Poly-Metric Study, part one

I had this idea a while back about exploring poly-metric in the strictest sense possible. The idea would be this: four voices, each in its own time signature, with the same bar repeated over and over again. The voices will then phase in and out of each other, at predictable but differing intervals; say you have three voices, in 3/4, 4/4, and 5/4 - the starts of the 3/4 and 4/4 bars will coincide every 12 quarter notes, the 4/4 and 5/4 every 20 quarter notes, the 3/4 and 5/4 every 15, and all three together every 60 quarter notes. One such full repetition of all voices, from being in sync to coming back in sync, seems a good length for the whole composition, as it will include all possible juxtapositions of all voices.

Now, there are some things that must be decided from the start; for instance, which time signatures? Another is that of structure, if there shall be another structural principle at work than just "from sync back to sync". In the latter, I've decided to structure it according to Schenkerian principles, albeit somewhat subverted. While not being a huge fan of Schenker, I am somewhat familiar with it. And, since this is a study on if strict poly-metric can yield pleasing results, it makes sense to structure it in an established framework for what makes pleasing music. (Again, I'm subverting it, in part by handwaving my own criteria for what makes a note structural or not, in part by extending the Schenkerian Urlinie to a tenth or twelfth, rather than the approved third, fifth or octave.)

As for which time signatures, my first trial had 4/4, 5/4, 6/4 and 7/4. I'm not really pleased with the result, so I'm starting over from scratch, this time documenting it. One reason I dislike it is that 4/4 and 6/4 have a common denominator in 2, meaning they have a tighter repetition, and that some juxtapositions between them simply will not occur. Now I'm thinking instead of using either 5/8, 7/8, 9/8, 11/8, or 7/8, 9/8, 11/8, 13/8. More to come.