I would have thought that my vigorous theoretical attacks on the venerated notions of “root progressions” and the like would have elicited vigorous theoretical defenses of those notions from those who do all that venerating. Alas, I have thus far been disappointed. Here’s a brief recap of some points that have been made by various interlocutors:
- The Texas Tech Theory Department noted that Roman numerals are easy to teach. (So are lots of bad theories; the headaches come only later, when one actually tries to apply them.)
- Scott Spiegelberg pointed out that Heinrich Schenker wrote a book called Harmony and even used Roman numerals in his magnum opus Free Composition. (The implication being, I guess, that Schenker must not have had any problem with the ideas of Rameau!)
- Matthew Guerrieri expressed a lack of interest in reexamining harmonic theory in view of its alleged “usefulness” (lucky for him that it didn’t stymie his own musical education for a decade), and the fact that, after all, no theory will ever be perfect (hence no need to bother replacing a bad theory with a better one!).
- Michael Monroe suggested that it might be unreasonable of me to be so emphatic and impractical in my approach (a fair criticism perhaps, but hardly a defense of harmonic theory).
- And, in the latest installment, Scott Spiegelberg, upon returning to the blogosphere, declines to address the specifics of my argument, being content merely to assert that harmony does, in fact, exist.
Spiegelberg’s “defense” of harmonic theory is particularly disappointing, because I actually went to the trouble of explaining in detail how it led Spiegelberg himself astray in his analysis of Chopin’s E-minor Prelude — and giving my own harmony-free analysis of the piece for comparison. Spiegelberg not only declines to challenge my analysis in favor of his own, he explicitly says that he doesn’t have a problem with my analysis! Why then does he bother trying to “defend the honor” of harmony, when he apparently agrees with me?
The answer, perhaps, is that he misunderstands what my “voice-leading analysis” (as he calls it) represents. It’s not merely a description of one aspect of the music (“voice-leading”); it’s a derivation sequence of the actual notes of the piece. Its purpose is to provide enough information to allow one to identify the specific “grammatical” function(s) of every single note in the score (i.e. whether it’s a passing tone, neighbor, borrowed tone, or what have you) — with the implication that reference to “harmony” is nowhere necessary for this purpose. If Spiegelberg disagrees with this conclusion, then he is obliged to tell us which notes in the score require the invocation of harmonic theory in order to be understood. Or, at the very least, he needs to explain how the virtues of a “harmonic” analysis (whatever those may be) are not provided by my analysis.
According to Spiegelberg, I am “attempting to move us back to pre-Rameau (1723) days where chords don’t exist, everything is counterpoint alone”. The implicit praise of Rameau aside, this is not accurate. It would be fairer to say that Spiegelberg and others are attempting to keep us back in pre-Westergaard (1975) days where notes weren’t properly accounted for.
Spiegelberg also claims that
Heinrich Schenker’s greatest realization was that the rules of counterpoint – set by 16th century compositional practice – had been altered by the evolution of tonality.
If that were true, then Schenker’s historical significance would be that of just another theorist with his own set of “exceptions” to the “rules of counterpoint”. Practically every theorist in Western history came to the “realization” that the “rules” that were set by his predecessors “had been altered” by the evolution of musical practice (whether or not they actually favored such “alterations” of “the rules”). Why else would they bother to keep writing new books?
No, indeed: Schenker’s most important contribution was the idea that complex musical structures can be explicitly and systematically understood as elaborations of simpler ones — all the way down to the simplest possible musical structures (the Ursatz, and finally the tonic triad itself).
If you study Schenker’s works chronologically, you’ll notice that the concept of harmonic progression becomes less and less fundamental as time goes on and his analyses become more refined. By the time you get to Free Composition, the only irreducible “progression” left is I-V-I; all the others have been reduced to “contrapuntal-melodic” or “voice-leading” events — in other words, operations on notes (see Figures 14-19 as well as §278; I-V-I itself was finally disposed of by Westergaard in section 8.2 of ITT). Of course, he had already said, in Masterwork II (“Elucidations”):
There are no other tonal spaces than those of 1-3, 3-5, 5-8. There is no other origin for passing-note progressions, or for melody. The first passing-note progression comprised by the Urlinie generates dissonance (second, fourth, seventh). Dissonance is transformed into consonance because only consonance, with its tonal spaces (as shown above), unlike dissonance, can promote new passing-note progressions and freshly burgeoning melodies. This comes about through prolongations in ever-renewing layers of voice-leading, through diminution, through motive, through melody in the narrower sense; but all of these hark back to the initial tonal space, and to the passing-note progressions comprised by the Urlinie. As the outcome [my emphasis -- J.C.] of all these transformations and unfoldings, there emerge the harmonic scale steps…
Now it’s true that if you don’t read Schenker very carefully, and in context, you might (depending on the passage) come away with the impression that he’s just as much a proponent of harmonic theory as everyone else. For instance, the very next sentence after the passage I just quoted is:
Despite the notes being sounded successively, the arpeggiation of a chord remains a harmonic phenomenon…
If, however, you’re reading this passage in the larger context of his analytical work, you’ll realize that all he really means is that the notes of the arpeggiation are to be thought of as sounding simultaneously at a deeper level of structure. The point here is that he’s contrasting the conceptual status of melodic skips (which create compound lines — i.e. those that are understood as generated by more than one line at a deeper level) with that of steps (which serve to define a single line). The defining notion of harmonic theory, namely that of “root progression”, is not involved here at all.
But we needn’t actually go into these kinds of subtleties in order to settle the question of which side of this debate Schenker would be on. For the purpose of dismissing once and for all the idea that Schenker believed in harmonic theory in the usual sense of the term, I submit for your consideration his essay “Rameau or Beethoven? Creeping Paralysis or Spiritual Potency in Music?” from Masterwork III (the one with the Eroica analysis). Here’s how it opens:
The histories of music all draw attention to Rameau’s Treatise on Harmony of 1722, extolling it as a major contribution to the field of music theory. They proclaim the new doctrine of fundamental bass and the inversions of a chord, of chordal construction in thirds and harmonic relations among those chords, as contained, virtually full-grown, in its pages.
What no music historian — or theorist, for that matter — has yet realized however is that even while J.S. Bach and Handel were still living, and before Mozart and Beethoven were even born, with this doctrine [i.e. "fundamental bass and the inversions of a chord, of chordal construction in thirds and harmonic relations among those chords" -- J.C.] the seeds of death had already been sown in [music] theory, and indirectly also in music composition!
Later, he continues:
In that he reduced all musical phenomena to fundamental basses and the progressions proper to them, Rameau detached what not even the layman can avoid seeing in front of his nose, namely the superimposition of notes, from the flux of horizontal voice-leading in which every superimposition has its origin [my emphasis -- J.C.]…
Still later,
What is more, even granting the significance of fundamental basses on his terms, Rameau really ought to have asked himself the question: Why is it that if generation of content (i.e. diminutions and their cohesion) is solely a matter of the vertical axis and its cadences — why, if this is so, do not these selfsame cadences left to their own devices give rise to a perpetuum mobile, so to speak, thereby turning the content into a perpetuum mobile too? What is it that offers resistance to such a perpetuum mobile? Where does the impetus come from ever to bring a composition to a close? If not from the vertical and its cadences, then does it not perhaps come from form? But where does the latter come from? The vertical and its cadences? Or is it not much more likely that it comes from the horizontal, and from the impetus at work there, the impetus of the law of the passing note? Instead of giving primacy to the horizontal, as the composing-out of the fundamental chord that yields content, and subordinating to it as a mere counterpoint the vertical, with its first arpeggiation of the fundamental chord and the derivatives of that, Rameau right at the outset shunned the horizontal in favor of the vertical, which offered his more lackluster French musical taste the enticing possibility of a cosier schematization. So it became Rameau’s sorry task in life to lure the musical ear away from voice-leading, instead of being the first to identify the latter and its laws.
And so on.
Let not my opponents in this debate dare cite Schenker as one of their own, whatever Roman numerals he may have written.
I’ll observe that, except for the francophobic outburst, Schenker got it exactly right in that latter paragraph. It is the “impetus of the law of the passing note” (which in other contexts he might have called “the necessity of composing out the triad via the Urlinie” or something similar), and not the alleged phenomenon of “harmonic pulls”, that differentiates “free composition” (i.e. real music) from counterpoint exercises (as Schenker conceived them).
To conclude, let me restate my challenge to the would-be defenders of Rameau and his successors. Here are my three main attacks on traditional harmonic theory (in order of increasing controversiality):
- It doesn’t explain anything that Westergaardian theory can’t explain (whereas Westergaardian theory explains quite a lot that harmony can’t explain).
- When both kinds of explanations are available, the Westergaardian explanation is always to be preferred to the harmonic explanation.
- The pedagogy of 20th century music would be greatly facilitated by adopting the Westergaardian viewpoint with respect to earlier music, because Westergaardian theory (or a slight modification thereof) is capable of unraveling the complex tonal structures that govern so-called “atonal” music. In contrast, harmonic theory has hidden these structures from us, because it does not permit a “tonal” analysis of music in which any collection of notes may be sounded simultaneously.
If 1. and 2. are true, that’s already enough to give harmonic theory the boot; 3. should just make us indignant that we had to put up with it for so long.
If you think that any of the above three claims are false, I challenge you to explain why. I’ll even help you out, by telling you what you would need to do:
- To refute 1., the weakest claim, your task will be the hardest: you will need to exhibit a passage of tonal music and show that Westergaardian theory is incapable of addressing some phenomenon in the passage that is successfully addressed by harmonic theory. Be prepared for two kinds of objections from me: (a) the phenomenon isn’t real (so you can’t just simply invoke harmonic theory in its own defense, and say something like: “the harmonic progression of this passage”); (b) you’re incorrectly characterizing the phenomenon (“what you think is Phenomenon X is in reality (Westergaardian) Phenomenon Y”).
- To refute 2. should in principle be a bit easier: all you need to do is compare and contrast a harmonic and a Westergaardian explanation of a passage or phenomenon and explain why the harmonic explanation is better.
- As for 3., I’d recommend holding off until I start posting some more analyses of this type (I’ve already done one on Schoenberg op. 19, no. 2). However, if you really feel strongly that this approach is destined from the start to be wrong, by all means, hit me with your best shot.
Well, there it is; now have at it!
August 31, 2007 at 12:27 pm |
god this is fun…
scott.. I believe the floor is yours…(if you dare)
August 31, 2007 at 11:47 pm |
Since you’ve asked so nicely, I’ll go through a point-by-point justification of my Chopin analysis in another post. In this comment, I’ve just got to say that you are the one reading Schenker through ideological goggles, not me. My take on Schenker is the same as that of David Beach, Matthew Brown, Felix Salzer, Steve Laitz, Neil Minturn, Charles Smith, etc. etc. etc. Yes, Schenker reduced all progressions down to I V I, and believed that the fundamental I V I was a linear expression of the tonic triad, which he called the Chord of Nature. But he was still starting with a chord, and observed this chord being stretched out through time by a series of transformations. These transformations include passing motions and neighbor motions that you include, but he also includes very important Harmonization and Tonicization transformations, which are vertical as much as horizontal. Right from the very beginning, the chord of nature is stretched out by an arpeggiation from 3 to one, which is then filled by a passing 2. Then, in all tonal pieces, this 2 is harmonized to become the fundamental V, creating the Ursatz I V I. As you say above, Schenker recognized the hierarchical nature of tonal music, though he didn’t invent this, there are several precursors in Viennese theory as well as Hauptmann’s ideosyncratic hierarchic of dialectic opposites in harmony. As we add more layers of transformations and diminutions, the piece becomes more complex, both melodically and harmonically. But Schenker would never have dreamed to divorce harmony from melody, which was his complaint of Rameau. He felt Rameau focused solely on harmony, ignoring voice-leading (a term of art in theory that is not the same as part-writing). What you are doing is focusing solely on voice-leading, ignoring harmony completely, so you are like Rameau in ignoring one important aspect of music. Read the quotes you cite above in with this interpretative lens, and see if you understand my perspective. I appreciated your voice leading analysis (and that is what any music theorist would call that) for revealing some interesting aspects of the Chopin. But it is not the complete answer.
September 1, 2007 at 7:33 am |
In this comment, I’ve just got to say that you are the one reading Schenker through ideological goggles, not me. My take on Schenker is the same as that of David Beach, Matthew Brown, Felix Salzer, Steve Laitz, Neil Minturn, Charles Smith, etc. etc. etc.
Since I’m not accusing you of “reading Schenker through ideological goggles”, and nor am I arguing from authority (as is apparently your intention in invoking such a list of names), I don’t see why this matters.
(When you sought to marginalize my position by calling it “odd”, I could have responded by saying I was only too happy to be grouped with such “oddballs” as C.P.E. Bach and Peter Westergaard. But I would prefer to stick to the actual theoretical substance.)
It’s true that my reading of Schenker is a post-Westegaardian one: for me the important question is how well Schenker understood (as compared to his predecessors) the principles of what would now be called Westergaardian theory (which I consider to be the best theory of tonal music yet proposed) — the answer being that he had a very well-developed understanding of these principles (despite his failure to completely eliminate the idea of harmonic progression). If you want to call this an “ideology”, that’s fine, so long as you realize that it’s an ideology that I am entirely prepared to argue for.
Yes, Schenker reduced all progressions down to I V I, and believed that the fundamental I V I was a linear expression of the tonic triad, which he called the Chord of Nature. But he was still starting with a chord, and observed this chord being stretched out through time by a series of transformations.
That’s just as true for Westergaard (and me) as it is for Schenker. It’s no concession to harmonic theory at all to speak of a single chord being elaborated over a span of time. What harmonic theory attempts to do is to explain successions of chords by reference to abstract “laws of progression” through the space of pitch class sets, as opposed to decomposing the chords into their constituent notes and explaining the individual functions of the latter. Despite what Schenker says, actually, it’s not really a question of the “horizontal” versus the “vertical”; it’s a question of a refined explanation (of the both the horizontal and vertical dimensions) versus a crude one.
These transformations include passing motions and neighbor motions that you include, but he also includes very important Harmonization and Tonicization transformations, which are vertical as much as horizontal.
Again, see above. “Tonicization” is a term that is explicitly used in ITT. As for “Harmonization”, the beauty of Westergaardian theory is that there is no need for such an operation, because it can be completely reduced to conceptually simpler operations (principally “borrowing”) involving concrete notes.
Right from the very beginning, the chord of nature is stretched out by an arpeggiation from 3 to one, which is then filled by a passing 2. Then, in all tonal pieces, this 2 is harmonized to become the fundamental V, creating the Ursatz I V I.
Here is how this process may be explained in Westergaardian terms: There are several underlying lines, each sounding a pitch the tonic triad, which we shall use to generate two textural voices, soprano and bass. The soprano arpeggiates (a form of borrowing) 3 and 1 over the 1 of the bass. Then, the 3 and 1 are connected via step motion. Finally, the bass arpeggiates (borrows) a 5 to coincide with the soprano’s 2, creating room for another triad (the dominant), which itself may be similarly elaborated.
Do you not agree that this is a clear, simple, specific, and elegant explanation of the Ursatz phenomenon? (Is it even fundamentally different from Schenker’s?)
But Schenker would never have dreamed to divorce harmony from melody, which was his complaint of Rameau. He felt Rameau focused solely on harmony, ignoring voice-leading
There’s no need to paraphrase Schenker’s complaint about Rameau; you can find the direct quotes above, which are pretty clear on the fact that he thought Rameau’s theory was fundamentally wrongheaded, not just incomplete. Also compare C.P.E. Bach’s remark to Kirnberger (quoted at the beginning of this very essay by Schenker): “You may state publicly that my principles, and those of my late father, are antithetical to Rameau’s.” Notice the strong wording: he doesn’t say that Rameau fails to capture the whole story; he says that his principles are antithetical to those of Rameau.
(a term of art in theory that is not the same as part-writing).
I don’t know what the point of this parenthetical comment could be, other than to suggest (implausibly) that I’m unfamiliar with the term “voice-leading”. However, since you make a contrast with part-writing, I’ll take this opportunity to remind you of Schenker’s complaints in Harmony about part-writing exercises in other harmony books, which he views as exercises in voice-leading that do not belong in a text on “harmony” (the abstract theory of scale-steps and their relations, a theory whose role he had already begun to restrict in Harmony itself).
What you are doing is focusing solely on voice-leading, ignoring harmony completely, so you are like Rameau in ignoring one important aspect of music.
What aspect are you talking about? What phenomenon did I fail to capture in my analysis of the Chopin? (You can’t just say “harmony” — that would of course be circular.)
Read the quotes you cite above in with this interpretative lens, and see if you understand my perspective.
I think I do understand your perspective (you can of course correct me if necessary): you don’t read Schenker to see how close he comes to eliminating harmony, because you’re not interested in eliminating harmony; it simply doesn’t bother you that you are invoking concepts that are logically superfluous — you’re not looking for the most parsimonious theory you can find. Like Matthew, you see no need to reexamine your theoretical inventory unless it causes some obvious practical difficulty.
Assuming this is accurate, I would say two things:
(1) Theoretical refinement may not be your most pressing concern (because you already “get” music), but a theory that is too crude will only allow you to communicate with people who already know how to read beyond your literal words. Some people may be able to get by on harmonic language (because they already have enough intuition to understand the concrete musical phenomena being talked about), but others (like me) may interpret your Roman numerals to literally mean this, if they don’t know any better.
(2) Harmonic theory does cause practical difficulties, as I have been arguing. I am inclined to suspect that the only people to whom these difficulites are not obvious are those who are unaware of (or insufficiently familiar with) alternatives to harmonic theory.
I appreciated your voice leading analysis (and that is what any music theorist would call that)
So what? It may be a voice-leading analysis, but it’s also more than that (unless you’re willing to identify “voice-leading analysis” with “derivation sequence of the notes”).
for revealing some interesting aspects of the Chopin. But it is not the complete answer.
Again, what’s missing?
September 1, 2007 at 4:07 pm |
James, I’ve been trying to understand your perspective, but don’t believe you have been trying to understand mine. This has made the discussion somewhat frustrating from my perspective. Your attempt at paraphrasing my perspective is not accurate, as I don’t believe Schenker is close to eliminating harmony at all. He was reintegrating vertical and horizontal aspects, which can be thought of as harmony and linear motion, though it is more complex than that. Clearly you disagree. And I definitely do not agree that harmony is logically superfluous. You can keep saying harmony is unnecessary, but it goes completely against the way I hear music. I can accept that to you harmony is unimportant. Can you accept that to me harmony is very important?
As for “voice leading analysis”, yes, it does include the concept of hierarchical generation, since it is an aspect or offshoot of Schenkerian analysis depending on the usage. Again, I’ve been trying to learn more about the nuances of Westergaardian theory, and have been trying to be gracious in acknowledging positive aspects of that theory. But you keep describing ludicrous versions of harmonic analysis that I have not been advocating and in fact have been working hard to correct in your comments and on my own blog. If you aren’t willing to read my attempts with an open mind, and continue to use only your own parody definition of harmonic theory, further communication will become too frustrating on my part to continue.
September 1, 2007 at 10:33 pm |
I just think Scott’s analyses are better than yours. By invoking harmony, Scott was able to discuss the expectations and denials we experience when listening to that Chopin Prelude. Sure, your “sketches” model the music, but they don’t lead to any interesting observations about it. Neither “How to make a Chopin prelude or “Read it and weep.” said anything worth contemplating about those wonderful pieces.
I personally believe that theories about music are only as good as the analyses they lead to. Unfortunately, your analyses fall short and have not convinced me that “Westergaardian theory” is any better than they theories we already have.
September 2, 2007 at 2:57 am |
James, I can only say that “the theory of roots and progressions. The latter is what “harmony” has meant since Rameau” is not my definition of harmony. Nor is “harmonic theory attempts to explain successions of sonorities by reference to abstract ‘laws of progression’ through the space of pitch-class sets.” Schenkerian theory is a harmonic theory. Riemannian theory is a harmonic theory. Hauptmann’s dialectic theory is a harmonic theory. Schechter, Weber, Crotch, Schoenberg, all of these people created visions of how sonorities relate to each other in a way that creates tonality. And that is my definition of harmony: how vertical sonorities relate to each other to create a sense of tonality. Linear motion is a crucial element of these relationships, as Schenker wisely showed. Thus linear prolongations is part of harmonic theory. Perhaps where you and I disagree is on how to define harmony. Because I don’t recognize your definitions as the harmonic theory I learned or that I teach.
September 2, 2007 at 3:32 am |
I have to second Scott in saying that you seem to argue with what you think we say rather than what we are actually saying. At no time did I ever express “a lack of interest in reexamining harmonic theory”. What I did express was the opinion that the idea of harmony and the traditional way of analyzing harmony remains useful. And no, it didn’t set back my education—perhaps because I don’t confuse theoretical analysis with the actual making of music. I respect theory that is aware that analysis is only a snapshot of the music, with the image loss that implies; theorists I find rewarding and vital will choose and tailor their methods to the facet of the music they’re trying to illuminate, without the implication that all other methods are automatically superseded in any other context.
It seems to me that you’re trying to come up with an objectivist way to explain musical practice—one method that will delineate the actual truth of how music is created and experienced. Problem is, music is a perspectivist art form. You’ve said that theory should enable one to recreate how a composer could have come up with the notes he or she did. Every composer I know is a perspectivist: they will use any and every method, theory, system, what have you, that they can get their hands on if they think it will get them closer to the musical idea they’re after, because the core substance of music is fundamentally beyond logical analysis—when something can only be apprehended obliquely, it’s best to come at it from as many angles as possible, and respect the view from each. A plurality of theoretical approaches, I think, will get you closer to the whole effect of the music than a single scheme.
September 2, 2007 at 3:53 am |
This whole debate is starting to parallel a Shaolin Kungfu (Scott) and Ninja (James) recent argument in the press. For a more complete description of what I mean, please click here.
September 2, 2007 at 5:48 am |
To Scott and Matthew, I think this debate might seem a little less abstract if you could provide some concrete example of a musical phenomenon that can be better explained through the lens of traditional harmonic theory than through the methods James is using. The harmonic theory James is attacking doesn’t seem to be the idea that vertical sonorities create a sense of tonality, but rather the attempt to catalog those sonorities and assign them specific functions via the roman numeral system.
When I was a student I was often frustrated by being asked to explain progressions that had no obvious chordal progression recognized by traditional theory. Those passages were often explained away by stating that the notes were justified by the voice leading. What James seems to be suggesting is that the same thing is true of passages that can also be neatly described in roman numeral progressions, so why bother with the traditional classification theory at all? That seems to be a good question to me. Until hearing about Westergaard I would have assumed the answer was that we had no convenient way to notate such a thing.
Now Scott and Matthew both seem convinced that a system which views vertical sonorities as the product of voice leading is missing something significant about the way music is understood and created. They both know more than I about the subject, so I’m willing to believe that’s true, but I’d still like to know just what that something is. I find it very plausible that all western music is based on voice leading and that chords are the incidental product of those rules. It seems to track much more closely with the way I hear music. Is there something special about those combinations of notes (admittedly vast) that are recognized by traditional theory that makes one hear those notes differently?
September 2, 2007 at 5:48 am |
Matthew writes:
Every composer I know is a perspectivist: they will use any and every method, theory, system, what have you, that they can get their hands on if they think it will get them closer to the musical idea they’re after, because the core substance of music is fundamentally beyond logical analysis—when something can only be apprehended obliquely, it’s best to come at it from as many angles as possible, and respect the view from each.. A plurality of theoretical approaches, I think, will get you closer to the whole effect of the music than a single scheme.
…and sometimes none at all, as I know plenty of good well respected and extremely educated composers that try to avoid theoretical systems like the plague (this one not included). If theoretical systems are used by a composer, it’s not just to generate an affect from the start. It can sometimes be used to analyze, justtify, and possilbly correct something that we have found either by instinct or by accident. In some sense, it can act on a psychological level to help keep us concentrated and justiified at our desk, instead of relying on our non-linear or unpredictable moods which we sometimes use to marginize our work depending on the moon phase and whether we ate Thai that day.
However, like all “belief” systems, music theory has its own internal traps and cults. Ultimately, the composer picks his religious poisons and observes his faith the best way he can – by observing and trusting in himself.
September 2, 2007 at 6:30 am |
Eric:
I don’t know if it makes someone hear it differently—everyone hears differently. (I will say that my own reactions to music are as much keyed by certain striking vertical sonorities as by the paths that took them there.)
Here’s one way I think about vertical sonorities: often times, the same ones turn up in similar situations so often that to deny that the composer regarded that collection of notes to be as much a vertical entity as a product of voice-leading seems to be missing the forest for the trees. When the vast majority of works written in what for better or worse we’ll call the Western tonal tradition contain one vertical sonority followed by another such that, if you stack them both up in thirds, the lowest notes of each chord are a fifth away from each other, I think that’s a significant enough commonality that to call it V-I (or dominant-tonic, or some other term of your choice) is a meaningful and useful abstraction of a certain musical practice. Not every one of those cadences are going to use the same voice leading—not every one is going to arrive there via the same path. But there’s an underlying similarity to the events that’s worth pointing out.
James is no doubt going to self-righteously rant on that Westergaardian theory is more detailed (maybe), closer to how the composer thinks (probably not), etc., etc. But if I point out to someone that at a particular place in a particular piece that the composer is trying to get us to hear a new pitch as a stable point of orientation, I think that saying that he or she does it by means of a V-I cadence is a pretty efficient way of communicating something essential about the compositional technique. And yes, it’s at least five syllables more efficient than “3-2-1 over 5-1″ or any description of borrowing from the bass and neighbor tones and the like.
ComposerBastard: Absolutely true. I’ll should add another way composers use theory—to try and figure out how to recreate something they’ve heard. That one, I tend to go through a host of methods—even if the first one seems to be apt.
September 2, 2007 at 2:08 am |
Scott, I think it’s a bit unfair to accuse me of not trying to understand your perspective. I may have misunderstood it — but I did specifically invite you to correct my misunderstanding, after all.
[Schenker] was reintegrating vertical and horizontal aspects, which can be thought of as harmony and linear motion, though it is more complex than that. Clearly you disagree
Why do you assume that I disagree? Is it not specifically in his reintegration of vertical and horizontal aspects into a unified conception that he departs from the tradition of Rameau?
And I definitely do not agree that harmony is logically superfluous. You can keep saying harmony is unnecessary, but it goes completely against the way I hear music. I can accept that to you harmony is unimportant. Can you accept that to me harmony is very important?
Please note that I did not say harmony was unimportant; I said it was logically superfluous. This should be a signal that I don’t believe this debate is actually about different ways of hearing music; it’s about different choices of theoretical vocabulary used to express one’s hearing of music. The point is that so-called “harmonic” phenomena admit a much better description in terms of Schenkerian/Westergaardian operations on basic tonal structures.
It is at least slightly ironic that you have accused me of attacking a straw man, because you have also repeatedly suggested that I am discounting the importance of the vertical dimension of music (something that people invariably do when I talk about harmonic theory being a bad theory — talk about frustration!). On the contrary: what distinguishes Schenker/Westergaard from Rameau is precisely that the horizontal and vertical structures are treated simultaneously, in an integrated framework. Before Schenker, people hadn’t realized that it was possible to explain so much of tonal music in terms of elaborations of the structures of strict counterpoint; they thought that many tonal phenomena were irreducibly “harmonic”. Schenker never completely gave up this idea; his Ursatz still contains the Stufengang I-V-I. However, look at what he accomplished in terms of eliminating harmonic explanations at the local level! (Even his Harmony is as much about what doesn’t constitute a Stufe as it is about what does.) All he had to do was go just a bit further to make harmony completely redundant.
To see what I’m talking about, it may help to contrast Schenker’s conception of species counterpoint with Westergaard’s. For Schenker, counterpoint is the “pure theory of voice-leading”; the effects of Stufen are not considered at all. (This is how you accuse me of hearing real music, is it not?) For Westergaard, however, so-called Stufen-effects are built into the rules of counterpoint: his formulation of species ensures that a species composition will be understood as an elaboration of the tonic triad — that it will be subject to “the impetus of the law of the passing note”, as Schenker put it. He does this by basing species compositions on the Ursatz; in effect, what used to be called I-V-I is now a basic part of contrapuntal theory! Westergaard thus integrates the vertical and horizontal to an even greater extent than Schenker. If you combine Westergaard’s contrapuntal theory with Schenker’s reduction of large- and small-scale harmonic progressions to voice-leading phenomena, you see (as Westergaard evidently did — hence ITT) that the concept of “harmonic progression” is simply not needed to explain anything — vertical or horizontal — in tonal music!
Again, I’ve been trying to learn more about the nuances of Westergaardian theory, and have been trying to be gracious in acknowledging positive aspects of that theory. But you keep describing ludicrous versions of harmonic analysis that I have not been advocating and in fact have been working hard to correct in your comments and on my own blog.
My passion should not be mistaken for a lack of graciousness; I have tried very consciously to mimic (at least approximately) the tone of my opponents, and not to be too unfair.
It is, however, frustrating to be accused over and over of neglecting the vertical dimension when what I am actually attacking is the theory of roots and progressions. The latter is what “harmony” has meant since Rameau; I don’t understand why you seem to consider that an absurd caricature. Do you actually disagree that “harmonic theory attempts to explain successions of sonorities by reference to abstract ‘laws of progression’ through the space of pitch-class sets?”
More generally, it should not be assumed that just because one criticizes a certain theory, one therefore is not interested in the phenomena that the theory purports to address. When I say that harmony doesn’t exist, it’s as if I said that phlogiston doesn’t exist — which doesn’t mean I think there’s no such thing as combustion.
September 2, 2007 at 1:29 pm |
Scott: Maybe under your definition, Westergaardian theory is a harmonic theory too!
Matthew:
It seems to me that you’re trying to come up with an objectivist way to explain musical practice—one method that will delineate the actual truth of how music is created and experienced.
No, that’s a misunderstanding. All I’m trying to do is raise awareness of Westergaardian theory as an alternative to harmonic theory, and make the case for preferring the former over the latter. I have no “absolute” committment to Westergaardian theory; it just happens to come much closer to the way I personally think about music than “traditional” theory does.
Here’s one way I think about vertical sonorities: often times, the same ones turn up in similar situations so often that to deny that the composer regarded that collection of notes to be as much a vertical entity as a product of voice-leading seems to be missing the forest for the trees.
You might as well say that “some times a particular melodic motive turns up in similar situations so often that to deny that the composer regarded that collection of notes to be as much a thematic entity as a product of tonal functions seems to be missing the forest for the trees”.
It may be perfectly true, but it simply doesn’t fly as an argument against using Westergaard as your tonal theory text.
When the vast majority of works written in what for better or worse we’ll call the Western tonal tradition contain one vertical sonority followed by another such that, if you stack them both up in thirds, the lowest notes of each chord are a fifth away from each other, I think that’s a significant enough commonality that to call it V-I (or dominant-tonic, or some other term of your choice)
You know, Westergaard does use the terms dominant and tonic (he even uses Roman numerals for diatonic scale degrees, thought not “chords”, of course). So if you want to talk about “V-I” as a shorthand for certain common processes, be my guest. (I’d bet Westergaard himself probably does this.) But let’s not pretend for a moment that that is how most people actually use “V-I”. They use it as a theoretical idea in itself: notes are to be understood as “part of a V chord”; G-B-D is followed by C-E-G because it’s a V-I, etc.
Even if people want to continue using expressions like “V-I”, they should be aware of the explanation for why that phenomenon exists. I wouldn’t have a problem with Roman numerals if everybody had read Westergaard and realized they were theoretically superfluous.
James is no doubt going to self-righteously rant on
Since when does passionate advocacy of a set of ideas equate to self-righteousness?
that Westergaardian theory is more detailed (maybe),
“Refined” would be the appropriate term.
closer to how the composer thinks (probably not),
Says who? It sure is a lot closer to how I think — which is what I really care about in the first place.
But if I point out to someone that at a particular place in a particular piece that the composer is trying to get us to hear a new pitch as a stable point of orientation, I think that saying that he or she does it by means of a V-I cadence is a pretty efficient way of communicating something essential about the compositional technique.
How about just saying that the pitch in question is tonicized? (ITT, sec. 8.5) That’s the real point anyway.
And yes, it’s at least five syllables more efficient than “3-2-1 over 5-1″ or any description of borrowing from the bass and neighbor tones and the like.
“Shorter” is not the same as “more efficient”. You also have to take into account the amount of information being conveyed. “V-I” may be slightly shorter than “2-1 over 5-1″, but the latter does such a better job of pinpointing the relevant phenomenon that it’s more than worth the trade-off.
CB:
However, like all “belief” systems, music theory has its own internal traps and cults. Ultimately, the composer picks his religious poisons and observes his faith the best way he can – by observing and trusting in himself.
This is a good point. Dogma isn’t necessarily bad so long as it’s productive. My “religious adherence” to (my own verison of) Westergaardian theory, in addition to providing me with a efficient and highly intuitive way to analyze “tonal” (i.e. old) music, and unlocking the gates of “atonal” (i.e. more recent) music, has also proven to be more creatively stimulating than pretty much any idea or way of thinking I have ever been exposed to.
September 2, 2007 at 2:15 pm |
Matthew, James:
Dogma isn’t necessarily bad so long as it’s productive.
I should also expand this just a wee bit by saying pre-factor or post-facto theoretics can indeed cripple a composers creative thoughts and efforts by intimidation and utilitarianism – regardless of their own level of mastery of the theoretical knowledge they might be exposed. There are two polarric dangers – avoiding it completely; or following it religiously.
Some composers avoid it because of their bad experiences, because of the mountain of knowledge in the field, or because they don’t want to sound like composers X and Y, or have any human element in their work – theoretical thought being one of them. Some composers spend their time making sure every note has justification to some qualitatve or quantitative law, and checking this over and over again.
In the first case, the composer abandons his work because he has no structure or psycho-intellectiual investment,
In the second case the composer abandons his work because it sounds lderivitive, is TOO structured, or lacks emotional investment related to the schemas he remembers or the life experience he has followed.
September 2, 2007 at 4:24 pm |
Brian Moseley:
I just think Scott’s analyses are better than yours. By invoking harmony, Scott was able to discuss the expectations and denials we experience when listening to that Chopin Prelude. Sure, your “sketches” model the music, but they don’t lead to any interesting observations about it. Neither “How to make a Chopin prelude or “Read it and weep.” said anything worth contemplating about those wonderful pieces.
Unfortunately, your analyses fall short and have not convinced me that “Westergaardian theory” is any better than they theories we already have.
First of all, let’s get one thing straight: Westergaardian theory is a theory that “we already have”: we’ve had it since 1975!
Secondly: you may not be interested in the same analytical questions that I am, but that doesn’t mean that my analyses don’t reveal “anything worth contemplating”. Anything? That’s a pretty strong statement, as is the notion that they “don’t lead to any interesting observations”. I mean, as hard as I have been on Scott, at least I acknowledged that he had “some interesting and worthwhile things to say” about the Chopin prelude. As for the Schoenberg, if you don’t consider the idea of an “atonal” piece turning out to be in the key of G major an “interesting observation” that would be “worth contemplating”, then we are living in different universes.
Now, you make a good point about listener expectations; perhaps I’ll try to address that more specifically in future analyses. But rest assured that Westergaardian theory is eminently capable of addressing questions of listener expectation, and indeed is highly preoccupied with doing so, as you would find out by reading chapters 7 and 8 of ITT.
In general, the purpose of my analyses has been to reveal the specific structural function of each note. (Are you not interested in this?) In the case of the Chopin post, I was also concerned with showing how harmonic theory gets in the way of understanding said structural functions, which is why I “went after” Scott’s analysis. You may not be interested in these topics, but I would at least urge you to consider the possibilty that revealing structural functions of notes has a lot to do with listener expectations. For example, showing a Schenkerian fundamental line implies that the arrival on the tonic represents the fulfillment of a certain expectation set up at the beginning. In the Chopin prelude, a lot of tension is created by delaying certain passing motions — something which can be clearly seen in the “sketches” I provided. (And yes, I think that to “sketch” a work in this manner is to reveal important information about it. If I were faced with a complex score I had never seen before, I would certainly love to have access to these sorts of “sketches”.)
May 29, 2008 at 11:32 am |
[...] by the way, how this undermines Scott Spiegelberg’s claim that his take on Schenker is the same as Salzer’s, since Spiegelberg very clearly does like [...]