# First Claim: Harmony and Counterpoint Constrain One Another



## millionrainbows

From _A Geometry of Music,_ Dmitri Tymoczko:

"Any two major chords can be connected by stepwise voice leading in which no voice moves by more than two semitones. This means you can write a harmonic progression without worrying about melody; that is, for any sequence of major chords, there is always some way to connect the notes so as to form stepwise melodies.
What about the chromatic cluster B, C, Db followed by E, F, Gb (its transposition by ascending fourth)? Here, none of the notes of the first 'chord' are within two semitones of any note in the second, and hence there is no way to combine a sequence of these chords so as to produce conjunct melodies. At the same time, however, the chromatic cluster can do things that the C major chord can't. It is possible to write contrapuntal music in which individual melodic lines move short distances _within_ a single, unchanging harmony. This is possible only because the chord's notes are all clustered together, ensuring that there is always a short path between any two of them."


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## EdwardBast

millionrainbows said:


> From _A Geometry of Music,_ Dmitri Tymoczko:
> 
> Any two major chords can be connected by stepwise voice leading in which no voice moves by more than two semitones. This means you can write a harmonic progression without worrying about melody; that is, for any sequence of major chords, there is always some way to connect the notes so as to form stepwise melodies.
> What about the chromatic cluster B, C, Db followed by E, F, Gb (its transposition by ascending fourth)? Here, none of the notes of the first 'chord' are within two semitones of any note in the second, and hence there is no way to combine a sequence of these chords so as to produce conjunct melodies. At the same time, however, the chromatic cluster can do things that the C major chord can't. It is possible to write contrapuntal music in which individual melodic lines move short distances _within_ a single, unchanging harmony. This is possible only because the chord's notes are all clustered together, ensuring that there is always a short path between any two of them.


All of the above is a quotation of Tymoczko's words? If not, please use quotation marks to indicate which words are his.


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## millionrainbows

EdwardBast said:


> All of the above is a quotation of Tymoczko's words? If not, please use quotation marks to indicate which words are his.


So, I sound like him, or he sounds like me? Either way, I'll take that as an insult. :lol:

That's just one of four claims, Edward. You can look forward to a nice slash-fest. Sharpen up your knife!


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## EdwardBast

millionrainbows said:


> So, I sound like him, or he sounds like me? Either way, I'll take that as an insult. :lol:
> 
> That's just one of four claims, Edward. You can look forward to a nice slash-fest. Sharpen up your knife!


It's perfectly obvious that Dmitri didn't write the second sentence. Did he write any of the rest of it beyond the first sentence?


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## millionrainbows

EdwardBast said:


> It's perfectly obvious that Dmitri didn't write the second sentence. Did he write any of the rest of it beyond the first sentence?


Duly noted. It's all a direct quote.

https://www.amazon.com/Geometry-Mus...metry+of+music\&qid=1590435888&s=books&sr=1-1


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## EdwardBast

millionrainbows said:


> Duly noted. It's all a direct quote.
> 
> https://www.amazon.com/Geometry-Mus...metry+of+music\&qid=1590435888&s=books&sr=1-1


It isn't quite, but it's pretty close to what he wrote on pp. 13-14. So, what interests you about this passage? Why are you quoting it? Is there a point you are trying to demonstrate or are you just trying to sell more copies of Tymozcko's book? 

You do understand that one should indicate where one's quotation deviates from a text one is quoting, right? If you need any help with how to do this I'd be glad to help.


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## millionrainbows

error...........


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## EdwardBast

Seriously though, it sounds like a very interesting book and perspective and I hope it generates some good discussion.


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## millionrainbows

EdwardBast said:


> Seriously though, it sounds like a very interesting book and perspective and I hope it generates some good discussion.


Uh-huh..............Me too.


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## Torkelburger

But doesn't he say "two major chords"? And "sequence of major chords"? B, C, Db and E, F, Gb are not major chord qualities so would not apply to what he is talking about.


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## millionrainbows

Torkelburger said:


> But doesn't he say "two major chords"? And "sequence of major chords"? B, C, Db and E, F, Gb are not major chord qualities so would not apply to what he is talking about.


I've abandoned this thread, Torkelburger. See the other one, with the "corrrected" quote, done for EdwardBast's benefit.

I'll paste your reply over there & reply to it.


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## millionrainbows

EdwardBast said:


> It isn't quite, but it's pretty close to what he wrote on pp. 13-14. So, what interests you about this passage? Why are you quoting it? Is there a point you are trying to demonstrate or are you just trying to sell more copies of Tymozcko's book?
> 
> You do understand that one should indicate where one's quotation deviates from a text one is quoting, right? If you need any help with how to do this I'd be glad to help.


EdwardBast: I consider your questioning of the citation as insulting. The rest of your posts are insulting, as well, and are condescending, designed to abort this thread from its outset. I have reported this to the mods, but they have apparently decided not to remove them.
I really don't understand how you are able to get away with these sorts of actions, unless you hold special favor as an 'inside' advisor to the mods.


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## Phil loves classical

I don't get the claim that harmony and counterpoint constrain each other, based on that quote in the original post. The conclusion reached by Dmitri is that you can write counterpoint within unchanging harmony, but that doesn't pose a limitation on the harmony that can be reached with counterpoint. I'll make a counter claim that there are unlimited possibilities in harmony that can be reached with counterpoint.


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## millionrainbows

What the OP shows us is that CP classical music is a self-fulfilling system which is virtually 'automatic' in nature; a no-brainer for composers like Mozart, Handel, Vivaldi, and Haydn. The diatonic scale, which divides the octave up so evenly, and fits together in such a closely-related cookie cutter fashion, is an easy environment in which to do counterpoint and compose conjunct melodies for; they practically compose themselves. you can look in any direction and find a closely related chord or voice which is a member of a chord; do you want harmony A, B, or C? A harmonic buffet; whatever suits your fancy.


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## Torkelburger

millionrainbows said:


> What the OP shows us is that CP classical music is a self-fulfilling system which is virtually 'automatic' in nature; a no-brainer for composers like Mozart, Handel, Vivaldi, and Haydn. The diatonic scale, which divides the octave up so evenly, and fits together in such a closely-related cookie cutter fashion, is an easy environment in which to do counterpoint and compose conjunct melodies for; they practically compose themselves. you can look in any direction and find a closely related chord or voice which is a member of a chord; do you want harmony A, B, or C? A harmonic buffet; whatever suits your fancy.


If that's the case, then it should be no problem for you at all to compose say, a double period or so of piano music equally as good or even better than Beethoven Sonatas 14, 17, 21, 23, 29. Since the composition is automatic and the music composes itself, this should take you a matter of minutes. Post your composition that proves your theory to the world one hour from now and let us be the judge.


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## millionrainbows

Torkelburger said:


> If that's the case, then it should be no problem for you at all to compose say, a double period or so of piano music equally as good or even better than Beethoven Sonatas 14, 17, 21, 23, 29.


But what would be the point? You could also compose a 12-tone piece which consisted of all fifths.



> Since the composition is automatic and the music composes itself, this should take you a matter of minutes. *Post your composition* that proves your theory to the world one hour from now and let us be the judge.


*Okay! How about over on the composer's thread? Would that work? (inside joke for Taggart)*

No, you're missing the point. What I've said is true, and simply repeats what the book said (albeit more abrasively): CP harmony is a fairly straightforward process because it is enabled by the diatonic scale and the triads laid out on its scale degrees.

I.e., if the harmonic scaffolding is there, any conjunct melodies or counterpoint are fairly easy to construct.

Thus, the thread title: "Harmony and Counterpoint Constrain (or enable) One Another."

This thread isn't about ME, or if I can write music "better than Beethoven."

This observation concerns the basics mechanics of the diatonic system, not "The Art of Beethoven."

Besides that, Beethoven was getting much more harmonically complex than the basic points I've covered.

Your post seems unconcerned with the ideas presented here, and more concerned with 'controlling' and 'challenging' and 'confronting.' It's all too psychological for me.


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## millionrainbows

Phil loves classical said:


> I don't get the claim that harmony and counterpoint constrain each other, based on that quote in the original post.


I think if you re-read the thread, and keep following the premise, the extreme simplicity of the idea will finally strike you.



> The conclusion reached by Dmitri is that you can write counterpoint within unchanging harmony, but that doesn't pose a limitation on the harmony that can be reached with counterpoint.


That would depend on what notes your counterpoint defines as its harmonic scaffolding, wouldn't it? If the notes you use make up a scale of five or more notes, then yes, almost anything is possible, depending on how large you can tolerate your melodic leaps (i.e. voice leading).

If you want conjunct melodies, then larger spacing begins to prohibit this.

It looks like we'd better present some definitions: https://en.wikipedia.org/wiki/Steps_and_skips

Conjunct: In music, a step, or conjunct motion, is the difference in pitch between two consecutive notes of a musical scale. In other words, it is the interval between two consecutive scale degrees. Any larger interval is called a skip (also called a leap), or disjunct motion.

*Melodic motion* in which the interval between any two consecutive pitches is no more than a step, or, less strictly, where skips are rare, is called *stepwise* or *conjunct melodic motion,* as opposed to skipwise or disjunct melodic motion, characterized by frequent skips.



> I'll make a counter claim that there are unlimited possibilities in harmony that can be reached with counterpoint.


But why make such a counterclaim? All this exposition is doing is explaining the nature of *tonality,* and its harmony and melodic aspects, and how they affect each other reciprocally. What is there to challenge?

Anyway, to say _"there are unlimited possibilities in harmony that can be reached with counterpoint"_ is fraught with inconsistency.
Tonality is not about "unlimited possibilities," is it? It's about how you divide up the octave. If your counterpoint consists of scale notes, then that's your harmony.

You only have 12 notes; what does "unlimited" mean? Dodecaphony? Now we are out of the realm of tonal harmony. 
But, yes, the "clusters" in the example are a form of harmony which generates melodic lines (counterpoint) which "burble and bubble" within a limited range of a chromatic cluster. Or you could say it's the counterpoint that's creating the clusters. It's a "chicken or egg" problem.


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## Torkelburger

I don't care how easy it is to compose a melody in the diatonic system. That has nothing to do with how good a piece is or how hard it was to compose. Beethoven's fifth symphony entire first movement is based more on extremely simple motifs than any "melody" and it is one of the greatest pieces in the history of music. It's what you do with it that matters. There's more to composition than just connecting dots and painting by numbers. That's not what composition is.


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## millionrainbows

Torkelburger said:


> I don't care how easy it is to compose a melody in the diatonic system. That has nothing to do with how good a piece is or how hard it was to compose.


Okay, I agree, but that's not the point of this thread, and I don't think this thread "contradicts" what you are saying. All it is saying is that the diatonic system facilitates the construction of conjunct melodies.



> Beethoven's fifth symphony entire first movement is based more on extremely simple motifs than any "melody" and it is one of the greatest pieces in the history of music. It's what you do with it that matters. There's more to composition than just connecting dots and painting by numbers. That's not what composition is.


I don't disagree with that. But the purpose of this thread is not to make value judgements, or to present ideas which contradict that. It's a simple exposition about the nature of tonality.


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## Torkelburger

That's the nature of all music, though. Atonality is not any different. Someone could just as easily say that 12-tone music is a self-fulfilling system which is automatic in nature, a no-brainer for composers (and that the chromatic scale divides the octave evenly) and that 12-tone music composes itself. All you have to do is follow the row and plug in the numbers for melodies and harmonies. The row tells you what notes to write. It’s a paint by numbers system.

Would they be correct? Wouldn’t Schoenberg, Berg, Webern, Boulez, Babbitt, Sessions, Stravinsky et al 12-tone music all sound the same then?

Does Bach, Mozart, and Beethoven sound the same? If the music composed itself and is automatic (meaning the composer has no control) then it would, but it doesn’t.

Same goes for composing with pitch-class sets or most any other post tonal technique.


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## Torkelburger

> CP harmony is a fairly straightforward process because it is enabled by the diatonic scale and the triads laid out on its scale degrees.


Again, CP is not alone this regard. It is a system just as any other system to compose with (12 tone, quartal, secundal, etc.) All systems make for a fairly straightforward process.


> I.e., if the harmonic scaffolding is there, any conjunct melodies or counterpoint are fairly easy to construct.


But the same is true for any system. Take quartal harmony. The harmonic scaffolding is there. And given that 5 contiguous perfect fourths yield the pitches of a pentatonic "scale", any conjunct melodies or counterpoint are fairly easy to construct.


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## isorhythm

The book looks like it could be interesting.


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## EdwardBast

millionrainbows said:


> EdwardBast: I consider your questioning of the citation as insulting. The rest of your posts are insulting, as well, and are condescending, designed to abort this thread from its outset. I have reported this to the mods, but they have apparently decided not to remove them.
> I really don't understand how you are able to get away with these sorts of actions, unless you hold special favor as an 'inside' advisor to the mods.


The actions you mention were all the result of your failure to clearly indicate whose words appeared in the OP. You didn't use quotation marks, so I asked what part of the post was attributable to Dmitry Tymoczko and what part was your writing. You then edited the post by putting quotation marks around the whole text and stating that it was a direct quotation of Tymoczko. This was false, and I knew it was false without even checking the original because of a grammatical error in your version that would not have gotten by an editor. Finally, I located the passage in Tymoczko's book and managed to get an accurate version of the passage. All of this could have been avoided had you simply quoted the source correctly.

As for why I was suspicious enough to go through these contortions to get an accurate quotation out of you, that should be obvious. In the past you have misused quotation marks to falsely attribute to me words I never wrote. Others have had this problem as well. You have damaged your credibility by playing fast and loose with quotation marks in the past, so you have little excuse for being insulted when people don't trust your citations.


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## Phil loves classical

millionrainbows said:


> I think if you re-read the thread, and keep following the premise, the extreme simplicity of the idea will finally strike you.
> 
> That would depend on what notes your counterpoint defines as its harmonic scaffolding, wouldn't it? If the notes you use make up a scale of five or more notes, then yes, almost anything is possible, depending on how large you can tolerate your melodic leaps (i.e. voice leading).
> 
> If you want conjunct melodies, then larger spacing begins to prohibit this.
> 
> It looks like we'd better present some definitions: https://en.wikipedia.org/wiki/Steps_and_skips
> 
> Conjunct: In music, a step, or conjunct motion, is the difference in pitch between two consecutive notes of a musical scale. In other words, it is the interval between two consecutive scale degrees. Any larger interval is called a skip (also called a leap), or disjunct motion.
> 
> *Melodic motion* in which the interval between any two consecutive pitches is no more than a step, or, less strictly, where skips are rare, is called *stepwise* or *conjunct melodic motion,* as opposed to skipwise or disjunct melodic motion, characterized by frequent skips.
> 
> But why make such a counterclaim? All this exposition is doing is explaining the nature of *tonality,* and its harmony and melodic aspects, and how they affect each other reciprocally. What is there to challenge?
> 
> Anyway, to say _"there are unlimited possibilities in harmony that can be reached with counterpoint"_ is fraught with inconsistency.
> Tonality is not about "unlimited possibilities," is it? It's about how you divide up the octave. If your counterpoint consists of scale notes, then that's your harmony.
> 
> You only have 12 notes; what does "unlimited" mean? Dodecaphony? Now we are out of the realm of tonal harmony.
> But, yes, the "clusters" in the example are a form of harmony which generates melodic lines (counterpoint) which "burble and bubble" within a limited range of a chromatic cluster. Or you could say it's the counterpoint that's creating the clusters. It's a "chicken or egg" problem.


There is still nothing in that quote that implies that Harmony and Counterpoint constrain one another. That is just from a logical standpoint.

You can have tonal music that incorporate any of the 12 tones in different ways with counterpoint. There is no limitation, as long as the voice leading is done right. ie. You can incorporate any "chord" vertically at least momentarily, as long as the voices are moving toward a certain goal. What do you mean by "If your counterpoint consists of scale notes, then that's your harmony"? There isn't one type of harmony based on scale notes. It can change, you can have different chords and combinations. Check out this fugue by Bach. The vertical harmony wouldn't make sense if taken out of its context. I'm sure he could have worked in any combination of notes vertically between the 3 voices. That's what I mean by unlimited possibilities.


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## millionrainbows

Torkelburger said:


> That's the nature of all music, though. Atonality is not any different. Someone could just as easily say that 12-tone music is a self-fulfilling system which is automatic in nature, a no-brainer for composers (and that the chromatic scale divides the octave evenly) and that 12-tone music composes itself. All you have to do is follow the row and plug in the numbers for melodies and harmonies. The row tells you what notes to write. It's a paint by numbers system.


What the book is saying (and this is only the first of four claims about the nature of tonality) is that if you have wide spaces in your harmonic components, you will have wide leaps in the counterpoint or melodic figurations you construct. It's a very simple idea. Since most tonal music uses scales, and if the scales divide the octave fairly evenly, constructing conjunct melodies or smooth voice leading is enabled.

You are on the wrong track. This is not about "how easy" it is to create good music; it simply tells us what _features _will facilitate conjunct vs. disjunct melody or counterpoint.


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## millionrainbows

Torkelburger said:


> Again, CP is not alone this regard. It is a system just as any other system to compose with (12 tone, quartal, secundal, etc.) All systems make for a fairly straightforward process.
> 
> But the same is true for any system. Take quartal harmony. The harmonic scaffolding is there. And given that 5 contiguous perfect fourths yield the pitches of a pentatonic "scale", any conjunct melodies or counterpoint are fairly easy to construct.


Yes, you're right. The book, and this idea, is exploring the features of tonality. It's not my purpose to argue with you.


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## millionrainbows

isorhythm said:


> The book looks like it could be interesting.


It is, if you want to know what tonality is from an 'outside the box' perspective. But isn't that true of anything? In order to know what it is, you must compare it with what it is not.


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## millionrainbows

Phil loves classical said:


> There is still nothing in that quote that implies that Harmony and Counterpoint constrain one another. That is just from a logical standpoint.
> 
> You can have tonal music that incorporate any of the 12 tones in different ways with counterpoint. There is no limitation, as long as the voice leading is done right. ie. You can incorporate any "chord" vertically at least momentarily, as long as the voices are moving toward a certain goal. What do you mean by "If your counterpoint consists of scale notes, then that's your harmony"? *There isn't one type of harmony based on scale notes.* It can change, you can have different chords and combinations. Check out this fugue by Bach. The vertical harmony wouldn't make sense if taken out of its context. I'm sure he could have worked in any combination of notes vertically between the 3 voices. That's what I mean by unlimited possibilities.


I'm not sure what it is that you're arguing about, or what it is about Dmitri's book that seems to offend you.

I never said that there is only one type of harmony based on scale notes, whatever you mean by that.

BTW, a scale defines harmonic content, and defines a tonality. See WIK. The first note of a scale presented represents the key note or tonic of a tonality. I don't wish to argue basics such as this.


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## millionrainbows

EdwardBast said:


> The actions you mention were all the result of your failure to clearly indicate whose words appeared in the OP. You didn't use quotation marks, so I asked what part of the post was attributable to Dmitry Tymoczko and what part was your writing. You then edited the post by putting quotation marks around the whole text and stating that it was a direct quotation of Tymoczko. This was false, and I knew it was false without even checking the original because of a grammatical error in your version that would not have gotten by an editor. Finally, I located the passage in Tymoczko's book and managed to get an accurate version of the passage. All of this could have been avoided had you simply quoted the source correctly.
> 
> As for why I was suspicious enough to go through these contortions to get an accurate quotation out of you, that should be obvious. In the past you have misused quotation marks to falsely attribute to me words I never wrote. Others have had this problem as well. You have damaged your credibility by playing fast and loose with quotation marks in the past, so you have little excuse for being insulted when people don't trust your citations.


From _A Geometry of Music, Dmitri Tymoczko:
"Figure 1.3.4 shows that any two major chords can be connected by stepwise voice leading in which no voice moves by more than two semitones. This means that Lyrico can write a harmonic progression without worrying about melody; that is, for any sequence of major chords, there is always some way to connect the notes so as to form stepwise melodies...
But what if Lyrico writes the chromatic cluster [B, C, Db] followed by [E, F, Gb], its transposition by ascending fourth? Here, none of the notes of the first 'chord' are within two semitones of any note in the second, and hence there is no way to combine a sequence of these chords so as to produce conjunct melodies (Figure 1.3.5). At the same time, however, the chromatic cluster can do things that the C major chord can't: Figure 1.3.6 shows that is possible to write contrapuntal music in which individual melodic lines move by short distances within a single, unchanging harmony. Clearly, this is possible only because the chord's notes are all clustered together, ensuring that there is always a short path between any two of them." -p.13-14_


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## Phil loves classical

millionrainbows said:


> I'm not sure what it is that you're arguing about, or what it is about Dmitri's book that seems to offend you.
> 
> BTW, a scale defines harmonic content, and defines a tonality. See WIK. The first note of a scale presented represents the key note or tonic of a tonality. I don't wish to argue basics such as this.


I'm arguing the premise of your claim on the thread title, which is not related to that quote. A scale can't define harmonic content, it's the choosing of the notes. Debussy used notes from the same scale as Mozart, but sounds vastly different.


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## millionrainbows

Phil loves classical said:


> I'm arguing the premise of your claim on the thread title, which is not related to that quote. *A scale can't define harmonic content*, it's the choosing of the notes. Debussy used notes from the same scale as Mozart, but sounds vastly different.


If it's a tonal scale, it defines a tonal relationship of the notes, i.e. a relationship of all the scale steps to a key note. I call this a "tonality" in the general sense of the term. If it's called a C scale, and is presented as starting on C, then it's understood that C is the tonic.

In the case of both Mozart and Debussy using a C major scale, I would hear the overall tonal effect as being drawn from the same scale, in this respect, and it would sound C-ish.

If you used the same 7 notes (C-D-E-F-G-A-B), and called it a G scale, then G is the tonic note, and it would be a mixolydian scale. 
Is this what you mean? Explain.


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## millionrainbows

Anyway, this is just the first of four claims about tonality that Tymoczko makes. At this rate, we'll never get to number two. This seems typical of the argumentative and confrontational aspect of the internet. It seems that everybody is stuck in their own little world, and many are revealed to be 'not at peace' with themselves; thus, it often ends in bickering over inconsequential details, misunderstandings, and more bickering. My advice to everyone is: do your thinking (homework, practice) before you post.


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## Phil loves classical

I downloaded the pdf of the book (for free here: https://www.academia.edu/18164732/Geometry_of_Music?auto=download)

The example he used to make the claim in the thread title was in pages 12 and 13, not the example you quoted.

Here is a real life example which proves him wrong (the fugue starting at 1:30). The fugue subject uses only major triadic notes and at certain times with more than one voice). First of all, it has unchanging harmony at times, which Dmitri (the writer, not Shostakovich ) said could only be accomplished with chromatic clusters. (ie. Conjunct melodies which step by 2 semitones maximum are not required for counterpoint which proves him premise wrong) Secondly, it's a great piece with beautiful harmony and nothing wrong with the counterpoint.


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## millionrainbows

Phil loves classical said:


> The example he used to make the claim in the thread title was in pages 12 and 13, not the example you quoted.


That's totally misleading, verging on lying.

This site will not allow me to post PDF images from my computer on this site _(I seem to have run out of privileges in that regard)_, so the 'corrected' quotation only refers to the figures without showing them. In the OP, I thought that would be confusing. That's why I left those references out of the first quote, and EdwardBast jumped on it.

Additionally, those figures on p. 12 and 13 refer to a different part of the text, which I did not quote at all.

You two guys are really something else!



> Here is a real life example which proves him wrong (the fugue starting at 1:30). The fugue subject uses only major triadic notes and at certain times with more than one voice). First of all, it has unchanging harmony at times, which Dmitri (the writer, not Shostakovich ) said could only be accomplished with chromatic clusters. (ie. Conjunct melodies which step by 2 semitones maximum are not required for counterpoint which proves him premise wrong) Secondly, it's a great piece with beautiful harmony and nothing wrong with the counterpoint.


Then you're misreading Tymoczko. He didn't claim that diatonic harmony could not be static. (Shostakovich sounds static to me quite often  ), or that static harmony could only be accomplished with chromatic clusters.That's just the way the examples turned out.

You don't understand the example, or the principle behind it, obviously.

It sounds to me like you're arguing just to be arguing.


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## Phil loves classical

millionrainbows said:


> That's totally misleading, verging on lying.
> 
> This site will not allow me to post PDF images from my computer on this site _(I seem to have run out of privileges in that regard)_, so the 'corrected' quotation only refers to the figures without showing them. In the OP, I thought that would be confusing. That's why I left those references out of the first quote, and EdwardBast jumped on it.
> 
> Additionally, those figures on p. 12 and 13 refer to a different part of the text, which I did not quote at all.
> 
> You two guys are really something else!
> 
> Then you're misreading Tymoczko. *He didn't claim that diatonic harmony could not be static*. (Shostakovich sounds static to me quite often  ), or that static harmony could only be accomplished with chromatic clusters.That's just the way the examples turned out.
> 
> You don't understand the example, or the principle behind it, obviously.
> 
> It sounds to me like you're arguing just to be arguing.


Dmitri came up with a pretty strong claim as in the thread title. His example can't back it up at all conclusively, just as the Shostakovich showed, nor by his looking at instances with very limited scope. At least he said the examples "suggests" his claim. Ultimately, counterpoint is not all about conjunct melodies that move within 2 semitones, just as it is not all about triadic notes as Shostakovich's more extreme example is (and still proves his overall claim wrong anyway). I thought you were all about 'thinking out of the box', or only when it's against CP harmony?

I'd be more interested in a more logical or mathematical proof. I see a lot of holes in his implication.


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## Bwv 1080

If you actually read the chapter, it’s not a strong claim to say that harmony and counterpoint constrain one another. The example on 12-13 compares counterpoint derived from a single major triad vs a three note semitone cluster and then observes that you can’t get conjunct melodies (defined as moving in whole or half steps) from the major triad without introducing passing tones that will then define a scale. The cluster has the opposite problem, you can obviously make conjunct melodies from the chord tones, but there is no way to link the ends of the cluster with a small number of passing tones - the cluster does not imply any sort of a scale. He certainly does not say that unchanging harmony can only be accomplished with clusters, so the Shostakovich example is irrelevant


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## millionrainbows

Phil loves classical said:


> Dmitri came up with a pretty strong claim as in the thread title. His example can't back it up at all conclusively, just as the Shostakovich showed, nor by his looking at instances with very limited scope.


This is typical of 'internet logic.' Tymoczko is making a generalization, a wide one, only one of four, and if you find any exception (like that irrelevant Shostakovich example), then you think you've 'disproved' the generalization.



> At least he said the examples "suggests" his claim. Ultimately, counterpoint is not all about conjunct melodies that move within 2 semitones, just as it is not all about triadic notes as Shostakovich's more extreme example is (and still proves his overall claim wrong anyway). I thought you were all about 'thinking out of the box', or only when it's against CP harmony?


This is only one of four claims, and these are to define the parameters of tonality in general ways. He does a great job in the book. 
But if you're not a 'generalist,' and are stuck in details, and don't really care to get a bird's eye view of the nature of tonality so that you can explore other areas, then this book and this kind of thinking are not for you.



> I'd be more interested in a more logical or mathematical proof. I see a lot of holes in his implication.


Well, if you look for something, chances are you will find it.


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## millionrainbows

Bwv 1080 said:


> If you actually read the chapter, it's not a strong claim to say that harmony and counterpoint constrain one another. The example on 12-13 compares counterpoint derived from a single major triad vs a three note semitone cluster and then observes that you can't get conjunct melodies (defined as moving in whole or half steps) from the major triad without introducing passing tones that will then define a scale. The cluster has the opposite problem, you can obviously make conjunct melodies from the chord tones, but there is no way to link the ends of the cluster with a small number of passing tones - the cluster does not imply any sort of a scale. He certainly does not say that unchanging harmony can only be accomplished with clusters, so the Shostakovich example is irrelevant


Thank you, Bwv 1080; you have proven that you understand what Tymoczko is getting at, and that you have a superior musical intelligence. Kudos! :tiphat:


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## Bwv 1080

Thought the passage was interesting enough that I bought the book on Kindle, maybe some others could as well and generate some interesting discussion


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## Phil loves classical

millionrainbows said:


> This is typical of 'internet logic.' Tymoczko is making a generalization, a wide one, only one of four, and if you find any exception (like that irrelevant Shostakovich example), then you think you've 'disproved' the generalization.
> 
> This is only one of four claims, and these are to define the parameters of tonality in general ways. He does a great job in the book.
> But if you're not a 'generalist,' and are stuck in details, and don't really care to get a bird's eye view of the nature of tonality so that you can explore other areas, then this book and this kind of thinking are not for you.
> 
> Well, if you look for something, chances are you will find it.


I actually went on to read the next part: "macroharmony and centricity are completely independent: it is entirely possible, for example, to write diatonic music in which no note is heard as a tonal center, just as one can write chromatic music with a very clear center." This is pretty obvious to me. Now I look back at the first claim in context, I do agree in the micro picture. I had thought he implied counterpoint and harmony constrain each other in the macro sense, which is obviously wrong, which I'm sure you know .


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## isorhythm

It seems as though Tymoczko is laying out some theorems the way a mathematician would, and will go on to develop a deeper argument in the book. His first claim about harmony and counterpoint is straightforwardly true, by definition. He isn't saying anything about tonal music "writing itself" or anything like that.


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## millionrainbows

isorhythm said:


> It seems as though Tymoczko is laying out some theorems the way a mathematician would, and will go on to develop a deeper argument in the book. His first claim about harmony and counterpoint is straightforwardly true, by definition. He isn't saying anything about tonal music "writing itself" or anything like that.


You'd argue with a fencepost, Iso. What I said was in context: "CP classical music is a self-fulfilling system which is virtually 'automatic' in nature; a no-brainer for composers like Mozart, Handel, Vivaldi, and Haydn. The diatonic scale, which divides the octave up so evenly, and fits together in such a closely-related cookie cutter fashion, is an easy environment in which to do counterpoint and compose conjunct melodies for; they practically compose themselves. You can look in any direction and find a closely related chord or voice which is a member of a chord."

I think that statement is true, and stand behind it. And I think Tymoczko implies the same thing.

When you take it out of context, it sounds more radical. I'm not sure what you're disagreeing with, or if it's just that _you don't like what I post,_ which is fine with me. I like to take some license, and be provocative. If you want to discuss the ideas, do so, but stop your "internet complaining" which is so characteristic of internet 'discussions.' I'm bored with your negativity.


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## BabyGiraffe

millionrainbows said:


> Y is an easy environment in which to do counterpoint and compose conjunct melodies for; they practically compose themselves. You can look in any direction and find a closely related chord or voice which is a member of a chord."
> [/COLOR]
> I think that statement is true, and stand behind it. And I think Tymoczko implies the same thing.


Not only diatonic, any 7 note note scale works for triadic counterpoint (but some may be dissonant). Diatonic scale can be thought as 5-limit 7-note consonant chord. In 12 equal it's tempered in meantone tuning, so it has no "wolf" intervals, which are essential, if you want "pure" sound.
You can even directly write in 7 equal and decide the tuning later (which is basically what modern pop producers do with "beatmaking pads" etc, quantizing the pads to some scale) or change the tuning to another.
12 equal also is also augmented and diminished tuning, so it's braindead easy to connect major and minor thirds, too. In 19 equal you need to deal with major/minor diesis (which are equalized). This means that 16-17-18th century music can be directly translated to 19 equal, but not 19th or 20th - chromatic mediants etc are real enharmonic modulations, not just existing on paper.

12 equal (the whole gamut, not just a subset) is also good for tetrads (13 note is the translation plane for 4 note chords, 7 is for 3 note chords) and 12 can be thought as 13 with 2 note equalized, so extended/jazz harmony is efficient.

31 equal is good for blues/barbershop type intervals, if you want efficient chord connections with consonance. With less consonance - 27, 26 and 22 can do the job.

Still, I wouldn't say that music writes itself, or everyone would be a composer...


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## millionrainbows

BabyGiraffe said:


> Still, I wouldn't say that music writes itself, or everyone would be a composer...


I wouldn't say that that music writes itself either, and I didn't. Are you _really_ going along with Isorhythm in his exaggeration/invalidation campaign of negativity? Too bad; I understand you so much more than he ever will. After all does he have the Just Intonation Primer?


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## BabyGiraffe

millionrainbows said:


> I wouldn't say that that music writes itself either, and I didn't. Are you _really_ going along with Isorhythm in his exaggeration/invalidation campaign of negativity? Too bad; I understand you so much more than he ever will.


Don't get hurt - it's just a little use of hyperbolization.

Since this topic is on Tymoczko - People, check his website - all his articles there are way better resource than his book, if you are after technical explanations behind his theory of voice leading (which, in the end doesn't give any novel insights, since 12 equal is pretty much very well explored as harmonic resource; but not as melodic one, judging from popular and classical music).


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## millionrainbows

BabyGiraffe said:


> Don't get hurt - it's just a little use of hyperbolization.
> 
> Since this topic is on Tymoczko - People, check his website - all his articles there are way better resource than his book, if you are after technical explanations behind his theory of voice leading (which, in the end doesn't give any novel insights, since 12 equal is pretty much very well explored as harmonic resource; but not as melodic one, judging from popular and classical music).


I'm not hurt; and I especially appreciate the link you so thoughtfully provided.

I'd like to hear you to say something good about our 12; like, it's almost stacked fifths except for that comma. Think you can muster it?


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## Bwv 1080

Interesting what he goes on to say about the limits of set theory. An awful lot of music has been written from <013568A>, not so much from the other 34 7-note cells


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## millionrainbows

Bwv 1080 said:


> Interesting what he goes on to say about the limits of set theory. An awful lot of music has been written from <013568A>, not so much from the other 34 7-note cells


Why do you suppose that is?


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## BabyGiraffe

millionrainbows said:


> Why do you suppose that is?


 Piano layout is my guess.


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## millionrainbows

BabyGiraffe said:


> Piano layout is my guess.


You think it might have to do with the layout of the scale intervals in the octave, which coincides with the piano layout, and is thus suited for CP harmonic practices? Get deeper. Your thoughts on this?


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## hammeredklavier

millionrainbows said:


> Debussy? Was his music full of counterpoint?


Debussy often sounds like he's overriding the constraints of counterpoint to achieve the kind of harmonic freedom he wants for his music.






compared to say,


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## millionrainbows

Yes, especially all those parallel major triads; those really sound contrapuntal.


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