lose all sense of direction! It's very much 'here-and-now' music. A music analyst might point out that there are some notes which return more often than others in some of Schoenberg's music (the G in "Musette" is an obvious one which is being discussed here), but this does not evoke any kind of tonality in my ears because that G is not drawing me anywhere. It's being played repeatedly, I can hear it being played repeatedly against the rest of the musical layers, and that's about as much as I gather from it. It's an interesting effect but not one which emphasises any sort of pivot...more like a nail in the wall with nothing hanging on to it!
> 
> Some of Debussy's pieces have been mentioned as apparently sounding more tonal than Schoenberg. This to me is mainly because Debussy uses common harmonies which appear in pieces associated with tonality (in addition to tempo and rhythm as Nereffid said), but in the end Debussy will often avoid function in the traditional sense. So to me it's a sort of deceptive or 'phantom tonality' which some of his pieces (such as Voiles) employ.
> 
> Anyway, that's just my approach to tonality. I admit I didn't give any sort of objective, rigorous definition of what tonality is, but only how I perceive it. I think it's impossible to give a rigorous definition really because everybody perceives music differently, and I think that tonality _is_ to do with perception to some degree.


This is a wonderful post, expressing better than any abstract philosophical discussion the essential nature of tonality as a complex subjective phenomenon. Subjective experiences can't be explained or transmitted from person to person, and if we want to describe or communicate them we're forced to resort to symbolic imagery (music itself being symbolic in part). Your images feel dead-on, and allow me to imagine that I hear the works you cite just as you do. I will forever imagine that repeated G as a straight line of nails hammered into the wall while the paintings on exhibit are hung around them. I would only add that "Voiles" is not typical of Debussy, but an extreme exercise in "phantomness"; most of his works have much more clear tonality in them, even when it's more implied than explicit.

EDIT: I also wanted to say that I like your observation that harmonic complexity can _intensify_ our sense of tonality. This truth balances the opposite view, rooted in a Darwinian-evolutionary theory of artistic progress and advanced by Schoenberg as he was developing his "post-tonal" language, that laid emphasis upon the obscuring of tonality resulting from increasing chromaticism and used that as a justification for the "necessity" of abandoning tonality altogether. Schoenberg backpedalled from this radical stance, of course, but the notion of atonality as a "logical" outcome of tonal enrichment and the way of the future took hold in a culture eager to be ahead of its time (an oxymoron if there ever was one). We can feel relieved that the future ended some time ago.


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## Dim7

TwoPhotons said:


> Some of Debussy's pieces have been mentioned as apparently sounding more tonal than Schoenberg. This to me is mainly because Debussy uses common harmonies which appear in pieces associated with tonality (in addition to tempo and rhythm as Nereffid said), but in the end Debussy will often avoid function in the traditional sense. So to me it's a sort of deceptive or 'phantom tonality' which some of his pieces (such as Voiles) employ.


I agree about the reason why Debussy is considered more tonal, however they don't really apply to Voiles, which of all Debussy pieces probably has the least to do with common practice major/minor tonality. I don't think it sounds any more tonal than Schoenberg, at least when the latter has pedal point, however I also think it is a rather cherry picked example.


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## SeptimalTritone

Let me be clear: my definition of tonality is the first sentence on wikipedia.

"Tonality is a musical system that arranges pitches or chords to induce a hierarchy of perceived relations, stabilities, and attractions."

This kind of definition of tonality includes common practice I-V tonality, but it includes far more beyond that.

Debussy does avoid common practice function in his mature pieces, but he is tonal, even in his piano preludes, and even in Voiles. Violes, or his other piano preludes aren't "phantom" tonal or "deceptively" tonal, they are tonal.

As far as Violes being "cherry picked" goes (really?) it's sole point was to show that even with whole tone scalarity, one can still have post-common practice tonality. That was it. People were making a huge fuss about the importance of the implications of a scale. Violes demonstrates that even with an equally spaced scale, there's tone relationships and centricity. It isn't even "less" tonal than other Debussy preludes or other piano works. It would be a horrific misunderstanding of my point to think that I cherry picked a Debussy example to show that he can be "as [not] tonal" as Schoenberg, it was merely to make a point about scales, and I have emphasized this many, many times. Both the Debussy and the Schoenberg are tonal, although post-common practice tonal.

It is true that Schoenberg goes through chromatic space much faster, and much less stepwise, than his surrounding early 20th century composers. But here are clear note relations and gravitation. Therefore, he is tonal.


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## Woodduck

SeptimalTritone said:


> Let me be clear: my definition of tonality is the first sentence on wikipedia.
> 
> "Tonality is a musical system that arranges pitches or chords to induce a hierarchy of perceived relations, stabilities, and attractions."
> 
> This kind of definition of tonality includes common practice I-V tonality, but it includes far more beyond that.
> 
> Debussy does avoid common practice function in his mature pieces, but he is tonal, even in his piano preludes, and even in Voiles. Violes, or his other piano preludes aren't "phantom" tonal or "deceptively" tonal, they are tonal.
> 
> As far as Violes being "cherry picked" goes (really?) it's sole point was to show that even with whole tone scalarity, one can still have post-common practice tonality. That was it. People were making a huge fuss about the importance of the implications of a scale. Violes demonstrates that even with an equally spaced scale, there's tone relationships and centricity. It isn't even "less" tonal than other Debussy preludes or other piano works. It would be a horrific misunderstanding of my point to think that I cherry picked a Debussy example to show that he can be "as [not] tonal" as Schoenberg, it was merely to make a point about scales, and I have emphasized this many, many times. Both the Debussy and the Schoenberg are tonal, although post-common practice tonal.
> 
> It is true that Schoenberg goes through chromatic space much faster, and much less stepwise, than his surrounding early 20th century composers. But here are clear note relations and gravitation. Therefore, he is tonal.


It seems we are down to a question of definitions. The definition you accept, _"Tonality is a musical system that arranges pitches or chords to induce a hierarchy of perceived relations, stabilities, and attractions,"_ is broad enough to describe any music in which tones are felt to influence one another, and some tones are given emphasis over others.

By that definition, it would be very difficult, if not impossible, to invent a piece of music using distinct pitches which would not qualify as tonal. But the definition fails to account for the structural and perceivable difference between music in which the "hierarchy of relations" is _systemic_ - inherent in the music's basic idiom (defined fundamentally by its scale) and therefore embedded in listener expectation and exploited through the music's manipulation of that expectation - and music in which a composer merely associates and privileges certain tones for a particular work.

From the perspective of the listener this difference is important. We can see it in the different ways in which a pedal point functions in Schoenberg's "Musette," Debussy's "Voiles," an Indian raga, and the stretto of a Bach fugue. The "tonal" significance is different in all four of these.

1) Bach's idiom is unambiguously tonal, utilizing a scale possessing an intrinsic hierarchy of great strength, orderliness, and complexity. Because of that hierarchy, which is familiar to his listeners before they hear his music, he can use a pedal point to create a passage of harmonic suspension or ambiguity, of great tension and tonal gravity, full of dissonances and uncertainties which are nonetheless comprehensible to a listener who awaits the return of the tonal center, knowing where in the harmonic system it will be but thrilled by the suspense of not being able to predict its time of arrival or what surprises there may be along the way.

2) The tonal center of an Indian raga is established by the drone - not technically a "pedal point," but similar in that it anchors music built on any of a number of scales which, like the scales used by Bach, are intrinsically hierarchical, meaning that the music made from them obeys a complex system of expected relationships (in this case melodic rather than harmonic as in Western common practice). As in the Bach, the listener knows what is "normal" in the idiom and the musician plays off of listener expectation.

3) Debussy's "Voiles" piques listener expectation too, utilizing two familiar devices to do it: triadic harmony and the pedal point. The mood of atmospheric vagueness depends on a continual _suggestion_ of tonality - I like TwoPhotons' expression "phantom tonality" - resulting from the refusal of the whole-tone scale to settle on any definite tonal direction or resolution (although there is a clearly tonal moment in the middle of the piece). The "tonality" is not explicit and structural, and whether we call the iridescent effect "tonal" or not doesn't matter, so long as we understand how its effect assumes a tonal sense in the listener and plays with it.

4) The repeated "G" in Schoenberg's "Musette," despite its prominence in the "hierarchy" of the piece, is not a tonal center belonging to a systemic hierarchy. There is no such hierarchy in Schoenberg's idiom, no system of relationships between the notes of his scale, which listeners are expected to understand in principle and bring to the experience of this specific work. Any differences in degrees of emphasis, any particular relationships which may be heard in the course of the work, have been devised for this particular work, and if there is to be listener expectation of any sort it will be based on rhythmic and melodic shape, continuation of patterns, and repetition (as with the "G").

The point is that, in the Schoenberg, _there are no intrinsic relationships within the idiom as such that determine progression and listener expectation._ As I understand tonality, that is the defining factor. Based on that, I'd call the Bach and the Indian raga definitely tonal, the Debussy vaguely tonal, and the Schoenberg not tonal.


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## Woodduck

Mahlerian said:


> http://symposium.music.org/index.ph...imary-musical-language-of-tonality&Itemid=124
> 
> "The specific twelve-tone row and the _method_ of its employment serve to assure that _E_-flat and _B_-flat are *significant absolute tonal reference points in the [Wind Quintet]*. "
> 
> *There ya go.* It's _really_ easy to find similar papers.


Just got around to reading this. There I _don't_ go.

This article is a heap of bad analogies, nonsequiturs, irrelevancies and sophistries. Basically, the only attempt it makes at an actual demonstration of tonality in Schoenberg's Wind Quintet is to show that major sections of the piece start with a Bb followed by an Eb to start the main theme. The use of this sequence of pitches to mark structural points is supposed to prove that they "function" as the music's dominant and tonic, respectively - and since we have a "tonic" and a "dominant" we must have tonality, right?

_"Significant absolute tonal reference points"?_ Yikes.

From my reading in Schoenberg's theoretical writings (which I hasten to say is far from exhaustive, and might prove exhausting), I get the impression that he put a lot of stock in these "analogues" to tonal music which some people seem to want to claim are the real thing. I don't think he was ever able to make up his mind as to whether he was really a traditionalist or a revolutionary. Actually I think he liked having it both ways. In any event he seems to have been as brilliant (and to have kept as busy) at rationalizing his artistic procedures and their significance as he was at actually writing music. And I think some people are still rationalizing. The author of this article works very hard at it and does a pathetic job. As soon as I read the following I was tempted to read no further:

_In his writings, Schoenberg gives us three distinct reasons for rejecting a theory of "atonality:" 1) his constant reference to music of the past as models for his own music; 2) his conservative harmonic concepts drawn directly from nineteenth-century Austrian pedagogy; and 3) his explicit disavowal of the term "atonality."
_

Did I really read that? Anybody who thinks any _one_ of those is a reason for redefining tonality to include the Wind Quintet and to find tonic and dominant in it needs to come out of the conservatory library and take a walk in the sunshine. Obviously the author hasn't come out for a while, and has himself convinced that Schoenberg's pseudo-tonal contrivances are "drawn directly from nineteenth-century Austrian pedagogy."

Pedagogy... Starts the same way as pedantry.


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## millionrainbows

Woodduck said:


> 1) Bach's idiom is unambiguously tonal, utilizing a scale possessing an intrinsic hierarchy of great strength, orderliness, and complexity. Because of that hierarchy, *which is familiar to his listeners before they hear his music,* he can use a pedal point to create a passage of harmonic suspension or ambiguity, of great tension and tonal gravity, full of dissonances and uncertainties which are nonetheless comprehensible to a listener who awaits the return of the tonal center, knowing where in the harmonic system it will be but thrilled by the suspense of not being able to predict its time of arrival or what surprises there may be along the way.


You make it sound like we "know" something, but all we do is hear, basically. I think even CP tonality is based on tone-centricity as heard by the ear, with not much need for 'knowing' anything about the CP Tonal system. It's the same procedure as listening to the raga you mention: it's all harmonic, and it's all there to begin with. In CP tonality, there is a lot that is spread out, but all of this boils down to interval relations to "1."



> 2) The tonal center of an Indian raga is established by the drone - not technically a "pedal point," but similar in that it anchors music built on any of a number of scales which, like the scales used by Bach, are *intrinsically hierarchical,* meaning that the music made from them* obeys a complex system of expected relationships (in this case melodic rather than harmonic as in Western common practice). *As in the Bach, *the listener knows what is "normal" in the idiom *and the musician plays off of listener expectation.


I think it's all done by ear. All the ear has to do is near-instantly recognize the relationship of one note to 'root' and he's got it. No difference in raga or Bach.


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## isorhythm

millionrainbows said:


> You make it sound like we "know" something, but all we do is hear, basically. I think even CP tonality is based on tone-centricity as heard by the ear, with not much need for 'knowing' anything about the CP Tonal system. It's the same procedure as listening to the raga you mention: it's all harmonic, and it's all there to begin with. In CP tonality, there is a lot that is spread out, but all of this boils down to interval relations to "1."


I think there are things in any particular tradition that are learned. I don't think I, as a Westerner with only passing familiarity with Indian music, hear or feel all of the relationships that someone versed in that tradition does.

To someone familiar with Western music, it often takes just one F# in C major to create a strong feeling of the center shifting to G. I doubt that feeling is nearly as strong for someone not familiar with Western music (though at this point, that's virtually no one on earth, since these devices are used in pop music).


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## isorhythm

EDIT: sorry for the double post, I meant to add this as an edit to the above:

This is hard to prove. I remember when I was first getting into early music, I would sometimes find, like many modern listeners, that chants or polyphonic pieces seemed to end on the "wrong" note or chord. I don't believe that a feeling of non-resolution was what people back then were going for. And in fact, the more familiar I became with the music, the less I felt that.


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## Mahlerian

isorhythm said:


> EDIT: sorry for the double post, I meant to add this as an edit to the above:
> 
> This is hard to prove. I remember when I was first getting into early music, I would sometimes find, like many modern listeners, that chants or polyphonic pieces seemed to end on the "wrong" note or chord. I don't believe that a feeling of non-resolution was what people back then were going for. And in fact, the more familiar I became with the music, the less I felt that.


The same was true of my relationship to the music called "atonal." Despite all people have said in this thread, it needs to be reemphasized that my descriptions are in large part a product of my experience, not of any theory or argument. Those came later.


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## SeptimalTritone

I am not arguing that the affect of the diatonic scale, or triads, or diatonic V->I or V7->I resolution, or counterpoint that avoids parallel fifths and resolves 2nds/7ths/tritones and 4ths with the bass, or (in the above example) secondary dominants, are only, or even mostly, a cultural phenomenon. All of these elements have an acoustic and voice leading basis, and together provide an affect, generally regardless of culture.

I am only arguing that Schoenberg's music post op 10, which usually avoids these elements as driving forces, still has expectation, gravitation, relationships, and progression. It is also not necessary for the listener to know any theory to feel the music at the gut level, just as in common practice tonality.

It does take time to acclimate to, but, at least for me, Beethoven, Brahms, and Mahler all took a lot of time to acclimate to. Perhaps I'm a terrible listener, but so much flies by the screen so quickly, and one has to recall and remember at the gut level a lot that flew by the screen. This takes a while to get used to. The case is also true, and even more true, with Schoenberg.


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## millionrainbows

isorhythm said:


> I think there are things in any particular tradition that are learned. I don't think I, as a Westerner with only passing familiarity with Indian music, hear or feel all of the relationships that someone versed in that tradition does.


Generally speaking, I thought we were talking about the nature of tonality, as experienced in music, any music of any culture, which creates a sense of tone-centeredness. As Woodduck said earlier, _"...tonal centricity is not just another way of constructing music, much less is it just the singular way Western music was constructed for 300 years. It is at root a cognitive phenomenon of enormous significance, overwhelming prevalence, and great power in the music of mankind, rooted in human nature (as well as the perception of tone, but I'll leave that to millionrainbows) and employed because it satisfies felt human needs for intellectual and emotional coherence and satisfaction."
_


> To someone familiar with Western music _(?)_, it often takes just one F# in C major to create a strong feeling of the center shifting to G. I doubt that feeling is nearly as strong for someone not familiar with Western music (though at this point, that's virtually no one on earth, since these devices are used in pop music).


If that includes everyone on Earth, then I would hesitate to call this strong feeling "Western," and it also degrades this already-flimsy premise that tonality is dependent on being enculturated or knowledgeable. As was said, perception of tonal centricity is a universal phenomenon of hearing, and is harmonic in nature.


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## millionrainbows

SeptimalTritone said:


> I am not arguing that the affect of the diatonic scale, or triads, or diatonic V->I or V7->I resolution, or counterpoint that avoids parallel fifths and resolves 2nds/7ths/tritones and 4ths with the bass, or (in the above example) secondary dominants, are only, or even mostly, a cultural phenomenon. All of these elements have an acoustic and voice leading basis, and together provide an affect, generally regardless of culture.


Good, then it sounds like you agree that the perception of tonal centricity, and the devices used to accomplish this, are ultimately rooted in acoustic phenomena, regardless of all the other trappings associated with these practices.



> I am only arguing that Schoenberg's music post op 10, which usually avoids these elements as driving forces, still has expectation, gravitation, relationships, and progression. It is also not necessary for the listener to know any theory to feel the music at the gut level, just as in common practice tonality.


Yes, but Schoenberg used various contrived devices as 'analogies' to those elements you mentioned. These included special considerations in row construction, tone emphasis in boundary areas, repetition, metric and rhythmic emphasis, and other kinds of musical logic which he wrote books on, like Fundamentals of Musical Composition and the Harmonielehre.

While he attempted to create tonality in these ways, the 12-tone method has no prevailing tonal hierarchy which asserts tonal associations in the local and macro-structures, like tonality does. If 12-tone *did *have a completely integrated system, like Babbitt and George Perle were after, then the result would not aid in the pursuit of a tonal-centric result, but would exhibit features pertaining to the row.



> It does take time to acclimate to, but, at least for me, Beethoven, Brahms, and Mahler all took a lot of time to acclimate to. Perhaps I'm a terrible listener, but so much flies by the screen so quickly, and one has to recall and remember at the gut level a lot that flew by the screen. This takes a while to get used to. The case is also true, and even more true, with Schoenberg.


Perhaps that is because what Woodduck said earlier applies: _"It's true that some listeners feel that such music is "unnatural," and that's because they share the statistically universal instinct which tells them that tonality is a natural phenomenon - which it is - and therefore they find that music which uses the familiar materials of tonal music - the notes of the chromatic scale, in this case - but frustrates their expectations by not organizing these notes tonally, sounds "wrong" to them."

_I think that any listener worth his salt would agree that Schoenberg is "not yer grandpa's tonality."

And beyond that, we need to keep talking about the ways this is accomplished, not just our subjective perception of it, because ultimately, the two go hand in hand. Otherwise, we are in la-la land again.

Let's keep up the rigor of this discourse.


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## millionrainbows

isorhythm said:


> This is hard to prove. I remember when I was first getting into early music, I would sometimes find, like many modern listeners, that chants or polyphonic pieces seemed to end on the "wrong" note or chord. I don't believe that a feeling of non-resolution was what people back then were going for. And in fact, the more familiar I became with the music, the less I felt that.


As Woodduck said, _"Although it's true that the sensation of tonal centricity is attenuated or suspended in some music written before Schoenberg's innovation, it is rarely absent for long and, more importantly, the presumption of its existence as a norm against which the music in question is to be heard is rarely if ever called into question. This is as true for the floating triads (with their inherent tonal suggestiveness) of Debussy as for the tonally ambiguous chromatic excursions of Wagner (which can only be ambiguous because they are fundamentally tonal)."

_And also holds true, I might add, for chants and polyphonic pieces. Although it's possible this was their artistic intent. At any rate, if the effect is a feeling of non-resolution, if it started out clearly in C and ended on F, then that's the effect, and that's the feeling. Maybe they were working with an inflexible system of tetrachords, like Schoenberg was.:lol:


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## millionrainbows

Mahlerian said:


> In my view, the idea that tonality is universal is based in either:
> 
> 1 - A belief that western music, and specifically the common practice era, is the most natural of all musics, which others aspire to be
> 
> 2 - A definition of tonality that covers everything except certain specific music in the 20th century, which definition, if examined, is inherently contradictory and nonsensical (because it requires music that's not tonal to also be tonal, unless you add in ad hoc arguments like Millionrainbows' stuff about ordered sets)
> 
> The idea that Schoenberg came along and wrote the first music that was ever in the history of humanity not tonal is historically short-sighted (tonality was, after all, only 300 or so years old) and Eurocentric (no other group of people ever developed tonality).
> 
> The third option, of course, is the very common dislike of Schoenberg and the belief, based simply in that dislike, that there's something inherently wrong (sometimes voiced as a claim that it's unnatural) with the music (and some or all of the rest of modernist music) because the person dislikes it.


That's not my reasoning, and I do believe that tonality is a universal phenomenon, based on the way the ear hears, and on the physics of sound (sonance), which can be expressed as ratios. Also, music which is tonal exhibits and uses these harmonic principles as its infrastructure. The harmonic model which manifests this truth is present in the structure of the music itself, as hierarchies of tones.

Highly chromatic and 12-tone musics are poor examples of how this works; they are the manifestation of tonality's weakening or dissolution, not meaning to sound negative. I like spicy food, too.


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## millionrainbows

Mahlerian said:


> The same was true of my relationship to the music called "atonal." Despite all people have said in this thread, it needs to be reemphasized that my descriptions are in large part a product of my experience, not of any theory or argument. Those came later.


I'm not sure what it is you are trying to say with this statement. Earlier, you were stating that the phenomenon of universal tonality was based on flawed subjective beliefs, prejudices, and ideas. Now you are saying that your subjective experience of tonality came before you had any theories about what tonality is.

It seems to me that you, too, are experiencing a very basic perception; one which exists in all men, through all history, and is based ultimately on the way we hear.

I, too, am basing my ideas about Schoenberg and tonality on my basic gut instincts; but I am humble enough, and rational enough, to know that there is a reason behind why I hear it this way, and that the devices and methods which produce this feeling of tonality in me are actually structural features, made manifest as sounds, and exist objectively in the music.

That's what I thought this discussion was about: the reasons why, and the various methods used, to create tonality, or a reasonable facsimile thereof. :lol:

Otherwise, we are back in subjective la-la land.


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## Mahlerian

millionrainbows said:


> I'm not sure what it is you are trying to say with this statement. Earlier, you were stating that the phenomenon of universal tonality was based on flawed subjective beliefs, prejudices, and ideas. Now you are saying that your subjective experience of tonality came before you had any theories about what tonality is.


No, I said that the idea of a universal tonality that does not include atonal music is based on bias and prejudice. If you want to define tonality as any kind of sustained and audible relationship between tones, go ahead.



millionrainbows said:


> It seems to me that you, too, are experiencing a very basic perception; one which exists in all men, through all history, and is based ultimately on the way we hear.


But not in the same way, clearly. If you say that there is a universal tonality, you must recognize that this includes plenty of things which might strike one at first as strange or disordered.



millionrainbows said:


> I, too, am basing my ideas about Schoenberg and tonality on my basic gut instincts; but I am humble enough, and rational enough, to know that there is a reason behind why I hear it this way, and that the devices and methods which produce this feeling of tonality in me are actually structural features, made manifest as sounds, and exist objectively in the music.


I didn't say I'm basing them on gut instincts. It's because I still cannot rationally justify the opposite, that all other music is tonal while Schoenberg's is not. There's just no quality about it that I perceive that would make that true.



millionrainbows said:


> That's what I thought this discussion was about: the reasons why, and the various methods used, to create tonality, or a reasonable facsimile thereof.


No, it's been a bunch of rationalizations for people's preconceptions that "atonal" music can't possibly be tonal, in the face of any evidence to the contrary. I've taken the weakest possible assertion for my position, that any other definition is self-contradictory, and the response consisted only of Isorhythm dithering over whether or not he could give any definition at all (except, of course, that Schoenberg simply HAS to be atonal).


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## millionrainbows

Woodduck said:


> I believe that tonality, though it may be encoded in certain compositional techniques or arrangements of tones, should not be thought of as a product or property of them, and cannot be created ad hoc by abstractly conceived systems of musical organization.


I don't, but you are short-changing the importance of the harmonic model, and over-emphasizing the subjective. The fact of harmonic relationships (sonance) is real, and is manifest as sound waves, and can be expressed as ratios. _It can be quantified._

The tonal system, or any music which creates a sense of tonality, (or even a guy playing a primitive string instrument 1000 years ago), _models_ the harmonic relationship of sound. So this 'model' is built-in to the system which creates the music, whether it be the CP Tonal system as manifest in a written score, or a simple bamboo flute, and the way holes were drilled into it to create a low fundamental with higher harmonics.



> I believe that tonality is a perceptual phenomenon which arises from a number of causes, essentially from the interaction of acoustical phenomena, the brain's ways of processing these, and other functions (some constant or universal, some variable) of the human psyche, its sensations, concepts, and emotions - all subject to a process of learning. Tonality is a perceived system of dynamic relationships between musical tones, entailing mutual influence and attraction between tones in more or less hierarchical relation to a central tone and to each other.


Yes, go on...



> ...These dynamic relationships are not inherent in sounds, yet - and this is crucial - _they are perceived as if they were._


Huh? Here's where we diverge. If ratios like 1:1 and 3:4 can exist as waves on a pond, they are real, just as sound waves are. The waves then get transferred to our eardrums, and become eardrum waves. That's pretty close to being real.



> And, just as crucially, _that perception cannot be created by design, but must evolve through experience._


Again, I cannot concur. They both seem to emerge at the same time.


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## millionrainbows

Mahlerian said:


> No, I said that the idea of a universal tonality that does not include atonal music is based on bias and prejudice.


You're confusing "universal tonality" as I use the idea (as a natural human experience because we hear with our ears that way, and because sound is that way) with systems of music, such as modernism).



> If you want to define tonality as any kind of sustained and audible relationship between tones, go ahead.


Not _any_ kind, but one based on harmonic relationships to a single note.



> If you say that there is a universal tonality, you must recognize that this includes plenty of things which might strike one at first as strange or disordered.


No, not "a" universal tonality. You're talking about it as if it were some kind of academic faction.

I love Expressionism, as well. You're making this sound as if anyone who doesn't like 12-tone music, or questions its 'tonal pedigree' is some sort of narrow-minded totalitarian, or worse.



> ...I still cannot rationally justify...that all other music is tonal while Schoenberg's is not. There's just no quality about it that I perceive that would make that true.


Schoenberg's post Op. 10 12-tone music is tonal just as Stevia is sweet. But for music to truly be tonal, it's structure must manifest the harmonic model, which is a ratio-based model, based on ratios to a "1". Schoenberg's 12-tone system is not ratio-based, but is based on quantitative absolutes.



> ...it's been a bunch of rationalizations for people's preconceptions that "atonal" music can't possibly be tonal, in the face of any evidence to the contrary. I've taken the weakest possible assertion for my position, that any other definition is self-contradictory, and the response consisted only of Isorhythm dithering over whether or not he could give any definition at all (except, of course, that Schoenberg simply HAS to be atonal).


In order for the music to be tonal, it, and the system which produced it, must reflect the harmonic model, which is ratio-based. 12-tone is not ratio-based, it is quantities. It can not possibly be tonal.

Schoenberg created a simulation of tonal procedures and devices, by using clever analogies. I like it a lot. It's great music, but it's not tonal.


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## Mahlerian

millionrainbows said:


> You're confusing "universal tonality" as I use the idea (as a natural human experience because we hear with our ears that way, and because sound is that way) with systems of music, such as modernism).


I hear Schoenberg's music as tonal, like all kinds of other things. It has centricity and definite harmonic relationships. Why doesn't it qualify for your universal tonality?



millionrainbows said:


> Not _any_ kind, but one based on harmonic relationships to a single note.


Like in Schoenberg.



millionrainbows said:


> No, not "a" universal tonality. You're talking about it as if it were some kind of academic faction.


Huh?



millionrainbows said:


> I love Expressionism, as well. You're making this sound as if anyone who doesn't like 12-tone music, or questions its 'tonal pedigree' is some sort of narrow-minded totalitarian, or worse.


I am? I don't believe that, just that there's no reason to say that atonality and tonality are separate categories.



millionrainbows said:


> Schoenberg's post Op. 10 12-tone music is tonal just as Stevia is sweet. But for music to truly be tonal, it's structure must manifest the harmonic model, which is a ratio-based model, based on ratios to a "1". Schoenberg's 12-tone system is not ratio-based, but is based on quantitative absolutes.


And it's also ratio-based. In fact, the ratios are the exact same ones found in other Western music.



millionrainbows said:


> BTW, 2+2 is 4.


If only the definitions of tonality offered here showed the same kind of respect for logic.


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## Woodduck

millionrainbows said:


> ... you are short-changing the importance of the harmonic model, and over-emphasizing the subjective. The fact of harmonic relationships (sonance) is real, and is manifest as sound waves, and can be expressed as ratios. _It can be quantified._
> 
> The tonal system, or any music which creates a sense of tonality, (or even a guy playing a primitive string instrument 1000 years ago), _models_ the harmonic relationship of sound. So this 'model' is built-in to the system which creates the music, whether it be the CP Tonal system as manifest in a written score, or a simple bamboo flute, and the way holes were drilled into it to create a low fundamental with higher harmonics.


I'm not sure how much we actually agree or disagree about the basis of tonal perception. I do agree that the most basic elements of certain tonal systems - at least a tonic, and very often a prominent position for the fifth scale degree - draw their raw material from the harmonic series, and that the hierarchy of overtones and ratios we hear _tends_ to privilege certain tones and harmonies over others in the making of music. But musical systems differ quite widely in their vocabulary - i.e. in the scales they employ. Our major scale and the tonal hierarchy built upon it adheres pretty closely to the hierarchy of the series, but other scales and tonal hierarchies diverge markedly. Many scales are clearly not derived from a preexisting harmonic archetype. I wonder what objective physical principles you would adduce to explain that.

I suspect that what you're calling my "overemphasizing the subjective" is my emphasis on the nature of perceptual organization, which, as gestalt psychologists explained long ago, is hierarchical both fundamentally and at every stage. The brain creates hierarchies whenever it perceives anything; it's how we get beyond sense perception to ideation. It's also how we make sense among the ideas we form, with the specific seeking context and reason in the general, the contingent and peripheral in the causal and fundamental. I believe that this is the most basic psychological mechanism which gives rise to the tendency to organize tones in systematic hierarchy, and that in carrying out this activity we find in the harmonic series an amazing gift of nature which presents to our ear - our brain - a hierarchy ready-made. But we aren't compelled to make any particular use of that hierarchy. Music, as such, is not a product of harmony, but of art. Music as an art may tend to follow, more or less, acoustically derived templates in the ways it organizes pitched sounds, because we perceive sounds within sounds and find them pleasing. But aesthetic cognizance of the harmonic series is not obligatory: there are scales consisting of only two or three notes (some American Indian music is like this), and still one will function clearly as a tonic, with the others functioning without audible relationship to partials and ratios.

There are other psychological, and even physiological, factors which make tonality appealing, e.g., the sense of stability, resolution, relaxation of tension. It's a common reaction to the concentration of dissonance in atonal music that it shortchanges this end of the feeling spectrum, that it's relentlessly tense. But of course tension is perceived in the context of style; dissonances seem less dissonant when all chords are dissonant. The objective degrees of dissonance in the harmonic series can't fully determine how dissonances are perceived subjectively in actual music.


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## millionrainbows

Mahlerian said:


> The idea that Schoenberg came along and wrote the first music that was ever in the history of humanity not tonal is historically short-sighted *(tonality was, after all, only 300 or so years old)* and Eurocentric (no other group of people ever developed tonality).


This statement shows that you are talking about something other than what I mean by 'universal tonality' and its being an innate feature of hearing and being human.

Our sense of tonality, tonal centers, and tone centricity came first, way before the CP Tonal period.


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## millionrainbows

Woodduck said:


> I'm not sure how much we actually agree or disagree about the basis of tonal perception. I do agree that the most basic elements of certain tonal systems - at least a tonic, and very often a prominent position for the fifth scale degree - draw their raw material from the harmonic series, and that the hierarchy of overtones and ratios we hear _tends_ to privilege certain tones and harmonies over others in the making of music.


What about unison (1:1) and the octave (2:1)? Those are harmonic ratios which give meaning to pitch equivalency, which is the way we all hear. All the other ratios follow from this: 2:3, 3:4, and so on. These are manifest as waves on our eardrums, like ripples on a pond. I don't question that, and that must be accepted as axiomatic if this discussion is to continue in a rewarding way.



> But musical systems differ quite widely in their vocabulary - i.e. in the scales they employ.


Why should that be problematic? There can be many possible harmonic models. A "model" does not have to adhere to the harmonic series; it can be any scale which covers an octave. Our ears and brain will hear the scale steps as ratios to "1" or the starting point.

If scales had to adhere strictly to the harmonic series, then our diatonic scale would be inaccurate, since the harmonic series features a flat-seven very early on.



> Our major scale and the tonal hierarchy built upon it adheres pretty closely to the hierarchy of the series, but other scales and tonal hierarchies diverge markedly.


Again, I am not talking about "the" harmonic series, but harmonic models. The "12" division of our octave is quite arbitrary. But _any_ division of the octave could be used to create a series of ratios built on its steps.



> Many scales are clearly not derived from a preexisting harmonic archetype. I wonder what objective physical principles you would adduce to explain that.


Again, we need to get on the same page. You need to first realise that a sense of tonality and tonal gravity can be created with any scale or octave division. This sense of tonality is primal, and existed long before the CP Tonal tradition.


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## millionrainbows

Mahlerian said:


> In my view, the idea that tonality is universal is based in...a
> belief that western music, and specifically the common practice era, is the most natural of all musics, which others aspire to be.


We're not on the same page. "A universal sense of tonality or tone-centricity" is innate to humanity and the way we hear. You're talking about tonality as if it were a variety of compositional practices.



> A definition of tonality that covers everything except certain specific music in the 20th century...is inherently contradictory and nonsensical...


The reason Schoenberg & company's music is not considered tonal is because it was produced using the 12-tone method, it's just that simple. Nothing against Schoenberg; I love the man & his music.

It's difficult to have an objective discussion about tonality when you keep bringing Schoenberg up in a personal way, as if he was being victimized; and the use of terms like 'prejudice' and 'bias.'



> The third option, of course, is the very common dislike of Schoenberg and the belief, based simply in that dislike, that there's something inherently wrong (sometimes voiced as a claim that it's unnatural) with the music (and some or all of the rest of modernist music) because the person dislikes it.


This can be a productive discussion if it stays objective. It should have nothing to do with 'like' or 'dislike' but only how tonality is created, and what features of the musical logic creates that.

The majority of all music throughout Man's history (using sustained pitches, not drum music, of course) is tonal, in that it creates a sense of tone centricity which feels and sounds natural, because it is based on natural principles. Likewise, 99 percent, if not all, of modern popular music is tonal.

The brilliance of Schoenberg is that he was able to create a method, and music, which is not tonal. That's why I was attracted and fascinated by it.


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## Mahlerian

millionrainbows said:


> This statement shows that you are talking about something other than what I mean by 'universal tonality' and its being an innate feature of hearing and being human.
> 
> Our sense of tonality, tonal centers, and tone centricity came first, way before the CP Tonal period.


Like I've said, your definition of tonal is fine, but you need to acknowledge that it also encompasses 12-tone music.


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## millionrainbows

Woodduck said:


> I suspect that what you're calling my "overemphasizing the subjective" is my emphasis on the nature of perceptual organization, which, as gestalt psychologists explained long ago, is hierarchical both fundamentally and at every stage. The brain creates hierarchies whenever it perceives anything; it's how we get beyond sense perception to ideation. It's also how we make sense among the ideas we form, with the specific seeking context and reason in the general, the contingent and peripheral in the causal and fundamental. I believe that this is the most basic psychological mechanism which gives rise to the tendency to organize tones in systematic hierarchy, and that in carrying out this activity we find in the harmonic series an amazing gift of nature which presents to our ear - our brain - a hierarchy ready-made.


I think it's based more on sensual phenomena than you do. Of course, the brain must process the input, but mustard tastes like mustard, red is red, and these are instantaneous reactions, requiring very little horizontal processing time.



> But we aren't compelled to make any particular use of that hierarchy. Music, as such, is not a product of harmony, but of art. Music as an art may tend to follow, more or less, acoustically derived templates in the ways it organizes pitched sounds, because we perceive sounds within sounds and find them pleasing.
> 
> But aesthetic cognizance of *the harmonic series *is not obligatory: there are scales consisting of only two or three notes (some American Indian music is like this), and still one will function clearly as a tonic, with the others functioning without audible relationship to partials and ratios.


This is a troublesome statement; if a note functions as a tonic ("1"), the subservient divisions _must_ be a ratio of that.

Also, you are again mistaking "the" harmonic series as what I refer to when I say tonality is based on harmonic principles. I use the term "harmonic" as an adjective, not as a noun. Please refer to this link to the definitions, and remember it:

~https://en.wiktionary.org/wiki/harmonic




> There are other psychological, and even physiological, factors which make tonality appealing, e.g., the sense of stability, resolution, relaxation of tension. It's a common reaction to the concentration of dissonance in atonal music that it shortchanges this end of the feeling spectrum, that it's relentlessly tense. But of course tension is perceived in the context of style; dissonances seem less dissonant when all chords are dissonant. The objective degrees of dissonance in the harmonic series can't fully determine how dissonances are perceived subjectively in actual music.


 I agree.


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## Woodduck

millionrainbows said:


> What about unison (1:1) and the octave (2:1)? Those are harmonic ratios which give meaning to pitch equivalency, which is the way we all hear. All the other ratios follow from this: 2:3, 3:4, and so on. These are manifest as waves on our eardrums, like ripples on a pond. I don't question that, and that must be accepted as axiomatic if this discussion is to continue in a rewarding way.
> 
> Why should that be problematic? There can be many possible harmonic models. A "model" does not have to adhere to the harmonic series; it can be any scale which covers an octave. Our ears and brain will hear the scale steps as ratios to "1" or the starting point.
> 
> If scales had to adhere strictly to the harmonic series, then our diatonic scale would be inaccurate, since the harmonic series features a flat-seven very early on.
> 
> Again, I am not talking about "the" harmonic series, but harmonic models. The "12" division of our octave is quite arbitrary. But _any_ division of the octave could be used to create a series of ratios built on its steps.
> 
> Again, we need to get on the same page. You need to first realise that a sense of tonality and tonal gravity can be created with any scale or octave division. This sense of tonality is primal, and existed long before the CP Tonal tradition.


I believe we are on the same page. I was just trying to be sure i understood your views. The only statement that confuses me in the above is "All the other ratios follow from this." What do you mean by "follow"? Physical phenomena don't "follow," they just are.


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## millionrainbows

Mahlerian said:


> Like I've said, your definition of tonal is fine, but you need to acknowledge that it also encompasses 12-tone music.


Why should I do that if the 12-tone method is incapable of producing truly tonal music? This is not a put-down of 12-tone or Schoenberg, either. I love Schoenberg, and I have all of his books and most of his music, and scores of his string quartets, and the Webern 2-piano reduction of Five Pieces for Orchestra.

When I listen to the String Quartet No. 3, I like it, but I know it's not tonal. I'm listen to it in more linear ways. The Fourth String Quartet is even more beautiful, but I do not hear it as tonal, nor do I think it's wise or productive to try to get tonality from it.

Of course, I love his tonal works as well. I'm listening to Chamber Symphony No. 1 as we speak.

We have to remain objective, and define our terms clearly, if we are to make progress.


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## millionrainbows

Woodduck said:


> I believe we are on the same page. I was just trying to be sure i understood your views. The only statement that confuses me in the above is "All the other ratios follow from this." What do you mean by "follow"? Physical phenomena don't "follow," they just are.


By "follow," I am talking about the way ratios progress from "1" into "infinity" towards zero. Picture fractions as occupying the space on a number line, starting at 1 and going to the left towards zero. 1, 1:2, 2:3, 3:4, 4:5, 5:6, 6:7, etc.

Consider a string stretched across this space, from zero to one. Any division you create on that string is a ratio. There are infinite ways of dividing it, just as there are infinite points.

If you want to criticize this as being too arbitrary for our ears, remember that our equal-tempered scale only approximates "just" simple intervals, and the actual ratios we hear are much more complex.

The way we quantify ratios "follows" a progression, from 1 to infinity, approaching zero, if you will.


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## Mahlerian

millionrainbows said:


> When I listen to the String Quartet No. 3, I like it, but I know it's not tonal. I'm listen to it in more linear ways. The Fourth String Quartet is even more beautiful, but I do not hear it as tonal, nor do I think it's wise or productive to try to get tonality from it.


Like I said, it's not any kind of effort on my part to hear the tonality in these works. It's just there, present, as I listen.



millionrainbows said:


> We have to remain objective, and define our terms clearly, if we are to make progress.


Exactly, and no one here has yet come up with a definition for a "Universal Tonality" that doesn't also include 12-tone music.


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## millionrainbows

Mahlerian said:


> Like I said, it's not any kind of effort on my part to hear the tonality in these works. It's just there, present, as I listen.


That's not good for a discussion on the nature of tonality. It defines nothing, it tells us nothing objective. You cannot demonstrate why it sounds tonal, and you can't offer any objective information which supports your assertion.



> ...no one here has yet come up with a definition for a "Universal Tonality" that doesn't also include 12-tone music.


Again, 'a sense of universal tonality' is innate, and existed from Man's earliest origins. I thought you agreed with that, but apparently not.

The Second Viennese School is an exception in modernism, since it by and large is 12-tone (don't throw Berg at me).

Generally, the only composer who comes close are Bartok, like in his violin sonata, but I understand it was 12-tone as well. And there's always Hauer.

Another major factor in the exclusion of 12-tone music as tonal is that, while all the rest of the modernists may be only vaguely tonal, they are still tonal, and use harmonic devices. Harmonic devices are a very tonal thing. This relates them in a very important way to tonality, as even the simplest triad has tonal centricity. A C-major triad always retains its identity, no matter how you stack it.

Schoenberg's Ode to Napoleon contained Eb triads in tribute to Beethoven's Eroica, but even there, there is no such thing as a "tonal triad" in serialism, because when you invert C-E-G you get C-Ab-F. Even the simplest tonal procedures, like chord imversion, have no tonal meaning or context in 12-tone methodology.

Also, the way Bartok has "nodes" or localized tonal centers should not be confused with Schoenberg's "note emphasis" points. The Bartok nodes can have tonal meaning and context, while the Schoenberg points do not, since there is no tonal infrastructure.


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## Mahlerian

This discussion has become an exercise in special pleading on the part of those who offer something as a clear exception to rules they care not to define.


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## Barbebleu

Don't you just love the fact that the original poster of this thread has never been heard of again since his original post? Clearly, his work here is done.


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## Woodduck

Mahlerian said:


> This discussion has become an exercise in special pleading on the part of those who offer something as a clear exception to *rules they care not to define.*


How ungracious. On the contrary, people are defining their terms as clearly as they can.

It seems to me that your assertion that "tonal centers" exist in Schoenberg's 12-tone music is the one thing in the discussion for which no real evidence has yet been produced (and not only in this thread). Examples of such "tonal centers" cited so far here - the pedal point "G" in the "Musette" cited by Septimal Tritone, and the recurrent Bb followed by Eb in the first movement of the Wind Quintet cited in the Graham Phipps article - are not true harmonic centers representing a tonal idiom, despite their structural functions in their respective works. They are "pseudo-tonal" devices, analogous to a pedal point and a key center, but without their tonal functions. The fact that you seem not to have noticed the difference, and could offer that article as evidence of tonality in the music, makes me suspect that when we talk about tonal centers we are just not talking about the same thing.

Unlike millionrainbows, my reading in Schoenberg's own writings is sketchy, but I wonder if he was not himself inconsistent about the matter of tonality in his own music, or at least whether he didn't undergo a shift in his thinking. At the time he was preparing the theoretical groundwork of his 12-tone method, he regarded tonality as a property of common practice harmony only (denying its presence in the church modes, for example). He used such expressions as "tones related only to each other" (rather than hierarchically to a tonal center) and "emancipation of the dissonance" (obscuring the difference between dissonance and consonance, which could only be achieved if the audible difference had no tonal meaning - if dissonance ceased to suggest tonal function). He seems to have been convinced that the complexity which tonal harmony had reached had brought tonality to the end of its effective usefulness as a way of structuring music (which may have applied to his own musical needs, but obviously wasn't relevant to other people who went right on writing tonal music of immense variety and freshness), and necessitated its replacement by some other organizing principle. What he replaced it with was a system in which vertical harmony would be extrapolated somehow from a horizontal sequence (row) chosen in such a way as to avoid tonal implications. He was explicitly concerned to _prevent_ the sense of tonal expectation from arising: non-repetition, the forbidding of doubling, and the avoidance of triadic harmony were various means of ensuring this (it amuses me that in practice the "emancipation of the dissonance" was achieved by the shackling of the consonance). Works like the Piano Suite and the Wind Quintet sound to me pretty explicit in pursuit of this goal, pretty strict in keeping any real tonal tendencies from arising, and that's consistent with what he said he was aiming for, "pseudo-tonal" devices such as the aforementioned notwithstanding. The fact that he relaxed enough to allow some suggestions of tonality into serial works, and even wrote some tonal music (feeling nostalgic for the call of nature, I assume), doesn't negate the radicalness of his new harmonic language or the theories he based it on.

My personal feeling is that if you're going to build harmonic music on the chromatic scale used in common practice music and write in forms similar to traditional forms, you're going to have a very challenging task to keep tonal suggestiveness at bay. The listener will be able to find _inside_ the music's textures continual hints of tonal direction even if the total harmonic context and trajectory of the music immediately and continually negates such direction. I consider such music - by Schoenberg and others - not simply _atonal_ (which could indicate simply a lack of awareness of tonality or an indifference to it) but _contratonal. _In that regard I agree that the term "atonal" is not specific enough.


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## Woodduck

Barbebleu said:


> Don't you just love the fact that the original poster of this thread has never been heard of again since his original post? Clearly, his work here is done.


We can only hope that he is contemplating the accumulated wisdom of his betters, and that he will soon emerge from his solitude having produced the Great American Opera.


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## Barbebleu

Woodduck said:


> We can only hope that he is contemplating the accumulated wisdom of his betters, and that he will soon emerge from his solitude having produced the Great American Opera.


Oh goodness, I hope not!


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## isorhythm

I think I've mentioned this before, but I'm just going to reproduce most of a letter Schoenberg wrote to Rene Leibowitz in 1947. You can find the whole thing on Google Books. He is answering questions posed by Leibowitz, and I don't know exactly what the questions were, but it's pretty easy to infer the gist. Bolding mine.



> Under the term of loosening the 'rigour' of the treatment of the twelve tones you mean probably the occasional doubling of octaves, occurrences of tonal triads and hints of tonalities. Many of the restrictions observable in my first works in this style, and what you call 'pure', derived more theoretically than spontaneously from a probably instinctive desire to *bring out sharply the difference of this style with preceding music.*
> 
> Avoiding doubling of octaves was certainly a kind of exaggeration because if the composer did it, nature denied it. Every single tone contains octave doubling. Curiously I still do it not all too frequently, though I am today conscious that it is a question of mere dynamics: to emphasize one part more distinctly.
> 
> As regards hints of a tonality and intermixing of consonant triads one must remember that the main purpose of 12-tone composition is: production of coherence through the use of a unifying succession of tones which should function at least like a motive. *Thus the organizatorial efficiency of the harmony should be replaced.*
> 
> It was not my purpose to write dissonant music, but to include dissonance in a logical manner without reference to the treatment of the classics: because such a treatment is impossible. *I do not know where in the Piano Concerto a tonality is expressed.*
> 
> It is true that the Ode at the end sounds like E flat. I don't know why I did it. Maybe I was wrong, but at present you cannot make me feel this.


Schoenberg, in 1947, did not think his 12-tone music was tonal - not even music like the piano concerto that a lot of people think "sounds tonal."

Editing to add: I expect one response will be that Schoenberg meant only "common practice" when he said "tonal," but that inference is clearly wrong and actually makes nonsense of everything he's saying. He clearly thinks that tonality can arise outside of common practice rules (end of his ode "sound like E flat," the whole idea of "hints of tonalities"). He just says that he doesn't do it much - and indeed that he consciously avoided it at first.


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## EdwardBast

Barbebleu said:


> Don't you just love the fact that the original poster of this thread has never been heard of again since his original post? *Clearly, his work here is done.*


Maybe he read the lot of us discoursing on the topic and decided he didn't want to learn it after all. Clearly _our_ work is done here!


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## Mahlerian

isorhythm said:


> Schoenberg, in 1947, did not think his 12-tone music was tonal - not even music like the piano concerto that a lot of people think "sounds tonal."


As I've explained before, by tonal, Schoenberg meant "in a key, expressed via functional harmony." This is clear from the context of remarks that are often used in support of the idea that he truly did believe in an atonal music. Even in the short excerpt, you didn't highlight the part that leads directly to the bolded section, where he says that tonality is the "treatment of the classics," by which he understood the classical tradition from Bach through Wagner, as in Harmonielehre.


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## isorhythm

Mahlerian said:


> As I've explained before, by tonal, Schoenberg meant "in a key, expressed via functional harmony." This is clear from the context of remarks that are often used in support of the idea that he truly did believe in an atonal music. Even in the short excerpt, you didn't highlight the part that leads directly to the bolded section, where he says that tonality is the "treatment of the classics," by which he understood the classical tradition from Bach through Wagner, as in Harmonielehre.


Your response and my edit anticipating it crossed.

He does not say that tonality is the treatment of the classics. He is actually saying the opposite; he seems to be responding to Leibowitz's claim that he's backsliding into tonality (that does seem to be what's going on here, right?) by saying that you can refer to the dissonance treatment of the classics in some ways without being tonal.

In short: the piano concerto has "cadences" that go dissonant --> more consonant. Schoenberg says that doesn't make it tonal. I don't know how much clearer he could be about it.


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## Mahlerian

isorhythm said:


> Your response and my edit anticipating it crossed.
> 
> He does not say that tonality is the treatment of the classics. He is actually saying the opposite; he seems to be responding to Leibowitz's claim that he's backsliding into tonality (that does seem to be what's going on here, right?) by saying that you can refer to the dissonance treatment of the classics in some ways without being tonal.
> 
> In short: the piano concerto has "cadences" that go dissonant --> more consonant. Schoenberg says that doesn't make it tonal. I don't know how much clearer he could be about it.


We've been over this before. Whenever Schoenberg uses the term tonality, he means functional, key-based tonality. He was adamant in that the music of the Neoclassicists, etc. was not tonal, but simply the use of triads that, when combined, cannot express a tonality, because they are not functionally related.

At other times, he suggested that the definition of tonality could be expanded to include his own music, saying that atonality is only a word for music the tonality of which has not yet been discovered.

There's a discussion here with Bethany Beardslee in reference to Babbitt, Schoenberg, and Webern, and Beardslee says that "All music is tonal." They remark how the idea that the emphasis of notes should be flat was a European notion with Boulez and Stockhausen and something that Schoenberg, Babbitt, and Webern certainly didn't believe in.


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## isorhythm

^You did not respond to my point above.

Schoenberg readily recognizes that there are such things as "hints" of tonality or that something can "sound like E flat" without, in the common practice sense, being properly in E flat.

That he may have written elsewhere that Stravinsky et al weren't tonal in the common practice sense is irrelevant. It does not mean that he failed to see a distinction between their musics' relationship to tonality and his own.


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## Mahlerian

isorhythm said:


> ^You did not respond to my point above.
> 
> Schoenberg readily recognizes that there are such things as "hints" of tonality or that something can "sound like E flat" without, in the common practice sense, being properly in E flat.


Yes, exactly. They weren't tonal in the common practice sense, which is how he defined tonality, so it can sound like it has hints of functional tonality without actually being constructed in that way.

I have never claimed that Schoenberg's later music is common practice, so I don't understand the relevance to this discussion.



isorhythm said:


> That he may have written elsewhere that Stravinsky et al weren't tonal in the common practice sense is irrelevant. It does not mean that he failed to see a distinction between their musics' relationship to tonality and his own.


Yes, he said that his music, unlike theirs, was an extension of tradition, and justified the dissonances it used, while theirs depended on the arbitrary whims of the composer.

I'm not saying he was right about that, but merely that he saw a distinction in terms of the relationship to common practice, and it was the opposite of what you're implying.


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## isorhythm

Mahlerian said:


> Yes, he said that his music, unlike theirs, was an extension of tradition, and justified the dissonances it used, while theirs depended on the arbitrary whims of the composer..


Well, now I'm curious - where did he say this?

I don't see how it could be true; Schoenberg's harmony, looked at vertically, is surely less related to common practice than Stravinsky's (pre-12-tone).


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## Mahlerian

isorhythm said:


> Well, now I'm curious - where did he say this?
> 
> I don't see how it could be true; Schoenberg's harmony, looked at vertically, is surely less related to common practice than Stravinsky's (pre-12-tone).


Look at his scathing comments on Neoclassicism. It's there. I don't have my copy of Style and Idea at hand, so I can't provide an exact reference, sorry.

I can understand how it could be true. Despite the lack of diatonic and triadic formations, Schoenberg's music applies the concepts of functional harmony to new kinds of harmonies, while Stravinsky's goes out of its way to obliterate functionality within the diatonic scale and uses triads against their former constructive meaning. Rosen says this as well in his book on Schoenberg.

At any rate, it's clear that neither composer wrote music that was common practice tonal, and we do agree on that, it's just whether or not the two should be put into separate categories or not that we disagree on.

Even there, I've suggested nonfunctional diatonic and nonfunctional chromatic as more accurate terms to replace Neoclassicism's version of tonality and expressionist/12-tone harmony, respectively.


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## Woodduck

I've been trying to discover what Schoenberg himself had to say about the presence of some sort of tonality in his 12-tone music. Over the course of these discussions he hasn't been quoted much, which seems odd considering that he turned out so much detailed and systematic theoretical writing, and that some here seem to know his writings pretty well. As both composer and theoretician he was nothing if not deliberate, thorough, and self-aware. If his 12-tone works are really tonal in some meaningful sense, Schoenberg could hardly have failed to comment on it and to attempt some explanation. But I have never seen any quote from him to substantiate the idea.

I know that Schoenberg viewed "tonality" as a property belonging entirely to Western harmonic music between approximately the Baroque and his own time. He considered the Medieval modes to be "devoid of tonality," or at best a confused stab at tonality; in fact he appeared not to understand their tonal organization at all (I was surprised to encounter statements such as "The effect of a fundamental tone was felt, but since no one knew which one it was, all of them were tried" - and "These reveal a remarkable phenomenon: the key of the underlying tonal series of which they are composed is different from the key in which the piece really exists.") He was also, apparently, not very curious about non-Western, and even Western ethnic, musics, with their diverse scales and tonal systems. I imagine he would have regarded them much as he did the church modes, as a primitive form of music which had not attained the logic of common practice harmony.

The other thing about Schoenberg's concept of tonality was that he seemed to view it primarily as a structuring device, a set of principles or laws by which music could be organized into parts both distinct and coherent: "I perceive in both of these functions, the conjoining and the unifying on the one hand, and on the other the articulating, separating, and characterizing, the main accomplishment of tonality" - and "The true reason for the marked development of tonality [was] to make what happens easily comprehensible. _Tonality is not an end in itself, but a means to an end."_ That last sentence seems key to his conviction that there was nothing to lose and everything to gain if he could devise a method of organizing music which would replace tonality's organizing function. And if he could - as he said he intended to do - what function would be left for tonality to perform? Why should it persist in any form?

The idea that Schoenberg sought to eliminate only common practice tonality, but not tonality as a more basic phenomenon, seems to me problematic, given the apparent lack of reference in his writings to any such "more basic" phenomenon, and particularly given the fact that the basic functions of common practice tonality and tonality as a larger phenomenon are fundamentally the same. The one unique characteristic of common practice music is the establishment of keys at different tonal levels and of modulation between them. But the notion that Schoenberg found it necessary to construct a system that produced a kind of harmony carefully calculated to prevent a sense of tonal stability from arising even moment-to-moment, merely in order to avoid the establishment of keys, is patently absurd. Wagner and Liszt had already achieved effective keylessness in the 1850s, although they had no interest in constructing a system around what was, for them, a specific expressive device; Schoenberg himself had done it in his own pre-12-tone works, using "free atonality" for the same kinds of programmatic, text-based works in which extremes of expression were required by a dramatic idea. Clearly, the reason Schoenberg felt he had to devise a new system of organizing music was that he wanted to write a kind of music - a music of extreme harmonic complexity and continuous development, yet in non-programmatic, "absolute" forms - which he knew _would not be coherent without the imposition of such a system._ And the reason it would not is simply that it would be without tonality: a system in which the notes of a scale perform recognized functions in relation to a central member of that scale. The listener's recognition of those functions is basic to all tonal systems, and where it is absent it is not merely common practice which has been abandoned.

I have never seen a statement of Schoenberg indicating a desire to retain any kind of tonality in his 12-tone works. But he certainly made statements indicating the intention of replacing tonality's functions, as he conceived them. Is it likely that there are significant aspects of his music, aspects so intimately bound up with his central concerns, that he never found it useful to discuss?


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## arpeggio

Manok said:


> I have a project that I think it would be best suited not to be tonal but I don't know anything other than 12 tone theory as far as modern music theory goes, can anyone help me out?


Check out Vincent Persichetti's _Twentieth-Century Harmony: Creative Aspects and Practice_: https://www.amazon.com/s/ref=nb_sb_ss_i_3_11?url=search-alias%3Daps&field-keywords=persichetti+20th+century+harmony&sprefix=persichetti%2Caps%2C125


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## isorhythm

arpeggio said:


> Check out Vincent Persichetti's _Twentieth-Century Harmony: Creative Aspects and Practice_: https://www.amazon.com/s/ref=nb_sb_ss_i_3_11?url=search-alias%3Daps&field-keywords=persichetti+20th+century+harmony&sprefix=persichetti%2Caps%2C125


Now we're talking! Thanks for the recommendation.


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## millionrainbows

Woodduck said:


> I've been trying to discover what Schoenberg himself had to say about the presence of some sort of tonality in his 12-tone music. Over the course of these discussions he hasn't been quoted much, which seems odd considering that he turned out so much detailed and systematic theoretical writing, and that some here seem to know his writings pretty well. As both composer and theoretician he was nothing if not deliberate, thorough, and self-aware. If his 12-tone works are really tonal in some meaningful sense, Schoenberg could hardly have failed to comment on it and to attempt some explanation. But I have never seen any quote from him to substantiate the idea.
> 
> I know that Schoenberg viewed "tonality" as a property belonging entirely to Western harmonic music between approximately the Baroque and his own time. He considered the Medieval modes to be "devoid of tonality," or at best a confused stab at tonality; in fact he appeared not to understand their tonal organization at all (I was surprised to encounter statements such as "The effect of a fundamental tone was felt, but since no one knew which one it was, all of them were tried" - and "These reveal a remarkable phenomenon: the key of the underlying tonal series of which they are composed is different from the key in which the piece really exists.") He was also, apparently, not very curious about non-Western, and even Western ethnic, musics, with their diverse scales and tonal systems. I imagine he would have regarded them much as he did the church modes, as a primitive form of music which had not attained the logic of common practice harmony.
> 
> The other thing about Schoenberg's concept of tonality was that he seemed to view it primarily as a structuring device, a set of principles or laws by which music could be organized into parts both distinct and coherent: "I perceive in both of these functions, the conjoining and the unifying on the one hand, and on the other the articulating, separating, and characterizing, the main accomplishment of tonality" - and "The true reason for the marked development of tonality [was] to make what happens easily comprehensible. _Tonality is not an end in itself, but a means to an end."_ That last sentence seems key to his conviction that there was nothing to lose and everything to gain if he could devise a method of organizing music which would replace tonality's organizing function. And if he could - as he said he intended to do - what function would be left for tonality to perform? Why should it persist in any form?
> 
> The idea that Schoenberg sought to eliminate only common practice tonality, but not tonality as a more basic phenomenon, seems to me problematic, given the apparent lack of reference in his writings to any such "more basic" phenomenon, and particularly given the fact that the basic functions of common practice tonality and tonality as a larger phenomenon are fundamentally the same. The one unique characteristic of common practice music is the establishment of keys at different tonal levels and of modulation between them. But the notion that Schoenberg found it necessary to construct a system that produced a kind of harmony carefully calculated to prevent a sense of tonal stability from arising even moment-to-moment, merely in order to avoid the establishment of keys, is patently absurd. Wagner and Liszt had already achieved effective keylessness in the 1850s, although they had no interest in constructing a system around what was, for them, a specific expressive device; Schoenberg himself had done it in his own pre-12-tone works, using "free atonality" for the same kinds of programmatic, text-based works in which extremes of expression were required by a dramatic idea. Clearly, the reason Schoenberg felt he had to devise a new system of organizing music was that he wanted to write a kind of music - a music of extreme harmonic complexity and continuous development, yet in non-programmatic, "absolute" forms - which he knew _would not be coherent without the imposition of such a system._ And the reason it would not is simply that it would be without tonality: a system in which the notes of a scale perform recognized functions in relation to a central member of that scale. The listener's recognition of those functions is basic to all tonal systems, and where it is absent it is not merely common practice which has been abandoned.
> 
> I have never seen a statement of Schoenberg indicating a desire to retain any kind of tonality in his 12-tone works. But he certainly made statements indicating the intention of replacing tonality's functions, as he conceived them. Is it likely that there are significant aspects of his music, aspects so intimately bound up with his central concerns, that he never found it useful to discuss?


As usual, another brilliant post by Woodduck. I completely agree with his statement: 
_
"...But the notion that Schoenberg found it necessary to construct a system that produced a kind of harmony carefully calculated to prevent a sense of tonal stability from arising even moment-to-moment, merely in order to avoid the establishment of keys, is patently absurd." 
_
...But I agree for perhaps other reasons, the prime one being that the 12-tone system cannot produce tonality because it is inherently a _quantitative_ system, not a _proportional_ one. Proportion (those ratios I'm always mentioning) is what harmony and tonality is, essentially: relations to "1."

So, 12-tone is not an "anti-tonal" method of doing things; it is simply not structured around pitch relations to a single note, but proportional in a relative way, in terms of relations of quantities (not specific pitches). This is better suited to the chromatic palette, using all 12 notes. Tonality lost its thrust when it became more chromatic. In tonality, less is more.

But instead, what 12-tone gives us is thematic and structural unity throughout the chromatic spectrum, which tonality, even constantly undulating and modulating tonality, cannot.

Schoenberg probably saw this as an advantage because 1.) he was already in a totally chromatic areas in which tonality had little specific meaning, and 2.) he was a thematic writer, and this was an excellent tool for doing themes and writing in counterpoint.


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## Mahlerian

millionrainbows said:


> As usual, another brilliant post by Woodduck. I completely agree with his statement:
> _
> "...But the notion that Schoenberg found it necessary to construct a system that produced a kind of harmony carefully calculated to prevent a sense of tonal stability from arising even moment-to-moment, merely in order to avoid the establishment of keys, is patently absurd."
> _


You see, I don't care for question-begging arguments. I prefer to make sure that my conclusion stays at the end rather than sandwiching it in the middle and hoping nobody notices.

But perhaps rhetorical flourishes can provide their own kind of brilliance to posts that depend on circular reasoning.


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## millionrainbows

Woodduck said:


> How ungracious. On the contrary, people are defining their terms as clearly as they can.


Hear, hear, and it can be tedious, but not as tedious as the replies.



> It seems to me that your assertion that "tonal centers" exist in Schoenberg's 12-tone music is the one thing in the discussion for which no real evidence has yet been produced (and not only in this thread).


 …and that assertion can easily be hidden behind subjectivity.



> Examples of such "tonal centers" cited so far here - the pedal point "G" in the "Musette" cited by Septimal Tritone, and the recurrent Bb followed by Eb in the first movement of the Wind Quintet cited in the Graham Phipps article - are not true harmonic centers representing a tonal idiom, despite their structural functions in their respective works. They are "pseudo-tonal" devices, analogous to a pedal point and a key center, but without their tonal functions. The fact that you seem not to have noticed the difference, and could offer that article as evidence of tonality in the music, makes me suspect that when we talk about tonal centers we are just not talking about the same thing.


…or that it's being obfuscated by constantly shifting the meaning of "tonality."



> Unlike millionrainbows, my reading in Schoenberg's own writings is sketchy, but I wonder if he was not himself inconsistent about the matter of tonality in his own music, or at least whether he didn't undergo a shift in his thinking. At the time he was preparing the theoretical groundwork of his 12-tone method, he regarded tonality as a property of common practice harmony only (denying its presence in the church modes, for example).


 I'll have to check in "Style and Idea" for the full context of that; I feel that surely Schoenberg had a general sense of what "experiencing tonality as a tonal center" was, in the general sense of the term (see Harvard Dictionary).

Like I've said before, to me, a general sense of tonality is established if an octave is divided into smaller constituent parts (becoming notes of a scale in relation to that octave), and the scale is based on that starting point. All functional relations follow from that naturally, forming a functional hierarchy, with no need to think about it.



> He used such expressions as "tones related only to each other" (rather than hierarchically to a tonal center) and "emancipation of the dissonance" (obscuring the difference between dissonance and consonance, which could only be achieved if the audible difference had no tonal meaning - if dissonance ceased to suggest tonal function).


Yes, but be sure not to confuse "tones" with "pitches." It's really a "pitch-abstract" set of relations. Dissonance and consonance now have no "tonal" or proportional meaning, but they do have a quantitative meaning, based on what interval sequence is created, forming an "interval template" which can start on any note ("transposition"), be inverted, and retrograded. It remains essentially the same, in a chromatic field. Tonality can't be this consistent. So now "dissonance" has no tonal or audible difference, but pitches have an exact quantity in relation to other.



> He seems to have been convinced that the complexity which tonal harmony had reached had brought tonality to the end of its effective usefulness as a way of structuring music (which may have applied to his own musical needs, but obviously wasn't relevant to other people who went right on writing tonal music of immense variety and freshness), and necessitated its replacement by some other organizing principle.


Yes, but other composers were not necessarily totally chromatic, as Schoenberg had been even in his later tonal works. I agree that he adopted the method for his own aims, but he was already on a chromatic trajectory.



> What he replaced it with was a system in which vertical harmony would be extrapolated somehow from a horizontal sequence (row) chosen in such a way as to avoid tonal implications. He was explicitly concerned to _prevent_ the sense of tonal expectation from arising: non-repetition, the forbidding of doubling, and the avoidance of triadic harmony were various means of ensuring this (it amuses me that in practice the "emancipation of the dissonance" was achieved by the shackling of the consonance).


I recall him saying that he avoided tonal tendencies in order to "test drive" the new system and see what it could do on its own terms. He seems to have been aware of the opposing tendencies, but I don't think he was out to "replace" or "subsume" tonality. He just had discovered a new way of structuring music, and since he was a classicist to begin with, he emulated forms and devices of that heritage, perhaps out of historical considerations of his stature and place in history…which seems to have worked.



> Works like the Piano Suite and the Wind Quintet sound to me pretty explicit in pursuit of this goal, pretty strict in keeping any real tonal tendencies from arising, and that's consistent with what he said he was aiming for, "pseudo-tonal" devices such as the aforementioned notwithstanding. The fact that he relaxed enough to allow some suggestions of tonality into serial works, and even wrote some tonal music (feeling nostalgic for the call of nature, I assume), doesn't negate the radicalness of his new harmonic language or the theories he based it on.


I agree; I hear no tonality whatsoever in those works.



> My personal feeling is that if you're going to build harmonic music on the chromatic scale used in common practice music and write in forms similar to traditional forms, you're going to have a very challenging task to keep tonal suggestiveness at bay. The listener will be able to find _inside_ the music's textures continual hints of tonal direction even if the total harmonic context and trajectory of the music immediately and continually negates such direction. I consider such music - by Schoenberg and others - not simply _atonal_ (which could indicate simply a lack of awareness of tonality or an indifference to it) but _contratonal. _In that regard I agree that the term "atonal" is not specific enough.


It does create confusion, and is very suggestive, because the 12-tone method is tonality's 'opposite,' if you are looking at the hierarchies of the systems themselves. 
I hesitate to say that 12-tone was intentionally created to oppose common practice tonality, but that was the dialectic it arose from: tonality was weakening beyond recognition. So, ironically, the net result is that 12-tone is indeed the exact opposite of tonality, in structural terms.

As it has panned out, 12-tone and serialism seem to have been treated to the 'lack of awareness' and 'indifference' you spoke of. So l propose, in half-jest, a new term for tonality: "aserial."

For me, increasing the chromaticism automatically weakens tonality. The challenge for listeners is to hear the music structurally, not tonally, and to listen for note-objects and thematic elements, which are linear and contrapuntal, not harmonic, or to listen to 'harmonic entities' which exist as events, without implying a harmonic goal. To me, hearing suggestions of tonality is a drawback, even in Schoenberg.

Elliott Carter is a chromaticist, and uses sets. Yet, he uses it in ways suited to a chromatic palette.


----------



## Mahlerian

millionrainbows said:


> So, ironically, the net result is that 12-tone is indeed the exact opposite of tonality, in structural terms.


There. Now we've hit rock bottom. This statement combines a lack of knowledge of the terms involved, confusion of categories, and a misuse of the word "ironic."


----------



## millionrainbows

Mahlerian said:


> You see, I don't care for question-begging arguments. I prefer to make sure that my conclusion stays at the end rather than sandwiching it in the middle and hoping nobody notices.
> 
> But perhaps rhetorical flourishes can provide their own kind of brilliance to posts that depend on circular reasoning.


You took Woodduck's statement out of context.

You are avoiding key issues: Wagner and others had already gotten rid of key areas (larger sense of tonality), but retained the common practice functions which had developed.

Since Wagner & others had already bypassed key areas, there was no need for Schoenberg develop a system specifically for this.

As Woodduck said,

"...the reason Schoenberg felt he had to devise a new system of organizing music was that he wanted to write a kind of music - a music of extreme harmonic complexity and continuous development, yet in non-programmatic, "absolute" forms - which he knew _would not be coherent without the imposition of such a system. And the reason it would not is simply that it would be without tonality: a system in which the notes of a scale perform recognized functions in relation to a central member of that scale. The listener's recognition of those functions is basic to all tonal systems, and *where it is absent it is not merely common practice which has been abandoned." *_


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## millionrainbows

Mahlerian said:


> There. Now we've hit rock bottom. This statement combines a lack of knowledge of the terms involved, confusion of categories, and a misuse of the word "ironic."


So what's it going to be? Common practice tonal function (which via Wagner and Liszt had already gotten rid of tonal centers i.e. key areas, but retained CP tonality's expressive functions), or larger-context tonality (sense of tone center)?

Which one do you hear in Schoenberg? CP functions or general tonality?

Because I think what Wooduck said is that in Schoenberg, the general sense of tone center is gone, and I agree. There's plenty of CP context and function and expressiveness in there, though, but I don't think you can tell the difference, judging by your reply.


----------



## Mahlerian

millionrainbows said:


> Because I think what Wooduck said is that in Schoenberg, the general sense of tone center is gone, and I agree. There's plenty of CP context and function and expressiveness in there, though, but I don't think you can tell the difference, judging by your reply.


If you'd ever read a thing I said, I have told you, Woodduck, and others countless times that what I hear in Schoenberg's music is tonal centers, in the general sense. I don't hear common practice, though I can hear the relation to it in the leading tone tendencies heard throughout. Now you're telling me I can't tell the difference? On what basis? Your differing perceptions?

I'm the only one on this thread who has been consistent in my definitions. The rest have all either avoided coming up with any or change them as needed to save their pet ideas of what Schoenberg is.


----------



## Mahlerian

millionrainbows said:


> Since Wagner & others had already bypassed key areas, there was no need for Schoenberg develop a system specifically for this.


Yes, and *THAT'S NOT WHAT HE DID*. That's why it's begging the question. He's attempting to prove that Schoenberg's music is atonal by saying that he went out of his way to avoid tonal centers in the general sense (he didn't).



millionrainbows said:


> As Woodduck said,
> 
> "...the reason Schoenberg felt he had to devise a new system of organizing music was that he wanted to write a kind of music - a music of extreme harmonic complexity and continuous development, yet in non-programmatic, "absolute" forms - which he knew _would not be coherent without the imposition of such a system. And the reason it would not is simply that it would be without tonality: a system in which the notes of a scale perform recognized functions in relation to a central member of that scale. The listener's recognition of those functions is basic to all tonal systems, and *where it is absent it is not merely common practice which has been abandoned." *_


Empty and meaningless, all of it. He's just stating the same point over and over, not arguing anything.


----------



## millionrainbows

Mahlerian said:


> Empty and meaningless, all of it. He's just stating the same point over and over, not arguing anything.


Then you don't recognize that the more sophisticated functions (CP tonality) developed out of general tonality (common to all tone-centered music), and you are unwilling to distinguish between the two, perhaps to obscure the issue.

The "issue" can only be clarified by recognizing and acknowledging this distinction (and connection).

_Tonality: a system in which the notes of a scale perform recognized functions in relation to a central member of that scale. The listener's recognition of those functions is basic to all tonal systems, and *where it is absent it is not merely common practice which has been abandoned."

*__T__hat doesn't__ sound empty and meaningless to me; quite the contrary. Does this threaten to expose your inability to articulate your position, which is: you hear tonality, but you don't know what it is, what caused it, or how it is created or minimized?_


----------



## Mahlerian

millionrainbows said:


> Then you don't recognize that the more sophisticated functions (CP tonality) developed out of general tonality (common to all tone-centered music), and you are unwilling to distinguish between the two, perhaps to obscure the issue.
> 
> The "issue" can only be clarified by recognizing and acknowledging this distinction (and connection).
> 
> _Tonality: a system in which the notes of a scale perform recognized functions in relation to a central member of that scale. The listener's recognition of those functions is basic to all tonal systems, and *where it is absent it is not merely common practice which has been abandoned."
> 
> *__T__hat doesn't__ sound empty and meaningless to me; quite the contrary. Does this threaten to expose your inability to articulate your position, which is: you hear tonality, but you don't know what it is, what caused it, or how it is created or minimized?_


What kind of functions? Are we talking about tonal function as a product of the relationships between triads, or are we using some other definition? Woodduck likes to use one and then pretend it was the other the second it loses its usefulness.

Speaking of which, why "recognized" functions? What purpose does that word serve there? We haven't even established what kind of functions we're talking about (not conclusively, anyway, because it'll change the next time we stop talking about common practice). Would a piece of music in some new system begin life as non-tonal and then become tonal once the functions of its notes are recognized?

There's a reason why common practice tonality is referred to interchangeably as functional tonality, because it was only with the rise of common practice that a harmonic system based on the functional relationships we think of today developed. Before then, there was no such thing, though perhaps we might hear some of the voice leading as an analogue to functional tonality, and since the 20th century, tonal function is no longer employed as it was throughout the whole common practice era. That's why the term nonfunctional tonality was created to describe the diatonic music of Stravinsky that actively diminishes the sense of tonal function by contradicting it constantly.

Listeners do not have to recognize functions in order to listen to music. Many are unable to do so and still enjoy it all the same. People who cannot identify the tonic chord when they hear it are still listening to the music, are they not? Then it is not the listener's recognition that matters, but the musical construction.

Of course I don't need to be able to explain how a piece is tonal to identify that it is. Isn't tonality, *according to you*, a matter of perception? I could hear tonality in common practice music before I could read a score, much less analyze one. Why should music in a less familiar idiom be different?

I could get into what I think causes the perception of tonality apart from common practice, but the fact is that we can't even explain what causes the sensation of tonality in common practice music itself. It is something heard, not something to be balanced like a spreadsheet, by the use of formulas.

I have offered two consistent definitions for tonality:

Tonality (general): Any kind of perceptible relationship among harmonies or notes

Tonality (specific): A particular way of relating harmonies and notes through functional triadic relationships with a diatonic basis, also called Common Practice Tonality

I have asked others here to offer some kind of consistent and meaningful definition of tonality that includes all music except that called atonal, but truth be told, I don't think it's possible, because there's absolutely nothing atonal about atonality.


----------



## Woodduck

Mahlerian said:


> You see, I don't care for question-begging arguments. I prefer to make sure that my conclusion stays at the end rather than sandwiching it in the middle and hoping nobody notices.
> 
> But perhaps rhetorical flourishes can provide their own kind of brilliance to posts that depend on circular reasoning.


What some people call "rhetorical flourishes" others just call "good writing." But thank you.

It would have been more useful if you had said what you think my "conclusion" is. In fact, I didn't intend to conclude anything, but to inquire as to whether Schoenberg had anything to say about the presence and nature of "tonality" in his serial works. I'm looking for statements from him, but have not yet turned up anything. I pointed out what I take to be his concept of tonality, and his denial that tonality exists in modal and other non-common practice music. That narrow (in my opinion, benighted and counterproductive) view of tonality could explain why he might have thought that avoiding common-practice made the word "tonality" irrelevant to what he was trying to do.

My conviction that his 12-tone music is _contratonal_ (I'm starting to like the term) is not the _conclusion_ of my post (I'm guessing that that's what you think my conclusion is) but rather its _thesis_. https://en.wikipedia.org/wiki/Thesis_statement It's an assumption, and so based not on arguments but on direct perception - _my_ perception. Anything I say about Schoenberg's music or theoretical intentions is an attempt to shed light on that assumption by seeking to understand the musical causes of the perception behind it. I'm thinking aloud, and I'm always happy to accept factual corrections, if I should mistake his meaning or mischaracterize his techniques. But the simple claim that Schoenberg's 12-tone writing is tonal is not a factual correction, and neither is an attempt to cite pseudo-tonal devices as manifestations of a tonal language.

As I understand him, Schoenberg said that he intended his method - the row and its permutations - to replace what he stated to be the primary function of tonality, which was the articulation of structure, a function lately made problematic by increasing chromaticism. He saw his innovation as a necessary solution to what he considered a historically inevitable and pressing musical problem: chromaticism had already weakened the traditional underlying diatonic basis of form, and in order to preserve, and even enhance, the expressive power of chromaticism without falling into chaos he had to find new ways to make music coherent, ways not dependent on the articulation of tonal levels.

The perspective that's emerging for me is that whatever merit Schoenberg's musical results may possess, his theoretical justifications were shaky, if not downright fallacious, and reveal him to have been very much a man of his time. Schoenberg was culture-bound in his definition of tonality (he mistook the _structure_ of the harmonic series and the chord-based bias of Western harmonic theory for the whole basis, essentially the sole relevant _cause_, of tonality and tonal perception); he was aligned with the popular thought of his era in his concept of musical "evolution" (chromaticism leading "logically" to the "higher" state of "pantonality" by some pseudo-Darwinian teleological process); and his assumptions about musical perception (about the way the brain organizes percepts, and about the capacity of listeners to identify, recognize, and integrate musical units) were made without scientific or experiential basis. I must also remark that his notion that dissonance could or should be "emancipated" - that any and all harmony would eventually be heard as consonant as the ear became accustomed to the more remote overtones, "as if there were no dissonance at all" (_Composition With Twelve Tones_, 1950) - may be felt to explain the constant dissonance of his own music, but as a notion of "evolutionary" progress and a condition to which music and listeners should aspire, it sounds like the dream of a mad scientist.

Insofar as chromatic harmony actually threatened musical coherence - and clearly this was a problem for Schoenberg, but not for other great composers who went on using tonality (including chromaticism) in a wondrous variety of ways - more coherence was lost by the renunciation of an intuitively felt and meaning-rich tonal hierarchy than could ever be replaced by a "harmony" resulting from the manipulation of pitch-templates compelled to run the gamut of an undifferentiated pseudo-scale without beginning, middle, end, or inherent quality or meaning.


----------



## Woodduck

Mahlerian said:


> *What kind of functions?* Are we talking about tonal function as a product of the relationships between triads, or are we using some other definition? *Woodduck likes to use one and then pretend it was the other the second it loses its usefulness.*
> 
> Speaking of which, *why "recognized" functions?* What purpose does that word serve there? We haven't even established what kind of functions we're talking about (not conclusively, anyway, because it'll change the next time we stop talking about common practice). *Would a piece of music in some new system begin life as non-tonal and then become tonal once the functions of its notes are recognized?*
> 
> There's a reason why common practice tonality is referred to interchangeably as functional tonality, because it was only with the rise of common practice that a harmonic system based on the functional relationships we think of today developed. *Before then, there was no such thing,* though perhaps we might hear some of the voice leading as an analogue to functional tonality, and since the 20th century, tonal function is no longer employed as it was throughout the whole common practice era. That's why the term nonfunctional tonality was created to describe the diatonic music of Stravinsky that actively diminishes the sense of tonal function by contradicting it constantly.
> 
> *Listeners do not have to recognize functions in order to listen to music.* Many are unable to do so and still enjoy it all the same. People who cannot identify the tonic chord when they hear it are still listening to the music, are they not? Then *it is not the listener's recognition that matters, but the musical construction.*
> 
> Of course *I don't need to be able to explain how a piece is tonal to identify that it is.* Isn't tonality, *according to you*, a matter of perception? I could hear tonality in common practice music before I could read a score, much less analyze one. Why should music in a less familiar idiom be different?
> 
> *I could get into what I think causes the perception of tonality apart from common practice,* but the fact is that we can't even explain what causes the sensation of tonality in common practice music itself. *It is something heard, not something to be balanced like a spreadsheet, by the use of formulas.*
> 
> *I have offered two consistent definitions for tonality:
> 
> Tonality (general): Any kind of perceptible relationship among harmonies or notes
> 
> Tonality (specific): A particular way of relating harmonies and notes through functional triadic relationships with a diatonic basis, also called Common Practice Tonality*
> 
> I have asked others here to offer some kind of consistent and meaningful definition of tonality that includes all music except that called atonal, but truth be told, I don't think it's possible, because there's absolutely nothing atonal about atonality.


Au contraire, my dear Watson! My idea of "function" has never wavered, wobbled or flipped! The idea that "function" can apply only to common practice harmony is of a piece with the idea that only that sort of music can be tonal. What gives common practice a monopoly on these terms? Tonality, of any sort, is all about how tones _function in relation to each other_ within a hierarchical system of functions centered on a specific pitch. Those functions may be few or many, simple or complex. But their specific nature identifies what tonal system we're working with, and they are determined by conventional usage and recognized and expected by listeners.

_Recognition_ is not the same as _conscious identification_. The functions of tones in tonal systems are _recognized intuitively_ by listeners familiar with music composed according to those systems. Based on their experience, listener's _recognize_ what happens in music, they have expectations of what might happen, and they sense when something unexpected happens. That's how tonality works. Listeners can learn, through experience, the functional presuppositions of different tonal systems, and experiments have shown that this learning can take place rather quickly. We can come to appreciate the functions of the tones in the scales of Indian or Chinese music by listening. Our basic sense of tonality - our brain's drive to organize data hierarchically - is so strong that very different tonal systems - basically, different scales and their associated conventions of melodic structure - will soon sound natural on their own terms.

Neither of your definitions of tonality includes the essential concepts: tone-centricity and hierarchy, as embodied in a scale. Your first definition could include virtually any music; after all, what is a "relationship"? If one tone is higher and another is lower, that's a relationship! But tonality it ain't. The second definition is merely a designation. It doesn't say what makes common practice tonal. If it did, it would reveal common practice to be a subspecies of tonality defined generally. Schoenberg seems to have lacked this understanding when he asserted that the modes and ethnic musics were not tonal.

Tonality is indeed a perceptual phenomenon, but tonal systems do have physical manifestations in written notation. The written indicators of common practice can be described in detail - here's the tonic note, here's the chord built on it, here's the dominant, here's the dominant seventh resolving deceptively to the submediant, etc., etc. Similar elements and movements could be designated for music in other tonal systems (and there may be names for these).

When you say you hear tonality in Schoenberg's 12-tone music, what elements, functions, and movements are you referring to? What do they look like in the score? You and SeptimalTritone pointed to examples in the Piano Suite and the Wind Quintet, but I have to call them "pseudo-tonal" devices which do not function as elements of a tonal system. What else ya got?


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## millionrainbows

Mahlerian said:


> Speaking of which, why "recognized" functions? What purpose does that word serve there? We haven't even established what kind of functions we're talking about (not conclusively, anyway, because it'll change the next time we stop talking about common practice).


We are not talking about functions "recognized" intellectually or cerebrally, but recognized instantly as sensation, as consonance or dissonance. This is a most basic way that we all hear. Some have learned the labels for these; others have not, and proceed intuitively.

It is obvious from this reply that you haven't really "grokked" the meaning of functions or intervals expressed as ratios. Thus, I feel somewhat embarrassed to keep giving out basic information in the hopes that it will "clear up" what is slowly being revealed to be some basic lack of understanding, which has been overlooked and replaced by not-deep-enough academic ideas.

The table that follows is what harmonic function is based on. Remember that 'function' refers to root movement, or one scale step upon which the triad is built, so we are talking about the relative consonance or dissonance of a root-note to tonic.

Most dissonant intervals to most consonant intervals, within one octave, using C as the reference, tonic, and "1" to which the ratios are part of:

1. minor seventh (C-Bb) 9:16
2. major seventh (C-B) 8:15
3. major second (C-D) 8:9
4. minor sixth (C-Ab) 5:8
5. minor third (C-Eb) 5:6
6. major third (C-E) 4:5
7. major sixth (C-A) 3:5
8. perfect fourth (C-F) 3:4
9. perfect fifth (C-G) 2:3
10. octave (C-C') 1:2
11. unison (C-C) 1:1

The intervals have a dissonant/consonant quality determined by their ratio, all in relation to a "keynote" or unity of 1; our ears/brain experience this as an instantaneous visceral sensation.

The intervals have a scale degree and place in relation to "1" or the Tonic, and triads can be constructed on these steps/notes. The chords thus constructed can then be given a "function" which is modeled after this harmonic relation to the keynote. Function is dependent on forward progression in time, and context, and both rely on memory.

This harmonic model is where all "linear function" originates, and is still manifest as ratios (intervals) which were derived from physical harmonic phenomena, which existed first.



> Would a piece of music in some new system begin life as non-tonal and then become tonal once the functions of its notes are recognized?


If it's non-tonal, it cannot have tonal function, since function is created by relationship to a key note.
Your question implies that harmonic function can be granted to music which started as non-tonal. The question doesn't make sense, since function is imparted by relation to "1" or tonic.



> There's a reason why common practice tonality is referred to interchangeably as functional tonality, because it was only with the rise of common practice that a harmonic system based on the functional relationships we think of today developed. Before then, there was no such thing…


While it's true that Western CP tonality developed and extended the notion of harmonic function, and _named _it that, the basic phenomenon of "function" existed from the beginning. Even the most "primitive" music can exhibit function when it gives preference to certain notes of the scale. The dominant V function is universal, because 2:3 is the most prominent relationship after 2:1 (the octave).

It's obvious from your reply that you do not have a general understanding of ratios and the physics of music, but are basing everything in academic terms, as if Western music had a monopoly on such basic physical concepts as "function."



> Listeners do not have to recognize functions in order to listen to music. Many are unable to do so and still enjoy it all the same. People who cannot identify the tonic chord when they hear it are still listening to the music, are they not? Then it is not the listener's recognition that matters, but the musical construction.


They recognize functions intuitively, as sound, and as degrees of consonance. That's why "V" is so important; it is more consonant sounding than 8:9, and draws us back to "1".



> Of course I don't need to be able to explain how a piece is tonal to identify that it is. Isn't tonality, *according to you*, a matter of perception? I could hear tonality in common practice music before I could read a score, much less analyze one. Why should music in a less familiar idiom be different?


It is nice to be able to explain what you hear. The purpose of terms and definitions is for communication with others.



> I could get into what I think causes the perception of tonality apart from common practice, but the fact is that we can't even explain what causes the sensation of tonality in common practice music itself. It is something heard, not something to be balanced like a spreadsheet, by the use of formulas.


I strongly disagree. The table of consonances above proves the point.



> I have offered two consistent definitions for tonality:
> 
> Tonality (general): Any kind of perceptible relationship among harmonies or notes
> 
> Tonality (specific): A particular way of relating harmonies and notes through functional triadic relationships with a diatonic basis, also called Common Practice Tonality


I agree with Woodduck, that your definitions fail to include tone-centricity, and that CP practices are merely elaborations of this, albeit very developed.



> I have asked others here to offer some kind of consistent and meaningful definition of tonality that includes all music except that called atonal, but truth be told, I don't think it's possible, because there's absolutely nothing atonal about atonality.


My definitions of tonality are consistent, and "atonality" or Woodduck's "contra tonality" are excluded from this, because they are based on non-tonal relationships.

Even the most "far-out" 20th century music, such as Debussy, I classify as tonal, although it is less tonal than CP music of earlier times. It's tonal for any number of reasons: because it still uses tonal hierarchies of notes, manifest as _vestiges_ of tonality, such as triads, chords, scales with starting points, use of unordered scales, pedal-points, symmetrical divisions of the octave, etc. In general, such tonal music is "harmonic" in nature, i.e., it is based on relations of pitches to a central pitch.

Even a simple triad in tonality reveals this harmonic relation: C-E-G is still a C triad, even if stated as E-G-C or G-C-E. It retains its harmonic identity and meaning under inversion. Not so with the non-tonal set C-E-G, or [0, 4, 7].


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## millionrainbows

Short answer, referring to my post #136 above:

Since tonality is based on audible relationships (see table above), then music using these relationships is instantly recognizable as being tonal, if the relationships are obvious and numerous enough. As music becomes weaker tonally, it gets more difficult to call, but is almost always still recognizable. Notice that this is an _inclusionary_ process; there is no obligation to identify "what kind" of tonality, so long as it is heard to be based on tonal and harmonic (adjective) sounds and sound relationships.

Conversely, music which is based on non-tonal (atonal) systems, namely 12-tone and serialism, is _instantly_ recognizable as being NOT tonal to almost all listeners. Notice that this is an _exclusionary_ process.

But most of the time, I don't worry about whether Second Viennese music is tonal or not. It just sounds good, is very expressive, and provokes all sorts of feelings and emotions most of the time.

How do you "hear" tonality in 12-tone Schoenberg? The music uses a non-tonal system, and is from square one already totally chromatic. We are already in a non-tone-centered environment, even if it is "tonality," and the term loses all meaning, unless we wish to use it to denote CP tonal context, devices, and practices; but that is also a contradiction, since the "mega-forms" of CP tonal practice, like harmonic goals and key areas and devices, were expanded on and extrapolated from the source of all tonality: the "one," the root, the "big note," our original tone-centered sense of tonality.

Let's face it: Schoenberg was not "attached" to tone-centricity. What he missed, in this new chromatic world, were the larger, expanded goals and forms of CP tonal practice. He missed the certainty, the context, the back-story, the "no-brainer" structure which he knew effortlessly inside and out, with the "through-system" infrastructure which tonality once provided, before it became an undulating, writhing, seething chromatic morass, as in R. Strauss' Metamorphosen, or the irritating vagaries of Wagner.

The 12-tone method provided this new structure and certainty, in spades. At last, he could have security in the form of the row, and become a thematic, contrapuntal writer again. Tonality? It had served its purpose, and now became a wandering in the dark, creating vagaries out of vagaries, with no certainty like before. It was artistic whim, like the early atonal-period works, wandering in a dark wood with no bread crumbs of connection to trace one's path, like Dante, before he entered the other realm...


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## Manok

All I simply meant was... I wanted to learn how to write music of the kind that is written by modern composers whenever that era officially began, not of the kind that was previous, Bach, Beethoven Brahms, Mozart etc. Simply as a way to expand my musical vocabulary. I can already write in styles similar, though not the same as those guys I already mentioned.


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## Guest

millionrainbows said:


> Again, 'a sense of universal tonality' is innate, and existed from Man's earliest origins.


It did? Says who? A recent study (though a trivial one ) offers an alternative view.

The fact that the publicly available* music over the last, say, 1000 years has followed a particular course of development does not mean that that development was in any way inevitable (except that any one specific point, you might say that it was almost inevitable, given what had immediately preceded it). In other words, there is nothing intrinsic to sound - not even the ratios that you regularly put forward as evidence of inevitability - that required man to have organised music in the ways that he did.

*I say 'publicly available' as we don't know what musical evolutions have taken place in private and are as yet undiscovered.


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## isorhythm

I think it's safe to say that octave equivalence is not culturally constructed - we can all agree on that, right?


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## Woodduck

isorhythm said:


> I think it's safe to say that octave equivalence is not culturally constructed - we can all agree on that, right?


I'm beginning to wonder whether we can all agree on the direction of up and down.

Octave equivalence is not culturally constructed, and neither is the predominance of the interval of the fifth - the most prominent overtone after the octave - in much of the world's music from ancient times to the present.

Apart from specific pitches, millionrainbows stated that "a _sense_ of tonality" - not any particular tonal system - has been present in humanity's music for as long as we can know. Its safe to say that the harmonic series, the human ear's ability to perceive its strongest partials, and the human brain's way of making sense of perceptions by ordering them hierarchically, have been what they are "from man's earliest origins."

Is anyone else getting weary of the "everything is cultural conditioning" argument?


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## millionrainbows

Woodduck said:


> I'm beginning to wonder whether we can all agree on the direction of up and down.
> 
> Octave equivalence is not culturally constructed, and neither is the predominance of the interval of the fifth - the most prominent overtone after the octave - in much of the world's music from ancient times to the present.
> 
> Apart from specific pitches, millionrainbows stated that "a _sense_ of tonality" - not any particular tonal system - has been present in humanity's music for as long as we can know. Its safe to say that the harmonic series, the human ear's ability to perceive its strongest partials, and the human brain's way of making sense of perceptions by ordering them hierarchically, have been what they are "from man's earliest origins."
> 
> Is anyone else getting weary of the "everything is cultural conditioning" argument?


That's also why I say that 12-tone and serialism are more "brain" music than "ear" music, although the results of 12-tone in actual sound-terms can be fantastic, strange, unsettling, mysterious, frightening, transcendently beautiful. But that's not based on my "ears" primarily, but is nonetheless based on the experience of hearing the music.

In visceral terms, the ear and body are opposed to the intellect as _feelings_ are opposed to _thinking. 
_
In this way, most of the 12-tone music of Schoenberg, Webern, and Berg evoke all sorts of "feelings" and states of being, because they are sensual and visceral sounds. This is in spite of the fact that the 12-tone method itself is not based on visceral principles, but on mathematical and quantitative principles which are in the realm of intellect and mind.


----------



## Pugg

isorhythm said:


> I think it's safe to say that octave equivalence is not culturally constructed - we can all agree on that, right?


Yes we can, if we do however, remains a question .


----------



## Guest

Woodduck said:


> Is anyone else getting weary of the "everything is cultural conditioning" argument?


Er, no - I don't think I've seen it - not '_everything_'.


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## Woodduck

MacLeod said:


> Er, no - I don't think I've seen it - not '_everything_'.


Then how about "every perception which is not shared by every human being, every belief that can't be proven to everyone's satisfaction, and every value judgment with which not everyone agrees"?

I was hoping to spare myself some work.


----------



## Guest

Woodduck said:


> Then how about "every perception which is not shared by every human being, every belief that can't be proven to everyone's satisfaction, and every value judgment with which not everyone agrees"?
> 
> I was hoping to spare myself some work.


I missed where someone said this...


----------



## JosefinaHW

After reading this thread I think it would be very interesting (certainly helpful to me) to look at several "pages" of the music section of original Quadrivium texts. My understanding is that music was included in the Quadrivium because it was considered one aspect of mathematics: the study of ratios. I don't know if using a monochord was one of the methods used to teach the subject: seems a bit too empirical, but it certainly would make sense. Has anyone ever seen samples of those pages/lessons?


----------



## millionrainbows

JosefinaHW said:


> After reading this thread I think it would be very interesting (certainly helpful to me) to look at several "pages" of the music section of original Quadrivium texts. My understanding is that music was included in the Quadrivium because it was considered one aspect of mathematics: the study of ratios. I don't know if using a monochord was one of the methods used to teach the subject: seems a bit too empirical, but it certainly would make sense. Has anyone ever seen samples of those pages/lessons?


Not the original urtext, but there is a little book on the Quadrivium. This is a neat series of little books. There's one about a parlor-device that "drew" pictures of intervals, called "Harmonograph."









​


----------



## JosefinaHW

millionrainbows said:


> Not the original urtext, but there is a little book on the Quadrivium. This is a neat series of little books. There's one about a parlor-device that "drew" pictures of intervals, called "Harmonograph."
> 
> :MillionRainbows: Thank you for your reply but I have already seen this book. I don't know if any of the original Quadrivium, Music "lessons" were ever written down. I think it would be very interesting to read about their understanding of tonality and how they go about describing music as representing cosmic harmony. For purposes of anyone interested in this thread I'm using "cosmic harmony" in the very narrow sense of "the natural order of the universe". One reason I think it would be very helpful is that the theologians of that time weren't coming at the problem with any agendas, so I imagine they would speak very directly about music from a "common sense" understanding. I don't mean any insult by mentioning "agendas". I will investigate further into this, but if anyone can make it easier, a link, explanation or examples would be greatly appreciated. TY again, MRainbows.


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## millionrainbows

From the Amazon description:
The quadrivium:
The classical curriculum comprises the four liberal arts of *number, geometry, music, and cosmology.* It was studied from antiquity to the Renaissance as a way of glimpsing the nature of reality. 
*Geometry is number in space;
music is number in time; 
and comology expresses number in space and time.

*Note that we are talking about 'number' here, which is a rather basic form of math. Likewise, geometry is number and relationships expressed visually; it's really the same, they all are the same thing expressed in different ways. That's why music, and intervals expressed as ratios (and tonality expressed as a ratio system) are essentially "basic math."
But don't let this fool you; there is much to be "grokked" on very basic levels, which many academically stilted thinkers have not yet grasped. But if you can 'grok' it, a whole new vista opens.
People used to think in relationships all the time, especially before measurement was standardized. The Egyptians built all their buildings using circles. The size of the circle was a length of leather cord stored on a stake, as long as the radius, and they put the stake in the ground, inscribed a circle, and all the relationships out of that circle became the building.
I find it amusing when I read those books about all the 'mystic numbers' and numerical coincidences in the Pyramids; of course they are there, because of the way it was circular to begin with.
Cosmology? Maybe tonality IS God, after all!


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## millionrainbows

I found EdwardBast's post #215 very illuminating and valuable. Here it is:




> Nice attempt at obfuscation, but you know perfectly well that I said "pitch hierarchy," not "tonal hierarchy." The latter term is best left for the discussion of common-practice tonal music. *"Pitch hierarchy," is a more general term uniting common-practice music, modal medieval music, folk music, rock, jazz, Indian classical music, etc.* Each of these styles has its own conventions for hierarchical relationships among tones, and they are usually more or less systematic within styles.


This, and having Woodduck's tacit agreement on the issue of 'general tonality' or 'Man's universal sense of tonality' has gone a long way in bringing clarity and light to the discussions on tonality and "what it is." Thank you both very much.


----------



## Mahlerian

millionrainbows said:


> I found EdwardBast's post #215 very illuminating and valuable. Here it is:
> 
> 
> 
> This, and having Woodduck's tacit agreement on the issue of 'general tonality' or 'Man's universal sense of tonality' has gone a long way in bringing clarity and light to the discussions on tonality and "what it is." Thank you both very much.


It's amazing how much clarity you and others here feel you have on a concept you either haven't defined or have defined inconsistently.

The statement you quoted, for example, is just saying "pitch hierarchy exists everywhere except where it doesn't." That isn't enlightening at all. It doesn't *say* anything. At any rate, Edward is completely wrong (as are you) if he thinks that I am attempting to obfuscate anything. I'm _trying_ to be as clear as possible, which has prompted you to criticize me as overly academic and obstinate.


----------



## Woodduck

millionrainbows said:


> I found EdwardBast's post #215 very illuminating and valuable. Here it is:
> 
> 
> 
> This, and having *Woodduck's tacit agreement* on the issue of 'general tonality' or 'Man's universal sense of tonality' has gone a long way in bringing clarity and light to the discussions on tonality and "what it is." Thank you both very much.


:lol: Tacit, only if you mean that words onscreen don't make noise (unless you have this http://www.naturalreaders.com/index.html ).

You're welcome.


----------



## Ukko

I want to learn non tonal theory?I have been reading that subject line question for a month now. It begs for a second sentence, perhaps "What is _wrong_ with me?"


----------



## millionrainbows

Mahlerian said:


> It's amazing how much clarity you and others here feel you have on a concept you either haven't defined or have defined inconsistently.
> 
> The statement you quoted, for example, is just saying "pitch hierarchy exists everywhere except where it doesn't." That isn't enlightening at all. It doesn't *say* anything. At any rate, Edward is completely wrong (as are you) if he thinks that I am attempting to obfuscate anything. I'm _trying_ to be as clear as possible, which has prompted you to criticize me as overly academic and obstinate.


Well, if your example and replies on the "What's your favorite non-Ionian mode" thread is any indication, that is questionable...

Perhaps you fail to see that our "inconsistency" is simply the result of your forcing us into a tighter and tighter spiral of clarifications, such as "tonal hierarchy" and "pitch hierarchy," which I think is a perfectly reasonable distinction when dealing with obstinacy.


----------



## millionrainbows

Woodduck said:


> :lol: Tacit, only if you mean that words onscreen don't make noise (unless you have this http://www.naturalreaders.com/index.html ).
> 
> You're welcome.


Alternate def. of tacit: implied but not explicit. And I can see that both of you have come to this conclusion independently, although judging from the reaction, we might be a conspiracy of wrongness and inconsistency.

Hey, I don't know about you guys, but I'm going to just relax, sit back, and enjoy this.


----------



## Mahlerian

millionrainbows said:


> Well, if your example and replies on the "What's your favorite non-Ionian mode" thread is any indication, that is questionable...


Oh? How so? I've been trying to get you to see how often you contradict your own stated views, sure, but my position has been consistent and I try to be clear.



millionrainbows said:


> Perhaps you fail to see that our "inconsistency" is simply the result of your forcing us into a tighter and tighter spiral of clarifications, such as "tonal hierarchy" and "pitch hierarchy," which I think is a perfectly reasonable distinction when dealing with obstinacy.


As I see it, your "clarifications" have consisted in repeating your original point. I got what you were saying before, it's just that what you are saying is internally contradictory and cannot possibly make any sense. You're defining those terms so loosely that they're next to meaningless, with the exception of keeping out certain kinds of music from a certain period. There you are extremely specific, and without any reasoning given.


----------



## EdwardBast

Mahlerian said:


> I have offered two consistent definitions for tonality:
> 
> Tonality (general): Any kind of perceptible relationship among harmonies or notes
> 
> Tonality (specific): A particular way of relating harmonies and notes through functional triadic relationships with a diatonic basis, also called Common Practice Tonality
> 
> *I have asked others here to offer some kind of consistent and meaningful definition of tonality that includes all music except that called atonal, but truth be told, I don't think it's possible,* because there's absolutely nothing atonal about atonality.


Of course it is possible. Several of us have done this repeatedly. A general definition requires three words: Systematic pitch hierarchy. Not "any kind of perceptible relationship among harmonies or notes," but systematic hierarchical ones.


----------



## Mahlerian

EdwardBast said:


> Of course it is possible. Several of us have done this repeatedly. A general definition requires three words: Systematic pitch hierarchy. Not "any kind of perceptible relationship among harmonies or notes," but systematic hierarchical ones.


What is the systematic hierarchy in Debussy's Brouillards, for example? It emerges from a juxtaposition of various harmonic and scale types. If there is any hierarchy present, it is synthetic, created by emphasis and context.

If you insist that these things can be tonal, well then so is Schoenberg, and your attempt to exclude him is incompatible with your own definition.


----------



## Woodduck

It isn't difficult to come up with a general definition of tonality, and it's possible to state it clearly in half a dozen or more ways, as we have done here. "Systematic pitch hierarchy" are the three essential concepts. A full definition would pull out two other implicit concepts: a specific scale out of which the hierarchy of pitches is made ; and a centrally important note of that scale (a "tonic") as occupying the fundamental position in the hierarchy. One might then point out the ways in which the tonic functions (as an ultimate point of resolution or rest) and the ways in which the other scale notes function in relation to it and to each other. 

Applying the general definition of tonality to actual music is more difficult, since scales and relationships among their tones differ in different tonal systems, and since any specific music can draw from or reference any system or combination of systems to any degree, from a clear and thorough exposition of its hierarchies (as in much music of the Classical period) to vague allusions (some extreme Impressionism and 20th century idioms). The choice to call certain musics "tonal" may be arguable, but the definition of tonality shouldn't be.


----------



## EdwardBast

Mahlerian said:


> What is the systematic hierarchy in Debussy's Brouillards, for example? It emerges from a juxtaposition of various harmonic and scale types. If there is any hierarchy present, it is synthetic, created by emphasis and context.
> 
> If you insist that these things can be tonal, well then so is Schoenberg, and your attempt to exclude him is incompatible with your own definition.


Nothing wrong with a synthetically created hierarchy. If there is a system to it, it fits the definition with no problem. And why do you think I would resist saying that some of Debussy's music isn't tonal? I think some of it isn't. I'm not trying to exclude Schoenberg from anything. Where did that come from?


----------



## Mahlerian

EdwardBast said:


> Nothing wrong with a synthetically created hierarchy. If there is a system to it, it fits the definition with no problem. And why do you think I would resist saying that some of Debussy's music isn't tonal? I think some of it isn't. I'm not trying to exclude Schoenberg from anything. Where did that come from?


Do you think Schoenberg's music doesn't use any hierarchies at all? That would be absolutely bizarre. Even if the system is synthetic, as in Scriabin or Debussy's prelude or in much Schoenberg, it's still present and controls the relationships between pitches and harmonies in a piece.

Perhaps you have not been saying that all of Debussy is tonal. That means that your definition is different from Woodduck's or Millionrainbows'.


----------



## EdwardBast

Mahlerian said:


> Do you think Schoenberg's music doesn't use any hierarchies at all? That would be absolutely bizarre. Even if the system is synthetic, as in Scriabin or Debussy's prelude or in much Schoenberg, it's still present and controls the relationships between pitches and harmonies in a piece.
> 
> Perhaps you have not been saying that all of Debussy is tonal. That means that your definition is different from Woodduck's or Millionrainbows'.


I think there are other categories besides tonal and atonal. And I suppose my three word definition does, or could, exclude a very small percentage of music that is not generally called atonal - for example, some whole tone works by Debussy, King Crimson, etc. I have seen no convincing demonstrations that Schoenberg's so-called atonal music or serial music is characterized by systematic pitch hierarchies, the operative word being systematic. Until I do, I will not include it in the tonal category.

As for the term atonal, it is somewhat like the term atheist. If one were to discover beings on one of the numerous exoplanets recently discovered to whom the notion of God never occurred, it would be silly to call them atheists. The term only applies in a context where theism is "a thing" and, moreover, a thing with respect to which one is concerned to define ones system of thought. Schoenberg lived in a context in which tonality was a thing and, moreover, a thing with respect to which he was concerned to define his musical thought, as copiously documented above by others. He made an issue of it. That is why the term has meaning used in relation to his music. It is also why the term sounds silly applied to Debussy's whole tone music. The opposition tonal versus atonal is just irrelevant to the composer and his audience. He didn't make an issue of it. Not a thing.


----------



## millionrainbows

Mahlerian said:


> What is the systematic hierarchy in Debussy's Brouillards, for example? It emerges from a juxtaposition of various harmonic and scale types. If there is any hierarchy present, it is synthetic, created by emphasis and context.
> 
> If you insist that these things can be tonal, well then so is Schoenberg, and your attempt to exclude him is incompatible with your own definition.


Are you saying that Schoenberg's 12-tone works are equivalent to Debussy (in Brouillards) in terms of pitch hierarchies? I disagree, as Debussy is using a *tonal* pitch hierarchy, and Schoenberg's hierarchy is based on a non-pitch-centric (non-tonal) and non-harmonic hierarchy.

Why?
The whole tone scale is a scale. It is unordered, and can be drawn from freely. Therefore, like all scales, it has a _pitch vector:_ every pitch is related to ALL other pitches, to create a harmonic set of intervals, which will create a tonality. It looks like this:

(Note that there are only 6 intervals: m2, M2, m2, M2, p4 and tritone. The rest are inversions of these basic intervals.)

Whole tone scale: C-D-E-F#-G#-A#

To get the interval vector, first determine every interval, starting with the first note and continuing to the last, eliminating redundancies along the way:

C-D: M2
C-E: M3
C-F#: tritone
C-G#: M3 (inverted m6)
C-A#(Bb): M2 (inverted m7)

Next, from D:
D-E: M2
D-F#: M3
D-G#: tritone
D-A#(Bb): M3 (inverted m6)
D-C: redundant, see C-D above

Next, from E:
E-F#: M2
E-G#:M3
E-A#(Bb): tritone
E-C: redundant (see C-E above)
E-D: redundant (see D-E above)

Next, from F#:
F#-G#: M2
F#-A#(Bb): M3
F#-C: redundant (see C-F# above)
F#-D: redundant (see D-F# above)
F#-E: redundant (see E-F# above)

Next, from G#:
G#-A#(Bb): M2
All others redundant, etc.

Lastly, A#(Bb):
All redundant

The sum, or interval vector, is usually shown in a table. Here are the results:

Whole tone scale:
M2: 6
M3: 6
tritone: 3

As you can see from the results, the whole tone scale is not varied harmonically; it has no fifths or fourths, which makes it unstable, no minor seconds, so no "spice", 3 tritones, which are unstable (and without minor seconds, useless as double-meaning dominants unless you use two adjacent WT scales, which Debussy did), and the largest number, 6 each, of M2s and M3s.

Whole Tone scale: C-D-E-F#-G#-A#

Furthermore, any scale creates an hierarchy of functions, based on degrees consonance/dissonance:

C - 1:1
D -8:9
E -4:5
F#- 45:32
G# - 8:5
A# - 16:9

Schoenberg's tone rows have no interval vector, or 'index of harmonic possibilities.' They are ordered, so the note C, for example, can only be interval-related to the preceding note, and the following note.

If anyone here would care to do an interval vector analysis of a 12-note row to demonstrate this, please feel free.


----------



## Mahlerian

EdwardBast said:


> Schoenberg lived in a context in which tonality was a thing and, moreover, a thing with respect to which he was concerned to define his musical thought, as copiously documented above by others. He made an issue of it. That is why the term has meaning used in relation to his music. It is also why the term sounds silly applied to Debussy's whole tone music. The opposition tonal versus atonal is just irrelevant to the composer and his audience. He didn't make an issue of it. Not a thing.


So you think Debussy was NOT consciously throwing out centuries of tradition when he started writing music that eschewed tonal function, traditional voice leading, and even the distinction between consonance and dissonance?

It's not as if Schoenberg agreed that the music he wrote was atonal or in opposition to traditional practice.


----------



## Dim7

millionrainbows said:


> Are you saying that Schoenberg's 12-tone works are equivalent to Debussy (in Brouillards) in terms of pitch hierarchies? I disagree, as Debussy is using a *tonal* pitch hierarchy, and Schoenberg's hierarchy is based on a non-pitch-centric (non-tonal) and non-harmonic hierarchy.
> 
> Why?
> The whole tone scale is a scale. It is unordered, and can be drawn from freely. Therefore, like all scales, it has a _pitch vector:_ every pitch is related to ALL other pitches, to create a harmonic set of intervals, which will create a tonality. It looks like this:
> 
> (Note that there are only 6 intervals: m2, M2, m2, M2, p4 and tritone. The rest are inversions of these basic intervals.)
> 
> Whole tone scale: C-D-E-F#-G#-A#
> 
> To get the interval vector, first determine every interval, starting with the first note and continuing to the last, eliminating redundancies along the way:
> 
> C-D: M2
> C-E: M3
> C-F#: tritone
> C-G#: M3 (inverted m6)
> C-A#(Bb): M2 (inverted m7)
> 
> Next, from D:
> D-E: M2
> D-F#: M3
> D-G#: tritone
> D-A#(Bb): M3 (inverted m6)
> D-C: redundant, see C-D above
> 
> Next, from E:
> E-F#: M2
> E-G#:M3
> E-A#(Bb): tritone
> E-C: redundant (see C-E above)
> E-D: redundant (see D-E above)
> 
> Next, from F#:
> F#-G#: M2
> F#-A#(Bb): M3
> F#-C: redundant (see C-F# above)
> F#-D: redundant (see D-F# above)
> F#-E: redundant (see E-F# above)
> 
> Next, from G#:
> G#-A#(Bb): M2
> All others redundant, etc.
> 
> Lastly, A#(Bb):
> All redundant
> 
> The sum, or interval vector, is usually shown in a table. Here are the results:
> 
> Whole tone scale:
> M2: 6
> M3: 6
> tritone: 3
> 
> As you can see from the results, the whole tone scale is not varied harmonically; it has no fifths or fourths, which makes it unstable, no minor seconds, so no "spice", an equal, 3 tritones, which are unstable (and without minor seconds, useless as double-meaning dominants), and the largest number, of M2s and M3s.
> 
> Schoenberg's tone rows have no interval vector, or 'index of harmonic possibilities.' They are ordered, so the note C, for example, can only be interval-related to the preceding note, and the following note.
> 
> If anyone here would care to do an interval vector analysis of a 12-note row to demonstrate this, please feel free.


None of that applies to Schoenberg's "free atonal" works though.


----------



## millionrainbows

Mahlerian said:


> So you think Debussy was NOT consciously throwing out centuries of tradition when he started writing music that eschewed tonal function, traditional voice leading, and even the distinction between consonance and dissonance?


He was throwing out many of the devices and functions of *CP tonal practice,* but his music, even Brouillards, was *tonal in the general sense,* because it retained many tonal harmonic devices: scales, triads, relationships.



> It's not as if Schoenberg agreed that the music he wrote was atonal or in opposition to traditional practice.


No, because he retained a semblance of CP tonal practices, because he was a classicist and wanted to keep that connection. He did reject a tone-centric (pitch) hierarchy. This makes it 'not tonal' and also 'not harmonically-based.'

This is fun; I've got it down, now.


----------



## millionrainbows

Dim7 said:


> None of that applies to Schoenberg's "free atonal" works though.


It depends on how he is using the 12 notes. Remember, there is still such a thing as a 12-note chromatic SCALE.

The deciding factor in the 12-tone method that makes it 'atonal' is the fact that it is ordered.

You could do an interval vector of it, as long as it is unordered. But the results, as you add more and more notes, become less and less "tonal." I've shown this chart before, and will show it again:

When Schoenberg began using ordered sets, he was creating atonality.

As to the "they all look alike," the cumulative effect of adding notes to an unordered set might be mistakenly seen as a creeping-in of "redundancy" and lack of variation, as this chart from Howard Hanson's Harmonic Materials of Modern Music shows:


> _p=perfect fifth (or fourth) _
> _m=major third (minor sixth)_
> _n=minor third (major sixth)_
> _s=major second (minor seventh)_
> _d=minor second (major seventh)_
> _t=augmented fourth, diminished fifth_
> 
> _doad (2 notes): p_
> _triad: p2 s_
> _tetrad: p3 n s2_
> _pentad: p4 m n2 s3_
> _hexad: p5 m2 n3 s4 d_
> _heptad: p6 m3 n4 s5 d2 t _
> _octad: p7 m4 n5 s6 d4 t2_
> _nonad: p8 m6 n6 s7 d6 t3_
> _decad: p9 m8 n8 s8 d8 t4_
> _undecad: p10 m10 n10 s10 d10 t5_
> _duodecad (12 notes): p12 m12 n12 s12 d12 t6_
> 
> _Each new progression adds one new interval, plus adding one more to those already present; but beyond seven tones, no new intervals can be added. In addition to this loss of new material, there is also a gradual decrease in the difference of the quantitative formation. _
> 
> _So the sound of a sonority, whether it be harmony or melody, depends on what is present, but also on what is not present. The pentatonic sounds as it does because it contains mainly perfect fifths, and also maj seconds, minor thirds, and one major third, but also because it does not contain the minor second or tritone._
> 
> _As sonorities get projected beyond the six-range, they tend to lose their individuality. _


Which is all fine and well when dealing with scale-sets in harmonically-related ways, as unordered sets.


----------



## millionrainbows

More on the whole-tone scale, and how it is tonal, from my blogs:

Serial row order can be 'stacked' to produce triads or anything else you wish, but there's only so far this will take you. 

The interval relations between the notes are what preserves the structural features of the row. If you do stack them, it should be in groups of 3, 4, 5 etc. consecutive notes of the row.

Good luck with the results, because this is not an inherently "harmonic" way of creating harmony.

The only thing that "function" does is project an hierarchy of triads, in relation to the tonic, by degree of consonance.

A mode does not, by itself, give structure to a piece. A whole-tone scale does not, by itself, give structure to a piece. Non-functional diatonicism does not, by itself, give structure to a piece. These are just "scales," and any "structure" must be put there by the composer, just like 12-tone music. There are 'automatic' consequences of these structures, though (see below).

The 12-tone method, likewise, does not give structure to a piece, but it does give overall unity to a piece, but it does not "structure" a piece.

In the case of "a mode," considered as the constituent scale, it has a tonic, and if triads are constructed on its scale-steps, an hierarchy of function will be automatically created, according to the degree of consonance present in relation to tonic, or I.

Example: D Dorian scale: D-E-F-G-A-B-C. Triads created: i-Dmin, ii-Emin, III-Fmaj, IV-Gmaj, v-Gmin, viø (half-diminished or min7b5)-Bmin7b5, bVII-Cmaj. I will not bother to rank them at this point.
_
So, to an extent, these structures are created "automatically" as a consequence of constructing triads on the scale-steps_. Surely, you would not dispute this obvious act, which any jazz player would know.

_In the case of the whole-tone scale, if it is referenced in a tonal context,_ it is inherently an unstable "deconstructing" element, *tonally speaking;* the best it can manage is a "suspended" feel, or altered dominant; but it can definitely be used to suggest tonal areas of function. 

Like Thelonious Monk did, it can be used as a dominant element, reinforcing a dominant 7 sound. 

Example: in C major, a whole-tone scale beginning on G (G-A-B-C#-D#-F) suggests a G aug 9, or a G7b5. Let's build some triads, from C: (C-D-E-F#(Gb)-G#(Ab)-A#(Bb).

I: C-E-Gb: Cb5, C-E-G#: C aug, which repeats on every scale step, since the scale is symmetrical. This makes it usable for those functions on each step. Any "modal" permutation (starting on D, E, F#, etc) are simply reiterations, and are essentially identical, and will yield the same content. Limited, but flexible.

Additionally, the whole-tone is a 6-note scale, so there are only 2 of them per octave. This allows 2 areas of tonality to be created, a semitone apart. Since the semitone can be a tritone substitution (the "chromatic/fifths" connection), this creates a "I-V" contrast which can be exploited tonally. Debussy did this. Schoenberg also used a row constructed on similar lines to "suggest" this same effect, although in essence, his tone-row is not "tonal" in a structural sense.


----------



## Mahlerian

millionrainbows said:


> He was throwing out many of the devices and functions of *CP tonal practice,* but his music, even Brouillards, was tonal in the general sense, because* it retained many tonal harmonic devices: scales, triads, relationships.*


Gee, just like Schoenberg did! Oh wait, I forgot, if you place something in an ordered set, it cannot be harmonic anymore. So a G major triad followed by a C major triad isn't a V-I cadence if you say it's part of an ordered set.











millionrainbows said:


> No, because he retained a semblance of CP tonal practices, because he was a classicist and wanted to keep that connection. He did reject a tone-centric (pitch) hierarchy. This makes it 'not tonal' and also 'not harmonically-based.'


Except that he didn't do that. The only kind of tone-centeredness he rejected was the specific hierarchies of common practice.


----------



## Woodduck

EdwardBast said:


> I think there are other categories besides tonal and atonal. And I suppose my three word definition does, or could, exclude a very small percentage of music that is not generally called atonal - for example, some whole tone works by Debussy, King Crimson, etc. I have seen no convincing demonstrations that Schoenberg's so-called atonal music or serial music is characterized by systematic pitch hierarchies, the operative work being systematic. Until I do, I will not include it in the tonal category.
> 
> As for the term atonal, it is somewhat like the term atheist. If one were to discover beings on one of the numerous exoplanets recently discovered to whom the notion of God never occurred, it would be silly to call them atheists. The term only applies in a context where theism is "a thing" and, moreover, a thing with respect to which one is concerned to define ones system of thought. Schoenberg lived in a context in which tonality was a thing and, moreover, a thing with respect to which he was concerned to define his musical thought, as copiously documented above by others. He made an issue of it. That is why the term has meaning used in relation to his music. It is also why the term sounds silly applied to Debussy's whole tone music. The opposition tonal versus atonal is just irrelevant to the composer and his audience. He didn't make an issue of it. Not a thing.


I agree with every word of this.

We can complicate this unnecessarily. It's probably my limitation that millionrainbow's numerical tables put me into an instant coma (), but I find the concepts of tonality, scale and hierarchy to be clear, and the phenomena they designate to be perceivable with little difficulty in the majority of cases. The appeal to borderline cases, such as Debussy's more extreme deployments of the whole tone scale, strikes me as mere evasion.

For the record, I don't see the whole tone scale as containing an inherent tonal principle. It can be used so as to convey a sense of tonality - it does, after all, contain an augmented sixth chord, which anyone familiar with common practice harmony is going to recognize, and if a certain note is dwelt upon the major third above it will be conspicuous - but it need not be so used. I hear Debussy as playing around with these possibilities in various works, varying the sense of tonality. We don't need to worry about which pieces have which foot on which side of the fence.

The 12-tone scale also contains no inherent structure. I have seen it distinguished from the chromatic scale, which consists of a diatonic scale and the additional five half steps. By that definition the _chromatic_ scale exhibits tonal hierarchy, and one can play with chromatic complexities and so weaken or strengthen the feeling of tonality. Chromaticism was not a 19th-century phenomenon; it was understood and employed even before Gesualdo reveled in it. His music has been referred to as "triadic atonality" - a nice name, but it doesn't matter what we call it. Chromatic ambiguity crops up again and again across the centuries, generally with some specific expressive (often text-based) or structural purpose. Wagner didn't invent it, he just concentrated it into one opera that made people's heads spin, and once his lovers attained their perfectly diatonic nirvana he was off to C-Major Nuremberg. He didn't cause a "harmonic crisis" that needed radical surgery.

Schoenberg's 12-tone music is not based on a hierarchically structured scale. If there is a tonic and its relations embedded somewhere in that music, let them stand up and be counted.


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## EdwardBast

Mahlerian said:


> So you think Debussy was NOT consciously throwing out centuries of tradition when he started writing music that eschewed tonal function, traditional voice leading, and even the distinction between consonance and dissonance?
> 
> It's not as if Schoenberg agreed that the music he wrote was atonal or in opposition to traditional practice.


I don't think Debussy ever abandoned the distinction between consonance and dissonance. I think he exploited it with great subtlety.

That aside, I see no reason to frame his aesthetically motivated actions as throwing anything out. And why "eschewing" tonal functions? Such constructions imply an intentional rejection of options and vocabulary Debussy was quite happy to use in a number of his works. If I had the skills and was going to paint the view of distant peaks I saw on this evening's loop over my local mountain, the palette would include subtle dusty shades of slate and gray and blue with maybe some pale hints of gold and shadowy green. These choices wouldn't imply a conscious rejection of red, the eschewing of orange, or a disdain for purple. The constructions you use would better fit the choices of a composer who was actively concerned with avoiding traditional functions and tone centricity and with redefining the parameters of dissonance, one who was consciously engaged with theoretical issues and whose consciousness of his place in history was in the forefront of his thinking. That doesn't sound like Debussy to me.


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## Mahlerian

EdwardBast said:


> The constructions you use would better fit the choices of a composer who was actively concerned with avoiding traditional functions and tone centricity and with redefining the parameters of dissonance, one who was consciously engaged with theoretical issues and whose consciousness of his place in history was in the forefront of his thinking. That doesn't sound like Debussy to me.


You're ignoring the many parallels between him and Schoenberg (who also didn't abandon the distinction between consonance and dissonance, just eschewed the traditional one, like Debussy did), who was far more traditionally minded.


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## Woodduck

Even if we accede to the use of the term "atonal" to describe certain music based on the whole tone scale - and I have no objection to it, provided that we understand what we're talking about - I find this constant citation of Debussy of no value in understanding Schoenberg. Nor do I find it a persuasive argument for rejecting the common use among musicians of the term "atonality." 

Schoenberg's atonal serialism, unlike Debussy's free use of alternative scales and "non-functional" harmony, was a carefully contrived system based on the assumption that tonality had spent its force in a hyperchromatic breakup of historic significance: that the clarity and strength of tonality had dissipated in a growing welter of chromaticism, that consonance and dissonance had lost their distinctness and thus much of their power to affect us, that the human ear and brain were constantly evolving to hear as consonant harmonies previously heard as dissonant, and that the inescapable way "forward" was to accept and complete this harmonic "emancipation of dissonance," to abandon tonality altogether, and to find a new basis for musical coherence which did not depend on tonal relationships. Schoenberg's writings describing and justifying his system and its importance make all this perfectly clear. (I think he was wrong about all of it, by the way, but that's another matter.)

I know of no evidence that Debussy's experiments with sonority had any such theoretical basis, and given his continued use of tonal harmony along with his "non-functional" floating triads and whole-tone effects, it's pretty obvious that his approach was not premised upon any distinct break with the past. I'm unaware that his procedures were based on any rationale other than their appeal to his ear.

As for the idea that Schoenberg meant to abandon only common practice tonality and not tonality as such, it sounds plausible, but I don't think it survives examination. Common practice is not peculiar in terms of what defines tonality; it's not alone in having a tonal center and a pitch hierarchy. It is distinguished by its explicit harmonic structure, its polyphony. If you are writing harmonic/polyphonic (as opposed to purely melodic) music, and you are preventing the establishment of a tonality (a "key") in the progression of your harmonies, exactly what form of tonality could you expect to retain? Some form which is not even relevant to the harmonic tradition from whose laws you are departing? If Schoenberg's harmony is traditional except with respect to the laws of the tonal relationships on which it's based, in what "nontraditional" sense is tonality still present? What is the tonal system now heard to be operating? What are its laws? How is it perceived?

I am unaware of any statements by Schoenberg expressing an intention to preserve tonality in his 12-tone music. All the theoretical groundwork he laid for his "method" appears to indicate the opposite. I would be delighted to find such statements as aids to better understanding what he actually did - or intended to do, whether he succeeded in doing it or not - but in their absence I find no reason to abandon traditional terminology - "atonality" - in describing the music itself.


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## millionrainbows

Woodduck said:


> Even if we accede to the use of the term "atonal" to describe certain music based on the whole tone scale - and I have no objection to it, provided that we understand what we're talking about - I find this constant citation of Debussy of no value in understanding Schoenberg. Nor do I find it a persuasive argument for rejecting the common use among musicians of the term "atonality."


Agreed.



> Schoenberg's atonal serialism, unlike Debussy's free use of alternative scales and "non-functional" harmony, was a carefully contrived system based on the assumption that tonality had spent its force in a hyperchromatic breakup of historic significance: that the clarity and strength of tonality had dissipated in a growing welter of chromaticism, that consonance and dissonance had lost their distinctness and thus much of their power to affect us, that the human ear and brain were constantly evolving to hear as consonant harmonies previously heard as dissonant, and that the inescapable way "forward" was to accept and complete this harmonic "emancipation of dissonance," to abandon tonality altogether, and to find a new basis for musical coherence which did not depend on tonal relationships. Schoenberg's writings describing and justifying his system and its importance make all this perfectly clear. (I think he was wrong about all of it, by the way, but that's another matter.)


I don't agree that what you say was his 'historic intent' was 'wrong,' because to me it's ultimately a non-issue, more about Schoenberg the man than the music itself. The 12-tone system itself is not 'wrong' because it is an alternate way. Remember that Webern was at the same time using the system in much more innovative ways, as far as the actual structural use goes. Not to minimize Schoenberg's artistry.



> I know of no evidence that Debussy's experiments with sonority had any such theoretical basis, and given his continued use of tonal harmony along with his "non-functional" floating triads and whole-tone effects, it's pretty obvious that his approach was not premised upon any distinct break with the past. I'm unaware that his procedures were based on any rationale other than their appeal to his ear.


I agree, and (appeal to the ear) that means Debussy was still using a _harmonic hierarchy,_ in which 2:3 would be more consonant than 9:8. Anyway, in my 'harmonic model,' as long as there is a scale, there is 'function.' To me, it doesn't matter if it's CP tonal function or not, since I understand 'function' in a general sense, which is simply a 'ranking' in order of consonance of the various ratios created by whatever scale or octave division is employed.



> As for the idea that Schoenberg meant to abandon only common practice tonality and not tonality as such, it sounds plausible, but I don't think it survives examination. Common practice is not peculiar in terms of what defines tonality; it's not alone in having a tonal center and a pitch hierarchy.


Agreed, totally. "Tonality as such" is the source of all tonality, including CP tonality.



> (Tonality) It is distinguished by its explicit harmonic structure, its polyphony. If you are writing harmonic/polyphonic (as opposed to purely melodic) music, and you are preventing the establishment of a tonality (a "key") in the progression of your harmonies, exactly what form of tonality could you expect to retain? Some form which is not even relevant to the harmonic tradition from whose laws you are departing? If Schoenberg's harmony is traditional except with respect to the element of the tonal relationships on which it's based, in what "nontraditional" sense is tonality still present? What is the tonal system now heard to be operating? What are its laws? How is it perceived?


Good question, one which I am still exploring. For example, Berg constructed the row for his Violin Concerto to suggest harmonic tonality. The row is G, B♭, D, F♯, A, C, E, G♯, B, C♯, E♭, F. This tone row consists of alternating triads, followed by a portion of an ascending whole tone scale. Although there is not an hierarchical relation to a tonic, there is still a harmonic effect. But these are at best allusions, which do not exhibit the meta-consequences of a tone-centered hierarchy, but only the consequences of the row structure. What if we did an interval-vector analysis of it? Remember, in an ordered tone row, only pairs of pitches can be compared.

Starting with G:
G-Bb: m3
Bb-D: M3
D-F#: M3
F#-A: m3
A-C: m3
C-E: M3
E-G#: M3
G#-B: m3
C#-Eb: M2
Eb-F: M2

Results: 
M2 (8:9): 2 
m3 (5:6): 4
M3 (4:5): 4

An equal number of m3s and M3s; and two Major seconds. These are within the row itself, before it is stacked or combined with other rows. Still, these are simply sonorities which do not refer to a tonic note. They are more consonant or dissonant only in relation to each other; the ratios are 'absolute' in this sense. They will be heard as a sonorous interval, but not in relation to a tonic; only to each other, or whatever other sonorities are created by combining other rows.



> I am unaware of any statements by Schoenberg expressing an intention to preserve tonality in his 12-tone music. All the theoretical groundwork he laid for his "method" appears to indicate the opposite. I would be delighted to find such statements as aids to better understanding what he actually did - or intended to do, whether he succeeded in doing it or not - but in their absence I find no reason to abandon traditional terminology - "atonality" - in describing the music itself.


And don't hold your breath waiting for any such evidence to be presented; only belittling ad-hominems.


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## Woodduck

millionrainbows said:


> Anyway, in my 'harmonic model,' as long as there is a scale, there is 'function.' To me, it doesn't matter if it's CP tonal function or not, since I understand 'function' in a general sense, which is simply a 'ranking' in order of consonance of the various ratios created by whatever scale or octave division is employed.


The term "function" has been bothering me. I take it as meaning the way notes or chords tend to relate to one another in particular musical styles or contexts - e.g., a certain tone "functions" as a tonal center, another "functions" as a leading tone, another "functions" as a secondary or subordinate area of tonal focus. I gather that the word is ordinarily used only in the context of common practice harmonic music, but I see no reason for so restricting it. Every kind of music has its system of relationships that determines what notes do and don't do in relation to one another - how they function. As with tonality itself, I can't see why common practice is peculiar in this regard.

As for your ranking of ratios, how does that relate to the concept of function, which Dictionary.com defines as "the kind of action or activity proper to a person, thing, or institution; the purpose for which something is designed or exists; role" ?


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## millionrainbows

Woodduck said:


> The term "function" has been bothering me. I take it as meaning the way notes or chords tend to relate to one another in particular musical styles or contexts - e.g., a certain tone "functions" as a tonal center, another "functions" as a leading tone, another "functions" as a secondary or subordinate area of tonal focus. I gather that the word is ordinarily used only in the context of common practice harmonic music, but I see no reason for so restricting it. Every kind of music has its system of relationships that determines what notes do and don't do in relation to one another - how they function. As with tonality itself, I can't see why common practice is peculiar in this regard.


As I said in an earlier blog, in tonality, the vertical dimension is derived from consonance/dissonance of intervals in relation to "1" or tonic. These are expressed as "fractions" of that "1", falling within the octave (1:1). This is "ranked" by degree of increasing dissonance: 1:1, 2:3, 3:4, 4:5, 5:6, etc. These vertical intervals are then "projected" into the horizontal dimension as "functions:" I, ii, iii, IV, V, vi, vii.




> As for your ranking of ratios, how does that relate to the concept of function, which Dictionary.com defines as "the kind of action or activity proper to a person, thing, or institution; the purpose for which something is designed or exists; role" ?



I guess you need to see the ratio first, because that is what will become root movement.

After you see that triads are built on those roots, and have the same consonance as the root considered in isolation, then 'function' of those triads is ranked in the same way, and you see that a 'distant key area' simply means 'more dissonant' or 'further away' from the tonic. They're inseparable, in this regard.

In another blog, I show examples:
A C major scale's horizontal functions correspond to these harmonic relations; and one can observe how these functions were derived:

I - 1:1
ii - 8:9
iii - 4:5
IV - 3:4
V - 2:3
vi - 3:5
vii - 8:15

Their importance in establishing the tonality is ranked by the order of consonance to dissonance, with smaller-number ratios being more consonant.

I - 1:1
V - 2:3
IV - 3:4
vi - 3:5
iii - 4:5
ii - 8:9
vii - 8:15

Using this model, a "function" hierarchy can be applied to any scale, after the degrees of dissonance are ranked.

Whole Tone scale: C-D-D-F#-G#-A#

C - 1:1
D -8:9
E -4:5
F#- 45:32
G# - 8:5
A# - 16:9

Whether or not you attach Roman numerals to the above is optional; but by the numbers, one can see a ranking:

C - 1:1
E -4:5
G# - 8:5
D -8:9
A# - 16:9
F#- 45:32

I hope this answers it. "Function" is just a scale member which takes on the role of a root of a triad, which was originally an interval (relating to the tonic). With a triad stacked on top, this makes the 'harmonic' or vertical dimension more immediately audible, I guess.

It's harder to hear how the single-note root station of, for example, a "ii" chord (D) relates to the root (C) 'by itself,' since both are not being sounded as an interval at the same time. It's all changing in time.

"Function" seems to be best understood 'in time' (horizontally) by most people, because it is a relation (in time) of 'changes' of roots or chords. It's a progression.

But the vertical dimension of function must also be understood, because the tension, or degree of dissonance, is what makes it want to go towards a certain direction, to either resolve or to go away from the tonic.

Schoenberg reduced these triad movements to root movements in his Structural Functions of Harmony book. It's true, just the 'interval itself,' without a triad, is sufficient to determine functionality, and 'tendencies' of root movement (strong and weak movement, or "to" and "away" from the tonic).


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## Woodduck

I can see how that works for common practice. But for other tonalities? In the whole tone scale, which has no first degree, I find tonality only as a "borrowed" effect, not as intrinsic. And in minor modes the very thing that makes them minor, the minor third - how does that fit into your scheme?


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## millionrainbows

Woodduck said:


> I can see how that works for common practice. But for other tonalities?


I define 'other tonalities' to mean a system of tone-centricity which can be accomplished using 'other scales,' and also 'other octave divisions.'

In my schema, 'tonality' is a more _general_ term, more accurately called a _pitch hierarchy,_ which means that any octave division, or any scale with a starting point, can be considered a 'tonality' (I didn't say how strong or weak), because _it creates an harmonic hierarchy of pitches within that octave which can be ranked in order of their sonance,_ and which can thus, if desired, be called 'functions' within that octave.



> In the whole tone scale, *which has no first degree,* I find tonality only as a "borrowed" effect, not as intrinsic.


For me, it's not accurate to say that the whole tone scale 'has no first degree' if _any note of the scale_ can be considered the starting note. This fits the definition of a scale, if it has a starting note and covers an octave.

I'm not concerned with how far these pitch hierarchies I speak of will go into the fog of weakened tonality, or fail your criteria of 'tonality' by using the whole tone scale as an example.

Perhaps your idea of a 'tonality' requires more centricity; perhaps you view the WT scale as only a way of weakening a tonality within a tonal context, which it certainly does; if so, you are being more specific in your requirements for a tonality than I am.

However, Debussy seemed to use the WT scale in _Brouillards_ as an end in itself, not just as a 'weakening agent.' The WT scale does have a distinctive harmonic, sonorous sound. Who cares if it has a 'tonic' if it sounds so good?

This effect may have been used by Debussy because of the better steel-string pianos in use at the time, better metals for the frames, and their tuning. _The WT scale sounds more sonorous, more evenly-sheened, in equal temperament,_ because ET is a more 'symmetrical tuning.' It would sound less sonorous in mean tone tuning.

_For me, a 'starting point' is a 1:1, and as such, defines a tonality, _because it is a center reference to which all other ratios relate; this includes whole tone scales and diminished scales as well.

If you maintain that a whole tone scale has no starting point, or refuse to recognize that it can be _considered_ to have a starting point, then that is a game changer, and we have nothing further to discuss. If you don't see the WT scale as a true 'tonal' entity in itself, but as a 'glitch' used to weaken tonality, then that's fine; the diminished scale is also such an entity.

But in my schema, 'tonality' is a more general term which means that any octave division, or scale, with a starting point, can be considered a 'tonality' (I didn't say how strong or weak), because _it creates an harmonic hierarchy of pitches within that octave which can be ranked in order of their sonance,_ and can thus, if desired, be called 'functions' within that octave.

If the octave division starts with a note, that note is 1:1, and to me, that means a tone-centered tonality is present.

However, please bear in mind that Debussy, Schoenberg, and Berg, all in their respective 'tonal' periods, used the WT scale to establish "areas" of what I would call 'tonality,' albeit a very vague and weakened form. This also might have required two versions of the scale, a semitone apart, to cover all 12 notes. Were these areas "tonalities?" I say yes, because the principles of tonality are in play.

Of course, being symmetrical, all of the 'modes' of the WT scale are identical. No matter which of the 6 notes is considered the starting point, the scale will be identical.

The WT scale lies in a 'grey area' of tonality. Besides being a scale, it is also the 'projection' of the major second, it divides the octave at the tritone, and it is symmetrical. These three characteristics are geometric in nature; they are based on mathematical 'geometric' structural features derived from the "12-ness" of our octave division. Now, we have opened a complex can of worms, which requires knowledge of several aspects of music theory.

Pythagoras did not start with 12 notes; I know that , and this was argued cruelly in "that other" thread I tried to start. I'm still bitter about the abuse I suffered there, with no sympathy from above.

I do maintain that our 12-note division of the octave is essentially a Pythagoran-derived concept, because Pythagoras 'stacked' fifths to get his scale, and if this procedure is extended and continued, we get a "stack" of 12 fifths, with the leftover Pythagoran comma at the end, which we compensated for in equal temperament. That's where we are today.

I do not care to have to prove my thesis all the way back to pre-history.



> And in minor modes the very thing that makes them minor, the minor third - how does that fit into your scheme?


A minor:

A: 1:1
B: 8:9
C: 6:5
D: 4:5
E: 2:3
F: 8:5
G: 16:9


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## millionrainbows

Woodduck said:


> The term "function" has been bothering me. I take it as meaning the way notes or chords tend to relate to one another in particular musical styles or contexts - e.g., a certain tone "functions" as a tonal center, another "functions" as a leading tone, another "functions" as a secondary or subordinate area of tonal focus. I gather that the word is ordinarily used only in the context of common practice harmonic music, but I see no reason for so restricting it. Every kind of music has its system of relationships that determines what notes do and don't do in relation to one another - how they function. As with tonality itself, I can't see why common practice is peculiar in this regard.


As far as function goes, I find Schoenberg's ideas in Structural Functions of Harmony to be very compelling, as well as proof that he truly "grokked" the meaning of intervals in both their vertical/harmonic and their horizontal/root movement senses.

1.) Schoenberg considered a root root movement of a _fifth up_ (identical with a _fourth down)_ to be tending towards weakening, or moving away from tonic.

If we hear a fifth (C with G on top), we hear the _bottom_ note as the "tonic." This means, in "moving" horizontal terms, that when our root moves up a fifth, it is moving "away" from the tonic; the top note has _weakened, _as in I-V.

2.) Schoenberg considered a root root movement of a _fourth up_ (identical with a _fifth down) _to be tending towards stregthening, or moving towards tonic.

If we hear a fourth (C with F on top), we hear the _top_ note as 'tonic.' The top note is _strengthened, _as in V-I.

This tendency to hear intervals in this way has to do with the way we hear harmonics of a fundamental tone.


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## millionrainbows

Further thoughts on Berg's Violin Concerto:

If the row is considered as a template for root movement (of harmonic entities , perhaps tertial, constructed on these steps), then we have root movement of "chords" in major thirds mostly, something that was done by Beethoven in his Ninth to quickly go to distant key areas; you can also see how this sort of arbitrary distancing of root movement could easily tie-in with Riemann theory.

M2 (8:9): 2 
m3 (5:6): 4
M3 (4:5): 4

The row (G, B♭, D, F♯, A, C, E, G♯, B, C♯, E♭, F) has plenty of thirds.

This 'even-spacing' of root movement would also be interesting because it is not full of root movements by fourths and fifths, or chromatically by minor seconds, which might get dense and boring as well.


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## bestellen

Check out Vincent Persichetti's Twentieth-Century Harmony: Creative Aspects and Practice.


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## millionrainbows

bestellen said:


> Check out Vincent Persichetti's Twentieth-Century Harmony: Creative Aspects and Practice.


If you will look inside the actual book, you will learn that this book is not concerned with "non-tonal theory" as the OP requested, but is really about "extended harmonic devices" that are traceable to tonality and harmonic practice. The same goes for Howard Hanson's book "Harmonic Materials of Modern Music." Both books are "tonal" in that they deal with harmonic aspects of music which are ultimately traceable to harmony, sonority, and qualities of tonality, however extended or expanded beyond CP practices and notions of tonality and harmony.


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