Akjaysma: Difference between revisions
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The '''akjaysma''' is a 7-limit [[unnoticeable comma]]. It is the difference between a stack of seven | The '''akjaysma''' is a 7-limit [[unnoticeable comma]]. It is the difference between a stack of seven [[105/64]]s and five octaves; {{monzo|47 -7 -7 -7}} in monzo and 0.33765160 cents in size. For equal divisions ''N'' up to 37316, this comma is tempered out only if 7 divides ''N''. Examples are [[7edo]], [[77edo]], [[217edo]], [[224edo]], [[441edo]] and [[665edo]]. | ||
== Temperaments == | == Temperaments == | ||
Tempering out the akjaysma splits the octave into 7 equal parts and maps 105th harmonic into 5\7. It leads to a number of regular temperaments including absurdity, brahmagupta, and neutron. | Tempering out the akjaysma splits the octave into 7 equal parts and maps 105th harmonic into 5\7. It leads to a number of regular temperaments including [[Syntonic-chromatic equivalence continuum|absurdity]], [[Ragismic microtemperaments #Brahmagupta|brahmagupta]], and [[Akjaysmic temperaments|neutron]]. | ||
Akjaysmic rank-3 temperament can be described as the 441&1848&2954 temperament, which tempers out 184549376/184528125 and 199297406/199290375 in the 11-limit. | Akjaysmic rank-3 temperament can be described as the 441&1848&2954 temperament, which tempers out 184549376/184528125 and 199297406/199290375 in the 11-limit. | ||
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Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
Comma list: 184549376/184528125, 199297406/199290375 | |||
Mapping: [{{val| 7 0 0 47 -168 }}, {{val| 0 1 0 -1 10 }}, {{val| 0 0 1 -1 5 }}] | |||
Mapping generators: ~29160/26411, ~3, ~5 | |||
{{Val list | POTE generators: ~3/2 = 701.968, ~5/4 = 386.332 | ||
Vals: {{Val list| 301, 364, 441, 742, 805, 1043, 1106, 1407, 1547, 1848, 2289, 2653, 2954, 3395, 4501, 5243, 6349, 8197 }} | |||
== See also == | == See also == | ||
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[[Category:7-limit]] | [[Category:7-limit]] | ||
[[Category:Unnoticeable comma]] | [[Category:Unnoticeable comma]] | ||
[[Category:Akjaysmic]] | |||
Revision as of 00:00, 29 April 2021
| Interval information |
5/7-octave comma
reduced subharmonic
The akjaysma is a 7-limit unnoticeable comma. It is the difference between a stack of seven 105/64s and five octaves; [47 -7 -7 -7⟩ in monzo and 0.33765160 cents in size. For equal divisions N up to 37316, this comma is tempered out only if 7 divides N. Examples are 7edo, 77edo, 217edo, 224edo, 441edo and 665edo.
Temperaments
Tempering out the akjaysma splits the octave into 7 equal parts and maps 105th harmonic into 5\7. It leads to a number of regular temperaments including absurdity, brahmagupta, and neutron.
Akjaysmic rank-3 temperament can be described as the 441&1848&2954 temperament, which tempers out 184549376/184528125 and 199297406/199290375 in the 11-limit.
Akjaysmic (441&1848&2954)
Subgroup: 2.3.5.7
Comma list: [47 -7 -7 -7⟩
Mapping: [⟨7 0 0 47], ⟨0 1 0 -1], ⟨0 0 1 -1]]
Mapping generators: ~1157625/1048576, ~3, ~5
POTE generators: ~3/2 = 701.965, ~5/4 = 386.330
11-limit 441&1848&2954
Subgroup: 2.3.5.7.11
Comma list: 184549376/184528125, 199297406/199290375
Mapping: [⟨7 0 0 47 -168], ⟨0 1 0 -1 10], ⟨0 0 1 -1 5]]
Mapping generators: ~29160/26411, ~3, ~5
POTE generators: ~3/2 = 701.968, ~5/4 = 386.332
Vals: Template:Val list