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:
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