[sdiy] Korg DW synths and phase in wavetables

[Tom Wiltshire]

Hi all,

I've been looking at the waveform data from the Korg DW8000 synth.  
For those of you that don't know much about it, it uses different  
wavetables for each octave. The wavetables are arranged so that  
higher octaves have less harmonic content. This avoids aliasing. At  
the bottom end of its range it uses 2048 8-bit samples per wave, with  
1024 further up, and 512 at the top end. Like this it is able to get  
all the wavetables it needs for a single waveform into only 8K, which  
I reckon is pretty good going. You could do the same thing at 16-bit  
resolution and still only use 16K, which would be blinding.

There are some things that it doesn't do that you'd probably want to  
include now, like interpolation between wavetable samples (it  
truncates the phase index), or interpolation between octave  
wavetables, but at the time they just didn't have the processor power  
for the price.

With this in mind, I was surprised to discover that it stores a full  
cycle of every waveform, even though every waveform in it is  
symmetrical, so you could easily just store half and read the same  
data out in reverse for the second half. If memory was expensive, why  
did they waste 50% of what they had? Then again, dealing with the  
reversed wavetable look-up addresses might have been worse...


This does bring up one question though; If you generate wavetables  
with all the harmonics starting at the same phase (0) then the  
wavetables will always have this property of rotational symmetry  
around the central point, which allows you to use half as much memory  
to store them. Given that the human ear can't really hear phase (only  
phase differences and the effects they cause) and can't tell the  
difference between a true square wave and any of the other waves that  
include the same amount of those odd harmonics, is there any reason  
why I _might_ want to store an entire cycle of a waveform in a  
wavetable synth?

T.