# Is this Atonal?



## peeyaj (Nov 17, 2010)

Is this section of the piece considered some kind of *atonal music*? The middle section of Schubert's D.959 sonata.






The section starts at 3:10 and end at 4:37.

Conversely, *what music pre-Schoenberg era that exhibits atonality? Those pieces and composers that seems to predict the atonality in music..*

Thoghts?


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## Mahlerian (Nov 27, 2012)

No, it's not atonal. It's very decidedly tonal, although it has some sharp dissonances (over pedal points, mainly).

If you intend atonal to mean "having no tonal center whatsoever", as many do, then I don't think Schoenberg ever wrote atonal music. The leading tone, the relation most important in post-Renaissance music for cadences, is still present, I feel.

If you mean "music that breaks from triadic functional relations", then there are examples of music before Schoenberg that exhibit these traits.

Liszt: Bagatelle sans tonalite (based heavily around tritone relations and strings of unresolved dissonances)





Many pieces by Debussy (and Impressionists in general) remove leading tone relations as a structural element and are more closely related to modal than tonal practice, but also with a de-emphasis on triads as the sole point of rest.




 (Schoenberg was already composing by this time, but had not composed any so-called atonal works.)


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## millionrainbows (Jun 23, 2012)

It starts out firmly in F sharp minor. The weirdness begins at around 2:47, with a diminished seventh F-Ab-B-D (which can easily function as the dominant of F sharp minor by simply putting a C# in the bass, making it a dom C#7b9...then at 2:52 it's a G7 to C#-E-G-A# (dim7) to C-Eb-Gb-A (dim7) to B-D-F-Ab (dim7 with G in bass, making it a G7b9 again) to "regular" G7, gateway V-i to C minor. Then surprise, at 3:19 to C# minor, then E minor to F minor, then at 3:36 to F# minor, then C# minor, the dominant minor area.

Now let's analyze this. The change from the established key of F#minor to the dim7 (F-Ab-B-D) is really just a i-V7, because by putting a C# in the bass, the Fdim7 is really an incomplete C#7b9 (F/E# is the maj3, Ab/G# is the 5th, B is b7, and D is b9).

These dim7/b9 chords can have more than one root; as a C#7b9, it can also function as a G7b9; Thus a tritone root shift, from C# to G7 is enabled.

All Dom7's contain a tritone, and the flat-seventh can be exchanged for a new root. In jazz, this is called tri-tone substitution.

This sort of tritone root movement basically turns a V-I into a chromatic descent; in our key of F# minor, instead of V-I (C# minor-F# minor) we are substituting the tritone G and going bii-i (G7-F# minor)

So no, it's not "atonal," but chromatic, using the ambiguity and dual-nature of dim7s to create chromatic root movements out of V-I's.

This _is_ what _led_ to atonality, though.


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## tdc (Jan 17, 2011)

millionrainbows said:


> It starts out firmly in F sharp minor. The weirdness begins at around 2:47, with a diminished seventh F-Ab-B-D (which can easily function as the dominant of F sharp minor by simply putting a C# in the bass, making it a dom C#7b9...then at 2:52 it's a G7 to C#-E-G-A# (dim7) to C-Eb-Gb-A (dim7) to B-D-F-Ab (dim7 with G in bass, making it a G7b9 again) to "regular" G7, gateway V-i to C minor. Then surprise, at 3:19 to C# minor, then E minor to F minor, then at 3:36 to F# minor, then C# minor, the dominant minor area.
> 
> Now let's analyze this. The change from the established key of F#minor to the dim7 (F-Ab-B-D) is really just a i-V7, because by putting a C# in the bass, the Fdim7 is really an incomplete C#7b9 (F/E# is the maj3, Ab/G# is the 5th, B is b7, and D is b9).
> 
> ...


This touches on an area I've found confusing, so you are saying that a C#7b9 could function as a G7b9, if I write out the notes of each of these chords we see they share 4 notes in common (the E# and G# having enharmonic equivalents in F and Ab respectively) we simply substitute the C# root for its tritone G.

C#7 b9 = C#,E#, G#, B, D
G7 b9 = G,B,D,F,Ab

I'm confused on the second part in bold, it suggests we substitute the flat 7 for a new root, but in this example the flat7 appears in both chords, so how is that note substituted? Secondly are you saying that Dom 7's can be substituted to multiple different key areas based on this b7, or just the tritone of the root?


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## peeyaj (Nov 17, 2010)

millionrainbows said:


> It starts out firmly in F sharp minor. The weirdness begins at around 2:47, with a diminished seventh F-Ab-B-D (which can easily function as the dominant of F sharp minor by simply putting a C# in the bass, making it a dom C#7b9...then at 2:52 it's a G7 to C#-E-G-A# (dim7) to C-Eb-Gb-A (dim7) to B-D-F-Ab (dim7 with G in bass, making it a G7b9 again) to "regular" G7, gateway V-i to C minor. Then surprise, at 3:19 to C# minor, then E minor to F minor, then at 3:36 to F# minor, then C# minor, the dominant minor area.
> 
> Now let's analyze this. The change from the established key of F#minor to the dim7 (F-Ab-B-D) is really just a i-V7, because by putting a C# in the bass, the Fdim7 is really an incomplete C#7b9 (F/E# is the maj3, Ab/G# is the 5th, B is b7, and D is b9).
> 
> ...


I don't fully understand but thanks anyway!


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## Guest (Apr 22, 2013)

I have to keep checking my calendar.

It still says 2013.

Next, it's going to say 2014.

It's never going to say 2009 or 1998 or 1939 or 1897 or... ever again.

Not that all of the things that happened in any of those years (and millions more) are lost forever or have become less important, but even those few things that survive are different in 2013 than they were in 2009 or 1998 or 1939 or 1897 or.

Here's a thought experiment for you. Imagine an online political chat group. The most persistent topic there, the one that generates the most heat, the one that generates the most activity, and gets the most locked threads and the most infractions for its posters is the topic of universal suffrage. (Though the Swiss posters might not see that as all _that_ odd. )


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## peeyaj (Nov 17, 2010)

some guy said:


> I have to keep checking my calendar.
> 
> It still says 2013.
> 
> ...


I don't understand what are you saying. I am generally curious about that section on the D.959 sonata.. Perhaps you have posted in the wrong thread.


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## millionrainbows (Jun 23, 2012)

tdc said:


> This touches on an area I've found confusing, so you are saying that a C#7b9 could function as a G7b9, if I write out the notes of each of these chords we see they share 4 notes in common (the E# and G# having enharmonic equivalents in F and Ab respectively) we simply substitute the C# root for its tritone G.
> 
> C#7 b9 = C#,E#, G#, B, D
> G7 b9 = G,B,D,F,Ab


Well, a diminished seventh falls into the "cracks" of the diatonic system, because they are built on all minor thirds. This creates difficulty in spelling them, because they have a "double-flatted" seventh. Triads and seventh chords should normally be spelled by skipping a letter, as in C7=C-E-G-Bb.

But diminished sevenths fall into an "enharmonic no-man's land." F dim7=F-Ab-Cb-*Ebb*. The "B" must be called "Cb" in order to adhere to the "skip a letter" rule, and the D must be called Ebb, not D. 
Likewise, to spell C dim7 with the proper skips, it must be C-Eb-Gb-*Bbb* (B double-flat). Note also the tritones F-Cb and C-Gb in these chords.

Diminished chords are recursive; the *root* can "cycle" through the pattern of minor thirds and be considered as any of the 4 notes.

For example, our *F dim* can be 
*F dim* (F-Ab-Cb-Ebb)
*Ab dim* (Ab-Cb-Ebb-Gbb)/*G# dim* (G#-B-D-F), 
*Cb dim* (Cb-Ebb-Gbb-Ab)/*B dim* (B-D-F-Ab) or
*D dim* (D-F-Ab-Cb).

The diminished scale is an *8-note scale;* there are 2 of them per octave, which "interlock." One is the "whole-half" scale, and the other is the "half-whole" scale, referring to the step-pattern.

The "whole-half" scale, _in half-steps,_ is 2-1-2-1-2-1-2-1-2. Starting on C, this is C-D-Eb-F-Gb-Ab-A-B. Unlike diatonic scales, a letter-note must be repeated, in this case (Ab-A). Spellings can vary according to the harmonic situation.

The "half-whole" scale on C is 1-2-1-2-1-2-1-2-1. Starting on C, this is C-Db-Eb-Fb-Gb-G-A-Bb. Note the repeated letter, (Gb-G).

Diminished seventh chords are members of this diminished scale. The dim7 (C-Eb-Gb-Bbb) can be given "new roots" and be transformed into 4 possible dom b9s. These 4 new roots are taken from the "left-over" notes of the diminished scale. Thus, (C-Eb-Gb-Bbb) can become D7b9, F7b9, Ab7b9, or B7b9, just like the regular dim chords had 4 roots.

Try this at the piano, and see my blog: *The dominant chord rules! *on page 6 of my blogs.



tdc said:


> I'm confused on the second part in bold, it suggests we substitute the flat 7 for a new root, but in this example the flat7 appears in both chords, so how is that note substituted? Secondly are you saying that Dom 7's can be substituted to multiple different key areas based on this b7, or just the tritone of the root?


In all dominant (b7) chords, there is a tritone. *This tritone will always be third/flat seventh.* Unlike other intervals (except the octave), the tritone is an "invertible" interval; when flipped over, it remains the same interval. It's symmetrical.

So, the tritone in a C7 (C-E-G-Bb), *E-Bb* (M3/b7th), can, via tritone substitution, can become *E-Bb* (b7th-M3), transforming it from being A *C7* to being an *(F#7 or Gb7)*, which is a tritone away from C. The M3 and b7th have "exchanged functions" in the "flip".

Actually, I should have said *"All Dom7's contain a tritone, and the flat-seventh/Major third can exchange function, by using a new root a tritone away."* Sorry if this confused you.

The best way to "grok" this info is to go to a piano!


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## peeyaj (Nov 17, 2010)

@millionrainbows

Do you think the section of this sonata predicts the upcoming atonality in music? Is it unique in post-Beethoven era?


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## Kazaman (Apr 13, 2013)

Similarly chromatic and non-functional uses of dominant chords are to be found in pre-Beethoven composers ... for example, Mozart often makes use of back-related dominants, and Bach is full of chromaticism employing chained dominants.


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## peeyaj (Nov 17, 2010)

Kazaman said:


> Similarly chromatic and non-functional uses of dominant chords are to be found in pre-Beethoven composers ... for example, Mozart often makes use of back-related dominants, and Bach is full of chromaticism employing chained dominants.


So, whats so unique about this movement? I can't name it but I think its so forward looking...


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## Kazaman (Apr 13, 2013)

I'm not all that familiar with the work, judging a cursory glance at the score and a listen to the video you posted the music seems to foreshadow the late romantic tendency toward suspended tonality, as seen in Wagner, Strauss, Scriabin, Mahler and friends.


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## Mahlerian (Nov 27, 2012)

peeyaj said:


> @millionrainbows
> 
> Do you think the section of this sonata predicts the upcoming atonality in music? Is it unique in post-Beethoven era?


Pre-Baroque music could sound pretty wild to modern, tonally-oriented ears. Ever heard Gesualdo?


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## peeyaj (Nov 17, 2010)

Mahlerian said:


> Pre-Baroque music could sound pretty wild to modern, tonally-oriented ears. Ever heard Gesualdo?


The crazy one! Nope.. I am not that enamored with Baroque music other than Bach and Handel


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## Kazaman (Apr 13, 2013)

peeyaj said:


> The crazy one! Nope.. I am not that enamored with Baroque music other than Bach and Handel


Gesualdo is of the Renaissance, and his music is really quite beautiful.


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## millionrainbows (Jun 23, 2012)

peeyaj said:


> So, whats so unique about this movement? I can't name it but I think its so forward looking...


Yeah, Beethoven had loads of b9s derived from dim7s. A striking example is in the final mvt of String Quartet in F, op. 135, about a minute in, where you can hear the dim7 being transformed into a domb9, as the bass note changes under it. 
Bach's Chromatic fantasy (just the name alone is a clue) also uses chromatically descending dim7s.

The Schubert example is abrupt in its changes, perhaps that's why. Modulations got quicker and quicker, until we now have "instant" modulations in soundtracks. (The new James Bond movie is an example of that.

The weirdest change, to my ear, in the Schubert is "...Then surprise, at 3:19 to C# minor, then E minor to F minor, then at 3:36 to F# minor, then C# minor, the dominant minor area."

The jump from C#m to Em is unusual, then Em to Fm is odd, as well.

Bach's Sinfonia (Three-Part Invention) No. 9 in F minor is unusual; 11 of the 12 possible notes occur in the first two measures. Lots of chromatic movement of the bass line. I suggest Glenn Gould's performance.


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## Guest (Apr 23, 2013)

peeyaj said:


> So, whats so unique about this movement?


Near as I can tell, it's so because you have said it's so.

The others have said, over and over again, in various ways, "No, it is not unique, at least not in the way you want it to be. It shares the qualities that you think make it unique with all sorts of other music, from both before and after Schubert."

You are free to accept or reject, but re-asking the question is not going to get you a different answer.

[Edit: Well, unless that last post from million, which just preceded my initial posting of this, counts as a different answer.]


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## norman bates (Aug 18, 2010)

peeyaj said:


> Conversely, *what music pre-Schoenberg era that exhibits atonality? Those pieces and composers that seems to predict the atonality in music..*


Liszt aside, William Billings composed Jargon in 1778





Smetana composed Macbeth and the witches in 1859, and while it is still a tonal work it has moments that border on Atonality





Abel Decaux composed his Clairs de lune, his only work, between 1900 and 1907





and a dutch composer, Jan Ingenhoven, composed in the same period some atonal piece (one is "Nous n'irons plus au bois"), but I have not been capable to find any of these pieces.


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## peeyaj (Nov 17, 2010)

millionrainbows said:


> *The Schubert example is abrupt in its changes, perhaps that's why. Modulations got quicker and quicker, until we now have "instant" modulations in soundtracks. (The new James Bond movie is an example of that.
> 
> The weirdest change, to my ear, in the Schubert is "...Then surprise, at 3:19 to C# minor, then E minor to F minor, then at 3:36 to F# minor, then C# minor, the dominant minor area."
> 
> ...


Thank you @millionrainbows.. You are very helpful. :thumbsup:  :cheers:


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## PetrB (Feb 28, 2012)

some guy said:


> I have to keep checking my calendar.
> 
> It still says 2013.
> 
> ...


My dear colleague:

I think in this instance you jumped the gun on your practiced homily to the infidels re: 'acceptance' of or 'embracing' atonality, including its seminal chromaticism starting with the early romantic.

Whether the study is informal or formal, Peeyaj was not the first nor will he be the last to have to struggle in thought, somewhat confusedly. with the shift from later classical to early romantic, as per what began to 'happen to harmony,' the incipient chromaticism, the modulating by thirds, the different use of chord function redefined, and all that jazz.

When I studied, I recall about half the class -- both the quickest and the slowest -- began to struggle, had to re-think, revise and expand their habitual perceptions when it came to the romantic era harmony. Some caught on quickly, the other half, not.

In guessing how many tend to think of this musical development, I recall this quote of Confucius:
_"If you want to change the society, first revise the language."_

I think many people 'build in' what seems to them as an innate (i.e. 'natural') resistance to post classical and later harmony, first via a gazillion exposures to music primarily built upon I - V / IV - I, and that done by the cumulative whole of listening to popular song and dance forms and earlier classical fare almost exclusively.

The other element? Even in music schools and conservatories, harmonic evolution is most couched in phraseology such as, "the breakdown / destruction of tonality." 
_Change the language!_ 
Instead, it should be thought of - taught as. "The continued further development / evolving of harmony."

Any 'takers?'


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## EddieRUKiddingVarese (Jan 8, 2013)

A broad mindset and ability to examine new ideas is always better in the long run. Continued further development of musical forms should always be encouraged, whether fitting accepted forms or new methods.

Not sure how the schools are where you are but evolution is widely accepted and taught in schools here as accepted fact.


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## KenOC (Mar 7, 2011)

PetrB said:


> In guessing how many tend to think of this musical development, I recall this quote of Confucius:
> _"If you want to change the society, first revise the language."_


Are you sure Confucius said this? I can't recall it, and it sounds a lot more like somebody from the School of Names.

http://plato.stanford.edu/entries/school-names/


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## millionrainbows (Jun 23, 2012)

PetrB said:


> I think many people 'build in' what seems to them as an innate (i.e. 'natural') resistance to post classical and later harmony, first via a gazillion exposures to music primarily built upon I - V / IV - I, and that done by the cumulative whole of listening to popular song and dance forms and earlier classical fare almost exclusively.


Well, what do you expect? Garbage in/garbage out. I think this "resistance to post-classical harmony" is simply a matter of what you have listened to. When I was beginning to _really absorb_ music, it was the Beatles, The Byrds, The Doors, Eric Burdon and The Animals, Motown, and The Rolling Stones that ruled the airwaves; and this was not simply I-IV-V Western harmony; it had a strong element of blues, jazz, and folk music.

I don't know about Peeyaj, whom I suspect was raised conservatively, but I had trouble understanding the simplicity of Handel and Haydn, and the simplistic sonatinas I was attempting to learn; I had already expanded my ears in another direction; I was already "corrupted" by jazz and my listening habits, and electric guitars.

For example, when I was studying diminished seventh chords in junior college first-year theory, I pointed out to the teacher the connection between dim7s and flat-nine dominants, a jazz idea; but n-o-o-o, she wouldn't hear of it.

I also questioned the consideration of vii as being a "B diminished." To me, it always sounded like an incomplete G7 chord. I was later proved correct in my intuition by Walter Piston's _Harmony,_ and Schoenberg's _Harmonilehre,_ both of which treated the resolution of vii as an incomplete G, resolving to C as normal.

The problem is the restricted experience, practices, mindset, and worldview, on the part of elite musical specialists who are so immersed in Western tradition that they are unable or unwilling to _really listen_ to _all kinds_ of music.



PetrB said:


> The other element? Even in music schools and conservatories, harmonic evolution is most couched in phraseology such as, "the breakdown / destruction of tonality." _Change the language!_ Instead, it should be thought of - taught as "The continued further development / evolving of harmony."...Any 'takers?'


I agree that harmony evolved and developed; and terms like "breakdown / destruction of tonality" create the perception that modernism is a destructive force. Like religious zealots who want evolution to be taught alongside creationism, tonality does not need defending, nor is modern chromatic thinking aimed at tonality's destuction.

There comes a time when it must be recognized that "harmonic evolution" is not tied inextricably to 18th century CP tonality. Tonality _did_ "break down" and become chromatic, but this was a natural evolution in musical thought, not a "modernist conspiracy."

If even relatively tame post-classical and later harmony is "naturally resisted," then there is something amiss; these people have been conditioned very strictly, and have not exercised their ears enough.

Also, there is a political component to this: "evolution" of music, and "progress in musical thinking" is seen as a justification for modernism, so the idea that late-tonal chromaticism led to a chromatic thinking which _broke_ with tonality cannot be entertained, as this might cause sensitive tonal advocates to feel "discriminated" against.


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## Guest (Apr 24, 2013)

PetrB said:


> Instead, it should be thought of - taught as. "The continued further development / evolving of harmony."


The lovely thing about definitions is exploring the margins. At what point does 'harmony' cease to be harmony? Presumably when it is realised that the language we use to describe music is inadequate to encompass change, not when someone writes music that is 'not harmony.''

Composing in particular ways merely establishes traditions, not inevitabilities of either development or evolution. The fact that some traditions have been long-established, and a musical establishment (either real or virtual) determined the 'rules' for that tradition ("Write this way and you are writing 'harmony"; write that way and you're not - and you'll be demonised/lionised if you do!") does not, in fact, give such particular ways an objective pre-eminence.

'Music' - on the other hand - does change. 'Evolve' and 'develop' somehow smack of forward progression (or, some might argue, forward regression!). As someguy says the only way is forward in time (however much we like to spend our hours exploring the merits and demerits of the past) but it means nothing more nor less than that. Music will go where it will: attaching terms that attract any sense of purpose or moral colour is not a valid activity for an objective analysis of what music _does_.


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## KenOC (Mar 7, 2011)

MacLeod said:


> ...for an objective analysis of what music _does_.


Agree with your post, but I'm not sure that the mythical thing you mention in your final phrase can or ever will exist!


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## Guest (Apr 24, 2013)

KenOC said:


> Agree with your post, but I'm not sure that the mythical thing you mention in your final phrase can or ever will exist!


Which? 'Music' or 'objective analysis'?


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## KenOC (Mar 7, 2011)

MacLeod said:


> Which? 'Music' or 'objective analysis'?


Exactly what I quoted:

"an objective analysis of what music does."


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## quack (Oct 13, 2011)

The thing about being objective: someone always objects.


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## millionrainbows (Jun 23, 2012)

MacLeod said:


> The lovely thing about definitions is exploring the margins. At what point does 'harmony' cease to be harmony? Presumably when it is realised that the language we use to describe music is inadequate to encompass change, not when someone writes music that is 'not harmony.''


Agreed; the only "inevitability" is the ear. This being a "given," all music is "harmonic." Harmony will not cease to be harmony; it will simply be subject to another language, or system.

CP tonality should not be synonymous with harmony; all music is harmonic. It got that way by being a sustained pitch. That's the only real criterion. If it's not a sustained pitch, it's rhythm.



MacLeod said:


> Composing in particular ways merely establishes traditions, not inevitabilities of either development or evolution. The fact that some traditions have been long-established, and a musical establishment (either real or virtual) determined the 'rules' for that tradition ("Write this way and you are writing 'harmony"; write that way and you're not - and you'll be demonised/lionised if you do!") does not, in fact, give such particular ways an objective pre-eminence.
> 'Music' - on the other hand - does change. 'Evolve' and 'develop' somehow smack of forward progression (or, some might argue, forward regression!). As someguy says the only way is forward in time...but it means nothing more nor less than that. Music will go where it will: attaching terms that attract any sense of purpose or moral colour is not a valid activity for an objective analysis of what music _does_.


While I see the underlying thrust of this argument, and its attempt to assuage and sidestep the issue of a "progressive or advanced tonality," tonality as a system of organizing harmonic principles _did _evolve and progress. To refuse not to see this is somewhat unrealistic, when faced with the "nuts and bolts" of our Pythagoran heritage.

CP tonality uses the 12-note chromatic scale as its foundation, and this is simultaneously the means of its sustainability and expansion. If tonality had wished to stay "pure," it should never have modulated, used minor scales, diminished chords, or chromatic notes.

Tonality is a "7-note system living in a 12-note world." Therein lies both its strengths and weaknesses. The expansion of harmonic ideas into chromaticism, and the consequent emergence of a truly different chromatic thinking, separate and different than CP tonality, based on symmetrical division of the octave, recursive interval projections, and localized, moving tone-centers, was built-in to the 12-note infrastructure.



MacLeod said:


> As someguy says the only way is forward in time (however much we like to spend our hours exploring the merits and demerits of the past) but it means nothing more nor less than that. Music will go where it will: attaching terms that attract any sense of purpose or moral colour is not a valid activity for an objective analysis of what music _does_.


That's a poetic way of looking at things, but in addition to going "forward in time," there is the inevitability of accumulation: after 7, there are 5 more notes, which add up to 12.


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## Guest (Apr 25, 2013)

millionrainbows said:


> While I see the underlying thrust of this argument, and its attempt to assuage and sidestep the issue of a "progressive or advanced tonality," tonality as a system of organizing harmonic principles _did _evolve and progress. To refuse not to see this is somewhat unrealistic, when faced with the "nuts and bolts" of our Pythagoran heritage.
> 
> I don't think I'm _refusing _to see that there was progression/evolution. I'm pointing out that such progression was not inevitable: that it was not the only way music might have 'progressed'. All that happened is that a dominant tradition emerged, enforced by those who had the power to direct what players should play and composers should compose until other powers enabled new traditions to emerge, challenge, dominate.
> 
> That's a poetic way of looking at things, but in addition to going "forward in time," there is the inevitability of accumulation: after 7, there are 5 more notes, which add up to 12.


I'm not sure I follow that last point - which seems to reflect the convenience of an agreed 12 note system, not the inevitability - but I'm very happy to be poetic!

For good reason, we have an agreed system of measuring time based on the movement of the Earth on its axis and through space. But we could, had we so _wished_, have a time system where a minute is actually worth only 42 of what we currently call seconds, and a second might be worth only 345 of what we currently call milliseconds...

And, of course, the 360 degrees through which the Earth moves could have been 240, had mathematicians determined that a 'degree' actually had a slightly different value.

So it is with music - and I'm not just referring, by analogy, to the frequency value of an individual tone.


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## PetrB (Feb 28, 2012)

KenOC said:


> Are you sure Confucius said this? I can't recall it, and it sounds a lot more like somebody from the School of Names.
> 
> http://plato.stanford.edu/entries/school-names/


Well,I am old, but I was not there. I read it as attributed to Confucius, am unaware of the 'school of names,' but good things get passed on, sometimes credit forgotten as to the originator, other times credit taken or re-assigned.

Confucius ~ 551-479 B.C.E. / School of names, ca. 479-221 B.C.E.
Confucius was first: take your pick, or 'go academic-scholarly,' to confirm


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## millionrainbows (Jun 23, 2012)

> While I see the underlying thrust of this argument, and its attempt to assuage and sidestep the issue of a "progressive or advanced tonality," tonality as a system of organizing harmonic principles _did _evolve and progress. To refuse not to see this is somewhat unrealistic, when faced with the "nuts and bolts" of our Pythagoran heritage....That's a poetic way of looking at things, but in addition to going "forward in time," there is the inevitability of accumulation: after 7, there are 5 more notes, which add up to 12.





MacLeod said:


> I'm pointing out that such progression was not inevitable: that it was not the only way music might have 'progressed'. All that happened is that a dominant tradition emerged, enforced by those who had the power to direct what players should play and composers should compose until other powers enabled new traditions to emerge, challenge, dominate.


The operant word here is "emerged." The new way of chromatic thinking was "in the air" as the new Zeitgeist.

Stravinsky, Bartok, and Shostakovich all arrived at and used it independently, not because it was "the style," but because they were musical thinkers.

Harmonic musical thinking, and its development along logical lines (as part of the Greek Quadrivium of Arithmetic, Astronomy and Geometry) was historically inevitable, as inevitable as the scientific discoveries in astronomy of new planets. It should be seen more as a logical, somewhat scientific Zeitgeist, and less as a artistic Parisian parlour-style or politically enforced "style" of academics, because the elements which caused this progression are concrete results of our 12-note system, not whim or arbitrary nomenclature.

This is a sticking-point for many listeners; they can't accept the "logical" and mathematical ties to music. To them, it's all art and emotion, conjured out of thin air.



MacLeod said:


> I'm not sure I follow that last point - which seems to reflect the *convenience* of an agreed 12 note system, *not the inevitability* - but I'm very happy to be poetic!


Well, we could have kept going around the circle, like the Chinese did, and had 17 notes, or 43, or an infinite spiral without limit; but we stopped at 12, because Pythagoras used *fifths* as his stacking sequence, because it was the most dominant harmonic, and because the circle appeared to close at 12...although it was off by a few cents.

To attack the 12-note division of the octave as being "arbitrary" or simply one of many possibilities is a desperate attempt to escape the inevitable consequences of such a system, as if simply "setting the building on fire" would prove something about its structure.



MacLeod said:


> For good reason, we have an agreed system of measuring time based on the movement of the Earth on its axis and through space. But we could, had we so _wished_, have a time system where a minute is actually worth only 42 of what we currently call seconds, and a second might be worth only 345 of what we currently call milliseconds...And, of course, the 360 degrees through which the Earth moves could have been 240, had mathematicians determined that a 'degree' actually had a slightly different value.


Bad analogy, because all you're doing is playing with quantities. Music, like all art, is more concerned with relationships (ratios) rather than fixed quantities.

I've offered principles which are built-in to the infrastructure of the 12-note system itself, and this can't be dismissed by simply calling it "arbitrary" and offering no concrete alternative. I doubt that you could conceive of any other possible system, much less offer reasons for its being.



MacLeod said:


> So it is with music - and I'm not just referring, by analogy, to the frequency value of an individual tone.


Maybe not, but the thinking here is still "literal" in terms of discrete quantities, not relationships.

Besides all this, the "12 note system is arbitrary" argument is contradicted by the form and existence of all the music we all enjoy on this forum; Shostakovich, Bartók, Stravinsky, even Beethoven. How absurd to even argue such a point. BTW, the Earth revolves around the Sun, not the converse. :lol:


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## PetrB (Feb 28, 2012)

MacLeod said:


> The lovely thing about definitions is exploring the margins. At what point does 'harmony' cease to be harmony? Presumably when it is realised that the language we use to describe music is inadequate to encompass change, not when someone writes music that is 'not harmony.''
> 
> Composing in particular ways merely establishes traditions, not inevitabilities of either development or evolution. The fact that some traditions have been long-established, and a musical establishment (either real or virtual) determined the 'rules' for that tradition ("Write this way and you are writing 'harmony"; write that way and you're not - and you'll be demonised/lionised if you do!") does not, in fact, give such particular ways an objective pre-eminence.
> 
> 'Music' - on the other hand - does change. 'Evolve' and 'develop' somehow smack of forward progression (or, some might argue, forward regression!). As someguy says the only way is forward in time (however much we like to spend our hours exploring the merits and demerits of the past) but it means nothing more nor less than that. Music will go where it will: attaching terms that attract any sense of purpose or moral colour is not a valid activity for an objective analysis of what music _does_.


Well damn my bleeding fine and very liberal music theory education: Harmony is the result of any two discrete pitches (_specific or less than_) which are sounding at the same time. So much for 'what is harmony.' 

That is wildly different from the emotional associations which many carry with them in 'their interpretation' of 'harmony / harmonious.'


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## Guest (Apr 25, 2013)

I'm not sure you did get the underlying thrust at all, actually. You seem to have interpreted my posts through the prism of a dialogue exclusively about 12-tone, atonal, chromaticism etc, and, worse, as an 'attack'.

My posts are meant as my attempt as expressing my understanding of how music came to be what it was through the ages, not what it was specifically around the time of the atonal zeitgeist (to clumsily throw your terminology together for shorthand.)

By all means tell me I got my understanding of 'change through time' wrong.



millionrainbows said:


> The operant word here is "emerged." The new way of chromatic thinking was "in the air" as the new Zeitgeist.
> 
> Stravinsky, Bartok, and Shostakovich all arrived at and used it independently, not because it was "the style," but because they were musical thinkers.
> 
> ...


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## Mahlerian (Nov 27, 2012)

MacLeod said:


> but if there are 12 tones, are there not a certain number of semi tones in between those whole tones? A tone is identified by its frequency isn't it?


Yes. In theoretical terminology, a half step is called a semi-tone. Certain composers have used pitches half-way in between those, which are called quarter tones, and others have subdivided in still more exotic ways.



MacLeod said:


> Presumably, the 12 tones could have been associated with different frequencies than they actually were? If Middle C is 261.63 Hertz (assuming I've got the right figures from a reliable website http://www.phy.mtu.edu/~suits/notefreqs.html) presumably a tone system could have been established where "Middle C" was called something else and was 240 Hertz.


Middle C has changed significantly over time. Tunings used to be widely variable from place to place (and still are to some degree) but were usually about a half step lower than today.


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## Guest (Apr 25, 2013)

PetrB said:


> Well damn my bleeding fine and very liberal music theory education: Harmony is the result of any two discrete pitches (_specific or less than_) which are sounding at the same time. So much for 'what is harmony.'
> 
> That is wildly different from the emotional associations which many carry with them in 'their interpretation' of 'harmony / harmonious.'


I agree. I was not rejecting the accepted technical definition of harmony. I was rejecting the idea that there was/is an inevitable progression or decline or development of harmony - that is why I used the terms 'harmony' and 'not harmony' to represent the minimum tech spec and, presumably, anything that does not meet that minimum spec. It avoids the argument that is, as you say, really about what is 'harmonious' or 'mellifluous'.


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## PetrB (Feb 28, 2012)

MacLeod said:


> I agree. I was not rejecting the accepted technical definition of harmony. I was rejecting the idea that there was/is an inevitable progression or decline or development of harmony - that is why I used the terms 'harmony' and 'not harmony' to represent the minimum tech spec and, presumably, anything that does not meet that minimum spec. It avoids the argument that is, as you say, really about what is 'harmonious' or 'mellifluous'.


I think arguments for the more inexorable "progression or decline" of 'harmony' or 'classical music' is already far too absolutist: the arbitrariness -- or caprice -- of history itself should be enough to remind us something more accidental or capricious is part of the time thread.

Monteverdi, high modal and polyphonic though he was, being in the time and place he was and nonetheless opting to compose in a way more leaning toward tonal and homophonic,' is one of many historic 'events' which seem to me both circumstantial and capricious, since many another turn of direction could have happened, where what Monteverdi did 'took.' 
So 'caprice' in that if the circumstance had the slightest spin in another direction, another small catalyzing event, change of thought, then music easily -- could have / perhaps would have -- gone in a completely different direction from that date.

Viewing History that way, I find nothing 'inevitable' about any of it.


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## millionrainbows (Jun 23, 2012)

I'm talking music, not history; if any history is involved, it is the history of thought processes, not stylistic caprices of composers. There _is _an inevitability to the _structures_ of music.

Western harmony is based on movements by fourths and fifths, which is how "12" notes were generated, by stacking these fifths: F-C-G-D-A-E-B-F#-C#-G#-D#-A#.

From there, harmony is based on triads built in thirds: C-E-G, etc.

These triad relationships are really based on and refer to just ratios: 2:3 (fifth) and 4:5 (major third).

These ratios are not fixed quantities, they are ratios (relation between 2 things).

So the chatter about A=440, ec, is irrelevant, since they are fixed quantities.

Modern music started moving away from traditional tonality by way of exploiting the INHERENT SYMMETRIES in the 12-note scale.

All of these ideas were 'in the air' so to speak, around the turn of the century, and were not unique to any particular composer ; examples of symmetry began showing up as early as R. Strauss, in his 'Elektra' and 'Metamorphosen,' before he retreated back into conservative classicism. Debussy, as most of us know, used the whole-tone scale in his music, most notably the prelude 'Voiles' from Book I. The 6-note whole-tone scale itself is a symmetrical projection of the major second, and there are only two of them; Debussy exploits this characteristic to create 2 areas of contrasting tonality. Schoenberg was influenced by this idea as well.

Historically, it was the tritone (in both V7-I's and in diminished seventh chords) which was the first emergent symmetry which led to the expansion of tonality; this interval was the color tone in the V7-I progression, being the major third and flat-seven, which would then exchange places for the next cycle. This gave rise to new roots, moving chromatically instead of by fifths. This was tied-in (as mentioned above) with 'flat-nine' dominant altered chords, which are closely related to the diminished seventh. The use of 'flat-nine dominants' as true V chords appears as early as Beethoven and Bach. The vii degree of the major scale, a diminished triad, has always been treated as an incomplete dominant ninth with G as the 'imaginary' root, and resolved as a V7 chord would be (to C).
So, it can be seen from all this that 'tonality' underwent great changes around the dawn of the 20th century; and one should not confuse this expanded chromatic version of tonality with Schoenberg's 12-tone method, which just confuses the issue.

In closing, this quote by co-authors George Perle and Paul Lansky:

"Perhaps the most important influence of Schoenberg's method is not the 12-note idea itself, but along with it the individual concepts of permutation, inversional symmetry, invariance under transformation, etc.....Each of these ideas by itself, or in conjunction with many others, is focused upon with varying degrees...by...Bartók, Stravinsky, Berg, Webern, Varèse, etc...In this sense the development of the serial idea may be viewed not as a radical break with the past but as an especially brilliant coordination of musical ideas which had developed in the course of recent history. The symmetrical divisions of the octave so often found in Liszt and Wagner, for example, are not momentary abberations in tonal music which led to its ultimate destruction, but, rather, important musical ideas which, in defying integration into a given concept of a musical language, challenged the boundaries of that language."


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## Guest (Apr 27, 2013)

millionrainbows said:


> I'm talking music, not history; if any history is involved, it is the history of thought processes, not stylistic caprices of composers. There _is _an inevitability to the _structures_ of music.


Ah, that's where we're going wrong: I wish you'd said earlier. I'm talking about the _history _of music, not the _structure _of music.


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## millionrainbows (Jun 23, 2012)

MacLeod said:


> Ah, that's where we're going wrong: I wish you'd said earlier. I'm talking about the _history _of music, not the _structure _of music.


Yeah, _music history!_ _That's_ the ticket! 

Still, I'm talking about _the history of musical thought,_ and how this _historically determined_ the outcome of 20th century music. Music is part of the Quadrivium, like Astronomy, Geometry, and Arithmetic.

Thus, this is similar to a history of physics or refrigeration; for example, efficient refrigeration is the natural outcome of principles, not caprices or arbitrary choices.

The "art" history you speak of is a history of personalities, cults, and caprices of parlours and schools.

Harmonic evolution into chromaticism is the principle at work, and the art which is wrought from these principles is a refection of these principles, not the generator.


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## Guest (Apr 27, 2013)

Million, I'm not really sure what point it is you are trying to make. I made what I thought was a simple observation a few pages ago which you have neither refuted nor endorsed in terms that a non-specialist might understand. You can keep telling me that music is one of the quadrivium, and that it is a maths as precise as physics, but your posts still don't seem to engage with the point I was trying to make.

I'm not asking you to rewind, however. I suspect we should give up.


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## millionrainbows (Jun 23, 2012)

OK, fine by me.


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## EddieRUKiddingVarese (Jan 8, 2013)

Good by me too


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## millionrainbows (Jun 23, 2012)

10-4, Eleanor


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