Friday, August 31, 2007

Chopin redux

The gauntlet has been thrown, and I shall strive to mix metaphors with it until the dead horse is whipped. First I will restate a point from my old analysis in italics, James Cook's response to it in plain text, and my rejoinder in bold, in fine debate format.

1. I said the prelude begins with a tonic triad which is in inversion, thus unstable.

JC - [I'll ignore the straw man version of harmonic theory James describes first. I made none of the claims he states about composer intent, thus I do not have to defend them.] "I think that, instead of saying it begins with a “tonic chord”, we ought rather to say that it begins with a B in the top voice, which is counterpointed by a G in the bass, along with a couple of inner voices starting on B and E. Each of these notes then sets off on a journey of its own through some region of diatonic space — in the process of which it elaborates (or “composes-out”) some particular gesture that the composer wished to convey."

SS - James' statement leaves out the idea that we have begun with the tonic note that will be the eventual goal of this piece. I find this to be an important point, that we as listeners have started in the place to which we shall return. We know it is the tonic triad, since Chopin starts with a conventional dominant pickup, identifying the melodic B as the dominant of the E minor triad. James' analysis also misses the idea that we begin with an uneasy sonority, since the triad is not in root position. Thus we listeners expect something to happen, even as the B sustains and the underlying chord pulses along. Plus James' statement suggests there is no relationship between each of the four voices, since they each has a journey of their own. Nay, in tonal music the voices journey together, even when they take different paths.

2. SS - "The next chord is the dominant chord, though with a suspension: the E refuses to let go."

JC - "Except for the “next chord” business, this is very well put."

SS - How can one have a suspension if there is no chord? The E is in dissonance to the other voices only if one considers harmonic relationships. If you are thinking only in contrapuntal interval relationships, then there is also a dissonance between the A and the B, but James doesn't state this.

3. SS - "When this suspension does resolve, Chopin "misspells" the chord with an Eb instead of a D#."

JC - He actually says nothing about this verbally. His graphs also don't say anything about the unusual nature of this Eb.

SS - Any musician would find the Eb odd, since it is not in the diatonic space of E minor. It sounds fine, since it is enharmonically the same as D#, and thus fits with the expected dominant chord. James' analysis does not show this at all.

4. SS - "The melody turns this dominant chord into a diminished seventh chord,"

JC - "To say that “the melody turns this dominant chord into a diminished seventh chord” is an extremely awkward way of saying “the B moves up to C”; but it also carries the suggestion that there is a sort of “conspiracy” among the voices — as if they said, “let’s now form a diminished seventh chord!”. Now, conspiracies of that sort can certainly happen in music, but this is not one of those occasions. Here, it seems, we simply have a note moving to its upper neighbor, without any concern whatsoever for what its fellow notes are doing at the same moment. (Just as in real life, it takes quite a lot of work to establish a musical conspiracy.)"

SS - James doesn't state his criteria for creating a conspiracy, much less show why my example is not one. My justifications are (a) the way Chopin chooses the notes spells a fully diminished seventh chord; (b) fully diminished seventh chords are very recognizable sonorities; (c) it is an expected sonority in the E minor pantheon, being an inversion of the viio7; (d) it is an expected chord to follow the V65 chord, since both are dominant functions and composers throughout the 17th, 18th and 19th centuries have had V7 chords move to vii07 chords; (e) it explains how the next chord makes sense, as it is quite unexpected in E minor diatonic spaces. And I said that it was a melodic motion, since it repeats the neighboring figure from the first measure. What is interesting here is that in the first three measures the melody is exactly the same, but the harmonic rhythm changes - measure 1 is one chord, measure 2 is two chords, and measure 3 is three chords. James' analysis misses this, probably since he doesn't have any truck for chords. But the speeding up of harmonic rhythm is something that Schenker appreciated, and an interesting way for Chopin to create variety while keeping the same melody and surface rhythm.

5. SS - "diminished seventh chord resolves as a common-tone chord to a secondary French augmented sixth chord!"

JC - "Well, a “French” augmented sixth chord is the kind that has scale degree 2 in it; thus in E minor we would be talking about pitch-classes C, A# (the augmented sixth), E, and F#. However, our chord is a secondary chord, meaning evidently that it is a French sixth when viewed from the perspective of some other key. Now, the pitch-class content of the sonority I presume Spiegelberg is talking about (namely the one on the first half-note of m.3, immediately following the “diminished seventh chord”) is F, A, Eb, B; if we thought of the Eb as D#, this would spell a French sixth in A minor. What Spiegelberg is claiming, then, is that, at least for the first half-note of m.3, we are locally in A minor — and in particular the Eb is a raised scale degree 4! Needless to say, I have absolutely no idea how one could arrive at such an analysis: as far as I am concerned (see the graphs above), there is nothing in the entire Prelude (least of all in the first three measures) that requires one to think in terms of any key other than E minor — not so much as a single secondary dominant, let alone a secondary French sixth!"

SS - And this is exactly where James' analysis misses something wonderful. First of all, the secondary French augmented sixth could resolve to an E minor triad, basically like a tritone substitution in jazz theory. This progression is somewhat rare, but found in Tchaikovsky and other High Romantic composers' works. However, we don't know if that will be, because the common-tone resolution of the viio7 from measure 2 has cast everything in doubt. By the way, James doesn't comment on this point, but a common-tone resolution of a diminished seventh chord holds one note steady (two, A and Eb, in this case) and moves the other voices by step, usually downward. This is opposite of the normal resolution of a fully-diminished seventh chord, where one note resolves upward by half-step, the local leading-tone to tonic resolution. In this case, we could be modulating to A minor, or staying in E minor, it just isn't known at this point. But the French Augmented Sixth chord is very unusual and therefore highly evocative.

6. SS - "By this point, only the third measure, the listener is quite confused as to where tonic is, even though the chords progress by very small steps with many common tones."

JC - "Not only am I not confused about where the tonic is, I don’t even see how one could be confused about that in this context. What note besides E is even a candidate for tonic status?"

SS - Play the first 2.5 measures to some listeners, stop right there and ask them to sing tonic. I guarantee that you will get at least two different answers, as long as your sample size is above 2. You ask what harmonic analysis has that Westergaardian analysis doesn't, and this is one of those things. Yes, you can explain abstractly how the voices progress by logical melodic motions, but it misses the tensions built up by the relationships of the voices to each other.

7. SS - "The augmented-sixth chord does not resolve correctly, instead shifting to a chord progression that fits best in the key of A minor: iiø43 - viio42 - V7. By half-steps the dominant chord gets transformed, leading us back to the key of E minor. A minor is hinted at several times, and the final cadence of each phrase (there are only two phrases in the 25-measure prelude) includes an oscillation between the dominant B7 chord and the A minor triad."

JC - [skipping the translation, though ø is not redundant as modal mixture is quite common in minor tonalities, plus the quality is part of my argument for the implied tonality.] "Well, we do indeed find an instance of that particular (partially-ordered-by-register-pitch-class-set)-sequence (for that is what a “chord progression” is) in mm. 3-4 — provided, of course, that we don’t take into account the C on the last quarter of m.3! (Remember that the presence of an exactly corresponding C in m.2 compelled Spiegelberg to posit a “diminished seventh chord” for that timespan — what’s the difference here?) The question, however, is whether this “progression” has the analytical significance that Spiegelberg is attributing to it. I don’t see any good argument for this at all. A “V7 chord”, for example, is by definition composed of scale degrees 5, 7, 2 and 4 — but is the E in the bass in m.4 a scale degree 5? Is the G# a scale degree 7? If so, when exactly did E cease to be scale degree 1, and why?"

SS - First, sometimes a melody note is a chord tone, sometimes it is not. Even in Westergaardian analysis one would add notes at different stages (I presume, it is certainly the case with Schenkerian analysis). In this case the C in measure 3 is a dissonance just as the C in measure 1 is, whereas the C in measure 2 is not. If Westergaardian analysis cannot make that distinction, then that is something else about tonal music that that theory cannot explain. Second, a V7 is not just scale degrees 5, 7 , 2, and 4, it is also a sonority of the major minor seventh chord – a major triad with a minor seventh added – which is a highly distinctive sonority. Play the first chord in measure 4 by itself and ask your sample of listeners to sing tonic, they will all sing A. Play the beginning of the Prelude through to the beginning of m. 4 and ask listeners to sing tonic, there may be two different answers. I certainly can hear both E and A as possibilities, hence my original claim. I also allow that there are people who are adamant in hearing E alone as tonic, such as James. In theory classes I often talk of flexible versus steadfast listeners, with no intent of casting aspersions on either type. Steadfast listeners want to stick with a given tonic, meter, or other established pattern despite potential disruptions. Flexible listeners float with any new direction in meter, tonality, or pattern. As an example, a steadfast listener is more likely to hear chromaticism as tonicization, whereas a flexible listener is more likely to hear it as modulation. I've practiced hearing in both manners, so as to better appreciate the positions of fellow performers and my students, whatever type of listener they are. James is clearly a steadfast listener for this prelude (I have no idea what type he is for others, I find people often change with different pieces), not giving up the idea of E as tonic regardless of Eb's, F naturals, Bb's, and G#'s. When I hear the combination of a distinctive half-diminished seventh chord* with a fully diminished seventh chord and a dominant seventh chord, with the roots following the tonally powerful pattern of descending thirds, this pulls me to a new tonic, or at least a tonicization of A at very local levels. In Westergaardian terms, the notes of measures 3 to 4.2 fit the A minor diatonic collection rather than the E minor diatonic collection.

8. SS - "By half-steps the dominant chord gets transformed, leading us back to the key of E minor. A minor is hinted at several times, and the final cadence of eac phrase (there are only two phrases in the 25-measure prelude) includes an oscillation between the dominant B7 chord and the A minor triad."

JC - "Spiegelberg and I agree that there are exactly two “phrases” in the prelude (although this is something of a contradiction on his part, since he has analyzed mm. 3-4 as a cadence in A minor!). However, to speak of “an oscillation between the dominant B7 chord and the A minor triad” is once again misleading, even if literally accurate. Yes, we do get the pitch-class set C-E-A occurring in measures 10 and 11; but this is the purely accidental result of simultaneous neighbor-note motions in the two lowest voices — a very mild conspiracy, in which the A is not involved at all (it just happens to be there, like an innocent bystander). In fact, far from being the “root” of an A-minor triad, this A is actually a dissonant 7th, as you will see by referring to Stage 2(b) of the above analysis (second page). Needless to say, I do not understand how this phenomenon could possibly be said to reinforce any sense of A minor, which is what Spiegelberg implies."

SS - I apologize for have the misleading "final" before the word "cadence" in my analysis, as it implies there is more than one cadence per phrase. That was not my intent, as I firmly believe each cadence ends a phrase, and firmly believe this piece has only two phrases, thus only two cadences. I did not, however, analyze mm. 3-4 as a cadence in A minor. I said that the progression makes sense in A minor, but did not say that it cadences there. Instead, I pointed out that the V7, which is far too unsettled both as a sonority and by harmonic rhythm standards to be a half cadence, gets transformed through linear motion (which I would have thought James would appreciate) back to E minor tonality. The dissolution of the G# to G natural leads the way, followed by many other fascinating progressions through m. 13. I admit that many of them are best understood by linear motion alone, rather than harmonic root motion, hence my original statement. As for being misleading while being accurate, I would apologize if I understood how that was possible. How could A not be involved in the progressions of m. 10-11, when it is in the melodic line, accented by a grace note in m. 11? As for claiming that it is a dissonant 7th, that is a reasonable interpretation at a midground level, but not at the surface level I was wallowing in. (I'm using Schenkerian terms here, I trust they equate reasonably to Westergaardian Stage 2 versus Stage 9+). Play beat four of measure 10 or measure 11 and there is no dissonance, but indeed a "literally accurate" A minor triad. I do not deny that this A minor triad is functioning as a iv6 that prolongs the dominant and the lovely Phrygian half cadence. But my statement of oscillation does not contradict this function either. What I was trying to imply was the neat design that Chopin created, whereby the A minor tonality that was implied in mm. 3-4 relates to the A minor triad in mm. 9-11 even though E minor is the governing tonality of the whole phrase.

9. SS - "This prelude is all about the tensions between the melody and the harmony, with the harmony clearly winning. But what is so striking is that the exotic harmonies are created by simple means, small little movements of the left hand, and this slow harmonic rhythm creates such emotional intensity."

JC - "Well, since I don’t believe there is such a thing as “harmony” (in the traditional sense), obviously I can’t agree that the harmony “wins”. The fact is that these “small little movements of the left hand” are perfectly comprehensible — if ingeniously and subtlely timed — melodic motions through various parts of the E-minor scale. It is, indeed, Chopin’s highly refined sense of timing (and not any exotic modulations to other keys) that is responsible for the mysterious magic of this Prelude."

SS - I stand by my statement. The melody is striving to move somewhere, but is stuck in these oscillating patterns while the harmonies pull in all sorts of directions. If Westergaardian analysis cannot capture this interpretation, then it does not capture how I hear the piece and is therefore incomplete. I am curious how James distinguishes "perfectly comprehensible [...] melodic motions through various parts of the E-minor scale" that don't form triads or seventh chords that are found in E minor tonality. As an example, shift the entire right hand part of the Prelude over by one beat, so it starts at exactly the same time as the left hand. The melodic motions of the top voice are the same, and the four voices have separate journeys, so the Westergaardian analysis should be the same, except possibly for the alignment of the upper voice with the lower voices. But then, each voice has a separate journey, so what difference does it make if they don't line up? Is it the intervals? But if we care about vertical intervals, why not vertical sonorities created by all four voices? How would the analysis be changed without referring to harmonies? Would the modified piece still be in the E minor tonality, and if so, to the same extent as the original Prelude? The last question is one that can be answered by harmonic analysis, but I don't see how it is answered by Westergaardian analysis.

Finally, harmonic analysis is not the Piston-ian straw man James is tilting windmills at. Harmonic analysis as it is taught in many music schools is a mash-up of Rameau, Schenker and Riemann, with Meyer/Narmour/Huron implication/realization, Hatten/Agawu topoi, and various tricks of form and the like thrown in in many places (I also bring up gender theory and disability theory sometimes). A classmate of mine, Ian Quinn, has been rocking the theory world with his system of harmonic function without primary triads that he has been teaching at Yale for the last few years. This might change things everywhere eventually, especially if Ian writes a textbook based on it. But harmonic analysis is not just slapping Roman numerals on and being done with it. If that is your experience with harmonic theory, then you had a crappy teacher, not a crappy theory.

*I always tell my students that I associate half-diminished seventh chords with a bittersweet striving that ultimately fails.

4 comments:

composerBastard said...

Holy Mother of GOD this is entertaining and fun!

I can't stop laughing...this is great stuff. Mr. Cook...you're up...

Scott Spiegelberg said...

Next thing I know, you will be saying "Dance, my little puppets, dance!" I could use some entertaining as well,y'know.

ComposerBastard said...

well you found me out. The more puppet dancing you guys do, the more time I get to write w/o having to worry about theorists looking in my window.

Seriously, I can't believe you two are drawing a line in the academic sand over a Chopin prelude and on Labour day weekend. A chess match maybe, but over a Polish bar room piano player's little dittie? (err...no offense to Poland folks...I contribute regularly to the Polish Folk Music Society and eat pierogi for breakfast ).

Maybe we should move on to Debussy and see a real boxing match?

james cook said...

For the convenience of readers coming across this post, my reply is here.