Unifying/Formalizing the ideas of cross-rhythm, polyrhythm and hypermeter

Question

I am interested in the notions of polyrhythm, cross-rhythm, and hypermeter, including acquiring more mathematically based concepts that can aid in quality music production. I have done extensive reading of papers which claim to unlock the mysteries of what makes a rhythm "good". The most generic, by far, is the paper by GodFried T. Toussaint, which identifies the Euclidean algorithm as being central to the intuitive human generation of good rhythm. The Euclidean algorithm has other applications such as computing the greatest common divisor between two numbers, so it is quite amazing that this has a strong connection to polyrhythm.

An additional useful notion is that of interlocking rhythm or cross-rhythm. Again, the mathematical workhorse for generating "groovy" cross-rhythms is Euclid's algorithm, however, now it is about superimposing two Euclidean rhythms in such a way that the result is pleasing to the ear.

What the Euclidean concept omits to include are the notions of hypermeter. All polyrhythms/cross rhythms generated by this method are essentially for one measure (if we think in terms of score 4/4 notation). The rhythm is pleasant for one measure, but looping it endlessly can by no means generate an interesting track.

I am particularly interested in electronic music such as house and tech-house. A common structure is hypermeter where a 4-loop is superimposed on an 8 loop which is superimposed on a 16 loop. Indeed one could think of the entire track as being a loop in and of itself which can be repeated.

The Euclidean concept does not account for such structures, yet they are extremely common in electronic music. Are there formalized mathematical structures that tie the Euclidean algorithm to hypermetric structures? If not what other mathematical concepts are relevant to such structures?

Note I am mostly interested in working with 4/4 tracks which have a 3:4 polyrhythm. Basically most pop/electronic music uses this paradigm.

Answer 1

the Indian rhythm system called konnokol gives a very good approach on applying rhythm in a musical and oral context. It connects the improvisation by using spoken rhythms in combination with keeping control with the clapping of your hands.

For example try this:

Speak "ta ki ta" repeatedly representing 3 notes with equal length. 
clap on every 1st, 4th, 7th etc. note that you speak. You place accents this way.

you will get a 3/4 beat, looking like this:

>        >        >        >        >
ta ki ta ta ki ta ta ki ta ta ki ta ta

Now, change the accentuation every four notes:

>           >           >           >
ta ki ta ta ki ta ta ki ta ta ki ta ta

This way konnokol can get you any rhythm and feel in all metres and note counts.