Scott Spiegelberg has taken up my challenge! So now, it’s time to roll up our sleeves for the second round (the first round is here):
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.]
Well of course he didn’t make such claims; they would be utterly ridiculous! What Spiegelberg has to defend is not any claims about the intents of specific composers, but rather the use of a vocabulary which is by its very nature suggestive of that sort of absurd compositional process.
JC – “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.
That idea is implicit in the fact that we’re thinking in terms of E minor — so that E is necessarily the tonic (and G the mediant, and so on).
James’ analysis also misses the idea that we begin with an uneasy sonority, since the triad is not in root position.
I specifically mentioned that the bass begins on G — which, if we’re thinking in terms of E minor, is not where it “wants” to be, simply by virtue of the fact that it’s not the tonic.
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.
No: what my statement suggests is that there is not necessarily any relationship among the four voices. Which is true: they could turn out to have any of an infinite number of degrees of relatedness or independence, according to the choice of the composer. The denial of this is for me one of the most offensive aspects of harmonic theory.
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.
A suspension is a rhythmic event, specifically a delayed stepwise resolution of a dissonant tone. The relevant dissonance here is that of the E with respect to the F# of the bass. If one understands the tied E as a delay of the chromatic passing tone Eb, then one can understand an underlying functional parallelism (ITT, sec. 4.4) between these two voices over the span of the first two measures. (If I had shown this in my graphs, it would have gone between Stages 7 and 8.)
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.
Perhaps any musician trained on harmonic theory would find the Eb odd; but for me it is a perfectly straightforward passing tone on the way from E down to D — scale degree 7.5, if you will. (And, by the way, D# isn’t in the diatonic space of E minor either — which doesn’t prevent it from having a perfectly comprehensible meaning in that key.)
As for the “expected dominant chord”, what is actually “expected” is that the alto voice will move downward in parallel motion with the tenor and bass:
Why might D#/Eb be expected instead of D? Are the mysterious laws of harmony at work here, dictating the content of a “V chord”? Not at all. The choice is between these two (linear) structures:
There’s nothing wrong with either of these, but if you’re expecting D# instead of D, it’s because you consider the first one to be simpler.
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.
It’s a complex question, but I’d recommend taking section 4.4 of Westergaard as the point of departure.
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
All five of these justifications assume the harmonic framework, without comparing it to the Westergaardian one; hence all five of them can be immediately dismissed.
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.
Again, Westergaardian theory provides an alternative (and much more refined and nuanced) account of what people refer to as “harmonic rhythm”; to construct this account, combine the considerations of chapters 4 – 8 of ITT. With respect to this passage of the Prelude, the point is basically that the linear operations of the various lines are applied over different timespans. To get specific: the soprano’s neighbor notes segment each measure; the alto moves chromatically from E to D over the three measures; the tenor and bass would be expected to arrive on G and E respectively in m.3, but the alto’s descent encourages them to spread out this motion over mm.1-4 rather than mm. 1-3 (with the bass edging chromatically downward in m.3). Thus, in m.1 only one linear operation is going on; in m.2 we have one at the measure level (soprano), one at a “3-measure level” that is delayed at the measure level (alto), and two others at what will turn out to be a 4-measure level (tenor and bass); in m.3 we have the same thing in the soprano, another measure-level delay in the alto, and a chromatic passing motion in the bass taking place over mm.2-4.
To emphasize: the thought process going on here is not a horizontal juxtaposition of vertical structures; it’s a vertical superimposition of horizontal structures.
JC – “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.
In other words, “secondary French 6th to I” is on the “list of permitted progressions”. Again, since the very idea of such a “list” assumes the horizontal-juxtaposition-of-vertical-structures model that I have explicitly rejected, I don’t know what Spiegelberg’s purpose is in informing me of this piece of data. I suppose I should at least be glad that the progression in question
is “permitted”, since it would be most unfortunate (as well as futile) if harmonic theorists were to forbid the simultaneous resolution of a raised scale degree 7, a lowered scale degree 2, and a scale degree 4 to their respective destinations.
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.
I don’t know what comment I should make, other than the fact that these two examples represent midstream snaphots of different processes. Again, Spiegelberg is speaking as though he conceives of a passage in terms of chords juxtaposed in time (otherwise the question of “to which other chord should this chord resolve?” would not come up), rather than linear processes overlain on each other. The fact that the first simultaneity of both examples happens to be a type [0369] is, from an abstract standpoint, a complete coincidence. Now, there’s nothing stopping a composer from turning this kind of coincidence into a motivic process specific to the work, but if Spiegelberg is going to claim that’s what’s going on here, he needs to show how the [0369] idea pervades the work. Otherwise there’s no point in using the term “diminished seventh chord”.
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.
That doesn’t answer my question. Maybe everybody in the world has their own opinion about what the tonic is. This doesn’t tell me anything about what the source of the alleged ambiguity is, or why my own hearing isn’t the best one.
I would, however, like to add some clarification to my own remarks about E minor versus A minor. I don’t actually want to deny that there are local aspects of A minor to be heard in various places in the Prelude. It is a consequence of the iterative, hierarchical nature of tonal operations that virtually all pieces temporarily focus the listener’s attention on other scale degrees besides the tonic. But only in some pieces does this process cause any ambiguity about what the underlying tonic actually is. The problem with Spiegelberg’s analysis in this regard is that it does not capture the fact that, for all that A may have the feel of a local “tonic” at certain points (especially if you focus on very short timespans), it never rises to the level of displacing E in the hierarchy. Contrast this situation with that of the second Prelude (op. 28 no. 2), which is an example of genuine tonal ambiguity. In that piece, not only are you forced to invoke subordinate diatonic collections in a way that isn’t true of the E-minor Prelude, but the clarification of the relative hierarchical status of these various tonalities takes place over the span of the entire composition. Whereas in op. 28 no. 4, E minor is established at the beginning and never displaced, despite a temporary focus on scale degree 4 at certain places.
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.
Bull-oney. One doesn’t just “explain abstractly how the voices progress by logical melodic motions”; one explains the hierarchical relationships within and among the voices, over various spans of time. These hierarchical relationships are the source of the tensions that Spiegelberg speaks of.
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.
Aha! Thank you for so beautifully making my point for me. Harmonic theory completely obscures the fact that these C’s are all on the same hierarchical level — they’re all neighbors to the B, added at the same stage (Stage 8 in my illustration). Simply because of the fact that the accidentally-resultant simultaneity in m.2 happens to be a “recognized chord”, whereas the other resultant simultaneities are not, we are forced to completely distort the conceptual process going on in the top line. Who decided that [0369] was so special, anyway? Why can’t the other sonorities be “chords”, too? (And besides, I thought that even in harmonic theory, a diminished seventh chord was considered a dissonance.)
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.
Would Spiegelberg agree that
is an example of a “sonority of the major minor seventh chord”? If so, then he must confront the fact that such a sonority is not an irreducible entity: it is made out of notes. In this example, we have G, D, F, and B. How does one understand such a thing? Answer:
In other words, if you play that chord on a piano, a listener is going to imagine a context for it, probably of the above form. But what does that context consist of? Answer: scale degree 7 progressing to 1, 4 to 3, 2 to 1, and 5 to 1. In other words, the effect of this “highly distinctive sonority” consists precisely in that it strongly suggests an interpretation of its constituent notes as scale degrees 5, 7, 2, and 4! So much for Spiegelberg’s claim that there is more to a V7 than that.
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),
Could that be because some pieces lend themselves more easily to “steadfast” listening than others?
It’s not really that my hearing of this piece is “steadfast”; it’s that it’s hierarchical. Whatever happens with A, it happens on a lower level than what happens with E. Context matters a lot; you might think A is tonic in m.4 if you’ve forgotten the opening. But if you take the opening into account, it’s hard to come up with a plausible analysis on which A is superordinate to E. The sense of B as scale degree 5 (indeed, the primary tone of the fundamental line, in Schenkerian terms) in the first measure is just too strong.
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?
The neighbor-note motions of the lower voices are not conceptually dependent on the A (as would be implied by saying that there is a “progression to an A-minor triad”). As for the A’s in the top voice, they are easily understood as borrowings.
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.
As if the degree of alignment of the voices were a mere detail, rather than the very essence of the matter!
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.
I would simply refer Spiegelberg to section 4.4 of ITT, which he obviously has not read.
Perhaps I’ll think about giving a systematic exposition of Westergaardian principles on this blog at some point — it seems to be badly needed (especially since the book is out of print).
