A bizarre coincidence: this morning I was reading about a role for the Möbius strip in music, but it had nothing to do with this!

It turns out orbifolds have an application in music theory. Orbifolds are a kind of generalization of a continuous manifold [0]. The mathematician Tymoczko (and others) used orbifolds to describe the abstract geometry of musical chords, in which the Möbius strip is the geometry of the dyad. The work was published in Science [1], and is quite short and readable, but is also summarized in a short article by the AMS [2].

[0]: https://en.wikipedia.org/wiki/Orbifold

[1]: https://dmitri.mycpanel.princeton.edu/files/publications/sci...

[2]: https://www.ams.org/publicoutreach/math-in-the-media/mmarc-1...

Oh, this is delightful. It's an exploration of how J. S. Bach used algorithms ("mathematical tricks") to compose and generate music.

A related recent post:

Beneath the surface of Bach’s music is a world of numerology and cunning craft

https://aeon.co/essays/look-into-the-secret-world-of-numerol...

https://news.ycombinator.com/item?id=28498605

Interesting discussion. I attended a concert / talk featuring Professor Du Sautoy and a performance of the Goldberg Variations a few days ago which was very engaging.

I do wonder whether the maths in Bach was a 'shortcut' in the sense that imposing constraints to follow particular patterns narrowed down the range of material that would work in particular compositions and that having chosen that material the composition was a matter of then working through those patterns.

(Du Sautoy's latest book is all about mathematical shortcuts)

This is the programmer's way.