non-linear scales ?

Hello,

Excuse me if my post results to be off-topic, but I could find no help with this anywhere
else.

I am trying to build an electronic musical instrument using non-linear systems of
equations instead of the traditional harmonic oscillators. If you find it interesting, you can
see all the stuff at:
http://www.nonlinearinstruments.com

My question arised when I tested equal temperament scales for midi keyboard controlling
this kind of instruments using the simplest approach of s=12?2. It does not work at all,
cause the oscillatory properties of the instrument change so much between notes, to say,
and even the same concept of "pitched note" seems to fail sometimes.

So I will try to put it from my poor understanding of scale theory in this words: If equal
temperament, or other scales, take their final sense from the fact that the sounds that will
be used to produce it have an harmonic spectrum (so the coincidence of pitches with
harmonic resonances), what kind of scale should be of appliance when the kind of sounds
to be used result to have chaotic properties ?

Maybe you will find this question excesively general, so perhaps you could help me with a
different approach: can a formulation in terms of Dynamical Systems of equations (linear
or non-linear) be made for a practical scale implementation ?

If anyone is interested I will be glad to comment it in more detail, and if someone can read
Csound code, I think the whole thing will result a lot more clear.

Thanks for your interest

Ignasi Alvarez Garriga
http://www.ignasialvarez.com