It's sort of amazing that one of the most popular living classical composers - Arvo Pärt, who runs neck and neck with John Williams in how often his music gets played live - uses a mathematical system to create his music. Here's a great video on how it works.
Briefly, he likes to compose with two voices, which he calls the M-voice and the T-voice. The M-voice plays melodies in a diatonic scale, which are often mathematically patterned. The T-voice is restricted to playing notes in a particular triad, following a precise rule. For example, it might play the lowest note in the triad that's above the M-voice.
This produces a unique effect. The restrictions, and Pärt's use of religious texts, give the music a vaguely medieval sound. But it's not really like that old music at all. Since the M-voice stays in a diatonic scale, and T-voice stays in one triad, the music sounds very 'pure'. But the rules sometimes put the T-voice just a tone or semitone away from the M-voice, hence dissonant. The result sounds both ancient and futuristic.
Here I haven't even gotten to the symmetries in Pärt's music! For that, watch the video. You'll be able to see the patterns while hearing them.
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