Nonlinear vs. chaotic

[Daniel Oberfeld]

Hi all,
> I would love to have a musical instrument
>that
	>could jump octaves like a wind instrument (i.e. with the same sort
>of
	>noisy transition, not just clean octave jumps), or generate chaotic
	>subharmonics like a Gyuto monk, or growl like a sax, or create

One point I'd like to make: you have to consider 'nonlinear' and 
chaotic seperately.
Most 'natural' sound-sources (Strings, reeds, tubes) are certainly 
nonlinear in several aspects but do not exhibit chaotic behavior.
On the other hand, nonlinear system (e.g. oscillators) can produce 
chaotic 'timeseries'.

Personally, I don't think chaotic systems are useful for musical 
synthesis, because chaotic sounds are best described as "irregular, 
unpredictable, noisy, uncontrollable, dirty and wild" (Bruno Degazio: 
Twards a chaotic musical instrument, 1993). Some aspects 
here are contrary to everyday musical use and benefit.

Nonlinear oscillators on the other hand can show interesting 
behaviour like amplitude dependent harmonic structure (think of hard 
stroked Rhodes reeds), the mentioned octave jumps (overblown 
Saxophone) or special attack/decay behaviour like descending pitch 
(bass drum). 

All these physical systems are quite straight-forward described (in 
an oversimplified manner, I have to admit) in readily available 
differential equations (see my other posting for literature). These, 
on the other hand, are easily implemented in 'analog computers 
(Op-amp integrator and differentiator systems like state-variable 
VCFs). Hal Chamberlin has some examples in his "Musical applications 
for Microprocessors"

Daniel