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{{Infobox Interval
{{Infobox Interval
| Icon =
| Ratio = 140 737 488 355 328 / 140 710 042 265 625
| Ratio = 140 737 488 355 328 /<br>140 710 042 265 625
| Monzo = 47 -7 -7 -7
| Cents = 0.33765
| Name = akjaysma, 5/7-octave comma
| Name = akjaysma, 5/7-octave comma
| Color name = Trisa-seprugu comma
| Color name = Trisa-seprugu comma
| FJS name =
| Sound =
}}
}}
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 0.338 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 an [[Unnoticeable comma|unnoticeable]] [[7-limit]] [[comma]]. It is the difference between a stack of seven [[105/64]]'s and five octaves; {{monzo| 47 -7 -7 -7 }} in monzo and 0.338 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 [[Syntonic-chromatic equivalence continuum|absurdity]], [[Ragismic microtemperaments #Brahmagupta|brahmagupta]], and [[Mistismic temperaments|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&ndash;chromatic equivalence continuum|absurdity]], [[Ragismic microtemperaments #Brahmagupta|brahmagupta]], and [[Mistismic temperaments|neutron]], all of which also temper out ([[128/105]])/([[39/32]]) = [[4096/4095]] in the 13-limit.


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.
In addition, akjaysma appears in temperaments whose period is a multiple of 7 (14, 21, 28, 35, etc.), however from a composer's standpoint it may not be the most prominent characterization of these temperaments due to a lot of inherent differences between multiples of 7edo. Tempering it out along with the [[landscape comma]] offers the aptly named 441 & 1407 [[akjayland]] temperament, that divides the octave into 7 x 3 = 21 parts.  


=== Akjaysmic (441&amp;1848&amp;2954) ===
=== Akjaysmic ===
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: {{monzo| 47 -7 -7 -7 }}
[[Comma list]]: {{monzo| 47 -7 -7 -7 }}


[[Mapping]]: [{{val| 7 0 0 47 }}, {{val| 0 1 0 -1 }}, {{val| 0 0 1 -1 }}]
{{Mapping|legend=1| 7 0 0 47 | 0 1 0 -1 | 0 0 1 -1 }}


Mapping generators: ~1157625/1048576, ~3, ~5
: mapping generators: ~1157625/1048576, ~3, ~5


[[POTE generator]]s: ~3/2 = 701.965, ~5/4 = 386.330
[[Optimal tuning]] ([[POTE]]): ~1157625/1048576 = 1\7, ~3/2 = 701.965, ~5/4 = 386.330


{{Val list|legend=1| 140, 224, 301, 441, 665, 742, 966, 1106, 1407, 1547, 1848, 2289, 2513, 2954, 3395, 4802 }}
{{Optimal ET sequence|legend=1| 140, 224, 301, 441, 665, 742, 966, 1106, 1407, 1547, 1848, 2289, 2513, 2954, 3395, 4802 }}


=== 11-limit 441&amp;1848&amp;2954 ===
In higher limits, akjaysmic rank-3 temperament can be described as the 441 &amp; 1848 &amp; 2954 temperament, and it tempers out 184549376/184528125 and 199297406/199290375 in the 11-limit. See [[7th-octave temperaments]].
Subgroup: 2.3.5.7.11


Comma list: 184549376/184528125, 199297406/199290375
== Etymology ==
 
This comma was named by [[Aaron Krister Johnson]] in 2011 after himself<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_99488.html Yahoo! Tuning Group | ''xenwiki comma update'']</ref>.
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
 
POTE generators: ~3/2 = 701.968, ~5/4 = 386.332
 
Optimal GPV sequence: {{Val list| 301, 364, 441, 742, 805, 1043, 1106, 1407, 1547, 1848, 2289, 2653, 2954, 3395, 4501, 5243, 6349, 8197 }}


== See also ==
== See also ==
* [[Unnoticeable comma]]
* [[Unnoticeable comma]]


[[Category:7-limit]]
== Notes ==
[[Category:Unnoticeable commas]]
 
[[Category:Akjaysmic]]
[[Category:Akjaysmic]]
[[Category:Commas named after composers]]
[[Category:Commas named after music theorists]]
[[Category:Commas someone named after themselves]]
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