Alternate tunings on the Matrix-6
The Matrix-6 has no explicit knowledge of tuning, but it's easy
enough to program it into any desired equal temperament: simply
alter the depth by which the keyboard modulates the oscillators. In
particular, I wanted to try 19-tone equal.
First understand modulation strengths.
An example: 19-tet
I found that to cancel out keyboard tracking takes 4(-63) mods by KEYB,
and a (+42) to clean things up. So the keyboard is hard-wired to mod
the oscs by 4(2/3) - 1/12 = 31/12. (To define these mod strengths, I'm
assuming that oscs have a 1 "volt"/octave response. A (+63) mod creates
a 16-semitone interval from a +2 signal, so it has a strength of 16/12/2
= 2/3.) For 19-tet, we want to reduce the tracking by a (19-12)/19
fraction. So we need downward mod by keyboard with a strength of
(31/12)(7/19) = 0.95175.
Well, 0.95175 = 0.66667 [-63] + 0.28509 [-57] - 0.00658
[eh, fix it by ear]. The fudge factor turns out to be about
-29 (don't ask me why it's negative). So (-63)(-57)(-29) is the right
combination, as far as I can hear. Doing this to both oscs eats six
The general approach
Let's say we want N-tet, with N greater than twelve (the
other case is similar). We have 12 tones per octave; we want N.
So reduce keyboard modulation by (N-12)/N. As keyboard
mod starts out at 31/12 "volts"/octave, this requires negative mod with a
"V"/oct strength of X = (31/12)·(N-12)/N.
Approximate X as a sum of a few mods, using the table below.
Enable one osc, set up these mods, play an octave, and add one more
mod for fine-tuning.