I put the 11-temperament programs which I had written but not used to work on this, and got [2,8,-11,5,8,-23,1,-48,-16,52] for the wedgie from the val side. I then plugged 81/80, 121/120 and 6144/6125 in, and found it had torsion. This was depressing until I found that

81/80, 121/120 and 176/175 (among other possibilities) also works.

If no one seriously objects I'll dub the linear 11-limit temperament with the above wedgie and kernel basis the "Arabic".

From the wedgie, I get as a period matrix

[ 0 1]

[ 2 1]

[ 8 0]

[-11 6]

[ 5 2]

This has generators a = 9.0053365/31 = 15.9772099/55; b = 1. This is, of course, the neutral third of about 11/9, or 348.59367 cents if you want to get picky.

badness = 293.7893492

rms = 6.681354997

g = 9.680613914

The 7-tone MOS is Mohajira:

[5, 4, 5, 4, 5, 4, 4]

[9, 7, 9, 7, 9, 7, 7]

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:

> The 7-tone MOS is Mohajira:

>

> [5, 4, 5, 4, 5, 4, 4]

> [9, 7, 9, 7, 9, 7, 7]

And the alteration with 5, rather than 3, homotetrachordal octave

species is the Arabic Diatonic: 5, 4, 4, 5, 5, 4, 4.

Whenever you find an MOS, you should always check if some alteration

of the MOS gives more homotetrachordal octave species.

In fact, Dave Keenan and I found a scale with three step sizes that

was omnitetrachordal. Although the scale had 22 notes, I think this

points out that one cannot assume that the melodically "nicest"

scales will always come directly from altering an MOS in this way.