2.7.11 subgroup

The 2.7.11 subgroup is the JI group consisting of the intervals reachable by stacking 2/1, 7/4, and 11/8, with the exclusion of 3/2 and 5/4 (adding which would result in the full 11-limit).

The basic otonal triad of 2.7.11 is 4:7:11 or the isoharmonic 8:11:14.

JI scales

Detempered Orgone[7]

8/7
77/64
11/8
16/11
128/77
7/4
2/1

Ternary detempering of 11edo

539/512
8/7
77/64
64/49
11/8
16/11
49/32
128/77
7/4
1024/539
2/1

Ternary detempering of 15edo

mLsmLsmLmsLmsLm, 5L(6m4s), [L, m, s] = [128/121, 539/512, 352/343]

A 3×5 parallelogram scale

539/512
49/44
8/7
77/64
14/11
64/49
11/8
16/11
49/32
11/7
128/77
7/4
88/49
1024/539
2/1

Temperaments

26edo is known for having both accurate 7/4 and 11/8.

Orgone (11 & 15), which equates a stack of three 11/8 neutral fourths (octave reduced) and two 8/7's, is a particularly efficient temperament in the 2.7.11 group. Amaranthine (5 & 26), which equates a stack of eight 8/7's with 32/11, is a more complex but still notably accurate 2.7.11 temperament, however it requires an accurate 7 to make sense in an edo.