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 ~~128~~/~~105s~~ and ~~two~~ 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]].

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 ==

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.

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Subgroup: 2.3.5.7.11

[[Comma list]]: 184549376/184528125, 199297406/199290375

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: [{{val| 7 0 0 47 -168 }}, {{val| 0 1 0 -1 10 }}, {{val| 0 0 1 -1 5 }}]

~~[[POTE generator]]s~~: ~3~~/2 = 701.968~~, ~5~~/4 = 386.332~~

Mapping generators: ~29160/26411, ~3, ~5

{{Val list~~|legend=1~~| 301, 364, 441, 742, 805, 1043, 1106, 1407, 1547, 1848, 2289, 2653, 2954, 3395, 4501, 5243, 6349, 8197 }}

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 ==

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[[Category:7-limit]]

[[Category:Unnoticeable comma]]

[[Category:Akjaysmic]]

@@ Line 10: / Line 10: @@
 }}
-The '''akjaysma''' is a 7-limit [[unnoticeable comma]]. It is the difference between a stack of seven 128/105s and two 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]].
+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 ==
-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&amp;1848&amp;2954 temperament, which tempers out 184549376/184528125 and 199297406/199290375 in the 11-limit.
@@ Line 33: / Line 33: @@
 Subgroup: 2.3.5.7.11
-[[Comma list]]: 184549376/184528125, 199297406/199290375
+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: [{{val| 7 0 0 47 -168 }}, {{val| 0 1 0 -1 10 }}, {{val| 0 0 1 -1 5 }}]
-[[POTE generator]]s: ~3/2 = 701.968, ~5/4 = 386.332
+Mapping generators: ~29160/26411, ~3, ~5
-{{Val list|legend=1| 301, 364, 441, 742, 805, 1043, 1106, 1407, 1547, 1848, 2289, 2653, 2954, 3395, 4501, 5243, 6349, 8197 }}
+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 ==
@@ Line 47: / Line 49: @@
 [[Category:7-limit]]
 [[Category:Unnoticeable comma]]
+[[Category:Akjaysmic]]