Dmitri Tymoczko | Visualizing Musical Structure

Talk kindly contributed by Dmitri Tymoczko in SEMF's 2022 Spacious Spatiality

TALK ABSTRACT
My talk will focus on the connection between geometry and music, beginning with the circle of fifths, continuing with Leonard Euler’s “Tonnetz”, and ending with the current state of the art. I will show how computers and technology allow us to visualize the infinite-dimensional space describing the voice-leading relationships among all possible chords, opening the door to new ways of conceiving musical structure.

TALK MATERIALS

DMITRI TYMOCZKO

SEMF NETWORKS

MUSIC

[archudzik]

Great presentation and very useful mathematical expressions!

[donbelisario]

I'm shivering right now, what an amazing talk I really appreciate the effort of all the people involve along this years to unvell the mechanism of music. Making music accesible to everybody is nothing trivial but a necessity of the soul and mind. I guess It's happening just what Rodchenko and many others predicted when they mentioned that we as humans needed to strive for a richer and meaningful development of arts based on science and separate them from the shallow ornamentation.

[TheMemesofDestruction]

Thank you so much Professor Tymoczco and y’all at SEMF! Happy Thanksgiving Everybody! ☮️ ❤️

[JuliusSmith]

Very enjoyable, thanks! Minor note: David Heinichen's circle was called a "musicalischer circul", or "musical circle", and is not a circle of fifths unless you skip neighbors.

[harryleblanc]

Still trying to digest this. I think I might need to play around on his website, then come back and view it again. But it feels like this is something huge.

[vitalitylight]

A few questions for teachers and students- Symbolic representation of sound is a fun topic, but which systems do you, ultimately, use to compose, and/or to understand music? The variety of Tonnetz (and other symbolic representations for Western modern music notation) is interesting, but which compositional aid (or other mode of understanding the music [RN, Macro, etc.]) is most comprehensive and streamlined system to date? When do we NEED a Tonnetz?

[pliniobarraza]

This is very cool. I myself like to compose using visual constructs that help me build structure. In college I used to write this way without even using a piano, and often the results were pleasantly surprising. Anyway, great stuff in here, thank you for this. Unbelievable this has only 13 likes. Will spread the word and share with all my musician friends.

[luizmenezes]

So, you used the Dirac's Belt Trick in music?!?

That's insane, man.

[pietruyssinck]

at 23:10 I don't understand why the adjacent tiles are upside down.

[nartoomeon]

43:21 (dont read it, its probably wrong) I think, is more right, if musically inert sequence on a right side is "inert", becose it didn`t cover a whole set, whole chromatic scale. And homotopic equivalence has nothing to do with it. It seems that the speaker misused the term... A closed path does not give exhaustive information about its homotopy class. This is about topology. If the tonnetz is continuous and is a torus, so only small loops are closed, and the ones that go around its small and large circles are not.

[CoreyLClark]

Aaah, so its like that! I understand everything now! (Doesn't get it at all)