# Different Ideas of Tonality



## millionrainbows (Jun 23, 2012)

There's more than one way to skin a cat, as the old saying goes. So what's the difference in common practice tonality, and "neotonality?"

First, we have to understand that 'tonality' as a term must not be interpreted in a rigid and academic way. We are interested in seeing how tonal centers are established in music, which gives it a sense of tone-centricity, and creates harmonic associations which are similar to CP tonality, but different in many ways.

Hindemith, in his textbook, developed 2 criteria of tonal stability. Series I is a range of how each pitch is related to a focal pitch or tonic. For the note C as center, these progress further away:

C-C-G-F-A-E-Eb-Ab-D-Bb-Db-B-F#

Like the harmonic series, this can be transposed to any pitch.

Hindemith's Series II, a ranking of harmonic intervals, and identified their roots. In modern terms, "consonant" and "dissonant" are relative, not absolute .

Harmonic force: Melodic force:
C with G above and G with C above: C is root. Harmonic force: 5/ Melodic force: 1
This corresponds with Schoenberg's classifications of root movements, detailed in his Structural Functions of Harmony.
C with E above, and E with C above: C is root. Harmonic force:4 Melodic force:2
C with Eb above/Eb with C above: C is root. Harmonic force:3 Melodic force:3
B with C above/C with B above: C is root. Harmonic force:2 Melodic force:4
C with Db above/Db with C above: Db is root. Harmonic force:1 Melodic force:5
C with F# above: No root. Harmonic force:0 Melodic force:0

Unlike the typical resolutions of intervals considered dissonant in CP tonality, neotonal theory uses the term *tense* rather than dissonant.

Two main features of neotonality: enharmonic equivalence is accepted (there are no key areas), and distinctions between consonance and dissonance are relative rather than absolute.


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## Cosmos (Jun 28, 2013)

? I haven't heard of the term "neo-tonality" before. Just looked it up, and I'm not exactly sure what the difference is. I feel the only difference comes from academic definitions

P.s. Sorry I jumped the gun before you finished editing your post


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## Mahlerian (Nov 27, 2012)

Cosmos said:


> ? I haven't heard of the term "neo-tonality" before. Just looked it up, and I'm not exactly sure what the difference is. I feel the only difference comes from academic definitions


Well, common practice tonality is based on the hierarchical relations between the tonic, subdominant, dominant, and their various substitutes. It is music that is in "a key", where that key's diatonic scale is conceived as normal and deviations from it must (usually) be resolved in some way. The relationship between tonic and dominant is the most important.

Post-common practice "tonality" is based on single notes, which are emphasized as tonic and thus related to whatever is put above them; the old categories and rankings of distance are replaced. The music is centered, rather than in "a key" in the traditional sense. The relationship between tonic and fifth is de-emphasized.

There is a distinct difference in perspective between these two; this is why a number of classical music listeners have a hard time with _any or most_ 20th century classical music, even "tonal" music of the era. On the other hand, I don't think there's nearly as much of a difference between the latter and "atonal" music. The real difference I hear between the new "tonality" and "atonal" music is simply the chromaticism of the pitch language and the prevalence of triads or non-triads as the case may be.


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## millionrainbows (Jun 23, 2012)

Mahlerian said:


> Well, common practice tonality is based on the hierarchical relations between the tonic, subdominant, dominant, and their various substitutes. It is music that is in "a key", where that key's diatonic scale is conceived as normal and deviations from it must (usually) be resolved in some way. The relationship between tonic and dominant is the most important...(in) post-common practice "tonality"...the relationship between tonic and fifth is de-emphasized.


You'll note that Hindemith's Series one also puts C-G (tonic-dominant in tonal terms) as closely related, with Series II giving it a harmonic force of 5, the highest. I'm seeing that the "acoustic truth" of the diatonic scale notes and their harmonic distance to the key note or tonic is very similar to Hindemith's neotonality because both are based on harmonic truths.



Mahlerian said:


> There is a distinct difference in perspective between these two; this is why a number of classical music listeners have a hard time with _any or most_ 20th century classical music, even "tonal" music of the era.


I'm seeing the similarities rather than differences. Tonality and neotonality are both based on* harmonic hearing: *tone-centricity and harmonic relatedness to a key or focal pitch. They just call them different things, "key" and "focal point," or "dissonance" and "tension."



Mahlerian said:


> On the other hand, I don't think there's nearly as much of a difference between the latter and "atonal" music.


I do, because of the "harmonic hearing" factor present in both CP tonality and neotonality. Debussy is an obvious example of how people can relate to neotonality. (BTW, I consider Debussy to be a neotonalist) :lol:



Mahlerian said:


> The real difference I hear between the new "tonality" (neotonality) and "atonal" music is simply the chromaticism of the pitch language and the prevalence of triads or non-triads as the case may be.


Not in my case. Let's agree to disagree on this point, and move on to more aspects of neotonality, shall we?


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## Mahlerian (Nov 27, 2012)

millionrainbows said:


> You'll note that Hindemith's Series one also puts C-G (tonic-dominant in tonal terms) as closely related, with Series II giving it a harmonic force of 5, the highest. I'm seeing that the "acoustic truth" of the diatonic scale notes and their harmonic distance to the key note or tonic is very similar to Hindemith's neotonality because both are based on harmonic truths.


I'd go so far as to say that the above clearly doesn't structure a piece any more than a tone row does. Hindemith's music often sounds harmonically odd to me in a way that Schoenberg's doesn't.



> I'm seeing the similarities rather than differences. Tonality and neotonality are both based on* harmonic hearing: *tone-centricity and harmonic relatedness to a key or focal pitch. They just call them different things, "key" and "focal point," or "dissonance" and "tension."


But I hear all of these things in "atonal" music as well. Methods like 12-tone and serialism may not provide harmonic hearing, but _*good composers inevitably do*_. I have heard music that is harmonically meaningless or that ignores the obvious tendencies of the notes in the language used, and much of it comes from amateur composers who don't know what they're doing.



> I do, because of the "harmonic hearing" factor present in both CP tonality and neotonality. Debussy is an obvious example of how people can relate to neotonality. (BTW, I consider Debussy to be a neotonalist) :lol:


Which people? There are many who find Debussy's music difficult, amorphous, or dissonant (in this case meaning unpleasantly noisy, rather than dissonant in a technical sense).



> Not in my case. Let's agree to disagree on this point, and move on to more aspects of neotonality, shall we?


I haven't even accepted your earlier terms and distinctions.

I agree that there is different thinking at work behind Hindemith as compared to Webern. There is also very different harmonic thinking at work between Hindemith and Stravinsky, and the latter two cannot be analyzed using the same methods any more than the former. None of the above, though, may be meaningfully analyzed by functional roman numeral analyses.


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## millionrainbows (Jun 23, 2012)

> Originally Posted by *millionrainbows*:
> 
> You'll note that Hindemith's Series one also puts C-G (tonic-dominant in tonal terms) as closely related, with Series II giving it a harmonic force of 5, the highest. I'm seeing that the "acoustic truth" of the diatonic scale notes and their harmonic distance to the key note or tonic is very similar to Hindemith's neotonality because both are based on harmonic truths.





Mahlerian said:


> I'd go so far as to say that the above clearly doesn't structure a piece any more than a tone row does. Hindemith's music often sounds harmonically odd to me in a way that Schoenberg's doesn't.


That doesn't go very far in explaining anything. This is just a totally subjective comment on a objective piece of information I so kindly provided, the net effect being "ignore."

My point, made clearly, is that there is an aspect of "harmonic force" in Hindemith's neotonal Structures. This makes it similar to CP tonality, in that dissonances (now called tensions) are resolved to less tense structures. So that means the concept of neotonality has a built-in structural harmonic aspect. 12-tone music does not.



> millions: I'm seeing the similarities rather than differences. Tonality and neotonality are both based on* harmonic hearing: *tone-centricity and harmonic relatedness to a key or focal pitch. They just call them different things, "key" and "focal point," or "dissonance" and "tension."





Mahlerian said:


> There is a distinct difference in perspective between these two; this is why a number of classical music listeners have a hard time with _any or most_ 20th century classical music, even "tonal" music of the era...But I hear all of these things in "atonal" music as well. Methods like 12-tone and serialism may not provide harmonic hearing, but _*good composers inevitably do*_.


That's the closest I've ever heard you come to conceding the point that "methods like 12-tone and serialism may not provide harmonic hearing" structurally, but has to be put there by a composer until it 'sounds good.'

That seems such an obvious point to have expended so much energy as I have with trying to gain acknowledgement of this point. Ah, well, no use complaining. I shall move on.



> ...because of the "harmonic hearing" factor present in both CP tonality and neotonality...Debussy is an obvious example of how people can relate to neotonality.





Mahlerian said:


> Which people? There are many who find Debussy's music difficult, amorphous, or dissonant (in this case meaning unpleasantly noisy, rather than dissonant in a technical sense).


Oh, yes, I forgot about your statement that "a number of classical music listeners have a hard time with _any or most_ 20th century classical music, even "tonal" music of the era." I was distracted by my grandmother playing "Claire de Lune" at the tea party in the other room.



Mahlerian said:


> I haven't even accepted your earlier terms and distinctions.


They're not mine; they're Hindemith's an all those other neotonalist composers: David Diamond, etc.



Mahlerian said:


> I agree that there is different thinking at work behind Hindemith as compared to Webern. There is also very different harmonic thinking at work between Hindemith and Stravinsky, and the latter two cannot be analyzed using the same methods any more than the former.


That second part about Hindemith and Stravinsky cancels out what you said about Hindemith and Webern.

The net effect of what you are saying is that every composer must be analyzed individually.

While I see your point, I am emphasizing similarities and commonalities in neotonal and harmonic _thinking,_ with plenty of back-up information.

Your emphasis of the individual differences in composers is starting to reveal itself as simply a subjective negation of my points, since none of your contentions has contained any real factual or documented information. It remains totally subjective and directed at invalidating the thread idea. Whatever floats your boat.



Mahlerian said:


> None of the above, though, may be meaningfully analyzed by functional roman numeral analyses.


True; after all, this thread is about "Different Ideas of Tonality."

I question your opening statement about CP tonality:



Mahlerian said:


> Well, common practice tonality is based on the hierarchical relations between the tonic, subdominant, dominant, and their various substitutes. It is music that is in "a key", where that key's diatonic scale is conceived as normal and deviations from it must (usually) be resolved in some way.


It's really not a simple as that when you consider minor tonality, and the way it is often "borrowed" from.


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## Mahlerian (Nov 27, 2012)

millionrainbows said:


> That doesn't go very far in explaining anything. This is just a totally subjective comment on a objective piece of information I so kindly provided, the net effect being "ignore."
> 
> My point, made clearly, is that there is an aspect of "harmonic force" in Hindemith's neotonal Structures. This makes it similar to CP tonality, in that dissonances (now called tensions) are resolved to less tense structures. So that means the concept of neotonality has a built-in structural harmonic aspect. 12-tone music does not.


No, it doesn't prove any such thing. You listed a series of intervals, explaining that they are treated in certain ways. But this doesn't give a piece structure or coherence any more than the rules of counterpoint give a piece structure or coherence. There's a lot more that goes into music than that.

And...see below.



> That's the closest I've ever heard you come to conceding the point that "methods like 12-tone and serialism may not provide harmonic hearing" structurally, but has to be put there by a composer until it 'sounds good.'
> 
> That seems such an obvious point to have expended so much energy as I have with trying to gain acknowledgement of this point. Ah, well, no use complaining. I shall move on.


*I NEVER ONCE CONTESTED THIS POINT.* I have simply questioned the relevance of it. I still don't understand why it matters whether the structure is there because of the composer being a human being that hears things in a certain way based on the properties of overtones or because the system the composer uses is already based on one particular way of treating those properties.



> Oh, yes, I forgot about your statement that "a number of classical music listeners have a hard time with _any or most_ 20th century classical music, even "tonal" music of the era." I was distracted by my grandmother playing "Claire de Lune" at the tea party in the other room.


Ridicule aside (and making fun of your opponent's argument is a way of avoiding answering it), there are still many who find Debussy's 20th century works (not Suite Bergamesque) difficult to understand or remember.



> They're not mine; they're Hindemith's an all those other neotonalist composers: David Diamond, etc.


But what you've cited are elements that apply only to the practice of specific composers and which do not apply generally to others of a neotonal persuasion.



> That second part about Hindemith and Stravinsky cancels out what you said about Hindemith and Webern.


How? I think it's complementary.



> The net effect of what you are saying is that every composer must be analyzed individually.
> 
> While I see your point, I am emphasizing similarities and commonalities in neotonal and harmonic _thinking,_ with plenty of back-up information.


I don't see it. You've listed Hindemith's table of relationships between individual notes, but this doesn't apply to any composer besides Hindemith. You haven't shown commonalities simply by citing an example and stating that it's obviously analogous to what came before (when listeners can tell the difference right off the bat). Although there are some listeners uncomfortable with Debussy and Ravel, there are many who are uncomfortable with Hindemith, and place him alongside Schoenberg as an atonal noisemaker.



> Your emphasis of the individual differences in composers is starting to reveal itself as simply a subjective negation of my points, since none of your contentions has contained any real factual or documented information. It remains totally subjective and directed at invalidating the thread idea. Whatever floats your boat.


No, I honestly have no clue what you're talking about, and I'm trying to show you why it doesn't make sense to me.


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## SONNET CLV (May 31, 2014)

Before we all get _too_ confused, perhaps these charts will help explain tonality more clearly:


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## Richannes Wrahms (Jan 6, 2014)

Mahlerian said:


> Hindemith's music often sounds harmonically odd to me in a way that Schoenberg's doesn't.


I think Hindemith's musical language is born mostly from modal counterpoint (just before it 'turned' into tonality). He integrally incorporates chromaticism in a similarly, often 'awkward', way the mannerists did. Schoenberg's musical language is born from tonal counterpoint with free chromaticism. The main objective of these chromaticisms is expression and colour and both eventually became systematized for constructive purposes.


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## Mahlerian (Nov 27, 2012)

Richannes Wrahms said:


> I think Hindemith's musical language is born mostly from modal counterpoint (just before it 'turned' into tonality). He integrally incorporates chromaticism in a similarly, often 'awkward', way the mannerists did. Schoenberg's musical language is born from tonal counterpoint with free chromaticism. The main objective of these chromaticisms is expression and colour and both eventually became systematized for constructive purposes.


Yes, that distinction makes sense to me. I don't dislike Hindemith, but his earlier expressionist and neoclassical music appeal to me more than the later works.


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## millionrainbows (Jun 23, 2012)

Mahlerian said:


> ...You listed a series of intervals, explaining that they are treated in certain ways...what you've cited are elements that apply only to the practice of specific composers and which do not apply generally to others of a neotonal persuasion.


No, I disagree.

I'm talking about* Hindemith as a theorist,* which he was. You and Richanne Wrahms seem to be discussing your subjective stylistic impressions.

Hindemith, like all good theorists, is trying to extrapolate principles which apply in general ways to any music. These principles include such things as harmonic tension, gravities, and relative strengths of such principles. Schoenberg did the same thing in his *Harmonielehre,* and *Structural Functions* *of Harmony* books.

Your attitude seems _*anti-theory*_ to me, if you take everything as a specific case and are _unable to extrapolate the underlying principles of musical thought._ Even Rameau wrote a theory book.



Mahlerian said:


> I don't see it. You've listed Hindemith's table of relationships between individual notes, but this doesn't apply to any composer besides Hindemith. You haven't shown commonalities simply by citing an example and stating that it's obviously analogous to what came before.


Either you get it, or you don't. These are general principles of harmonic gravity and tension, applicable to any music you care to compose. These are much more flexible ways than CP tonality, with all its major/minor restrictions and rules. Maybe this upsets academics because new, flexible ways of seeing music threatens their precious CP tonality mindset.

VIVA Modernism!


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## Jobis (Jun 13, 2013)

millionrainbows said:


> No, I disagree. Hindemith, like all good theorists, is trying to extrapolate principles which apply in general ways to any music. These principles include such things as harmonic tension, gravities, and relative strengths of such principles. Schoenberg did the same thing in his Harminielehre, and Structural Functions books. You attitude seems anti-theory to me, if you take everything as a specific case and are unable to extrapolate the underlying principles of musical thought. Even Rameau wrote a theory book.
> 
> These are general principles, applicable to any music you care to compose. You must be upset because they threaten your precious CP tonality.


I don't understand what you two are arguing about, can you keep on topic before this discussion goes south?


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## millionrainbows (Jun 23, 2012)

Jobis said:


> I don't understand what you two are arguing about, can you keep on topic before this discussion goes south?


Tell it to Mahlerian. I'm staying on-topic by discussing theory, and new conceptions of tonality. I've already provided plenty of information for discussion. In that spirit, what do you think of Hindemith's theoretical ideas about "harmonic force"?


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## Jobis (Jun 13, 2013)

millionrainbows said:


> Tell it to Mahlerian. I'm staying on-topic by discussing theory, and new conceptions of tonality. I've already provided plenty of information for discussion. In that spirit, what do you think of Hindemith's theoretical ideas about "harmonic force"?


While I enjoy his music a lot and have much respect for Hindemith, I can't deny that he was quite a conservative in terms of music theory. That's not a bad thing, but he was attached to an idea of functional tonality, updated and unique to him, but not progressive like his contemporaries. He might be viewed as a bit of a dead end, because adopting his neo-tonality as a composer now would be mere appropriation.


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## millionrainbows (Jun 23, 2012)

Jobis said:


> While I enjoy his music a lot and have much respect for Hindemith, I can't deny that he was quite a conservative in terms of music theory. That's not a bad thing, but* he was attached to an idea of functional tonality, updated and unique to him, but not progressive like his contemporaries. He might be viewed as a bit of a dead end, because adopting his neo-tonality as a composer now would be mere appropriation.*


This is akin to saying that all serialists sound the same. Or that "serialism is a dead end."

It is possible, as in any discipline, that Hindemith is merely uncovering "harmonic truths" which exist anyway, but were obscured by the rigidity of CP tonality. This is the same way we can see "modes" in a modern way, as scales, rather than being beholden to a traditional conception of their use.

Yes, Hindemith's system of tonality had harmonic function, updated, and applicable in a general way. After all, Hindemith was a theorist, and music theory seeks to extrapolate general principles, and by nature is not "unique." If it frees-up CP tonality and harmonic function, and makes it more flexible, I'm all for it.

Hindemith was a good theorist, and developed a whole new set of harmonic criteria for resolving tension, and it makes total sense in a pervasive way, applied to all music. It really frees-up the old academic theories about "dissonance," yet it is still "tonality" which functions harmonically.

Schoenberg's Harmonilehre is one of the greatest, if not the greatest, music theory book.

Peter Schat, the Norweigan theorist and composer, has a book about his "tone clock," which is a harmonically-based system of creating tonalities using triads.

CP tonality was rigid and dated. It was good in its time, but time marches on. Modernism has proven that there is still plenty of music to be written which will be "tonal" in the broad sense, and can have *competing harmonic systems* as well.


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## Jobis (Jun 13, 2013)

millionrainbows said:


> This is akin to saying that all serialists sound the same. Or that "serialism is a dead end."
> 
> It is possible, as in any discipline, that Hindemith is merely uncovering "harmonic truths" which exist anyway, but were obscured by the rigidity of CP tonality. This is the same way we can see "modes" in a modern way, as scales, rather than being beholden to a traditional conception of their use.
> 
> ...


Its not the same at all; Hindemith's system presupposes certain relationships between tones as you said, serialism leaves it entirely up to the composer to establish proportions and relationships.

I believe it can be a little problematic when composers are too rigid and dogmatic in defining their theories or their styles; I understand that guidelines are necessary when in the process of free-composition, but isn't it all a bit arbitrary, searching for justification in nature and the harmonic series for one's musical developments? Isn't it up to the musicologists and analysts, at least in part, to do the theorising, after the event?


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## millionrainbows (Jun 23, 2012)

Jobis said:


> Its not the same at all; Hindemith's system presupposes certain relationships between tones as you said, serialism leaves it entirely up to the composer to establish proportions and relationships.


Or rather, "the row" establishes proportions and relationships.

I don't see comparisons of neotonality with atonality to be productive or relevant, since serialism is not inherently harmonic, or inherently tonal.

Any system of 'tonality' (i.e., a system which organizes the pitch resources in relation to a tonic pitch) is going to involve "harmonic gravity" of intervals, since by its nature, tonality relates all of its constituent notes to a central "home base" or tonic.

Serialism is not concerned with tonality, or the establishment of a central note. The ordering and non-repetition of the 12 notes insures this; no single note is emphasized over another. Rather, the relationships in serialism are intervallic, and are generalized away from specific pitches, but only in relationships.

There are only 6 intervals: m2,M2,m3,M3,4th, and tritone. The rest are inversions. If serialism is going to be comprehensible, it will be through these intervals and their qualities. If one wanted to, one could rank these intervals along a continuum of relative sonance, and thus "control" to an extent the harmonic results of tone rows, but why? It would be better to see intervals as "colors" unto themselves, with no ranking, and create our meanings by the preponderance and statistical occurrence of these different interval/colors.

Webern does this, when he uses a preponderance of a particular interval.

But, serialism makes no inherent distinction between consonance and dissonance, or rather, this distinction is irrelevant in serialism, since structurally, as a system, it does not concern itself with this.

Hindemith's system does, and places these along a continuum. It's a lot freer than CP tonality, but still takes into account the ear's ability to hear sonance as relative, not absolute.



Jobis said:


> I believe it can be a little problematic when composers are too rigid and dogmatic in defining their theories or their styles; I understand that guidelines are necessary when in the process of free-composition, but isn't it all a bit arbitrary, searching for justification in nature and the harmonic series for one's musical developments?


All music ends up having a harmonic effect on our ears. Any kind of "harmonic music" has its basis in the overtone series model, or in the case of intervals, the relationship of one note to another.

Tonality, and establishing it, is a somewhat different aspect, and that hinges on relationships to a central tonic note, and these relationships have to be defined by something. The most obvious way is our ears, and the way our ears hear. This is harmonic.

If you're not interested in establishing tonality, then interval relationships can be taken in isolation, with no reference to a central note, but as an isolated relationship. That's why rows can be transposed freely; the intervals produced do not depend on specific pitches.


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## MoonlightSonata (Mar 29, 2014)

Are there any other neo-tonal systems than Hindemith's?


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## millionrainbows (Jun 23, 2012)

Howard Hanson wrote an excellent text called Harmonic Materials of Modern Music. It might be a mistake to view Hindemith's or Hanson's ideas as "systems." These are intuitive ideas which were "in the air" so to speak. Hanson's ideas on "interval projection" are also called "interval multiplication," (see WIK entry) and were used by Boulez as well as Bartok.

http://en.wikipedia.org/wiki/Multiplication_(music)

Also, it might be a mistake to view such ideas as neo-tonal, since they can be applied to serial material as well. The "12" of our octave division comes back in many forms to haunt us, and becomes a mathematical verity, even in harmonic, tonal music.


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## Richannes Wrahms (Jan 6, 2014)

So, What's next in the agenda? The music theory of Galilei (Vincenzo), Kepler, Descartes, Euler etc...? Babbitt? Dmitri Tymoczko, Paul Erlich, William Sethares, etc...?


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## PetrB (Feb 28, 2012)

Jobis said:


> Its not the same at all; Hindemith's system presupposes certain relationships between tones as you said, serialism leaves it entirely up to the composer to establish proportions and relationships.
> 
> I believe it can be a little problematic when composers are too rigid and dogmatic in defining their theories or their styles; I understand that guidelines are necessary when in the process of free-composition, but isn't it all a bit arbitrary, searching for justification in nature and the harmonic series for one's musical developments? Isn't it up to the musicologists and analysts, at least in part, to do the theorising, after the event?


Absolutely and Bravo!

Acoustics, played with any particular way, and the 'golden numbers' proclaimed by this theorist or another, are about as readily manipulated to advocate one M.O. over another as are statistics, and whenever that is done, it is essentially, "Telling lies with numbers." How can any of it, no matter 'what the system,' be anything *but* "organic." "Organic" in relation to acoustics is no valid argument at all.

Then we have Hindemith, who so believed in his particular take of codification that his later works sound interchangeable, and a near parody of his earlier more creative self. That's where "belief in theory" vs the composer's ear and intuition becomes a detriment to the end-product.


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