Music & Mathematics

A Mathematician

First of all, on the fundamental relationship between mathematics and music: yes, the chromatic scale is based on simple geometric ratios, but beyond this (and a few other things perhaps), I think saying “Music comes from mathematics” or “Music is founded upon mathematics,” or anything similar, are more subtle statements than one might let on. It’s very philosophically grounded in whether one thinks mathematics can exist to be touched upon without having defined it first, or whether one sees mathematics as a lens through which physical and theoretical phenomena can be analyzed. Certainly mathematics has played an important part in serialism, which utilizes set theory and algebra, but can we say it has played a similar role in either the creation or musical essence of a Beethoven piano sonata? Certainly we can analyze the music in a mathematical fashion, but does this make it fundamentally an object of mathematics?

There are two unsupportable (because nothing is so black and white, right?) positions on this topic:

a) you are a quantophiliac, who looks for deterministic mathematical relationships to aesthetics, forgetting that music is art and therefore cannot be fully defined by the sum of any set of empirical observations.

b) you are a quantophobe, for whom mystical inspiration is all and you simply ignore the fact that mathematics is often a useful tool in achieving and describing aesthetic objectives.

Certainly, composers have taken direct inspiration from mathematics. Bartók used golden mean proportions, Ligeti used strange attractors and other fractal phenomena, etc. Music is not mathematics any more than architecture is mathematics, but as Thelonious Monk said, all musicians are subconsciously mathematicians.

I have also wondered if there is not a musical connection to playing chess via a (subconscious?) mathematical ability: e.g. Prokofiev apparently was a very good player.

Certain mathematicians have remarked upon proofs, etc., with the words “elegant” and “beautiful,” with some openly suspicious of any series of equations that shows too much sweat and not enough grace as being on the wrong path.

I have, however, been bored to tears by articles in scholarly musical journals going through “permutations of sets” blah blah fucking blah! For an elite who might claim they can actually hear such things in a work and follow them, fine.

You can interpret anything mathematically (with probably mixed results) but what is the point? You can interpret things however you want, and call it a world view. But that would be ignoring the world, and the various ways that people experience existence, let alone art.

There are composers who probably use a mathematical-like mindset for composition. But there are plenty of composers who probably couldn’t give a flying fuck about such methods (Birtwistle springs to mind, and man have you seen one of his scores?).