[sdiy] Casio CZ resonant waveforms / Windowed Sync

[Tom Wiltshire]

Hi Richie,

> I like your "ghetto demo" board where you can freely alter the saw oscillator (modulator) and sine oscillator (carrier) pitches with the pots. Very useful for quickly getting a handle on how it sounds, and it sounds good!

Thanks.

> The way you have it coded at the moment,  (sinusoidal carrier with no DC offset,  windowed by the sawtooth modulator)  mimics the sound of a sawtooth being passed through a resonant BANDPASS filter. (You can see this in the output waveform  -  It looks like a sawtooth would look like had it been passed through a sweepable resonant bandpass filter.  The low-frequency downward slope of the sawtooth waveform itself isn't visible in the output, only the resonant ringing.)

Yeah, I recognise the basic waveform from all my experiments with SSM2164 SVF filters, discussed here previously. That gave me direct experience of the visual effect (read 'time domain', I suppose) of LP, HP, and BP filters on waveforms. It's a bit odd but not unpleasant to see similar things happening an entirely different way! I find it very interesting how much these various techniques (both analog and digital) overlap - hard sync, windowed sync, filtering (HP, LP, BP) - all can produce similar effects, although all have things that they only can do.

> You can actually mimic different resonant filter responses by slight modifications to the carrier waveform before you multiply it with the modulator...

Aha! Now this is a list of things I'll have to try....

<snip the list>

> The nature of the resonance that this CZ algorithm imparts is quite interesting because it does not behave like a constant-Q filter.  As you sweep it, it does not boost all frequencies by the same amount of dB's.  It is highly resonant at high frequencies and runs out of steam if you like at low frequencies.  I find this interesting because many real world analogue filters that are held in high regard like the TB-303 also display similar characteristics.

Do you think we can do a CZ303?! It's an interesting notion...

> Fascinating stuff indeed.  All the best techniques are in the old kit it seems!

The impressive thing about this particular technique for me is the simplicity. It's *very* easy to do, and not at all demanding computationally speaking (e.g. your oldest dog-slow processor can still manage it) and yet it manages to produce a good range of fairly analogue-sounding filteresque noises without much overhead. That's pretty brilliant, really. I mean, I know Casio get a hard time (and the CZ presets really *are* cheesy!), but they must have have *someone* quite bright working for them back then.

Thanks,
Tom