Casio CZ/ VZ/ FZ - Pro Series

>> > "linear piecewise phase distortions". I think!

> Hm, to you, too. Could you give me a reference for your specific
> term? I'm eager to learn!

nothing fancy, just means a function that's made out of line segments
(in this case a transfer function for distorting the phase)
http://en.wikipedia.org/wiki/Piecewise_linear_function

this is how the cz produces the initial waveforms (system iii in the
patent). then there's an FM stage implemented as a hard reset of the
phase ("higher harmonics control signal generator", or system iv in
the patent), with a rather clever smoothing algorithm (just multiplies
by a decreasing ramp at the modulation frequency! sweet.)

anyway, since 1983 people have come up with many additional
interesting phaser distortion functions, ellipses and cycloids being
particularly friendly. i find that sticking with various chopped up
linear functions, and wavetables with pretty simple harmonic content
(1st through 5th order or so), still gives more than adequately rich
timbral results.

> Karplus-Strong algorithm,
now there's quite another beastie altogether.

http://music.calarts.edu/~ebuchla/karplus_strong_patent.pdf

that's KS's original idea for a digitar based on the excitation of a
virtual string by random noise bursts. i made some programs a while
ago (following the lead of folks like david jaffe at stanford), using
a KS-like model of masses connected by springs, but introducing more
complexity by using nonlinear terms in the force equations for the
springs, and doing crazy stuff like connecting them all in a ring
instead of a bridge-termination, and making arbitrarily weighted
connections between non-adjacent masses (ending up with something more
like a "spherical membrane" than a string, or anything else in the
real world...)... also using these things as chaotic resonantors by
using audio input for excitation rather than saws, impulses, or random
number bursts...

then lo and behold, recent releases of ableton live include a rather
sophisticated stringlike physical modelling synth (called...
"tensor"?), complete with nonilnearity, different excitation
functions, variable damping, all kindsa stuff. neat!

in general this kind of thing is lumped together under the umbrella of
waveguide synthesis. jaffe and julius smith at stanford have written
quite a lot about it.

smith maintains his extensive collection of papers for free on his website.
http://ccrma.stanford.edu/~jos/

perry cook at princeton has a nice book about synthesis inspired by
physical models. it's useful without being overly math-y. "real sound
synthesis for interactive applications."

places to find patents on the intertubes:

patentstorm.us (gives you the text, pay for the figures)
pat2pdf.org (free pdf conversion if you know the patent number already)

ok

/eb