Topos Approach to Bach’s Music?

I don’t know if there are any other fans of the CBS TV show Numb3rs out there, but I and my family are devotees. There was an odd, throw-off sort of line in last Friday’s episode, in which something (in an otherwise mathematical conversation) was likened to a “topos approach to Bach’s music,” to which another character commented, “See, I told you it was complicated.” This caught me off guard because

1) the idea of musical topic, as Leonard Ratner has formulated it, derives from the Greek word topos;
2) those of us who had the real Ratner treatment at Stanford began with some exercises in Bach preludes, identifying topics etc., before going on to use those tools in other music (Bach cantatas, Viennese classical music etc.); and
3) I believe that “topos approach” means something else in mathematics, something I probably could not even begin to understand, but if so I’m wondering how the devil Bach’s music came into it, in comment that was both unmotivated and un-followed-up.

Any ideas? As a Ratner disciple, I had the odd sense that aliens were trying to communicate with me without being noticed, or something on that order.

On to the City of the Angels! Very appropriate, given the setting of Numb3rs.

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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2 Responses to Topos Approach to Bach’s Music?

  1. James Martin says:

    I don’t know – but this is probably relevant:
    “The Topos of Music: Geometric Logic of Concepts, Theory, and Performance” by Guerino Mazzola.
    Topos theory is indeed an area of mathematics. Not for the faint-hearted, but try

  2. Oddly enough, I just saw that Mazzola book on the circulation desk at our music library. Kismet, or some such thing. Anyone recall if topos appear(s) in Hofstadter’s “Goedel, Escher, Bach”? That would seem to be the closest thing to a widely known contact point between math and JSB.

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