Phase transitions: The math behind the music

phys.org ^ | May 23, 2019

[BenLurkin]

balance between order and disorder, or entropy, he said.

"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," he said.

Berezovsky ... he's uncovering the "emergent structures of musical harmony" inherent in the art, just as order comes from disorder in the physical world. He believes that could mean a whole new way of looking at music of the past, present and future.

Berezovsky said his theory is more than just an illustration of how we think about music. Instead, he says the mathematical structure is actually the fundamental underpinning of music itself, making the resultant octaves and other arrangements a foregone conclusion, not an arbitrary invention by humans.

His research, published May 17 in the journal Science Advances, "aims to explain why basic ordered patterns emerge in music, using the same statistical mechanics framework that describes emergent order across phase transitions in physical systems."

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

The theory also speaks to why we enjoy music—because it is caught in the tension between being too dissonant and too complex.

A single note played continuously would completely lack dissonance (low "energy"), but would be wholly uninteresting to the human ear, while an overly complex piece of music (high entropy) is generally not pleasing to the human ear. Most music—across time and cultures—exists in that tension between the two extremes, Berezovsky said

[Reily]

It was Umar the Muslim conqueror of Alexandria who said with the burning of the library - paraphrasing “ If its in the Koran we already have it, if its not we don’t want it!”

Technically speaking the library suffered fire damage from Julius Caesar’s occupation of Alexandria & from rioting between Christians & Jews during the reign of Theodosius I (roughly 400 AD).

[Kommodor]

Phil Keaggy - Sounds

Especially the jam at the end.

https://www.youtube.com/watch?v=jmjveOt-u0I

[Skooz]

bfl

[norwaypinesavage]

;>)

[Intolerant in NJ]

Instead, he says the mathematical structure is actually the fundamental underpinning of music itself, making the resultant octaves and other arrangements a foregone conclusion, not an arbitrary invention by humans...back in the day when I was attending the university in Philly I had a few courses to kill and decided I'd try one being offered on musical composition - I can't tell a B flat from a glissando, but I love music and thought this would be a chance to find out more about the "technical" side of the artistic work I knew - the mentor for the course was George Rochberg, a composer of considerable repute, and twice a week for two semesters he would tell the five or six of us who were taking the course about the fine points of codas, crescendos, and counterpoints and we would go home to "compose" appropriate "music" using the various points we had heard about - there was no way I could actually "hear" the music in my head and then get it down on paper, but by then I had had twelve credits or so of calculus and analytic geometry, and it soon became obvious somehow that there were clear mathematical relationships between the various notes we were dealing with which would make them sound "good" - I guess harmonious - and "bad" - in various combinations - so I went through most of the year counting the thirds and fifths and all and producing my little ditties - kind Dr. Rochberg would gather us around the piano and play our tunes each week, offering as much encouragement as he could - "That's an interesting melody" or "That has some possibilities" - I ended up with two "A"'s - surely out of sympathy rather than for my totally lacking musical genius - and an awe to this day of how a bunch of notes that can so rile our imagination and emotions depends at base on the demands and precision of mathematics - Olga Kern and the finale of Rachmaninoff's Third Concerto.....

[lonevoice]

:-)