I do have one question is the presence of the borrowing operation the only significant difference between Westergaardian and Schenkerian theory?
The short answer is: definitely not. The long answer (a discussion of the relationship between Schenkerian and Westergaardian theory) is too long for this comment, but is something I plan to write about in the future. For now, be it noted simply that the two theories are quite distinct (for all that Westergaardian theory owes to Schenker as a predecessor) -- and, in particular, a criticism of Schenker can by no means necessarily be taken as a criticism of Westergaard, and vice-versa (see below).
For me the most distinctive advantage of Westergaardian analyses is that it respects the fact that notes do not have to “line up” according to a certain chord structure. Notes that are sounding at the same time may be performing different functions, whereas harmonic theory dictates that notes sounding at the same time are usually “part of a chord” which is performing some harmonic function.
The way I like to put it is that in Westergaardian theory, the function of a note is defined by its relationship to other notes in its line (and to the local tonic, of course), and not by its relationship to the “root” of the “chord” to which it belongs (as in harmonic theory).
A corollary of this seems to be that Harmonic analyses work fine when the notes do consistently line up according to their function
If by “work fine” you mean that it is in fact possible to identify the “appropriate” Roman numerals to assign in such cases, sure, I’ll give you that. But what is such an “analysis” telling you? Taken literally, it means that you should understand the notes in the passage in terms of the indicated progression of “roots”. Which, in turn, implies that in order to hear the passage in your head, you should first, according to the analyst, imagine the succession of roots (which often, indeed typically, move by skip), and only then imagine the other notes by relating them to the roots—with the connection of notes in such a way as to form lines being a further, third step. To me, this is self-evidently a preposterously circuitous procedure when compared with the alternative of imagining lines as the fundamental construct, within which notes move by step—without any notion of “roots” entering at all.
Having said that, my biggest worry with Westergaardian theory is that it is almost too powerful. Whereas Harmonic theory constrains you to producing notes that do sound in some sense tonal (for a very powerful example of this see here)
I am as profoundly unimpressed with that “demonstration” as I am with that whole book and its author—of which, I must say, this example is entirely characteristic, in its exclusive obsession with the most superficial aspects of musical hearing and near-total amputation of the (much deeper) musical phenomena that I care most about and find most interesting. As far as I am concerned, there is no aesthetic difference between any of the passages (a) through (d) for the simple reason that all four of them are too short to possess much of any aesthetic characteristics in the first place: they all consist of three bars of four chords each. They are stylistically distinct, I suppose (though not actually very much, in the scheme of things), but any of them could be continued into something interesting or something less than interesting. One thing, however, is certain: if any of them were to be continued in the way they were generated (i.e. at random), the result would be nothing short of awful—and equally so in all four cases.
The essence of musical composition—at least its most fundamental and “elusive” aspect—has to do with projecting coherent (i.e. recognizably human-designed) gestures over long time spans. (How long “long” is depends on context: even if you’re writing a ten-second piece, you will want to carefully design its global structure.) The point being that multileveled thinking—control of all the various degrees of locality and globality and their interrelationships—is at the core of this art form. For that, you need a hierarchical or “reductive” theory (the very thing that our author explicitly says he doesn’t want, even claiming that to hear this way is beyond human cognitive capacities—I’m not making this up, see the last part of Chapter 7), which harmonic theory isn’t. To be impressed by the difference between (a) and (d) -- as readers are apparently expected to be—is to miss most of the point of what music is about.
Westergaardian theory seems to allow you to do almost anything whether it sounds musical or not.
Not as Westergaard sees it (see e.g. the last paragraph of p. 294 of ITT). I actually think he’s wrong about this, and that the theory should allow any note to happen at any time; the theory after all is supposed to constrain analytical choices, not compositional ones. A composer can write anything, and the question for the theorist or analyst is how a given listener understands what the composer writes.
While it is very easy to come up with a Westergaardian analysis, it is very difficult for me to understand why someone who had a certain framework in mind would have performed the operations that would have led them to the music in its actual form. The main culprits of this seem to be anticipatory notes and borrowing.
It’s hard to address this without a specific example to discuss.
That’s not an interesting critique of Schenker, let alone Westergaard (who is not mentioned or cited even once). It basically goes like this:
(1) Schenker did not adhere to rigorous philosophical standards in his rhetoric.
(2) I disagree with (or don’t understand) some of Schenker’s analyses and those of his disciples.
(3) Therefore, harmonic theory is correct.
I’ll also note that while some of the criticisms of Schenker are legitimate (if boring), others are completely wrong (e.g. the idea that the highest structural dominant is necessarily the final one).
Here is my attempt at fleshing out a more specific example: http://i.imgur.com/ruEYlhD.png I can’t figure out how to generate those using using Westergaardian theory
Thanks, this operation being notably absent in Schenkerian theory (I think).
The short answer is: definitely not
I suppose I will have to live with that for now.
If by “work fine” you mean that it is in fact possible to identify the “appropriate” Roman numerals to assign in such cases, sure, I’ll give you that
By work fine, I mean the the theory is falsifiable, and has predictive power. If you are given half of the bars in a Mozart piece, using harmonic theory can give a reasonable guess as to the rest. I’m not that confident about Mozart though, certainly pop music can be predicted using harmonic theory.
As far as I am concerned, there is no aesthetic difference between any of the passages (a) through (d) for the simple reason that all four of them are too short to possess much of any aesthetic characteristics in the first place: they all consist of three bars of four chords each.
...
The essence of musical composition—at least its most fundamental and “elusive” aspect—has to do with projecting coherent (i.e. recognizably human-designed) gestures over long time spans … To be impressed by the difference between (a) and (d) -- as readers are apparently expected to be—is to miss most of the point of what music is about
Could it be that your subjective experience of music is different than most people? It certainly sounds very alien to me. While its true that listening to the long range structure of a sonata is pleasurable to me, there are certainly 3 to 4 bar excerpts that I happen to enjoy in isolation without context. But you think that 3 bars is not enough to distinguish non-music from music.
You also claim that the stylistic differences are minor, yet I would wager that virtually 100% of people (with hearing) can point out d) as being to only tonal example.
the question for the theorist or analyst is how a given listener understands what the composer writes
This is very strange to me; suppose mozart were to replace all of the f’s in sonata in c major with f sharps. I think that the piece of music would be worse. Not objectively, or fundamentally worse. Just worse to a typical listener’s ears. A pianist who was used to playing mozart might wonder if there was a mistake in the manuscript.
Thanks, this operation being notably absent in Schenkerian theory (I think).
On the contrary, Schenker uses it routinely.
By work fine, I mean the the theory is falsifiable, and has predictive power. If you are given half of the bars in a Mozart piece, using harmonic theory can give a reasonable guess as to the rest.
If you’re talking about the expectations that a piece sets up for the listener, Westergaardian theory has much more to say about that than harmonic theory does. Or, let me rather say: an analyst equipped with Westergaardian theory is in a better position to talk about that, in much greater detail and precision, than one equipped with harmonic theory.
You might try having a closer look at Chapter 8 of ITT, which you said you had only skimmed so far. (A review of Chapter 7 wouldn’t hurt either.)
Could it be that your subjective experience of music is different than most people?
Not in the sense that you mean, no. (Otherwise my answer might be “I should hope so!”) I’m not missing anything that “most people” would hear. It’s the opposite: I almost certainly hear more than an average human: more context, more possibilities, more vividness. (What kind of musician would I be were it otherwise?) I’m acutely aware of the differences between passages (a) through (d). It’s just that I also see (or, rather, hear) a much larger picture—a picture that, by the way, I would like more people to hear (rather than being discouraged from doing so and having their existing prejudices reinforced).
But you think that 3 bars is not enough to distinguish non-music from music.
That is not what I said. You would be closer if you said I thought 3 bars were not enough to distinguish good music from bad music. But of course it depends on how long the 3 bars are, and what they contain. My only claim here is that these particular excerpts are too short and contain too little to be judged against each other as music. And again, this is not because I don’t hear the effect of the constraints that produced (d) as opposed to (a), but rather most probably because: (1) I’m not impressed by (d) because I understand how easy it is to produce; and (2) I hear structure in (a) that “most people” probably don’t hear (and certainly aren’t encouraged to hear by the likes of Tymoczko), not because they can’t hear it, but mostly because they haven’t heard enough music to be in the habit of noticing those phenomena; and, most, importantly, (3) I understand the aesthetic importance of large-scale design, which is absent from all four excerpts (as is implicit in my calling them “excerpts”).
Music can have great moments, and I enjoy such moments as much as anyone else; but to listen to music as a sequence of isolated moments is a very impoverished way to listen to music. (And to anyone who knows a lot of music, (d) just isn’t that great of a moment.)
You also claim that the stylistic differences are minor, yet I would wager that virtually 100% of people (with hearing) can point out d) as being to only tonal example.
Far fewer than 100% of people know what the word “tonal” means. (I also suspect that you overestimate the aural skills of the average human: more people than you probably realize would simply hear all four as roughly “a bunch of piano chords, (a) having more high notes”.) Regardless, the fact that the differences are eminently perceptible does not imply that they are aesthetically significant. (Imagine if some of the excerpts were loud, and others were soft. A very hearable difference, but a stylistically minor one, given how often loud and soft mix freely in the same piece. Similarly, I feel that I could fairly easily compose a piece that incorporated all four excerpts.)
suppose mozart were to replace all of the f’s in sonata in c major with f sharps. I think that the piece of music would be worse. Not objectively, or fundamentally worse. Just worse to a typical listener’s ears. A pianist who was used to playing mozart might wonder if there was a mistake in the manuscript. Its also not clear to me that Westergaardian theory would predict that this set of notes is unusual, whereas harmonic theory would.
Replacing the F’s with F sharps would severely undermine the C-major tonality, for starters. That’s an assertion that can be made just as easily in Westergaardian theory, Schenkerian theory, or harmonic theory. But Westergaardian theory tells you even more: that by undermining the tonality, you necessarily undermine the rhythmic structure.
After looking at Chapter 8, its becoming obvious that learning Westergaardian theory to an extent that it would be actually useful to me is going to take a lot of time and analyses (and I don’t know if I will get around to that any time soon).
Regarding harmony, this document may be of interest to you—its written by a Schenkerian who is familiar with Westergaard:
The short answer is: definitely not. The long answer (a discussion of the relationship between Schenkerian and Westergaardian theory) is too long for this comment, but is something I plan to write about in the future. For now, be it noted simply that the two theories are quite distinct (for all that Westergaardian theory owes to Schenker as a predecessor) -- and, in particular, a criticism of Schenker can by no means necessarily be taken as a criticism of Westergaard, and vice-versa (see below).
The way I like to put it is that in Westergaardian theory, the function of a note is defined by its relationship to other notes in its line (and to the local tonic, of course), and not by its relationship to the “root” of the “chord” to which it belongs (as in harmonic theory).
If by “work fine” you mean that it is in fact possible to identify the “appropriate” Roman numerals to assign in such cases, sure, I’ll give you that. But what is such an “analysis” telling you? Taken literally, it means that you should understand the notes in the passage in terms of the indicated progression of “roots”. Which, in turn, implies that in order to hear the passage in your head, you should first, according to the analyst, imagine the succession of roots (which often, indeed typically, move by skip), and only then imagine the other notes by relating them to the roots—with the connection of notes in such a way as to form lines being a further, third step. To me, this is self-evidently a preposterously circuitous procedure when compared with the alternative of imagining lines as the fundamental construct, within which notes move by step—without any notion of “roots” entering at all.
I am as profoundly unimpressed with that “demonstration” as I am with that whole book and its author—of which, I must say, this example is entirely characteristic, in its exclusive obsession with the most superficial aspects of musical hearing and near-total amputation of the (much deeper) musical phenomena that I care most about and find most interesting. As far as I am concerned, there is no aesthetic difference between any of the passages (a) through (d) for the simple reason that all four of them are too short to possess much of any aesthetic characteristics in the first place: they all consist of three bars of four chords each. They are stylistically distinct, I suppose (though not actually very much, in the scheme of things), but any of them could be continued into something interesting or something less than interesting. One thing, however, is certain: if any of them were to be continued in the way they were generated (i.e. at random), the result would be nothing short of awful—and equally so in all four cases.
The essence of musical composition—at least its most fundamental and “elusive” aspect—has to do with projecting coherent (i.e. recognizably human-designed) gestures over long time spans. (How long “long” is depends on context: even if you’re writing a ten-second piece, you will want to carefully design its global structure.) The point being that multileveled thinking—control of all the various degrees of locality and globality and their interrelationships—is at the core of this art form. For that, you need a hierarchical or “reductive” theory (the very thing that our author explicitly says he doesn’t want, even claiming that to hear this way is beyond human cognitive capacities—I’m not making this up, see the last part of Chapter 7), which harmonic theory isn’t. To be impressed by the difference between (a) and (d) -- as readers are apparently expected to be—is to miss most of the point of what music is about.
Not as Westergaard sees it (see e.g. the last paragraph of p. 294 of ITT). I actually think he’s wrong about this, and that the theory should allow any note to happen at any time; the theory after all is supposed to constrain analytical choices, not compositional ones. A composer can write anything, and the question for the theorist or analyst is how a given listener understands what the composer writes.
It’s hard to address this without a specific example to discuss.
That’s not an interesting critique of Schenker, let alone Westergaard (who is not mentioned or cited even once). It basically goes like this:
(1) Schenker did not adhere to rigorous philosophical standards in his rhetoric.
(2) I disagree with (or don’t understand) some of Schenker’s analyses and those of his disciples.
(3) Therefore, harmonic theory is correct.
I’ll also note that while some of the criticisms of Schenker are legitimate (if boring), others are completely wrong (e.g. the idea that the highest structural dominant is necessarily the final one).
Use octave transfer (ITT sec. 7.7).
Thanks, this operation being notably absent in Schenkerian theory (I think).
I suppose I will have to live with that for now.
By work fine, I mean the the theory is falsifiable, and has predictive power. If you are given half of the bars in a Mozart piece, using harmonic theory can give a reasonable guess as to the rest. I’m not that confident about Mozart though, certainly pop music can be predicted using harmonic theory.
Could it be that your subjective experience of music is different than most people? It certainly sounds very alien to me. While its true that listening to the long range structure of a sonata is pleasurable to me, there are certainly 3 to 4 bar excerpts that I happen to enjoy in isolation without context. But you think that 3 bars is not enough to distinguish non-music from music.
You also claim that the stylistic differences are minor, yet I would wager that virtually 100% of people (with hearing) can point out d) as being to only tonal example.
This is very strange to me; suppose mozart were to replace all of the f’s in sonata in c major with f sharps. I think that the piece of music would be worse. Not objectively, or fundamentally worse. Just worse to a typical listener’s ears. A pianist who was used to playing mozart might wonder if there was a mistake in the manuscript.
On the contrary, Schenker uses it routinely.
If you’re talking about the expectations that a piece sets up for the listener, Westergaardian theory has much more to say about that than harmonic theory does. Or, let me rather say: an analyst equipped with Westergaardian theory is in a better position to talk about that, in much greater detail and precision, than one equipped with harmonic theory.
You might try having a closer look at Chapter 8 of ITT, which you said you had only skimmed so far. (A review of Chapter 7 wouldn’t hurt either.)
Not in the sense that you mean, no. (Otherwise my answer might be “I should hope so!”) I’m not missing anything that “most people” would hear. It’s the opposite: I almost certainly hear more than an average human: more context, more possibilities, more vividness. (What kind of musician would I be were it otherwise?) I’m acutely aware of the differences between passages (a) through (d). It’s just that I also see (or, rather, hear) a much larger picture—a picture that, by the way, I would like more people to hear (rather than being discouraged from doing so and having their existing prejudices reinforced).
That is not what I said. You would be closer if you said I thought 3 bars were not enough to distinguish good music from bad music. But of course it depends on how long the 3 bars are, and what they contain. My only claim here is that these particular excerpts are too short and contain too little to be judged against each other as music. And again, this is not because I don’t hear the effect of the constraints that produced (d) as opposed to (a), but rather most probably because: (1) I’m not impressed by (d) because I understand how easy it is to produce; and (2) I hear structure in (a) that “most people” probably don’t hear (and certainly aren’t encouraged to hear by the likes of Tymoczko), not because they can’t hear it, but mostly because they haven’t heard enough music to be in the habit of noticing those phenomena; and, most, importantly, (3) I understand the aesthetic importance of large-scale design, which is absent from all four excerpts (as is implicit in my calling them “excerpts”).
Music can have great moments, and I enjoy such moments as much as anyone else; but to listen to music as a sequence of isolated moments is a very impoverished way to listen to music. (And to anyone who knows a lot of music, (d) just isn’t that great of a moment.)
Far fewer than 100% of people know what the word “tonal” means. (I also suspect that you overestimate the aural skills of the average human: more people than you probably realize would simply hear all four as roughly “a bunch of piano chords, (a) having more high notes”.) Regardless, the fact that the differences are eminently perceptible does not imply that they are aesthetically significant. (Imagine if some of the excerpts were loud, and others were soft. A very hearable difference, but a stylistically minor one, given how often loud and soft mix freely in the same piece. Similarly, I feel that I could fairly easily compose a piece that incorporated all four excerpts.)
Replacing the F’s with F sharps would severely undermine the C-major tonality, for starters. That’s an assertion that can be made just as easily in Westergaardian theory, Schenkerian theory, or harmonic theory. But Westergaardian theory tells you even more: that by undermining the tonality, you necessarily undermine the rhythmic structure.
After looking at Chapter 8, its becoming obvious that learning Westergaardian theory to an extent that it would be actually useful to me is going to take a lot of time and analyses (and I don’t know if I will get around to that any time soon).
Regarding harmony, this document may be of interest to you—its written by a Schenkerian who is familiar with Westergaard:
http://www.artsci.wustl.edu/~rsnarren/texts/HarmonyText.pdf