It seems counterintuitive that something as intimate and personal as music can be created using a formula. And by saying formula, we’re not talking about predictable cookie-cutter ballads but rather music composed using complicated mathematical principles.
Though this technique seems to be a modern phenomenon of the computer age, the process of goes back to Mozart, who employed probability using dice to compose music, and the Greeks before him. Here are our top five practitioners of mathematics:
1. Iannis Xenakis wrote the book on formalized music, in which he explains his process of dynamic stochastic synthesis. Simply, it means that he used mathematical algorithms and probabilities to create entirely logical compositions. His work and writings have influenced a generation of composers who followed him and even inspired an iPhone app.
2. The son of a mathematician, Milton Babbitt studied math as an undergraduate at the University of Pennsylvania before he transferred into NYU’s music program. Still, his ease with numbers and formulas proved a solid frame for his music, if not the most soothing listening experience. One of Babbitt’s goals, he wrote in his article known as “Who Cares If You Listen?”, was to have music appreciated on the same level as philosophy, math and the sciences.
3. Mathematicians have long known that certain numbers and patterns reoccur within the nature. One of these is the Fibonacci sequence, where starting with two 1's every number in the series is the sum of the previous two (1, 1, 2, 3, 5, 8, 13, …). Bela Bartok is thought to have used the sequence in some of his compositions, along with a complex symmetrical architecture of the keys and tempos he chose.
4. John Cage often looked to probability and chance to dictate the music that he wrote. He famously used the Chinese fortune-telling I ching—a complicated head-or-tails games with eight outcomes—to dictate his compositional process, such as in the 1952 piece “Williams Mix.”
5. In his recent installation, “The Transfinite” at the Park Avenue Armory, the Japanese composer/artist/mathematician Ryoji Ikeda created a score, monumental projection on three 54-foot wide screens and several smaller video installations, all based on binary code. In his artistic statement, Ikeda wrote: “To me the purest beauty is the world of mathematics.”
Weigh in: Do you appreciate a piece of music more knowing that it is built on mathematical principals? Who is your favorite "mathematical" composer?