## 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
mod routings...

#### 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.
- mod
- "V"/oct
- 42
- 1/24
- 46
- 1/12
- 50
- 1/8
- 53
- 1/6
- 55
- 5/24
- 56
- 1/4
- 57
- 7/24
- 58
- 1/3
- 60
- 5/12
- 61
- 1/2
- 62
- 7/12
- 63
- 2/3