Random frequency modulation (was [sdiy] Interesting f vs. t graphs of pitch instability)

[Tom Wiltshire]

Scott,

On 7 Oct 2008, at 14:21, Scott Gravenhorst wrote:

> The sample rates of the GateMan synths are 1.0MHz for the monosynth  
> and 250KHz for
> the poly.  The NCOs are based on a phase accumulator design, so  
> they emulate linear
> CV for pitch.  Because of this I had to compensate for the control  
> voltage's action
> as it moves through it's range.  This is done by multiplying the  
> noise amplitude by
> the "CV" (in quotes because it's digital, and the pitch control  
> signal is an
> emulation of CV, linear) so that it is scaled properly.  This gives  
> a consistent
> effect across the entire pitch range of the synth.

This makes the pitch fluctuation a constant percentage of the pitch,  
rather than constant number of Hertz, doesn't it?
My own digital osc design is based on the Korg DWGS oscillators, a  
phase accumulator followed by a series of bandlimited wavetables. I  
have a 16-bit "Pitch" variable which represents 8 octaves of  
frequency, represented logarithmically (A V/Oct CV, if you like).  
This is then converted via a lookup table into a linear frequency  
increment.
So I can add the noise modulation to either the pitch variable  
(logarithmic) or the frequency increment (linear).

> What I did was to filter the noise through a simple single stage  
> IIR filter to roll
> off more and more high frequency energy in the noise waveform to  
> control whether it's
> just slow drift (very low Fc) or jumpy drift (medium Fc) or audible  
> noise (high Fc).
>  The lower the Fc, the slower the noise signal moves.  Lower Fc  
> also lowers the
> overall amplitude of the noise, so there's a multiplier value to  
> amplify it when
> needed.

This sounds good. Single-stage IIR is something that even a dsPIC  
should be able to handle! Will I find filter details in the Gateman  
notes in any form I can understand?

> What I have can do drift times in the 10s of seconds which causes  
> the NCOs
> to drift slowly in and out of tune and exhibit the characteristic  
> slow phasing we all
> love (the monosynth has 4 NCOs, the poly has 4 NCOs per voice).

How much accuracy does the filter need to be able to cope with such  
long times? 10's of seconds at the sample rates you mentioned is a  
LOT of samples. I'd have expected noise to build up in an IIR after  
so long, but I'm not well versed in digital filtering.

> The system stays in tune within the bounds of the noise signal  
> because the noise
> causes the pitch to drift back and forth across "perfect tune" by  
> even amounts on
> both sides of it.

Yeah, isn't that a handy property of a good-quality noise signal?!

> I just get a very nice in-tune, but randomly wandering phase change  
> sound.

Sounds lovely, Scott. Good work.

Thanks for the useful comments too.

Regards,
Tom