Ah, rhythmic melody! Yes, I’ve been wondering about the sequential permutations of rhythmic units, and it may be the missing piece for a gap I’m mulling over. At the beginning of this discussion, I brought up how 16 ticks (each corresponding to a 16th note) could be grouped and how the groupings could be permuted, e.g. [6,6,2,2], [8,4,4]. It’s a constricted rhythmic melody which doesn’t delve into “irrational rhythms”, but I think it’s the same idea. Most of the resources shared up to this point have been about steady rhythms. I want to explore “melodic” rhythms next.

I think the “counterpoint” of two rhythmic melodies would involve their syncopation. The mathematical procedure I’ve stumbled upon for determining syncopation is to compare the partial sum series of the two rhythms. E.g. [6,6,2,2] has a partial sum series of (6,12,14,16) while [8,4,4] has a series of (8,12,16). Because the smaller series is not a subset of the larger series, the two rhythms can be said to syncopate. (Also, their composite rhythm has partial sums of (6,8,12,14,16), corresponding to a rhythm of [6,2,4,2,2].) I think the independence of two rhythms depends on the degree to which they syncopate.

I think the bridge between melodic and harmonic rhythm has to do with periodicity. That’s what I’m mulling over at the moment.

An update by the way (addressing the thread):

After reading Stockhausen and exploring these resources, my horizons have broadened. What I previously called a “note” I’ve generalised as a “phoneme”, and what I called an abstract “motif” is now an abstract “chronomorph”, literally a shape in time. I think the theory suggests something far more ambitious than the code. After all, the implementation is merely a 4/4 tonal music generator