![]() The idea being that music was confined to a certain key and if it deviated, it had to return to that key. ![]() Tonality was a guiding principle in music from around 1600. It's a tonality that gives us harmony - perhaps a similar sense of harmony to that which Pythagoras saw in the stars. The human ear yearns for such familiar structures, sounds that resolve, or "frames of reference," as Maor puts it. A ratio of 3:2, meanwhile, gives you a perfect fifth - from the root to the "top note" of a basic "major triad" chord. His theory of universal harmony may have failed, but his ratios live on.Ī ratio of 2:1 gives you an octave - two of the same note, with one pitched at double the frequency of the other. I might not know I'm controlling the bit crusher but my ears tell me 'Oh, that sounds good,' and the more I move my finger to the left, the more extreme the sound gets, I can add dynamics to the sound," says Black. It has as a X/Y pad that lets you influence sounds by moving your finger up and down, and left and right. But it's also got mathematical principles built right into the user interface. Read more: One Thousand Hear Change of Note in World's Longest ConcertĪs a piece of computer software, it relies heavily on math. In February, Black's music label, Ninja Tune, released an iPad app for digital music production and performance called Jamm Pro. I was never very good at math, I was into chemistry," says Black, "but I do have that respect for it. "And people say music is basically mathematics - like harmony, relationship. My talking to you now is being mediated through mathematical operations on ones and zeros," says Matt Black, a musician and creative software pioneer, who has a background in science. "Everything is math when you get down to it. That didn't stop a group of scientists at Yale University in the 1970s, among them Willie Ruff, a jazz musician and musicologist, from turning Kepler's inaudible planetary calculations into sound using computer synthesis. "Finally, he realized the idea was wrong." I dare say that 30 years of his short life were wasted, searching for the orbit of the planets in musical laws of harmony," Maor says. The idea influenced science "negatively," says Maor, for a few thousand years, right up until the astronomers Johannes Kepler and Galileo Galilei came along. "And from that he made this huge leap of faith to say that the whole universe ran according to these simple numbers," says Maor. Read more: In-App Purchases: a mobile app developer's key to 'consumer lock-in' Pythagoras and his followers believed numbers ruled the universe Image: Public Domain He found that if you divide a string by a ratio of 2:1, 3:2 or 4:3, and pluck the string, as you would on a guitar or violin, the resulting notes have a "harmonious relationship." They are in consonance. As a result, little or no written records survived.īut we do know that Pythagoras experimented with vibrating strings. They swore to keep their discussions secret. "Music was ranked equal to science and they used it to explain the orbits of the planets and stars." They looked at the cosmos as a single "unity of music, astronomy, geometry and number theory, which they called arithmetic," says Maor. Led in large part by Pythagoras, their motto, as it were, was "numbers rule the universe." Eli Maor, professor of history of mathematics and life-long music lover Image: Privat The ancient Greeks were the first "real mathematicians," says Eli Maor, a retired professor of the history of mathematics and author of Music by the Numbers. Call it human, a natural instinct - our species is desperate to understand and control nature, if not the entire universe.
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