Exponental/Linear Modulation of Phase, + new circuit idea

[Sean Costello]

Haible Juergen wrote:

> Well, that makes me think of the Interpolating Scanner, of course.
> What would this "foldover" courve look like ? A "zigzag" courve
> comprising of triangles (easy) - or rather of sawteeth (not so easy) ?

Just triangles. I used it simply to make sure that the modulation signal
stayed within the proper bounds. Sawteeth would be more of a "wrapping"
effect, where the modulation would go instantly from the highest value
to the lowest, or something like that. I tried this in Csound, and the
results were hideously ugly sounds. Not good hideous, either.

> I only have exponential inputs on my module. Does "foldover" stage -> expo
> make sense ?

I think so. The "foldover" stage isn't particularly scientific - it's
just a way of keeping the modulation signal in the proper range in my
circuit. The sound is different for exponential and linear modulation,
with maybe more of a noisy edge with exponential modulation, but they
both sound similar.
 
> I'm not sure what exactly you mean by "all pass coefficients".

This refers to the gain coefficient of the feedforward/feedback amount
in the difference equation used in Csound. The allpass equation looks
like this:

y(n) = g*x(n) + x(n-1) - g*y(n-1)

where x(n) is the input, x(n-1) is the previous input, y(n) is the
output, y(n-1) is the previous output, and g is the gain coefficient. g
MUST be between -1 and 1; otherwise, the whole thing "blows up" almost
instantly, with the amplitude quickly exceeding the range of the
floating point representation. The "fold over" was originally used as a
way of dealing with this problem - it was somewhat accidental that I
discovered it sounded good.

> There is no limit to modulate fo from subaudio to ultrasonic values, in
> an analogue solution. Where would you place the "fold over" points ?
> (There is a certain point where there would be not much audible change
> anymore, of course. Any directions to choose the foldover points ?)

Easy - just set the foldover points so that the maximum and minimum
sweep voltages for the phaser correspond to the maximum and minumum
voltages (before foldover) of the foldover network.


> But while you can surely make the pitch periodically increase and decrease,
> I can't see thru-zero FM involved yet (but I haven't looked too close) -
> please explain !

I'm not sure if it would be true through-zero FM. However, it displays
some of the characteristics, in that a modulation signal exceeding a
certain limit will cause a phase reversal, instead of a stalling out of
the phase. I would bet that a more refined version of phase modulation
could be developed, to create more through-zero effects. However, the
technique I stumbled across can be used to obtain some nifty effects
from the combination of two modules that synth-diy folks might already
have around. Plus, I like the "foldover" method of dealing with control
voltages that exceed a certain range, as it sounds better than plain
"saturation," where exceeding a certain point just results in the
voltage not exceeding a certain threshold. 

Sean Costello