If I may ask, what was your issue with Westergaard?
(As a polyglot composer, I agree that there is an analogy of language proficiency to musical composition, but would draw a different conclusion: harmonic theory is like a phrasebook, whereas Westergaardian theory is like a grammar text. The former may seem more convenient for certain ad hoc purposes, but is hopelessly inferior for actually learning to speak the language.)
I don’t have any particular issue with Westergaard, I just couldn’t make it through the book. Perhaps with more more effort I could but I’m lacking motivation due to low expectancy. It was a long time ago that I attempted the book, but If I had to pinpoint why, there are few things I stumbled over:
The biggest problem was that I have poor aural skills. I cannot look at two lines and imagine what they sound like so I have to play them on a piano. Add in more lines and I am quickly overwhelmed.
A second problem was the abstractness of the first half of the book. Working through counterpoint exercises that didn’t really sound like music did not hold my attention for very long.
A third problem was the disconnect between the rules I was learning and my intuition. Even though I could do the exercises by following the rules, too often I felt like I was counting spaces rather than improving my understand of how musical lines are formed.
I think that your comparison is very interesting because I would predict that a phrasebook is much more useful than a grammar text for learning a language. The Pimsleur approach, which seems to be a decent way to start to learning a language, is pretty much a phrase book in audio form with some spaced repetition thrown in for good measure. Of course the next step, where the actual learning takes place, is to start trying to communicate with native speakers, but the whole point of Pimsleur is to get you to that point as soon as possible. This important because most people use grammatical rules implicitly rather than explicitly. Certainly grammar texts can be used to improve your proficiency in a language, but I highly doubt that anyone has actually learned a language using one. Without the critical step of communication, there is no mechanism for internalizing the grammatical rules.
(Sorry for taking such a long tangent into language acquisition, I wasn’t initially planning on stretching the analogy that far.)
Thanks for your feedback on the Westergaard text. I think many of your problems will be addressed by the material I plan to write at some indefinite point in the future. It’s unfortunate that ITT is the only exposition of Westergaardian theory available (and even it is not technically “available”, being out of print), because your issues seem to be with the book and not with the theory that the book aims to present.
There is considerable irony in what you say about aural skills, because I consider the development of aural skills—even at the most elementary levels—to be a principal practical use of Westergaardian theory. Unfortunately, Westergaard seems not to have fully appreciated this aspect of his theory’s power, because he requests of the reader a rather sophisticated level of aural skills (namely the ability to read and mentally hear a Mozart passage) as a prerequisite for the book—rather unnecessarily, in my opinion.
This leads to the point about counterpoint exercises, which, if designed properly, should be easier to mentally “hear” than real music—that is, indeed, their purpose. Unfortunately, this is not emphasized enough in ITT.
I think that your comparison is very interesting because I would predict that a phrasebook is much more useful than a grammar text for learning a language
Thank goodness I’m here to set you straight, then. Phrasebooks are virtually useless for learning to speak a language. Indeed they are specifically designed for people who don’t want to learn the language, but merely need to memorize a few phrases (hence the name), for—as I said—ad hoc purposes. (Asking where the bathroom is, what someone’s name is, whether they speak English, that sort of thing.)
Here’s an anecdote to illustrate the problem with phrasebooks. When I was about 10 years old and had just started learning French, my younger sister got the impression that pel was the French word for “is”. The reason? I had informed her that the French translation of “my name is” was je m’appelle—a three syllable expression whose last syllable is indeed pronounced pel. What she didn’t realize was that the three syllables of the French phrase do not individually correspond to the three syllables of the English phrase. Pel does not mean “is”; rather, appelle means “call”, je means “I”, and m’ means “myself”. Though translated “my name is”, the phrase actually means “I call myself”.
A phrasebook won’t tell you this; a grammar will. If you try to learn French from a phrasebook, you might successfully learn to introduce yourself with je m’appelle, but you will be in my sister’s position, doomed to making false assumptions about the structure of the language that may require vast amounts of data to correct. (It’s no defense of a wrong theory that it didn’t prevent you from learning the right theory eventually.) Whereas if you learn from a grammar, not only will you learn je m’appelle without thinking pel means “is”, but you will also be able to generalize outside the scope of the “Greetings” section of your phrasebook and produce apparently unrelated phrases such as “I call you” (je t’appelle).
I think your comments are revealing about the mindset of people who resist or “don’t get” my attack on harmonic theory. It seems to be assumed that of course no one actually learns musical thinking from a harmony book. Likewise, in defending phrasebooks, you help yourself to the assumption that the learner is going to have access to extensive amounts of data in the form of communication with speakers, and that this will be where the “actual learning” is going to occur. Well in that case, what do you need a phrasebook for? You can, after all, learn a language simply by immersion, with nothing other than the data itself to guide you. If you’re going to have any preliminary or supplementary instruction at all, it surely may as well be in an organized fashion, aimed at increasing the efficiency of the learning process by directing one toward correct theories and away from incorrect ones—which is exactly what grammar books do and phrasebooks don’t do.
Harmony is actually worse than a phrasebook, because at least a phrasebook won’t cause you to make worse mistakes than you would make otherwise; and it doesn’t pretend to be a grammar of the language. With harmony, the situation is different. Harmony books are written as if they were presenting an actual musical theory, something that would be useful to know before sifting through vast amounts of musical data doing, as you put it, “actual learning”. But then, when push comes to shove and it is pointed out how terrible, how actively misleading the harmony pseudo-theory is for this purpose, its defenders retreat to a position of “oh, well, of course everybody knows that you can’t actually learn music from a book”—as if that were a defense against an alternative theory that actually is helpful. It’s enough to drive one mad!
(You’ll understand, I hope, that I’m not reacting particularly to you in the preceding paragraph, but to my whole history of such discussions going back a number of years.)
Alright I’ve read most of the relevant parts of ITT. I only skimmed the chapter on phrases and movements and I didn’t read the chapter on performance.
I do have one question is the presence of the borrowing operation the only significant difference between Westergaardian and Schenkerian theory?
As for my thoughts, I think that Westergaardian theory is much more powerful than harmonic theory. It is capable of accounting for the presence of every single note in a composition unlike harmonic theory which seems to be stuck with a four part chorale texture plus voice leading for the melody. Moreover, Westergaardian analyses feel much more intuitive and musical to me than harmonic analyses. In other words its easier for me to hear the Westergaardian background than it is for me to hear the chord progression.
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. For example its not always clear to me that a tonic chord in a piece (which harmonic theory regards as being a point of stability) is really an arrival point or a result of notes that just happen to coincide at that moment. The same is true for other chords.
A corollary of this seems to be that Harmonic analyses work fine when the notes do consistently line up according to their function, which happens all the time in pop music and possibly in Classical music although I’m not certain of this.
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), Westergaardian theory seems to allow you to do almost anything whether it sounds musical or not. 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.
One of his criticisms is that you can have harmonic consistency without following contrapuntal rules . 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.
A corollary of this seems to be that Harmonic analyses work fine when the notes do consistently line up according to their function, which happens all the time in pop music and possibly in Classical music although I’m not certain of this.
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
Note that when analyzing tonal music with Westergaardian analysis, it is generally the case that anticipation and delay tend to occur at relatively shallow levels in the piece’s structure. The deeper you go, the more notes are going to be “aligned”, just like they might be expected to be in a harmonic analysis. Moreover, the constraints of consonance and dissonance in aligned lines (as given by the rules of counterpoint; see Westergaard’s chapters on species counterpoint) will also come into play, when it comes to these deeper levels. So it seems that Westergaardian analysis can do everything that you expect harmonic analysis to do, and of course even more. Instead of having “harmonic functions” and “chords”, you have constraints that force you to have some kind of consonance in the background.
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:
One more question. Do you also think that Westergaardian theory is superior for understanding jazz? I’ve encountered jazz pianists on the internet who insist that harmony and voice leading are ABSOLUTELY ESSENTIAL for doing jazz improvisation and anyone suggests otherwise is a heretic who deserves to be burnt at the stake. Hyperbole aside, jazz classes do seem to incorporate a lot of harmony and voice leading into their material and their students do seem to make fine improvisers and composers.
Oh, and for what its worth, you’ve convinced me to give Westergaard another shot.
Do you also think that Westergaardian theory is superior for understanding jazz?
Yes. My claim is not repertory-specific. (Note that this is my claim I’m talking about, not Westergaard’s.)
More generally, I claim that the Westergaardian framework (or some future theory descended from it) is the appropriate one for understanding any music that is to be understood in terms of the traditional Western pitch space (i.e. the one represented by a standardly-tuned piano keyboard), as well as any music whose pitch space can be regarded as an extension, restriction, or modification of the latter.
I’ve encountered jazz pianists on the internet who insist that harmony and voice leading are ABSOLUTELY ESSENTIAL for doing jazz improvisation and anyone suggests otherwise is a heretic who deserves to be burnt at the stake.
How many of them are familiar with Westergaardian (or even Schenkerian) theory?
I’ve encountered this attitude among art-music performers as well. My sense is that such people are usually confusing the map and the territory (i.e. confusing music theory and music), à la Phil Goetz above. They fail to understand that the concepts of harmonic theory are not identical to the musical phenomena they purport to describe, but instead are merely one candidate theory of those phenomena.
jazz classes do seem to incorporate a lot of harmony and voice leading into their material and their students do seem to make fine improvisers and composers
Some of them do—probably more or less exactly the subset who have enough tacit knowledge not to need to take their theoretical instruction seriously, and the temperament not to want to.
Oh, and for what its worth, you’ve convinced me to give Westergaard another shot.
I’m delighted to hear that, of course, although I should reiterate that I don’t expect ITT to be the final word on Westergaardian theory.
Some of them do—probably more or less exactly the subset who have enough tacit knowledge not to need to take their theoretical instruction seriously, and the temperament not to want to.
This was my hypothesis as well (which is what the jazz musician responded with hostility to). If this is true though, then why are jazz musicians so passionate about harmony and voice leading? They seem to really believe that its a useful paradigm for understanding music. Perhaps this is just belief in belief?
why are jazz musicians so passionate about harmony and voice leading?
It’s difficult to know what other people are thinking without talking to them directly. With this level of information I would make only two points:
1) It doesn’t count as “passionate about harmony and voice leading” unless they understand Westergaardian theory well enough to contrast the two. Otherwise it just amounts to “passionate about music theory of some kind”.
2) It doesn’t have anything to do with jazz. If they’re right that harmony is the superior theory for jazz, then it’s the superior theory of music in general. Given the kind of theory we’re looking for (cf. Chapter 1 of ITT), different musical traditions should not have different theories. (Analogy: if you find that the laws of physics are different on different planets, you have the wrong idea about what “laws of physics” means.)
I don’t think that we disagree all that much. We both agree that there are some people who are able to learn structural rules implicitly without explicit instruction. We typically call these people “good at languages” or “good at music”. Our main disagreement therefore, is how large that set of people is. I happen to think that it is very large given that everyone learns the grammatical rules of their first language this way, and a fair number of polyglots learn their second language this way as well (Unless you deny the usefulness of Pimsleur like approaches). If I understand you correctly, you think that the group of people who are able to properly learn a language/music this way is smaller, because it often results in bad habits and poor inferences about the structure of the language. I would endorse this as well—grammatical texts are useful for refining your understanding of the structure of a language.
Well in that case, what do you need a phrasebook for? You can, after all, learn a language simply by immersion, with nothing other than the data itself to guide you. If you’re going to have any preliminary or supplementary instruction at all, it surely may as well be in an organized fashion, aimed at increasing the efficiency of the learning process by directing one toward correct theories and away from incorrect ones—which is exactly what grammar books do and phrasebooks don’t do.
Because it is scary to learn to swim without arm floats even if there is someone else helping you (I think that phrase books are analogous to arm floats). Other than that I would agree with most of this. If you want secondary instruction in a language then you should probably use a grammar book and not a phrase book and I may return to Westergaard after I have taken some composition lessons. Also I would go one step further and say that not only is it possible to learn a language via immersion, it is necessary, and any other tools you may use to learn a language should help to support this goal.
I would endorse this as well—grammatical texts are useful for refining your understanding of the structure of a language.
Tentatively—grammatical texts have a complex relationship with language. They can be somewhat useful but still go astray because they’re for a different language, with the classic example being grammar based on Latin being used to occasionally force English out of its normal use.
I suspect the same happens when formal grammar is used to claim that casual and/or spoken English is wrong.
Yes, accurate grammars are better than inaccurate grammars. But I think you are focusing too much on the negative effects and not noticing the positive effects. It is hard to notice people’s understanding of grammar except when they make a mistake or correct someone else, both of which are generally negative effects.
Americans are generally not taught English grammar, but often are taught a foreign language, including grammar. Huge numbers of them claim that studying the foreign grammar helped them understand English grammar. Of course, they know the grammar is foreign, so they don’t immediately impose it on English. But they start off knowing so little grammar that the overlap with the other language is already quite valuable, as are the abstractions involved.
If I may ask, what was your issue with Westergaard?
(As a polyglot composer, I agree that there is an analogy of language proficiency to musical composition, but would draw a different conclusion: harmonic theory is like a phrasebook, whereas Westergaardian theory is like a grammar text. The former may seem more convenient for certain ad hoc purposes, but is hopelessly inferior for actually learning to speak the language.)
I don’t have any particular issue with Westergaard, I just couldn’t make it through the book. Perhaps with more more effort I could but I’m lacking motivation due to low expectancy. It was a long time ago that I attempted the book, but If I had to pinpoint why, there are few things I stumbled over:
The biggest problem was that I have poor aural skills. I cannot look at two lines and imagine what they sound like so I have to play them on a piano. Add in more lines and I am quickly overwhelmed.
A second problem was the abstractness of the first half of the book. Working through counterpoint exercises that didn’t really sound like music did not hold my attention for very long.
A third problem was the disconnect between the rules I was learning and my intuition. Even though I could do the exercises by following the rules, too often I felt like I was counting spaces rather than improving my understand of how musical lines are formed.
I think that your comparison is very interesting because I would predict that a phrasebook is much more useful than a grammar text for learning a language. The Pimsleur approach, which seems to be a decent way to start to learning a language, is pretty much a phrase book in audio form with some spaced repetition thrown in for good measure. Of course the next step, where the actual learning takes place, is to start trying to communicate with native speakers, but the whole point of Pimsleur is to get you to that point as soon as possible. This important because most people use grammatical rules implicitly rather than explicitly. Certainly grammar texts can be used to improve your proficiency in a language, but I highly doubt that anyone has actually learned a language using one. Without the critical step of communication, there is no mechanism for internalizing the grammatical rules.
(Sorry for taking such a long tangent into language acquisition, I wasn’t initially planning on stretching the analogy that far.)
Thanks for your feedback on the Westergaard text. I think many of your problems will be addressed by the material I plan to write at some indefinite point in the future. It’s unfortunate that ITT is the only exposition of Westergaardian theory available (and even it is not technically “available”, being out of print), because your issues seem to be with the book and not with the theory that the book aims to present.
There is considerable irony in what you say about aural skills, because I consider the development of aural skills—even at the most elementary levels—to be a principal practical use of Westergaardian theory. Unfortunately, Westergaard seems not to have fully appreciated this aspect of his theory’s power, because he requests of the reader a rather sophisticated level of aural skills (namely the ability to read and mentally hear a Mozart passage) as a prerequisite for the book—rather unnecessarily, in my opinion.
This leads to the point about counterpoint exercises, which, if designed properly, should be easier to mentally “hear” than real music—that is, indeed, their purpose. Unfortunately, this is not emphasized enough in ITT.
Thank goodness I’m here to set you straight, then. Phrasebooks are virtually useless for learning to speak a language. Indeed they are specifically designed for people who don’t want to learn the language, but merely need to memorize a few phrases (hence the name), for—as I said—ad hoc purposes. (Asking where the bathroom is, what someone’s name is, whether they speak English, that sort of thing.)
Here’s an anecdote to illustrate the problem with phrasebooks. When I was about 10 years old and had just started learning French, my younger sister got the impression that pel was the French word for “is”. The reason? I had informed her that the French translation of “my name is” was je m’appelle—a three syllable expression whose last syllable is indeed pronounced pel. What she didn’t realize was that the three syllables of the French phrase do not individually correspond to the three syllables of the English phrase. Pel does not mean “is”; rather, appelle means “call”, je means “I”, and m’ means “myself”. Though translated “my name is”, the phrase actually means “I call myself”.
A phrasebook won’t tell you this; a grammar will. If you try to learn French from a phrasebook, you might successfully learn to introduce yourself with je m’appelle, but you will be in my sister’s position, doomed to making false assumptions about the structure of the language that may require vast amounts of data to correct. (It’s no defense of a wrong theory that it didn’t prevent you from learning the right theory eventually.) Whereas if you learn from a grammar, not only will you learn je m’appelle without thinking pel means “is”, but you will also be able to generalize outside the scope of the “Greetings” section of your phrasebook and produce apparently unrelated phrases such as “I call you” (je t’appelle).
I think your comments are revealing about the mindset of people who resist or “don’t get” my attack on harmonic theory. It seems to be assumed that of course no one actually learns musical thinking from a harmony book. Likewise, in defending phrasebooks, you help yourself to the assumption that the learner is going to have access to extensive amounts of data in the form of communication with speakers, and that this will be where the “actual learning” is going to occur. Well in that case, what do you need a phrasebook for? You can, after all, learn a language simply by immersion, with nothing other than the data itself to guide you. If you’re going to have any preliminary or supplementary instruction at all, it surely may as well be in an organized fashion, aimed at increasing the efficiency of the learning process by directing one toward correct theories and away from incorrect ones—which is exactly what grammar books do and phrasebooks don’t do.
Harmony is actually worse than a phrasebook, because at least a phrasebook won’t cause you to make worse mistakes than you would make otherwise; and it doesn’t pretend to be a grammar of the language. With harmony, the situation is different. Harmony books are written as if they were presenting an actual musical theory, something that would be useful to know before sifting through vast amounts of musical data doing, as you put it, “actual learning”. But then, when push comes to shove and it is pointed out how terrible, how actively misleading the harmony pseudo-theory is for this purpose, its defenders retreat to a position of “oh, well, of course everybody knows that you can’t actually learn music from a book”—as if that were a defense against an alternative theory that actually is helpful. It’s enough to drive one mad!
(You’ll understand, I hope, that I’m not reacting particularly to you in the preceding paragraph, but to my whole history of such discussions going back a number of years.)
Alright I’ve read most of the relevant parts of ITT. I only skimmed the chapter on phrases and movements and I didn’t read the chapter on performance.
I do have one question is the presence of the borrowing operation the only significant difference between Westergaardian and Schenkerian theory?
As for my thoughts, I think that Westergaardian theory is much more powerful than harmonic theory. It is capable of accounting for the presence of every single note in a composition unlike harmonic theory which seems to be stuck with a four part chorale texture plus voice leading for the melody. Moreover, Westergaardian analyses feel much more intuitive and musical to me than harmonic analyses. In other words its easier for me to hear the Westergaardian background than it is for me to hear the chord progression.
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. For example its not always clear to me that a tonic chord in a piece (which harmonic theory regards as being a point of stability) is really an arrival point or a result of notes that just happen to coincide at that moment. The same is true for other chords.
A corollary of this seems to be that Harmonic analyses work fine when the notes do consistently line up according to their function, which happens all the time in pop music and possibly in Classical music although I’m not certain of this.
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), Westergaardian theory seems to allow you to do almost anything whether it sounds musical or not. 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.
One more thing: Have you read “why I am not a Schenkerian” by Lodewidjk Muns? Here is the link: http://lmuns.home.xs4all.nl/WhyIamNotaSchenkerian.pdf
One of his criticisms is that you can have harmonic consistency without following contrapuntal rules . 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.
Note that when analyzing tonal music with Westergaardian analysis, it is generally the case that anticipation and delay tend to occur at relatively shallow levels in the piece’s structure. The deeper you go, the more notes are going to be “aligned”, just like they might be expected to be in a harmonic analysis. Moreover, the constraints of consonance and dissonance in aligned lines (as given by the rules of counterpoint; see Westergaard’s chapters on species counterpoint) will also come into play, when it comes to these deeper levels. So it seems that Westergaardian analysis can do everything that you expect harmonic analysis to do, and of course even more. Instead of having “harmonic functions” and “chords”, you have constraints that force you to have some kind of consonance in the background.
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
One more question. Do you also think that Westergaardian theory is superior for understanding jazz? I’ve encountered jazz pianists on the internet who insist that harmony and voice leading are ABSOLUTELY ESSENTIAL for doing jazz improvisation and anyone suggests otherwise is a heretic who deserves to be burnt at the stake. Hyperbole aside, jazz classes do seem to incorporate a lot of harmony and voice leading into their material and their students do seem to make fine improvisers and composers.
Oh, and for what its worth, you’ve convinced me to give Westergaard another shot.
Yes. My claim is not repertory-specific. (Note that this is my claim I’m talking about, not Westergaard’s.)
More generally, I claim that the Westergaardian framework (or some future theory descended from it) is the appropriate one for understanding any music that is to be understood in terms of the traditional Western pitch space (i.e. the one represented by a standardly-tuned piano keyboard), as well as any music whose pitch space can be regarded as an extension, restriction, or modification of the latter.
How many of them are familiar with Westergaardian (or even Schenkerian) theory?
I’ve encountered this attitude among art-music performers as well. My sense is that such people are usually confusing the map and the territory (i.e. confusing music theory and music), à la Phil Goetz above. They fail to understand that the concepts of harmonic theory are not identical to the musical phenomena they purport to describe, but instead are merely one candidate theory of those phenomena.
Some of them do—probably more or less exactly the subset who have enough tacit knowledge not to need to take their theoretical instruction seriously, and the temperament not to want to.
I’m delighted to hear that, of course, although I should reiterate that I don’t expect ITT to be the final word on Westergaardian theory.
This was my hypothesis as well (which is what the jazz musician responded with hostility to). If this is true though, then why are jazz musicians so passionate about harmony and voice leading? They seem to really believe that its a useful paradigm for understanding music. Perhaps this is just belief in belief?
It’s difficult to know what other people are thinking without talking to them directly. With this level of information I would make only two points:
1) It doesn’t count as “passionate about harmony and voice leading” unless they understand Westergaardian theory well enough to contrast the two. Otherwise it just amounts to “passionate about music theory of some kind”.
2) It doesn’t have anything to do with jazz. If they’re right that harmony is the superior theory for jazz, then it’s the superior theory of music in general. Given the kind of theory we’re looking for (cf. Chapter 1 of ITT), different musical traditions should not have different theories. (Analogy: if you find that the laws of physics are different on different planets, you have the wrong idea about what “laws of physics” means.)
I don’t think that we disagree all that much. We both agree that there are some people who are able to learn structural rules implicitly without explicit instruction. We typically call these people “good at languages” or “good at music”. Our main disagreement therefore, is how large that set of people is. I happen to think that it is very large given that everyone learns the grammatical rules of their first language this way, and a fair number of polyglots learn their second language this way as well (Unless you deny the usefulness of Pimsleur like approaches). If I understand you correctly, you think that the group of people who are able to properly learn a language/music this way is smaller, because it often results in bad habits and poor inferences about the structure of the language. I would endorse this as well—grammatical texts are useful for refining your understanding of the structure of a language.
Because it is scary to learn to swim without arm floats even if there is someone else helping you (I think that phrase books are analogous to arm floats). Other than that I would agree with most of this. If you want secondary instruction in a language then you should probably use a grammar book and not a phrase book and I may return to Westergaard after I have taken some composition lessons. Also I would go one step further and say that not only is it possible to learn a language via immersion, it is necessary, and any other tools you may use to learn a language should help to support this goal.
Tentatively—grammatical texts have a complex relationship with language. They can be somewhat useful but still go astray because they’re for a different language, with the classic example being grammar based on Latin being used to occasionally force English out of its normal use.
I suspect the same happens when formal grammar is used to claim that casual and/or spoken English is wrong.
Modern descriptive grammars (like this one) aren’t anywhere near that bad.
Yes, accurate grammars are better than inaccurate grammars. But I think you are focusing too much on the negative effects and not noticing the positive effects. It is hard to notice people’s understanding of grammar except when they make a mistake or correct someone else, both of which are generally negative effects.
Americans are generally not taught English grammar, but often are taught a foreign language, including grammar. Huge numbers of them claim that studying the foreign grammar helped them understand English grammar. Of course, they know the grammar is foreign, so they don’t immediately impose it on English. But they start off knowing so little grammar that the overlap with the other language is already quite valuable, as are the abstractions involved.