He Blinded Us With Science!

Jonathan Bellman

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.

About jonathanbellman

Professor of Music History and Literature and Head of Academic Studies in Music at the University of Northern Colorado. Author, *The _Style Hongrois_ in the Music of Western Europe* (Northeastern University Press, 1993), *A Short Guide to Writing About Music* (2e, Longman, 2008), *Chopin's Polish Ballade: Op. 38 as Narrative of National Martyrdom* (Oxford University Press, 2010), Editor, *The Exotic in Western Music* (Northeastern University Press, 1998), author of bunches of articles and reviews and so on. Likes to play the piano, the mandolin, and even guitar sometimes. A. M. and Jo Winchester Distinguished Scholar at UNC, 2011.
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7 Responses to He Blinded Us With Science!

  1. I haven’t had a chance to read the paper or play with the pretty-making toys, but there’s a general principle at stake that I’d like to address: “Music is not medicine; it is art.”
    Actually, it’s a little of each. Music exists as a particular set of ways in which the physical properties sound interact with the ears and brains of humans. The system of western Tonality is a particular aesthetic perspective on physical phenomena; and any aesthetic perspective is coded in the ways our brains are structured and programmed. All of these things can be reasonably described in scientific terms — although most of it is beyond our current capability. Finding ways to analyze these relationships can help us determine which aesthetic preferences are driven by which physical factors — for instance, if there are chords that sit very close to commonly used chords in this map but which are not themselves used, what does that tell us about the nature of our aesthetic preferences?
    Certainly there’s a danger, as you observe, that these new tools will be misused — that insignificant similarities will be overvalued by tools that are used to look for the wrong things. But I can also easily think of ways in which even this particular model might be useful to traditional music theorists and historians.
    Suppose you want to isolate personal style traits in the work of individual composers from period style traits. You could run orbifold analyses of a few hundred stylisticaly similar pieces and graph the number of times particular harmonic moves were made. Moves that show up often are common style traits, and moves that show up rarely overall but commonly for certain composers are individual traits. The same analysis could be done to quantify the core harmonic differences between different eras — exactly which sets of common traits are different between, say, baroque and romantic music. We have a general sense of a lot of this, but probably not much hard data. Having done those analyses, you could then find which composers were the first ones to employ the harmonic strategies that became common during subesquent periods, and you could trace the influence from composer to composer, following the memetic propogation of particular harmonic strategies through the culture. Which personal style traits of which composers became common style traits 50 years later? All of this stuff could be directly relevant to the kinds of things you’re interested in.
    Ultimately, the usefullness of any given analytical tool lies in asking the right questions. Maybe this particular tool won’t turn out to be useful for answering any questions that are worth answering, or maybe nobody will think to ask the worthwhile questions that it can be used to answer. But developing these kinds of tools is still be useful even if this particular one is not, because sooner or later somebody will find one that’s helpful.
    It’s true that “one doesn’t explain Shakespeare’s dramatic sense by comparing his uses of “it is” and “’tis””, but that asks the wrong question. You certainly could use statistical analyses of word choice and sentance structure to determine whether some other work was also written by him — this strategy has most famouly been used for determining the authorship of some of the Federalist Papers. There’s plenty of questionably attributed music out there, too — maybe the orbifold analysis can tell us once and for all whether Josquin or Champion wrote the great “De Profundis.”
    On the other hand, I completely agree that Lemonick clearly doesn’t know what he’s talking about. All too common in Time ever since they stopped employing actual music critics for their classical music articles.

  2. Jonathan says:

    Many thanks for the thoughtful and thought-provoking response. I do know about the statistical analyses of word use in literary works (you mention the Federalist Papers; I’m thinking of authenticity studies of Shakespeare). These are not, ultimately, analogous cases. Taking your one point about orbifold analyses of “a few hundred stylistically similar pieces”: that is not analysis of how the piece (or paper) “works” in the aesthetic sense of musical analysis (cf. my comparison about paint compounds). What’s more, even when one asks a hard-data kind of question and farms the results, it isn’t necessarily what one thinks.
    My doctoral research had to do with Chopin, and I interlibrary-loaned a great number of studies that I thought MIGHT have something to do with my subject. One of them was a dissertation from Eastman, in Theory I think (though I’m not sure), that was a statistical tabulation of the frequency of Chopin’s use of a wide variety of different chords: major, minor, dominant seventh, major ninth, etc. The Preface to the diss acknowledged several other dissertations and masters theses, using similar methodologies but investigating the works of different composers. Clearly, this was the greater research program of a particular faculty member, and the grad students were sent off to do his data-retrieval.
    The problem was–a fatal one in Chopin–that there was no methodological distinction between a major ninth chord and a major triad with a held-over 9-8 suspension from the previous dominant harmony. Thus, no distinction between the *function* of the ninth scale degree over the tonic; was it truly a ninth chord, or a melodic suspension? They are heard quite differently. Ultimately, the hideously time-consuming process of chord counting therefore amounted to nothing at all, because the statistical rating of pitch aggregates completely ignored the context in which they were heard.
    The researchers had been sent to count cells, in other words, when they needed to be looking at much bigger phenomena and comparing them, but not lumping them all together.
    I’m not sure this story even has a moral, but I have been deeply suspicious of aesthetic analyses–which is to a large extent what I *think* Tymoczko is about–that are based on “data.”

  3. kevin r hollo says:

    i’d like to give you a bit of my mind on this subject, b/c is seems to parallel much of my own research agenda with perfomative literacy. what you call ‘aesthetic analyses’ can be done conversely with so-called scientific or numerical languages (computer programming languages come to mind). people have been writing code poetry for some time now, and i recently published a paper looking at the metonymic functions of text archiving languages like XML. it seems you’re absolutely right about CONtext, but there’s much more than meets the eye/ear/etc with most languages (all languages?), so much more that a marriage of the technical with the aesthetic will almost always produce something good. almost.
    i’ve got a favor to ask of you, tho i realize we’ve only shared a bit of dialogue these last few months. our wedding is less than a month away, and we’ve got a string quartet for prelude and ceremony duties. the contact person has given us a list of songs they do, and frankly, i’m very underread when it comes to classical music of any sort. i’m wondering if you wouldnt mind taking a look at the list, just circling a few that you think might be nice, i respect your work on the blog so much that i’m sure it would be more effective than me trying to hunt them down on mp3.
    either way, keep up the good work.

  4. Jonathan says:

    I would *never* choose anyone’s wedding music! The risks are too great. Thanks for responding.

  5. Jonathan —
    The combined forces of my day job and my inability to resist the urge to respond to the copyright issue on the AMS list have prevented me from the kind of serious response that your response to me deserves, and from checking out the software so I have a clearer idea of what we’re dealing with. But I get the sense that the bulk of our disagreement may simply be in what kinds of methodologies we’re prejudiced toward and against.
    Kevin — I helped a friend pick string quartet music for his wedding last summer, and found that the repertoire is pretty limited in terms of wedding-appropriate music. For the recessional we actually ended up with an excerpt of a Brandenberg concerto which was strings-oriented to begin with arranged for quartet, which was easy. That was the one I helped pick — I think the processional was an arrangement of Simple Gifts. Anyway, my suggestion would be to broaden your search to things like baroque concerti and string orchestra music. I recall thinking that the slow movement of the Beethoven 7th Symphony, which is strings-dominated, could be a lovely processional, for instance. Any string quartet worth having will be able to learn most of the kind of rep that would be appropriate for the occasion.

  6. Phil Ford says:

    I’m not suggesting anything for anyone’s wedding, but I’ll tell you what was played at mine:
    music before the ceremony: Brahms G major violin sonata, 1st mvt.
    processional: Beethoven Bagatelle op. 126 no. 3 in E flat
    recessional: a pair of Scarlatti sonatas, can’t remember the Kirkpatrick #s offhand.
    This was one of the few times where having mostly musicians for friends really paid off.
    Sorry to threadjack.

  7. kevin r hollo says:

    thank you to both galen and phil for the kind responses.
    i understand the ridiculousness with which this kind of request might be receieved, but understand that i am only asking for pointers, and would certainly listen to anything recommended before making decisions. cracy as it might seem to ask (perfect) strangers about music for such a special occasion, if someone in a classical field came to me and said, “kev, i need your help choosing some songs for an avant-pop wig out/mid-80’s dancehall computer sleepover/obscure 70’s butterfunk potluck” i would be so excited and very much up to the task. so again, thank you for some suggestions, i’m going to track them down if i can and give a listen.
    funny how these blogs bring us together (cue the muzak)…

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