When I was younger I got very involved in the issues of pitch analysis,
and the more I learned about both ethnic music and signal processing, the
more I realized that it becomes a question of what one is trying to find
out and why. I doubt that divisions smaller than a semitone in any
particular culture or even among the performances of any one family or
performer in that culture are part of a repeatable system, and rather they
represent an expressivity that has to do with fine tuning of pitch and
timbre. The ustads of the music of India can sing different forms of a
note, and I have heard an ustad (Viliyat Khan) demonstrate singing
different forms of Sa, the base note that is never supposed to vary, in
one raga, because it suddenly struck him that it was what he wanted to
improvise musically at that point, and he had the musical vocabulary to do
it within the context of the raga. However, I doubt that these different
forms are invariant from one raga to another, and a performer could
purposely vary these very small nuances of pitch even within one
performance. The listener may not be consciously be perceiving how low a
flattening actually is or how sharp a sharpening actually is. However,
the listener will hear it as a change of mood or shading of expression in
the music, and we can definitely hear the difference between these singers
and singer who does not know these skills. Arabic maqam singers and
Eastern European folk violinists also use very fine gradations of pitch as
an expressive tool. I strongly doubt that any type of system can be made
out of any this.