Fractal Music

Pulse Trains

What if we want to listen to more than one pulse train at a time?

If we were to play the percussive tracks from the previous examples simultaneously, we would only hear the highest frequency click; coincident pulses would all sound the same.

One solution might be to adjust the volume of the clicks in proportion to their depth.

This can work, but only to a limited extent; rapid, subtle changes in volume are difficult for the ear to discern clearly.

A better approach is to use different voices to represent different depths.

Here are the voice assignments for this orchestrated rendition of the same piece:

Pulse Instrument Eighth note Claves Quarter note High Wood Block Half note Tambourine Whole note Open Cuica 8 beat Tom-Tom/Bass Drum 16 beat Open Triangle Generally speaking, lower frequency pulse trains dominate all coincident pulses belonging to higher frequency pulse trains. Consider, for example, the way the thump of a bass drum or slap of a bass guitar can momentarily overshadow other voices. The following graph helps illustrate this concept of dominance. At any given time, only the largest pulse depth is represented. If the smallest feature represents one sixteenth note (half of an eighth note), then the largest feature corresponds to a whole note and the entire graph represents four measures of music in 4/4 time. Return to Pulse Trains. © 2004 Harlan Brothers