tri 2 saw modualtion

[Don Tillman]

   From: Martin Czech <martin.czech at itt-sc.de>
   Date: Mon, 27 Oct 1997 13:11:22 +0100 (MET)

   Well, I did some simulation and produced a 8 bit soundfile of 10 seconds.
   The result was disappointing. Maybe 8 bit is too poor to hear these.
   It is certainly not the same as going from saw to sine
   in a FM-synth (should be better PM synth, phase modulation).
   Certainly the Bessel functions don't apply here, but it could SOUND
   almost the same.

If you look at the harmonic spectra of the waveform you'll see for the
triangle case that every even harmonic is nulled out, and as you
change the symmetry, those "nulls" will slide up in frequency over the
harmonics and move farther apart, up until the wave is a full sawtooth
shape where there are no more nulls.  A Bessel function describes the
amount of each harmonic.

(This is a guess from the harmonic spectra of a PWM square wave -- I
haven't done the actual math.  The same mechanism applies though.)

You should be able to hear these nulls sliding around, it should be a
very pretty vocal sound, something like a phase shifter.  Especially
with a few of them playing simulataneously each with a sine LFO.

Note the difference here between changing the symmetry and
crossfading; in crossfading the strength each harmonic would just
creep from it's triangle value to it's saw value but in changing the
symmetry the nulls go flying up and down in frequency.

   Audio modulation: Hmm, this is the same as using the linear FM-Input with
   a strange pre-warped input , isn't it? Will it be that much different?
   I doubt.

No, it would be closer to audio modulation of a PWM square wave.  But
warmer. 

   From: Haible Juergen <Juergen.Haible at nbgm.siemens.de>
   Date: Mon, 27 Oct 1997 16:49:32 +0100

   Great idea!

Thanks.  

I've been puzzling over how to build symmetry modulation into a VCO
for a long time.  I would love to build it right into the VCO process
(the equivalent of a symmetry pot on a waveform generator) but I can't
find a way to do it that wouldn't mess up the pitch.  Frustrating.

This idea isn't as good because it's not built into the VCO itself,
and you might have some glitches in the waveform as the slope changes,
but it has the advantage that you can plug other waveforms into it.

   Works fine in Simulation, as long as the rising/falling slope ratio
   is not too large.
   For an almost-sawtooth wave you'd need very large CV's, however.
   (the old 1/x problem raises its ugly head ...)

Right.  

However there probably aren't any especially interesting sounds at the
last 1% of the range.

  -- Don