An article by Michael D. Lemonick on p. 57 of the 5 February 2007 issue of Time magazine is titled “The Geometry of Music,” with the subhead: “A composer has taken equations from string theory to explain why Bach and bebop aren’t so different.” Hmm. (And the still, small voice within sings Leonard Cohen: “Baby, I’ve been here before…”) Here’s the first sentence: “When you first hear them, a Gregorian chant, a Debussy prelude and John Coltrane improvisation might seem to have almost nothing in common—except that they all include chord progressions and something you could plausibly call a melody.”
First off, it is not too geekily musical to observe that Lemonick must not know what either chord progressions or Gregorian chant actually are, since chant is monophonic—a single voice, or several voices singing in unison—and therefore chord progressions are pretty much out of the question. Yes, you find chord progressions realized melodically in, for example, Bach violin sonatas and partitas, but that doesn’t apply—the liturgical chant repertories of the Roman Catholic Church evolved (meaning no offense to those who believe that the music was quite literally dictated to St. Gregory by a dove) before the codification of traditional western tonal grammar. End result of first sentence: the reader knows that the writer is about to spend an entire page talking about something of which he has no understanding.
No blame for the journalist’s fumbling attempts to explain what this is about should be borne by Dmitri Tymoczko, the composer/theorist in question. Lemonick does direct us to the composer’s website to understand his plan, and several links to papers and publications are provided there. The opening of the abstract that appeared in Science magazine, titled “The Geometry of Musical Chords,” reads: “A musical chord can be represented as a point in a geometrical space called an orbifold. Line segments represent mappings from the notes of one chord to those of another. Composers in a wide range of styles have exploited the non-Euclidean geometry of these spaces, typically by using short line segments between structurally similar chords.” Links on the website show us different pieces with dancing dots and segments on orbifolds.
The first line gives me pause: “A musical chord can be represented as a point in a geometrical space called an orbifold.” OK, but why would one do that? Is there any indication that composers—outside of maybe Skrjabin—would have been thinking of music as somehow being represented in three-dimensional space? Tymoczko is quoted in the Time article as saying “Composers have been exploring these maps without really knowing.” I am skeptical, but that might have more to do with my disciplinary background than with the entire business being a great big larf.
A colleague in Music Theory recently told me that he believes all analysis should proceed from the notes themselves, not from historical aesthetic approaches or treatises or anything else. “We tend to leave that to our colleagues in Music History.” Nice dig. We can take it further; theorists might consider themselves the equivalents of modern physician-researchers, pursuing Scientific Truth, while music historians like me are advocating—umm—“historically informed medicine,” practicing analysis in clumsy, wrongheaded ways analagous to having barbers lop off limbs, treating infections with leeches and bloodletting, and treating insanity by seeking to remove the Stone of Folly, etc. (Though I’m willing to try that last in one or two high-profile cases…) Joke’s on music historians; why can’t we simply base results on scientifically derived data? This is how the music works! See, we’ve got data!
One remembers, here, Hans Keller’s famous distinction between anatomy and physiology. Music historians might find, in theorists, something of (say) cell-counting (or molecule-counting) in a way that completely obscures the big picture, and how things actually work. Music is not medicine; it is art. One does not explain painters’ aesthetics by studying the chemical compounds of their paints, because that is another kind of research, and one doesn’t explain Shakespeare’s dramatic sense by comparing his uses of “it is” and “’tis.” So I wonder about Tymoczko’s premises and conclusions. Because the chords can be represented visually…so? In western tonal music we’ve got twelve pitches and a tonal structure; those are givens, so a lot of the miraculous correspondences between various tonal musics are built into the system.
I do not yet see how coming up with a new way to visually represent a very finite number of aspects about any music, and then comparing various of these newly minted representations, tells us anything. For me, better explanations about composers’ aesthetics and how their music worked will come from period-specific understandings: how music was taught, learned, though about, and heard, not how in can be represented or depicted in some way I dream up…today. If we begin by positing a “system” (look! if we put music on the orbifold, different pieces look similar…), then certain patterns that may or may not be real correspondences look significant, and have the additional attractiveness of Discovery Channel-type graphics to “prove” the case. Look! You can see it right there!
Or, being a music historian, maybe I Just Don’t Get It. I invite Dial M readers to do their own prospecting in the Chord Geometries section of “Publications” on Tymoczko’s site and opine on the idea of whether or not great truths are revealed therein. My feeling is that there is less here than what very attractively meets the eye, but am willing to be educated.