## 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

 (go to my front-door page) eli+w3@cs.cmu.edu19 Jan 2002