Phase Transitions: Know The Mathematics Behind Music

You will, anyway, if you spend some time talking to Jesse Berezovsky, an associate professor of physics at Case Western Reserve University.

The response in physics, and music, Berezovsky argues, is called "phase transitions" and occurs because of a balance between order and disorder, or entropy, he said.

"We can see a balance, or a competition, between the dissonance and the entropy of the sound, and see that phase transitions can also occur from the messy sound to the ordered structures of the music," he said.

Mixing math and music is not new. Mathematicians have been fascinated by the structure of music. The American Mathematical Society, for example, dedicates part of its website (https://www.ams.org/publicoutreach/math-and-music) to explore the idea (Pythagoras, anyone?) There is geometry in the buzz of the strings, there is music in the spacing of the spheres. "

But Berezovsky makes arguments that much of the thinking, until now, has been a top-down approach, applying mathematical ideas to existing musical compositions as a way of understanding existing music.

He argues that he is discovering the "emerging structures of musical harmony" inherent in art, just as order comes from disorder in the physical world. He believes that this could mean a new way of seeing music from the past, present and future.

"I think this model could shed light on structures of harmony, particularly in Western music," Berezovsky said. "But we can take it further: these ideas could provide a new lens for studying the whole system of adjustment and harmony between cultures and throughout history, perhaps even a roadmap to exploring new ideas in those areas.

"Or for any of us, maybe it's just another way of appreciating music: to see the emergence of music the way we do the formation of snowflakes or precious stones."

Emerging structures in music.

Berezovsky said that his theory is more than an illustration of how we think about music. Instead, he says that the mathematical structure is actually the fundamental basis of the music itself, making the resulting octaves and other arrangements an inevitable conclusion, not an arbitrary invention on the part of humans.

His research is published on May 17 in the journal Science Advances. It focuses to explain why basic patterns come together in music, using the same framework of statistical mechanics that describes the emerging order through phase transitions in the systems physical.

In other words, the same universal principles that guide the arrangement of atoms when they are organized in a crystal from a gas or liquid are also behind the fact that "phase transitions occur in this model from disordered sound to the discrete sets of tones, including the 12 -the octave division used in Western music ".

By: Preeti Narula

Content: https://www.sciencedaily.com/releases/2019/05/190523092552.htm