Regular readers know by now that I am not a fan of certain music-theoretical ideas, namely those having to do with “harmony” and “chord progressions”. They also, I hope, understand my reasons, which I have tried to convey (and will continue to try to convey) within the context of musical analysis. However, it occurs to me that I should probably devote at least one post specifically to presenting my case against these notions — to help avoid misunderstandings of the sort that tend to arise in these discussions. It will also provide an opportunity for those who may disagree to explain their reasoning. (I am entirely open to having my mind changed if someone can give a good enough argument.) So, here goes.
The first thing to point out is that the concepts in question are nothing more than excess theoretical baggage: that is, they are not needed in order to explain or describe any musical phenomenon. One should already begin to suspect this upon reading Schenker’s later witings, such as The Masterwork in Music and Free Composition; but in any case it was later demonstrated conclusively by Peter Westergaard, who built on Schenker’s work and devised a theory of tonal music that is completely harmony-free. Westergaard’s efficient and elegant theory allows one to explain every note in a tonal compostion in terms of operations on pitches and rhythms alone — no abstract superstructures such as “chords” or “progressions”. What I like best about this theory is what I would call its “honesty”: if you understand it, you will also understand how to actually make (compose and perform) tonal music (rather than just how to talk about it).
That is actually the crux of the matter, and leads directly to the second point. If harmony were merely redundant, that would be one thing. After all, sometimes theoretical concepts that are superfluous from a strictly logical standpoint can nevertheless be illuminating. For example all of mathematics can in principle be reduced to set theory, but no one actually wants to do away with numbers, groups, topological spaces, or even triangles (except for Jean Dieudonné in the last case). Harmony, however, is not in this category. It belongs instead with gods, witches, phlogiston, and élan vital in the hallowed hall of Bad Theories — those that are such that to retain them after they have been “reduced away” would actually obscure the true explanation for the phenomenon they were invented to explain. The simple fact is that “harmonic” explanations of musical events do not accurately reflect musical intuition. (Again, just as I did before, I invite readers to compare and contrast a harmonic explanation and a Westergaardian explanation of a simple passage.)
All this, of course, has been (or certainly should have been) known since at least 1975, when Westergaard’s book An Introduction to Tonal Theory was published. However, harmonic theory has yet another bad consequence, which I haven’t yet seen anybody point out explicitly (though it was hinted at, for example, by Roger Sessions): it encourages people to think about music in ways that cause them to totally miss the deep connections between 20th-century music and earlier music. Discourse about the art music of the past 100 years makes it seem as if the activity that Bach, Mozart, and Beethoven were involved in has ceased to exist as a profession. It was for this reason that, as a child (when the only writings on music I knew were those that can be found in bookstores), I resented composers like Schoenberg and Boulez — not for their music, which I had never heard, but for what I thought their music represented, based on what I had read in music dictionaries and the like.
But it didn’t have to be that way. If Westergaardian theory had been the standard theoretical framework for discussing music in 1900, the concept of “atonality” would probably never have been invented in the first place. Why not? Because no one would have thought that unfamiliar coincidences of notes required a new theory of music. Oh sure, people would still have bitched about Schoenberg’s music, but they would have done so within the confines of the existing theory. Instead of saying “This music fundamentally violates the principles that have governed music for centuries”, they would have said “You know, Herr Schoenberg, when you pile on more than 50 layers of elaboration over a 20-measure timespan, I really have a hard time following you.” And they might have added: “Even Reger, curse him, only goes up to about 30 layers over such a span.”
Can you imagine how much more reasonable the history of 20th-century music would have looked? Babbitt’s notion of The Composer as Specialist would have been understood from the outset; people would have realized that the new music was difficult for the simple reason that it was quantitatively more complex than, and not qualitatively different from, the music of the past. There would be none of these silly arguments about whether it is appropriate for today’s music students to study the “common practice style”; it would be axiomatic that one begins with older music, because older music is simpler — and later music builds on earlier music by adding additional layers of structure. Most importantly, young aspiring composers would not have experienced existential crises upon discovering that “one doesn’t write that kind of music any more”, since it would have been understood that, from a composer’s standpoint anyway, there is only one “kind” of music. (Recall Schoenberg’s comment about twelve-tone composition, to the effect that one devises the row, and continues to compose as before.)
To sum up:
- There is nothing that can be explained with harmonic theory that can’t be explained without it;
- Harmonic theory provides only bad explanations in the first place; and
- If harmonic theory were replaced with a better theory, then 20th-century (and later) music wouldn’t seem so alien.
So that is why I feel so strongly that we need to get rid of “harmony”. The sooner, the better.
August 21, 2007 at 2:49 pm |
That’s it! Here’s the crux of our disagreement:
The simple fact is that “harmonic” explanations of musical events do not accurately reflect musical intuition.
I don’t think any analytical explanation accurately reflects musical intuition. At best, it’s a post-hoc abstract representation of what the intuitive process might have been. In rare cases (sketch analyses and the like) the guesses are more educated, but they’re still guesses. So I look at any theoretical concept on pragmatic terms—how easily does it allow me to talk about the music at hand? It’s sort of like economic laws, where usefulness lies in how well they predict behavior, not how well they describe “reality.”
In that sense, “harmony” is useful for predicting the behavior of so much music from such a wide swath of traditions and periods that to toss it away seems a baby-bathwater proposition. It’s not a coincidence that the majority of Western music written between 1750 and 1900 adopts what we call a V-I cadence at the close. It’s not a question of whether the composers’ intuitive processes were closer to a Westergaardian concept (I doubt it anyways, based on the evidence of figured bass). “V-I” and the like is a useful shorthand for a widespread harmonic practice that’s a hallmark of a great chunk of the repertoire.
And if you’re serious about understanding how a piece of music works, you simply can’t approach it in an ahistorical way. The fact is, if a composer learned harmony, then harmonic concepts became part of his or her musical intuition—they can either utilize it or ignore it, but in some sense, they’re reacting to it in a personal way. Think of it this way: if you don’t consider why Wagner’s contemporaries found his harmonies so startling, you won’t understand why he did a lot of the things he did. I’m not advocating the historical arrow of progress—subsequent musical practice doesn’t invalidate previous musical practice. But music isn’t created in a vacuum, either. Composers (and composer-on-the-spot improvisers) are using and reacting to the musical practices they’ve been taught, they’ve picked up, or happen to be around them in their own particular milieu. And for almost all of post-1700 Western history, that’s included harmonic ideas.
20th century music doesn’t seem particularly alien to me, but if you’re going to try and explain why it does to a lot of people, the main difference isn’t in form, or voice-leading, it’s in the resulting vertical sonorities—harmony, in other words. You can find a theoretical system to explain that the underlying practice isn’t so different, but that won’t explain why the results inspire such divergent reactions. Listeners respond to vertical simultaneities—whether that’s because of conditioning or not is another story, but the fact is, they do—so it’s useful to have a theory that can at least explain how those verticals are different, and why successions of verticals in atonal music don’t have the same effect on listeners as successions of verticals in tonal music.
And one more plea for harmony: rock and pop. An awful lot of that repertoire utilizes Roman-numeral progressions with no concern for voice leading whatsoever—block, root-position, often registrally and contrapuntally disjunct chords. And yet that music is still well-formed enough to be recognizably and agreeably musically grammatical.
August 21, 2007 at 3:53 pm |
Are there non-aleatory compositions using only the traditional Western pitch set that aren’t susceptible to a meaningful Westergaardian analysis? If not, I’d question its value; I can’t imagine that every way of throwing notes at a page can be understood as music. If you can think of such a work, what is it?
August 21, 2007 at 10:25 pm |
Matthew:
I don’t think any analytical explanation accurately reflects musical intuition. At best, it’s a post-hoc abstract representation of what the intuitive process might have been.
Once again, let’s not confuse analytical explanation with historical research. The purpose of analysis, as I see it, is to answer the question, “How could I, too, have composed this music?” Getting into the actual composer’s head is a different kind of task — one which would, however, have to start from some analytical understanding of one’s own of the piece, if it is to be fruitful.
So I look at any theoretical concept on pragmatic terms—how easily does it allow me to talk about the music at hand?
Westergaardian theory makes it very easy — much easier than harmonic theory.
It’s sort of like economic laws, where usefulness lies in how well they predict behavior, not how well they describe “reality.”
Suppose you have two theories, A and B, that do an equally good job of predicting behavior. Suppose, however, that theory A actually provides an explanation for the behavior in terms of fundamental principles, in addition to describing the behavior itself. Which theory do you choose? (This should be a rhetorical question!)
It’s not a coincidence that the majority of Western music written between 1750 and 1900 adopts what we call a V-I cadence at the close.
Who said it was? Some of us just happen to be interested in why this might be the case. (For the answer, see section 8.2 of An Introduction to Tonal Theory.)
It’s not a question of whether the composers’ intuitive processes were closer to a Westergaardian concept (I doubt it anyways, based on the evidence of figured bass).
What do you mean? Figured bass was one of the cornerstones of Schenker’s musical thought (which led to Westergaard). It serves better as evidence against harmonic theory (as representing the intuitions of composers) than in favor of it.
“You may state publicly that my principles, and those of my late father, are antithetical to Rameau’s.” — C.P.E. Bach, to J.P. Kirnberger.
“V-I” and the like is a useful shorthand for a widespread harmonic practice that’s a hallmark of a great chunk of the repertoire.
So is “3-2-1 over 5-1″ and the like!
The fact is, if a composer learned harmony, then harmonic concepts became part of his or her musical intuition—they can either utilize it or ignore it, but in some sense, they’re reacting to it in a personal way.
Neither Purcell nor Bach ever learned harmony; to apply such a theory to their music would be nothing if not to “approach music in an ahistorical way”. I’m not sure to what extent Haydn, Mozart, and Beethoven were familiar with Rameau, but they certainly weren’t “reacting to it in a personal way”; their theoretical heritage was Fux and figured-bass. And, as Schenker puts it, “Brahms would have none of it!” Perhaps that’s “reacting to it in a personal way”; but in any case it’s evidence in my favor, not yours.
Think of it this way: if you don’t consider why Wagner’s contemporaries found his harmonies so startling, you won’t understand why he did a lot of the things he did.
Why do you assume that, if we dispensed with Rameauvian theory, we could no longer “consider why Wagner’s contemporaries found his harmonies so startling”?
And for almost all of post-1700 Western history, that’s included harmonic ideas.
This is historically inaccurate. See above.
You can find a theoretical system to explain that the underlying practice isn’t so different, but that won’t explain why the results inspire such divergent reactions.
Again, who said? This is a completely unjustifed assumption.
Listeners respond to vertical simultaneities—whether that’s because of conditioning or not is another story, but the fact is, they do—so it’s useful to have a theory that can at least explain how those verticals are different, and why successions of verticals in atonal music don’t have the same effect on listeners as successions of verticals in tonal music.
Look: the correct theory will explain successions of veritcals just as much as everything else. Indeed, the whole point is that the notes that constitute those “successions of verticals” are not arbitrary accidents.
And one more plea for harmony: rock and pop.
That is hardly going to be an effective example for the purpose of convicing me, but I’ll humor you…
An awful lot of that repertoire utilizes Roman-numeral progressions with no concern for voice leading whatsoever—block, root-position, often registrally and contrapuntally disjunct chords.
Well, the authors of such music did, after all, learn harmony, so it’s not terribly surprising they construct their music in this way. In fact, let me turn it around: the fact that harmonic theory regards, say, Bach’s music as if it were constructed in the manner of contemporary popular music is surely a point against it, is it not?
But here’s the point (especially if you want to be historical): “chord progressions” like “V-I” did not originally arise from the abstract idea of “root movement”. They arose from cadential melodic progressions of the sort described in section 8.2 of ITT. Those cadential patterns have become very familiar — so familiar, in fact that it’s easy to recognize them even through the fog of complicated register transfers, etc. This, I strongly suspect, is what the practicioners and listeners of popular music (as well as most people who think or claim to think “harmonically”) are really doing.
Look, I don’t mean to be impertinent, but I can’t resist asking the following question: while you may think you’re making a principled case in defense of harmonic theory, is not the fact of the matter that you’re just unfamiliar with Westergaard’s book? If you had originally learned music theory from ITT, would we even be having this disagreement?
August 21, 2007 at 10:56 pm |
Jason:
Are there non-aleatory compositions using only the traditional Western pitch set that aren’t susceptible to a meaningful Westergaardian analysis? If not, I’d question its value; I can’t imagine that every way of throwing notes at a page can be understood as music.
From the Westergaardian perspective, the purpose of analyzing a piece (or a collection of notes thrown on a page) is not to differentiate good music from bad music, but rather to understand how one conceives of the notes. This is actually a prerequisite to aesthetic evaluation. (Westergaardian theory does contain a sort of primitive aesthetic criterion in the form of the notion of “interest”, discussed in chapter 4 of ITT.)
Instead of regarding Westergaardian theory as one candidate for a theory of how music behaves (which would in any case be a historical theory, not an analytical one), it’s better, I would argue, to think of it as a proposal for how to approach music in the first place — almost more of a metatheory than a theory, if you like. My use of the term “Westergaardian theory” is perhaps (like my use of “Schenkerian theory”) more general than other’s uses, but I think what’s important about ITT is not just what’s in the book, but what follows after reading the book.
The effectiveness (and thus value) of a theory can be thought of as the product (result of multiplying) its scope and its specificity; those two quantities aren’t necessarily inversely proportional (otherwise all theories would be equally valuable).
August 22, 2007 at 3:51 pm |
I’m interested enough that I ordered a copy of the book – I look forward to receiving it. I didn’t fully express my reason for asking the question above, and I think it has been misunderstood.
Whether you think of Westergaardian theory as a theory of how music behaves or a proposal for how to approach music, the theory is about music. If you apply the analytical techniques derived from a theory about music to an assembly of notes that is not music – and I assume that a such compositions exist – then the results of those techniques should not make sense. Otherwise, it’s not a theory about music, but about a broader category of which music is a part, something like “sounds made up only of changing combinations of pitches from a 12-tone division of the octave and their octave displacements”. If that’s the case, it can tell us about how music works as a part of that larger category, but not as music – either in intent or perception.
If you understood that as my underlying question before, I must be missing how your reply addresses it. Can you clarify?
August 22, 2007 at 9:30 pm |
I’m interested enough that I ordered a copy of the book – I look forward to receiving it.
That’s wonderful!
Whether you think of Westergaardian theory as a theory of how music behaves or a proposal for how to approach music, the theory is about music. If you apply the analytical techniques derived from a theory about music to an assembly of notes that is not music – and I assume that a such compositions exist – then the results of those techniques should not make sense.
It depends, of course, upon what you mean by “music” in the first place, and you need a theory of music in order to answer that question. It also depends on what you mean by “make sense”, and for this you need a metatheory: something that tells you what your theory is supposed to accomplish. Westergaard gives his answers to both of these questions in Chapter 1 of ITT; far be it for me to spoil the book for you!
For the moment, though, let me point out that there’s nothing inconsistent about a single theory being able to describe both what music is (as opposed to non-music), and how it works — indeed, it may even be necessary, since whether something is or is not music could turn out to depend on “how it works”! In other words, it’s incorrect to assume that something must already be established as “music” in order to be able to meaningfully apply “music theory” to it.
I’ll give you my own take on the matter. In my view, “musicality” is a property not of a certain kind of object “out there”, but rather of a particular mode of human perception. That is to say that any collection of sounds could be regarded as music, if one wished to hear it that way. What is “that way”? Basically, it consists of listening to sounds with the aim of perceiving interesting or pleasing (it’s not at all easy to untangle those two concepts from each other) structure. Now, of course, it is quite obvious that some collections of sounds (particularly those designed for the purpose) are better suited to being listened to in this way than others! But the purpose of musical analysis itself is simply to describe the structure (or lack thereof) that one perceives; aesthetic evaluation (which, in informal language, may take the form of answering the question, “Is this really music”?) proceeds from there.
August 23, 2007 at 10:18 am |
[...] In response to my last post, commenter Matthew writes: In that sense, “harmony” is useful for predicting the behavior of so [...]
October 14, 2007 at 8:28 pm |
[...] Westergaardian vertical dimension, Part 1 Having done enough harmony-bashing for the moment, I’ll try to advance the discussion in a more positive manner, by presenting [...]
February 22, 2008 at 10:41 am |
Have you guys heard of theory of musical lexicon? To know anything is good…? Right ? If you can invent something new it’s even better. Maybe you will have to break some rule of music theory…but if you don’t know it…what you will be going to break…How you gonna know it’s even new? Music theory = music grammar …there are many ways to think about it.. It has its own periods of history and ways of explaining how things work…but don’t be misled of statements like somebody writes here…Don’t try to invent the bike again…improve…ok…go ahead…but don’t waste time on it digging through simple -invented stuff already…also there is some common musical language rules to communicate with other musicians…how you will communicate to other musicians who spent all their lives studding music…What you gonna say? Oh..it’s crap…let’s be inspired…”I:can you play that three note chord for me?…II: What do you mean? I: you know C,E,G …C major chord….?II: I don’t know….I hate music theory!!!! “Music theory helps you to get out of your own small thinking box and only looser and lazy musician try to ignore it…There is no easy and simple way to music only slow, calm listening and studding and creating something new from what you already know and have heard…the more you have in your brain and in you vision-heart the more you’ll give joy to listeners…After seeing listeners enjoying your music… you’ll receive 10 times bigger joy back…and that’s how music should work. Just banging on some sounds without shapes won’t give you or listeners any pleasure…if you’ll be deaf…and you will think listeners and I enjoy my banging…One day you’ll realize…..that all these years you were slamming a hammer on musical pitches… Study, study and study and don’t turn away any thought suggested about music….
April 24, 2008 at 4:35 pm |
[...] I invariably get reactions like “But…but…of course harmonic theory is correct (or useful) — look how ubiquitous progressions like I-IV-V-I [...]