The math behind the music

The next time you listen to a favorite song or marvel at the beauty of a natural sound, you can also question the calculus behind the music.

Anyway, you'll be discussing with Jesse Berezovsky, an associate professor of physics at Case Western Reserve University. A long-time research scientist and part-time violist, it was necessary to understand and explain the connective tissue between the two disciplines – specifically, how the orderly structure of music emerges from the general chaos of sound.

"Why is music made up of so many rules, why do we organize sounds in this way to create music?" He poses a short explanation video about his research. To answer this question, we can borrow methods from a related question:

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

Transition phase in physics, music

According to Berezovsky, physics and music are called "phase transitions" and result from a balance between order and disorder, or entropy, he said.

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

Mix math and music is not new. Mathematicians have long been fascinated by the structure of music. The American Mathematical Society, for example, devotes part of its web page to exploring the idea (Pythagoras, whoever?) There is geometry in the buzz strings, there is music in the space of the spheres. ")

But Berezovsky argues that much of the thinking, up to now, was a top-down approach, applying mathematical ideas to existing musical compositions as a means of understanding an already existing music.

He claims to discover the "emerging structures of musical harmony" inherent in the art, just as order comes from disorder in the physical world. He thinks it could mean a whole new way of looking at the music of the past, the present and the future.

"I think this model could illuminate the very structures of harmony, especially in Western music," Berezovsky said. "But we can go further: these ideas could provide a new perspective for studying the whole system of tuning and harmony across cultures and through history – perhaps even a road map to explore new ideas in these areas.

"Or for one of us, it's perhaps just another way to appreciate the music: see the emergence of music as we form snowflake formation 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 in fact the fundamental foundation of the music itself, making the resulting octaves and other arrangements a foregone conclusion, and not an arbitrary invention by humans.

His research, published May 17 in the newspaper Progress of science, "aims to explain why basic ordered patterns emerge in music, using the same statistical mechanics framework that describes an emergent order through phase transitions in physical systems."

In other words, the same universal principles that guide the arrangement of atoms when they are organized in crystal from a gas or a liquid are also the cause of the fact that "phase transitions are produce in this model disordered sounds to discrete sets of pitches, division by octave used in Western music. "

The theory also explains why we value music because it is caught in the tension between being too dissonant and too complex.

A single continuously played note would completely lack dissonance (low "energy"), but would be totally uninteresting to the human ear, while a piece of music too complex (high entropy) would not generally appeal to the Human ear. Most music – across time and cultures – exists in this tension between the two extremes, said Berezovsky.