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.