Bach and the musical Möbius strip

plus.maths.org

94 points·CarolineW··9 comments

If this seems interesting to you, I would suggest reading: "Gödel, Escher, Bach: An Eternal Golden Braid" [1]

[1] https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden...

I think Westworld naming the next episode "The Well-Tempered Clavier" could, somehow, lead to a resurgence in interest in GEB -- lots of people on /r/westworld seem to be interested, for sure! (For one, I've heard that the show's creators have admitted that they are creatively indebted to the book in some ways.)

I think it might have something to do with the structure of the fugue.

> a contrapuntal composition in which a short melody or phrase (the subject) is introduced by one part and successively taken up by others and developed by interweaving the parts.

Westworld also did some interesting hints to "The Origin of Consciousness in the Breakdown of the Bicameral Mind" by Julian Jaynes a book that if you haven't read it yet you should. It's up there with GEB.

Came here to suggest this book. You were faster.

Related is Tymoczko's geometry of musical chords [1] see also [2].

[1] http://dmitri.tymoczko.com/geometry-of-music.html

[2] http://dmitri.mycpanel.princeton.edu/voiceleading.pdf

[3] http://dmitri.mycpanel.princeton.edu/ChordGeometries.html

He gave an interesting presentation at a recent AAAS meeting in DC - really intriguing ideas.

http://arstechnica.com/science/2016/03/mathematics-meets-mus...

[2] is fantastic. I was just thinking about strategies to voice lead a set of block chords correctly while minimizing overall intervallic distance.

An actual music möbius strip: https://www.youtube.com/watch?v=3iMI_uOM_fY

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