The Corner

Re: Chomsky/Silver/Cost

Dan, I thought of the distinction you discussed—the masses-of-data approach vs. the classical or Galilean approach—while listening to a piece of music yesterday. It was the last movement of Mendelssohn’s String Symphony No. 8. (Score; recording. The recording is lightning-fast and a little anemic and I don’t love it, but it’s the best I can find on YouTube. If you can, try Kurt Masur with the Leipzig Gewandhaus Orchestra—of which, incidentally, Mendelssohn was once the music director.)

I was appreciating the many subtle differences between the exposition and the recapitulation. There is a harmonic change that is mandated by the genre, but Mendelssohn also introduces all kinds of tiny motivic and contrapuntal embellishments. Look at the second-violin and viola parts in measures 402–409 vs. measures 69–76. It’s wonderful. “He didn’t have to do that, you know,” as a theory teacher of mine used to say about passages in Bach that amazed him. The variation is especially welcome since Mendelssohn repeats the primary theme of the exposition (and recapitulation) as its secondary theme, and monotony could easily set in.

Then I was thinking about how we recognize the morphological relationship between passages despite their surface variation. Take measures 17–19 compared with measures 361–363. Looking at the first-violin parts in 18 and 362, for example, you see they have some notes in common, but we wouldn’t say every case of G–F#–E–F# is morphologically related to G–C–F#, even if the rhythms were exactly as they are here. We have to discern the deeper harmonic structure. We can do this by reducing each passage to the same progression of block chords. We then look back at what Mendelssohn actually wrote and see it as an elaboration of this basic structure.

How does this relate to the masses-of-data/Galilean distinction? Imagine some extraterrestrial scientist who can’t actually hear music but can nonetheless perceive sequences and groupings of notes (he could be looking at a score, or detecting sound wavelengths through an instrument). He feeds this information through a computer to try to discover statistical relationships in the arrangement of notes—this one goes with that one, this one follows that one, etc. Since in tonal music certain progressions are “correct” (satisfying) and others “incorrect” (unsatisfying), we have standard progressions, and they partially determine the sequences and groupings of notes. So the alien will find higher probabilities that some notes lead to others, or go with others, within certain definable contexts. He’ll notice e.g. that what we call an F keeps going to what we call an E when he looks at what we call a V4-2 chord resolving to what we call a I6 chord in C Major. The masses-of-data approach will thus help him learn, at least to some extent, what we call harmony.

Except he won’t really be learning harmony, because he can’t hear the music.1 He won’t penetrate to its fundamental principles—what I almost want to call its inner life—as we can. And without those principles, he won’t be able to see measures 17–19 and measures 361–363 as morphological variations of the same structure, even if he can detect a pattern relation between them. His entire process is a crude and massively complicated way of grasping incompletely what Heinrich Shenker grasps in a glance, what Mendelssohn or Bach just does without having a theory (though he has learned from other composers’ examples), and what we can just hear without analysis—which is the best way to listen to music.


1. I don’t mean that he will lack a “subjective auditory experience of the music.” I mean that he will not be able to form our concepts of harmonic function. Two examples. First, a pivot chord, a point of transition into a new key. We analyze it as having two different functions, depending on the key in which we hear it. But the alien music theorist is just looking for statistical relationships in the sequences of notes. For him, then, the pivot chord will not be different in kind from any other chord whose type has been found, empirically, to be followed by more than one other type of chord—and that will be true of pretty much every chord, whether or not the music containing it changes key. Second, suppose he has been analyzing tonal compositions and then happens upon twelve-tone and serial music. Statistics will not enable him to understand that he has encountered a completely different system, with a completely different set of rules. He will think, “And here is another way the tones can be arranged . . .” [Third example: enharmonic equivalence. 5/10/2013]

What I say may not be true if he has non-auditory means of perceiving consonance and dissonance, perhaps by analyzing pitches as waves. He would then be able to notice that a given stretch of music begins and ends with a certain group of consonant tones (say, a C-major chord), and that types of dissonance resolve to types of consonance in characteristic ways, regardless of the particular tones that instantiate them. From this he may arrive, however painstakingly, at something like our idea of key signature and harmonic function. But he has now moved beyond a masses-of-data approach and combined it with the study of qualitative relationships between pitches. If we imagine him simply looking at scores and trying to find statistical relationships between the marks on the page, his understanding will be limited in the ways that I have described. [He might attain a proto-understanding of enharmonic equivalence even if he lacks means of detecting consonance and dissonance. Suppose he lacks such means, but does possess an instrument that, exposed to a tone of definite pitch, displays a symbol of his own language representing the pitch. If he has also a library of musical scores and recordings, he can play the recordings for his instrument and compare its readings with the score. He will see, for example, that the notes in the score designating C-double-flat and B-flat correspond to a single symbol on his instrument. Keeping statistics, he will find probability relationships between the alternative spellings in the score and the notes that precede and follow them. But this is not an understanding of harmonic function. “Why two score symbols for the same thing?” he will ask himself. “Do these silly humans write a redundant notation? Or am I not noticing something?” And he will never stop scratching his head. 5/12/2013]

It is interesting to think about him in connection with David Hume’s ideas on causation. Remember, though, that it is we who arrange tones, and that we can point to examples of arranged vs. non-arranged tones, and of something (someone) that arranges them vs. something (someone) that doesn’t. (1/30/13)

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