2.7.11 subgroup: Difference between revisions
From Xenharmonic Reference
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[[26edo]] is known for having both accurate 7/4 and 11/8. | [[26edo]] is known for having both accurate 7/4 and 11/8. | ||
[[Orgone]] ( | [[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. | ||
{{Cat|JI groups}} | {{Cat|JI groups}} | ||
Revision as of 03:16, 12 March 2026
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).
JI scales
LsLmLsL
8/7
77/64
11/8
16/11
128/77
7/4
2/1Ternary detempering of 11edo
539/512
8/7
77/64
64/49
11/8
16/11
49/32
128/77
7/4
1024/539
2/1Ternary detempering of 15edo
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
2/1Temperaments
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.
