Scale generators and ASR/OTTO tuning resolution

>Marion tells us:
>There are matrix methods, which multiply sets of frequency
>ratios, and there are cycle methods which multiply a single ratio
>iteratively. All of them quickly generate a lot of scales, but
>they are, for the greater part, scales that can not be accurately
>reproduced on contemporary instruments. Also, these methods are
>mostly indifferent to the consonance of the scales they produce.

Sad but true. The especially odd part is that oscillator chips have pretty
good resolution but making them represent ET scales cuts this down
significantly.

For instance, The OTTO chip in the ASR-10 has an 11-bit fractional phase
accumulator. This means that a sample from unity up to an octave can
resolve 2048 different intervals. An octave above that this number doubles
for each octave, and each octave below this is halved.

The tuning tables are represented as 7 bits between semitones, which is 1524
steps or .78 cents. However, the exponential table used to convert linear
frequency isn't long enough, which is why you really only get 768 steps or
the 1.5 cent resolution measured by Carter Scholz a number of years ago.
(Thanks to Bill Mauchly for this info)

What's needed is some kind of 'ratio mode' which calculates this directly
and sets up integer ratios between different voices. Don't look for this in
any sort of product from us any time soon, though. If you have a Soundscape
card it is possible to hit the OTTO chip directly from the PC and put in
your own ratios. Writing some Forth code to do this and implement Marion's
variable loop length tuning method has been on my project stack for a while.
The only big problem is that the Soundscape waveforms are in ROM, but you
could possibly find different waveforms of different lengths and match them up.

regards,

Steve Curtin
Ensoniq Corp


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