In Defense of Theory

Kyle Gann has posted a letter from Jean Lawton that takes issue with set theory or any applications of math to music composition. She particularly names Allen Forte (though misspelling his first name), Milton Babbitt, and Robert Morris as “Musical Josef Mengeles.” The latter two are both composers and theorists, the former the dean of American music theory. They have all written about the application of math to music. Babbitt and Morris have written music based upon mathematical principles. To Jean, this results in the flensing of “ligaments of language, the tendons of cultural connotations, the muscles of synaesthaesia, and all the skin of extra-mathematical supra-logical aspects from music left us with set of bleached bones.” I will approach my apologia from two fronts. First, I will claim that Jean sets up false dichotomies of vague descriptions vs. equations and logic, language vs. math in discussions of music. Second, I will point out some horrible misuses of cognitive science in supporting her claims that set-theoretic music is un-natural. And third, I will provide reasons why logical views of music are beneficial, especially to performers.

Jean claims that the choices for musical discussion are to A) not talk about music, B) reduce music to equations and logic, or C) rely upon vague isms. This ignores options such as counterpoint, texture, motives, harmonic categories (Hindemith, Schenker, Riemann, extended chords or basic triadic harmony), rhythm, hermeneutics, semiotics (though Jean does quote Nattiez), reception theory, phenomenology, or a whole slew of other means of analysis that don’t have equations as the answer. They do rely upon logic, but usually logic of the artistic kind, rather than symbolic logic. Schenker’s theories talk about transformations and operations as if it is math, but he designed these operations upon the logic that tonal music follows, not upon artificially-imposed mathematical rules. This is basically the same for other types of analysis, with various levels of assumptions or empirical bases.

Next, I would challenge Jean to make the distinction between language and math. Math is a language, designed to communicate ideas either precisely or imprecisely, just as other languages can. It is not inhuman, as Jean suggests, as it was designed by humans. It can describe abstract ideals or pragmatic facts, and do so elegantly or clumsily. The English language also shares these qualities, and can be just as stultifying as any mathematical description. And how much math is considered unacceptable? Bach was fond of encoding numerological symbols in his music, Bartòk utilized the Fibonacci Series/Golden Section in much of his music, Hindemith made ‘3’ significant in Mathis der Maler, and Crumb made ‘7’ and ‘13’ significant in Black Angels. Is that too much to talk about? What about neo-Riemannian functions in the harmonic progressions of Brahms or Wagner? Even simple ideas like tuning and intervals rely upon mathematical principles.

Jean supports her claims of the failure of set theory by citing James Clerk Maxwell (who was actually responding to Helmholtz’s new acoustic theories rather than any set theories, as they didn’t exist yet), PET scans that suggest the connection between pitch perception and visual imagination, Leonard Meyer, L.S. Lloyd, and 4th graders. First a response to the pitch perception idea: cross-cultural studies have shown that notational formats determine physical analogies for pitch and rhythm. Because the Western system of notation places high frequency pitches higher on a staff, we associate pitches in a vertical framework. Studies with people who do not know or use Western notation use different descriptions of pitch. It is not a hard-wired universal, nor are Meyer’s claims of timbre descriptions. In Chinese instrumental playing timbres are described by the gestures that produce them. Studies by Kendall and Carterette have shown discrepancies between German and American concepts of timbre, that “sharp” is not as relevant as “nasal” is to American ears. For every cognitive fact that Jean can find that could support the “unnatural” aspects of set-theoretic music, I could find one that shows the perceptual salience of inversions and retrogrades. It really comes down to aesthetics, which is a much more personal issue.

I am a bit uncertain whether Jean is complaining about theorists analyzing music with mathematical tools, or composers creating works using mathematical processes. The first mention is of analysis, one of her alternatives for talking about music. But then she critiques music composed by Babbitt, so it seems that she has it in for both sides. First a defense of theorists: as another reader, Adam Baratz, points out to Kyle, it is better to engage music by what’s inside the piece, rather than from a purely ideological stance. I disagree about the cheesiness of Philomel, as I think it is a devastating piece, full of the emotion and violence of rape. But it is worthwhile to examine the inner workings of a piece of music with all the tools at hand. This helps in aesthetic arguments, in performance decisions, and in finding common ground for any discussions about music.

As for set-theoretic music, by which I think Jean really means serial music, integrated serial music specifically, Sturgeon’s Law applies to that group of pieces as much as any other. 90% of total serial music is utter crap, including some by Babbitt, Boulez, and Stockhausen. Perhaps even more than 90% in this case, though I think it just seems that way because we are still too close to that period. But some serial pieces do acheive a transcendent beauty. I would place Messiaen’s Modes des valeurs et d’intensités in that category. Jean is right that music needs an emotional underpinning, a connection with the human listeners. But that connection is not dependent upon a specific process of composition, or a single musical language.

For what it’s worth, I do agree with Kyle about the benefits of genre labels, as a shorthand for communicating features that many pieces share. It also helps to establish the aesthetic expectations an audience will need to appreciate a given work.