2.7.11 subgroup: Difference between revisions
Created page with "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). {{Cat|JI groups}}" |
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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 '''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 substring scale|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. {{Adv|[[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}} | ||
Latest revision as of 05:21, 14 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).
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
2/1Ternary 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
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
2/1Temperaments
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.
