If you happen to have a subscription to JSTOR, Karlheinz Stockhausen’s 1962 article “The Concept of Unity in Electronic Music” is a classic explanation of some of the concepts I’m about to describe. It turns out that some musical parameters, such as rhythm and frequency, are in fact manifestations of one underlying mathematical principle.
Consider a simple rhythm, for instance, a pulse that divides a second into three equal beats. We can view the speed of this rhythm as 3 Hz. If we speed this pulse up until it is several hundred Hz, we will no longer process it as a rhythm but instead as a pitch with a frequency, as the following audio example demonstrates:
More interestingly, suppose we take a polyrhythm. That is, we take a single pulse, let’s say, 1 Hz, and divide it evenly into two different parts. One of the simplest possibilities is a 3:2 pattern, which would initially start out as a 3 Hz : 2 Hz ratio. Again, if we speed this polyrhythm up until it is several hundred Hz, our brains begin to perceive the rhythm as frequency. In particular, we will hear a perfect fifth, since the ratio of the frequencies is 3:2. Try to determine in the middle of the following audio example where you stop perceiving the sounds as a rhythm and start perceiving them as frequency:
Here’s a similar example, but with a 4:3 ratio, so that the frequencies play a perfect fourth:
And the irresistible 6:5:4 ratio, which produces a major triad:
It may seem counterintuitive, but these examples demonstrate that rhythm and frequency are in a certain sense the same concept. It’s merely our perception of them that varies.
(Note: I’ve coded all the musical examples in Gamma.)