Music, Mathematics: Idle Thoughts

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You can measure music in time and metre, and this has led some, who feel inclined, to explore the mathematical possibilities of this. But I have never thought of music as having an essential link with mathematics or an essential mathematical content.

People sometimes think that Arnold Schoenberg was more interested in the mathematical side of music, perhaps because of his 12-note method. But his music is far more about melodic invention and elaboration than maths. There is as much if not more mathematics in J.S. Bach.

I often have visions of large architectural geometries when listening to Beethoven’s or even Sibelius’s symphonies – but the image changes frequently.

Thinking however in terms of analytical mathematics, equations, progressions, parametrizations, charts, etc., many composers seem to be hooked on this and pay a great deal of attention to them in their compositions, e.g. Stockhausen, Cage, Boulez. I am not sure this is a good thing, because the mathematical method (virtually irrelevant to the listener) just relates to a means of producing the notes – the music seems to get lost in the process.

Does a musician or a composer need to be a mathematician or a scientist? No. Maybe a musician needs some rudiments of mathematics, then so do many other professions – accountancy for example.

It may be interesting for mathematicians to point to analogies between the two subjects. More interesting may be the analogies with the plastic arts (painting, sculpture), indeed Schoenberg (himself a painter) paid great attention to this. But ultimately music has to stand on its own feet without these props.

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