[sdiy] Wavetable info

[David Cornutt]

On Thursday, January 1, 2004, at 01:50  PM, Scott Gravenhorst wrote:

> Hi all, and Happy New Year.
>
> I've often thought that it would be interesting to do waveform drawing,
> but I've also wondered just how useful it is ?  For what I know, a 
> static
> waveform is just a pile of harmonics, regardless of whether it's 
> generated
> by a waveform specific VCO or a hand drawn deal.  If the harmonics 
> don't
> change in some way over time, then the waveform itself is not 
> interesting.

To avoid cluttering up the list with a discussion that has already 
cluttered up
Analogue Heaven, I'm going to avoid the "what makes a good oscillator"
philosophical discussion and stick to some technical aspects...

It's more correct to state that any static waveform is a pile of 
overtones.
With the waveforms that we commonly use in (particularly) analog
synthesizers, the overtones have a particular harmonic structure.  You
can change this to an extent with a filter, but beyond a certain point
it becomes very difficult to do with subtractive synthesis.  Consider, 
for
example, what fixed filter banks do; they create a pattern of peaks and
valleys in the Fourier transform that may look very different from what
originally went in to the filter.  These are typically used for fixed 
formats,
but what if you want them to track pitch?  Building a set of 15 or so 
good-
quality VCFs, and getting them all to track together, could be a very
expensive undertaking.

Drawing waveforms gives you a sort of escape from the limitations of
conventional subtractive synthesis.  You can draw a waveform that has
a wildly different set of overtones to begin with, and now your filters 
and
other processors have something very different to chew on.  As an
example, there are techniques for drawing waveforms that have
non-harmonically-related overtones.  (More than two crossings of the
X-axis per cycle will usually yield some strange overtone combinations.)
Conventionally, in subtractive synthesis, we do this sort of thing using
a patch that involves FM or a ring modulator, but as we all know,
these can be unpredictable and hard to control because the outputs
aren't logarithmically related to the inputs.  On the other hand, if you
have a mixed-overtones waveform that you are extracting from a sampler
or a wavetable oscillator like a Miniwave, you have a lot more control
over the resulting pitch and it's easier to play melodically, and you'll
get timbres that you would never get with just pulses and sawtooths.

>  If one could draw several waveforms and then morph through them, this
> might give an interest dynamic change over time, but increases the
> complexity of the software required.  Then I ask myself, how would this
> differ from using modulated VCFs, modulated waveshapers, or any of the
> other common (and simple) methods for making interesting dynamic 
> sounds?

I won't deny that, like any static waveform, it needs processing to make
it interesting to the ear.  But you are starting with a very different 
set
of overtones, so your conventional modulations may produce some
very different and unique sounds.  That ugly philosophical thing sticks
its head in again here, but I'm just going to swat it on the nose and
send it back to its time-out corner. :-)

> Also, there seems no correlation between a waveform that 'looks cool' 
> and
> one that sounds cool.  Watching a scope, I see some pretty 'ugly'
> waveforms that sound very nice.  So how can one then visually design 
> good
> waveforms without wasting a lot of time?

Um, well, actually that's the hard part.  You have to do a lot of 
experimenting.
I have managed to divine a couple of rules:

0.  Start with simple stuff, like sine waves, and work your way up.
Even things that you think are standard, like pulse waves, may
surprise you when you draw them.

1.  When you are drawing, make everything as smooth as you can.
Any bumps or jerks in the waveform will translate to a prominent
high-frequency overtone, usually unpleasant and (for some reason)
difficult to filter out without destroying the basic timbre of the 
waveform.

2.  If you draw a waveform where the integrations of the various
wave halves (the area under each part of the curve, between it
and the axis) has large variations, you will create a waveform with
a very wide spectrum of overtones ranging from bass rumble to
high-pitch squeal, all in one waveform.  This can be interesting, but
if you overdo it, it starts to sound like one of those bad digital
white-noise generator chips.