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]
<syntaxhighlight> 8/7 77/64 11/8 16/11 128/77 7/4 2/1 </syntaxhighlight>
Ternary detempering of 11edo
<syntaxhighlight> 539/512 8/7 77/64 64/49 11/8 16/11 49/32 128/77 7/4 1024/539 2/1 </syntaxhighlight>
Ternary detempering of 15edo
mLsmLsmLmsLmsLm, 5L(6m4s), [L, m, s] = [128/121, 539/512, 352/343]
A 3×5 parallelogram scale
<syntaxhighlight> 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 </syntaxhighlight>
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.
