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Tuesday, May 28, 2019

Phase transitions: The math behind the music | Mathematics -

Next time you listen to a favorite tune or wonder at the beauty of a natural sound, you might also end up pondering the math behind the music, notes

We can look at a balance--or a competition--between dissonance and entropy of sound--and see that phase transitions can also occur from disordered sound to the ordered structures of music.
Photo: Jesse Berezovsky/Case Western Reserve University

You will, anyway, if you spend any time talking with Jesse Berezovsky, an associate professor of physics at Case Western Reserve University. The longtime science researcher and a part-time viola player has become consumed with understanding and explaining the between the two disciplines—more specifically, how the ordered of emerges from the general chaos of sound.

"Why is music composed according to so many rules? Why do we organize sounds in this way to create music?" he asks on a short explainer video he recently made about his research. "To address that question, we can borrow methods from a related question:

'How do atoms in a random gas or liquid come together to form a particular crystal?".

Phase transitions in physics, music
The answer in physics—and music, Berezovsky argues—is called "phase transitions" and comes about because of a balance between order and disorder, or entropy, he said...

Mixing math and music is not new. Mathematicians have long been fascinated with the structure of music. The American Mathematical Society, for example, devotes part of its web page to exploring the idea (Pythagoras, anyone? "There is geometry in the humming of the strings, there is music in the spacing of the spheres.")
Read more... 

Additional resources
Jesse Berezovsky, The structure of musical harmony as an ordered phase of sound: A statistical mechanics approach to music theory, Science Advances (2019).  
DOI: 10.1126/sciadv.aav8490