Exponental/Linear Modulation of Phase, + new circuit idea

[Haible Juergen]

	>I have been performing some experiments in Csound, using several
cascaded
	>allpass stages (i.e. phase shift stages), with the allpass
coefficient being
	>modulated at an audio rate. Some of the things I have found:
	>
	>- This is a VERY nice way of getting FM effects. Using a sine
oscillator as a
	>carrier, and another as a modulator, I could get results that were
very close to
	>classical FM sounds, with the amount of harmonic content rising
with the volume
	>of the modulator.

Hi Sean, and list,

I've made such experiments, though by far not as extensive and systematic
ones
as you describe. I used a six stage 13700 based phaser. Actually it's the
Variable
Slope Filter/Phaser. I tried audio rate FM on the filter, and discovered the
FM
phase sounds by occasionally switching to phaser mode. It's important that
you can switch the phaser to "all pass only" mode (i.e. direct signal not
mixed
to the output) for the most prominent FM effect. I have a pot that does a
continuous mix between dry and all pass (of low pass) signals, so that works
fine.
(Feedback to create resonance peaks is interesting, too, but this is more
into
the "Filter FM" than "oscillator FM" palette of sounds again.)

	>- Using the mirror opcode (an opcode that implements "foldover" of
a waveform,
	>in a manner similar to the middle section of the Serge Wave
Multiplier) on the
	>modulating signal allows for more dramatic FM effects, similar to
the
	>through-zero FM on Yamaha synths. I implemented it out of
necessity, as the
	>allpass stages will "blow up" if the allpass coefficient (g) is
outside of the
	>range -1<g<1.

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) ?

	>- Running the modulating signal through an exponential function -
i.e. amod2 =
	>exp(amod) - does not result in a shifting pitch center with
increased modulator
	>amplitude. This is in contrast to the FMing of an
exponentially-controlled
	>oscillator, where the pitch center rises with increased modulator
amplitude.

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

I'm not sure what exactly you mean by "all pass coefficients".
Asuming one stage, an all pass would be

H(jw) = (1+ jw/wo) / (1- jw/wo),        w = 2*pi*f, wo = 2*pi*fo.

What I can modulate, is fo, the pole/zero frequency, which also describes 
the frequency where the delay time of the stage goes down.

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 ?)

	>- Any signal can be subjected to FM in this way, not just
oscillator signals.
	>The results aren't always pretty, but I'm sure this would be useful
in many
	>cases, especially for processing unpitched percussion instruments
with sweeping
	>oscillator frequencies.

Modulating Delay Lines is a nice way to impose FM on a complex signal. The
Roland (We don't buy new Roland gear anymore, do we ?) VP-330 uses
a short delay line for its Vibrato effect. (Modulated by an exceptional
implementation
for a delayed sine LFO, btw. I've cloned it for my upcoming JH-720 synth
...)
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 guess All Pass stages would show a very similar behaviour. The delay time
is not constant with frequency anymore, but I'd expect the basic behaviour
for
FM application to be quite similar.

	>Does anyone have the circuitry where they could test this idea out?


I'll give it another try on the JH-3. Give me some hint how to set
the piece wise linear transfer courve for the fold over effect you have in
mind !

JH.