Phase transitions: The math behind the music

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).

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.....

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