I’m currently developing the theory of my music algorithm alongside its implementation. I think this theory could be a starting point for other composers and musicians, so I’m eager to publish it.

Anyways, as I was examining the relationships that comprise a musical system, I couldn’t help but think that the space-domain relationships (e.g. pitch consonance, chord membership, voice independence) suggest time-domain relationships (of which I can name none).

My question for discussion is: **what relationships exist for polyrhythmic textures?** Is there anything comparable to a chord in terms of layered durations, or are there rules to ensure rhythmic independence, or (as the title of this post suggests) is there a notion of rhythmic consonance or dissonance? The less of my algorithm I leave to pure chance, the more consistent the quality of its output. Because there are evidently some rhythms that sound good together and some that sound awkward.

Some terminology I’m toying with for this discussion:

Tick - an atom of abstract time (versus a unit of concrete time, e.g. the second)

Span - a unit of abstract time, comprising ticks, the first of which is accented (e.g. 4 ticks in a span)

Rhythm - a permutation of spans adding up to one measure (e.g. for a measure of 16 ticks, the following are some of its rhythms: [12,4], [8,8], [4,4,8])

Feel free to use traditional terminology: e.g. I heard somewhere that layering eighths on top of quarters is like a parallel fifth in harmony.

It looks like there’s stuff in the literature behind paywalls. I’ll share here what I find.