Exponental/Linear Modulation of Phase, + new circuit idea

[Sean Costello]

Don Tillman wrote:
> 
> I finally read Sean's phase modulation discussion...
> 
> I think SC is building a basic DSP implementation of an all pass
> filter stage.  Very basic, because the modulation source isn't
> modulating the tuning frequency, it's modulating the DSP coefficients
> directly, bypassing the z-tranform.
> 
> This will make the modulation nonlinear, especially at the high end of
> the range.

Very true. I haven't implemented a version of the unit generator where the
frequency is determined in Hz. I need to map out what is going on, and figure
out what the modulation is doing. So far, I haven't needed to have direct
control over the tuning frequency of the allpass stages, as I have primarily
used the ugen for phasing sounds, which it does very well. When creating
phase-shifting sounds, the cutoff frequency of each individual stages ends up
being rather arbitrary, as the "pitch" of the phase shift is very dependent on
how many stages there are. I have found that using a waveform that resembles an
inverted FWR sine wave for modulation, and setting the "bias" level by ear (i.e.
adding a constant to the sine wave) works best for phasing sounds.  Generally, I
find that the high end of the range is useful, and that the coefficients tend to
range in between -.99 and .25 or so for effective phasing.

Sorry if this is getting a little too digital, but can you think of applications
where having the frequency of the allpass set by Hz would be useful? I would
imagine that this could be useful in physical modelling applications, but I
would think that custom designed allpass filters that are tailored for the
application (say, switchable coefficients for a passive nonlinearity) might be
more useful. I have already created a Hilbert ugen that uses these allpass
structures internally, and am working on an improved Hilbert ugen that allows
the user to control the number of stages in the phase differencing network,
frequency range, etc,; the Hilbert ugen calculates the coefficients internally,
based on the poles derived from Weaver's approximations and the sampling rate.
For my plain vanilla allpass chain unit generator, I have avoided specifying the
tuning in Hz so far, as it would greatly increase the computation time needed
for the unit generator.

Anyway, I'm sure that you are right, and that audio rate modulation of my
allpass network is resulting in something that is neither exponential nor linear
modulation. Still, it sounds very nice, and I would like to experiment with
analog versions of the same effect. I originally tried it as a way of "warming
up" the sound a little bit, as the phasing sound was a little too "clean." With
just a touch of self-modulation, the results are similar to the distortion most
analog phasers feature.

I may try hacking into my Maestro phaser and experiment with audio-rate
modulation of phase in that way. My Maestro is one of the later, Moog-made
models, that looks like a silver wedge. It uses CA3094's as the phase-shifting
elements, and so should be easier to convert to audio rate modulation than a
photocell phaser like my Mutron II. Unfortunately, I can't figure out how to
take the unit apart! The unit has large plastic "wheels" that are attached to
the pots in mysterious ways...

Back to work,

Sean Costello