Actually I've published academic papers in computational musicology, I'm very familiar with the math of music, rather a newcomer to philosophy and wondering what y'all have to add to the conversation - but I agree it's a good puzzle!

What I meant was that the idea of a "mode of limited transposition" didn't exist as something worth naming until exactly the moment when it was used by Messiaen (at least that's my understanding).

I don't doubt that there's math in music, but I think the process by which math becomes musically relevant is fascinating and potentially understudied (or I just haven't found the right resources).

Thanks for your thoughts! I'm also interested in the idea of a musical theory as something that's made to be broken, and even going beyond that, of theory as something that can be generated at the same time as the thing it's describing. For instance, Messiaen (a famous composer) invented "modes of limited transposition" as he was first using them. Do you think that relates to any mathematical or scientific use of the word "theory"?