Quartaminorthirds

Quartaminorthirds is the 7-limit linear temperament with wedgie
[9, 5, -3, -21, 30, -13] and period matrix
[[1, 1, 2, 3], [0, 9, 5, -3]]. It tempers out 1029/1024, 6144/6125
and their product, 126/125. It is covered by 31, 46, 77 and 108
among others, but 139 gives almost exactly the rms optimal values
with the generator 9/139. It has MOS of size 15 and 16, which in
139 terms are [(9)*14, 13] and [(9)*15, 4]. The first is more
regular, but the second I think is more interesting because like
Blackjack it can be described in terms of a linear array of tetrads.

The complexity measure most useful if we are interested in complete
tetrads is Graham complexity, and here we have a value of 12, as
opposed to 13 for miracle. The signature is of unital type,
[-7,1,17]. From a complexity of 12 we conclude we have four major and
four minor tetrads, and these can be identified with the tetrads from
[0,0,0] to [0,0,7], which give us the steps defined by the generator
running from -3 to 12.

--- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
From a complexity of 12 we conclude we have four major and
> four minor tetrads, and these can be identified with the tetrads from
> [0,0,0] to [0,0,7], which give us the steps defined by the generator
> running from -3 to 12.

This should be the tetrads from [0,0,0] to [0,7,0], of course.