[sdiy] top octave gneration

[Don Tillman]

Brock Russell wrote:

> Just happen to have the 9 bit top octave divide list on my desk.
> (2 MHz typical input)
> Equal tempered scale; a few Just scales from Vanessa Else (Polyphony May 84)
> C (hi)  239             210     360     630     24
> B       253             224     384     672     26
> A#      268             240     400     720     27
> A       284             252     432     756     28
> G#      301             270     450     810     30
> G       319             280     480     840     32
> F#      338             330     512     900     33
> F       358             315     540     945     36
> E       379             336     576     1008    39
> D#      402             360     600     1080    40
> D       426             378     640     1120    42
> C#      451             405     675     1225    44
> C (lo)  478             420     720     1260    48

I'm sure I've said it a couple times before whenever the topic of top octave
generators comes up, but it's been a while...

The divide-by-239 to divide-by-478 is the classic top octave chip, like the
5024.  It has roughly twice the error of the gear-based Hammond organ tone
generator (that's 1938 technology!)

The reason is that instead of a 1/N approach the Hammond uses a pair of gears
for each note, and thus an M/N approach, which gives you bettter accuracy with
smallish integers.

This suggests a couple things.  One is that you might want to aim for better
accuracy than a 1938 organ.  Another is that it might be fun to copy the Hammond
ratios exactly with twelve 4046 PLLs and 24 dividers.

  -- Don

--
Don Tillman
Palo Alto, California, USA
don at till.com
http://www.till.com