[sdiy] wavetable lookup waves

[Grant Richter]

Hi All,

Just wanted to drop a note. The Wiard Waveform City, Blacet Mini-Wave and
Doepfer A-112 Sampler all use the same binary file format. So these files
can be used by all three devices, hopefully making for a larger interest in
the wavetables. Wiard and Blacet will be selling wavetables that took a
great deal of engineering and programming. But the intent of the Mini-Wave
is to supply an inexpensive device for your own experimentation.

In other words, the Mini-Wave project has never been about money, but to
provide an inexpensive module which is a freaking blast to play with! As
such, my input to the list is NOT advertising, but to try and make the whole
thing more fun for people who love their Mini-Waves.

> 
> I want to scare you some more. Far fewer non-redundant combinations than 3.2
> x 10^616
> 
> If the wavetable is used alone and for audio only, then we can delete phase
> and symmetries:
> * The bit pattern shifted by one or more bits (phase) will sound the same.
> * Vertical mirrors (amplitude) will sound the same.
> * Horizontal mirrors (time) will sound the same.

I agree with the above statements. To generate all possible waveforms in
this format, we run through the first bytes 256 values, then we set the
second byte to 1 and run through the first 256 again and so forth for all
bytes. While very large, the problem is computable.

The most significant problem is deciding which waveforms will be useful. In
order to do this we need a waveform indexing system which can assign a
waveform index to each waveform. Mike Firman and I have approached this by
calculating the Shannon information entropy for both the amplitude portion
and the FFT. These two numbers map an index onto an 8 x 8 "entropy
chessboard". Darwin Grosse has named the technique "entropometry" and we
have written custom software for it.

A very loose interpretation of the information entropy is to look at it as
an index of complexity. If you look on the Wiard group file site on Yahoo
groups, I have posted the manual for the new "Socket Rocket" chip with
entropometer plots of the waveforms.

Most acoustic musical waveforms map to and amplitude entropy of 4 bits or
more and a spectral entropy of 4 bits or more. This eliminates 3 quadrants
of the "chessboard" and considerably reduces the number of waveforms that
need to be considered.

> 
> * Any combination that yields fo in less than 256 Bytes isn't making best
> use of the wavetable. If the pattern is complete in 128 Bytes and then
> repeated in another 128 Bytes it will sound an octave higher but not the
> most efficient use of the wavetable.

It does have a particular sound to it. If you consider the number of bytes
in the waveforms as establishing the sampling rate, a 128 byte waveform has
half the sampling rate of a 256 byte waveform. This mean the the wavefrom
can not be transposed as far before aliasing tones appear as part of the
signal. As it happens, these aliasing tones have a signature sound and
resampling PPG or Prophet VS waveforms to 256 bytes eliminates part of their
character.

> 
> *Any combination that does not include maximum and minimum amplitude in the
> sample. It will sound the same, just noisier.

Complete cycles which do not use the entire length or amplitude of the
wavetable, can still be useful. Waveforms which complete in less than 256
byes can form formants like the VOSIM method, or inharmonic partials.

In the "Prayer Wheels" section of the Socket Rocket, I encoded ASCII text
from the Bible, Koran, Hindu and Buddhist texts. While these do not use the
entire amplitude range, they are interesting as control voltage sequences.
You can listen to the tone sequence formed by the Lords Prayer for example.
And as audio waveforms, they are surprisingly musical, like bagpipe
chanters. (assuming any bagpipe is musical ;^)

> 
> Now, since all of these bits are available, but there is significant
> redundancy is there some clever method of building wavetables of greater
> resolution in the same size ROM?
> 
> Could waves be mirrored; count up then down?

Using the A/D drive method in the Mini-Wave, this is accomplished by driving
the input with a triangle wave instead of a sawtooth.
> 
> Could waves be mirrored; count, change sign then count again?

Similar?
> 
> Could waves be segmented into parts A, B, C, and D?

If the MSB of the Mini-Wave A/D converter is routed to a CMOS counter (4024)
and a simple R-2R DAC is put on the first 4 bits, then a staircase voltage
is generated which will increment the wave input after a single pass of each
waveform. So now the entire wavebank (4096 bytes) will play contiguously.
> 
> Could wave segments be stored on ROM B and then be pointed at by ROM A?
> (Sorta, kinda like a state machine.) (Granular sound?)

To do this simply cascade two Mini-Waves. Should be very crazy!!
> 
> ----- Original Message -----
> From: matti <matti at devo.com>
> To: <synth-diy at dropmix.xs4all.nl>
> Sent: Friday, December 28, 2001 3:40 AM
> Subject: RE: [sdiy] wavetable lookup waves
> 
> 
>> On Fri, 28 Dec 2001, Colin Fraser wrote:
>> 
>>> 
>>> Eh ?
>>> 
>>> 8 bits * 256 bytes = 2048 bits.
>>> Possible combinations = 2 ^ 2048 = 3.2 x 10 ^ 616
>>> 
>>> Colin f
>> 
>> oh. less scary. thanks.
>> 
>> 
>> -
>> the chatter has stopped. oh joy. achmed, yon achmed, make my felt.
>> 
>> 
> 
>