Phase transitions: the math behind the music | Hacker News Reader

Phase transitions: the math behind the music

thedaily.case.edu

48 pointsfurcyd8 comments

This is basically a fluff piece. Here's a link to the actual research paper: https://advances.sciencemag.org/content/5/5/eaav8490.full

Kept waiting to delve into the theory... and waiting...

It feels like a whole article made up of first paragraphs!

Another mathematical theory using group theory is: The Topos of Music: Geometric Logic of Concepts, Theory, and Performance by Guerino Mazzola. He shows that music lives in the Z12 group and chords are invariant subgroups. Interesting read.

The joke about Mazzola is that people who know enough about music to see through his theories are bamboozled by his maths, and vice versa.

If you want to explore that space, Tymoczko's A Geometry of Music is more rewarding.

But this misses the point. Music isn't just mathematical consonance and dissonance. Music is the practice of using consonance, dissonance, timbre, rhythm, form, and historic and cultural references, with aesthetic intent - i.e. creating metaphors and other complex cognitive experiences out of musical material.

The difference between a composer and a dabbler is that composers either work at this level consciously and deliberately, or they have unusually effective musical instincts and use them to decide if something "sounds right" or "works."

Any naive mathematical description - which includes all of the work on ML in music - misses this ability of musical material to create those extra levels of expression and meaning.

>which includes all of the work on ML in music

As of yet :)

Hmm, i suppose it would be hard to generate music with ML that make cultural or emotional references, the ML would need to resemble a human in order to understand these, or otherwise understand humans like we understand ourselves. However, current ML sytems might succeed in making references in its music involving a simpler context, like an arcade game, or common physics.

https://openai.com/blog/musenet

https://magenta.tensorflow.org/music-transformer

https://www.aiva.ai/creations

A great deal of music can be transcribed into 31-tone equal temperament without loss of fidelity. Guess what happens to the Z12 group invariances.

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