Music and mathematics

I read with great interest an Independent article by Cambridge mathematician Tim Gowers about what he calls the “myth” of a link between mathematical and musical ability. I’d heard this theory before, usually framed in the form of a reproach to my child self ca. 1989-1995 for not having worked hard enough at my maths homework. I was pretty good at maths, or at least I was until they brought in all that calculus business, but truthfully, it never provoked any interest or excitement in me the way music did.

It’s true, as Gowers notes, that many mathematicians play an instrument well. But so do many scientists, librarians, and academics in all fields. People who are academically bright as children often learn to play an instrument, and their intellectual quickness and diligent study habits mean they can get quite good at it. Is this a sign of mystical interconnection of abilities, or simply an indicator of the type of personality that doesn’t mind being shut in a room for long periods of time developing a challenging skill?

In an attempt to find a comparison, Gowers points out certain intuitive connections that we can make between the rules of Mozartean phrase structure and “A is to B as C is to D” mathematical logic problems. I wonder if these might also be applied to one of the forms of music theory and composition that really is directly related to mathematics: that is, serialism. I don’t know if the “big three” of the Second Viennese School deliberately set out to write mathematical music: there is, after all, a charming anecdote about the young Anton Webern most unscientifically crossing note names off a piece of scrap paper while composing a twelve-tone row. But Milton Babbitt, a mathematician and theorist as well as composer, was able to fit mathematical terms such as “combinatoriality” and “semi-combinatoriality” to Arnold Schoenberg’s row transformation techniques, opening up new possibilities of total serialism to post-war composers.

Some concert-goers do find twelve-tone music a bit difficult to listen to. Perhaps it’s the very “mathiness” of it that makes it such a challenge. I confess that it didn’t set my own heart aflame until one of my theory professors at university introduced me to theorist-composer George Perle’s startling detective work into Alban Berg’s Lyric Suite, within whose tone-rows which we can find clues and insights into the composer’s forbidden and hitherto undiscovered love affair with Hanna Fuchs-Robettin. After that, I couldn’t get enough Second Viennese School. Maybe a passionate teacher is all that mathophobes and dodecaphobes alike need to give these subjects more of a chance?

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