Brian Greene: Perhaps the most familiar kind of interval in music is the octave where you have C and another C They sound kind of the same but the second one is higher pitch relative to the first. Mathematically we know how those two waves, those two vibrations relate to one another. So when two notes are an octave apart the wavelength of one is twice the wavelength of the other or said differently the frequency of the higher one is twice the frequency of the lower one. So that is a very simple relationship between how quickly the note, the string if it is producing that note is vibrating, and if it’s vibrating twice as fast, it’ll be an octave higher.
There’s a lot of math in music in that the relationship between vibrations can be phrased mathematically. The art of music of course goes beyond the math in doing things that don’t really come out of a formula, don’t come out of some well defined system of going from one note to the next but using sort of creative genius to do things unexpectedly. That’s where I think the music happens.