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Akjaysma: Difference between revisions

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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]].
The '''akjaysma''' ({{monzo|legend=1| 47 -7 -7 -7 }}) is an [[unnoticeable comma|unnoticeable]] [[7-limit]] [[comma]] with a size of about 0.338 cents. It is the difference between a stack of seven [[105/64]]'s and five octaves.  


== 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]], all of which also temper out ([[128/105]])/([[39/32]]) = [[4096/4095]] in the 13-limit.
[[Tempering out]] the akjaysma splits the octave into 7 equal parts and maps 105th harmonic to 5\7. For [[edo]]s ''N'' up to 37316, this comma is tempered out only if 7 divides ''N''. Examples are [[7edo]], [[77edo]], [[217edo]], [[224edo]], [[441edo]] and [[665edo]].


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.  
It can be further tempered to a number of rank-2 temperaments such as [[absurdity]], [[brahmagupta]], and [[neutron]], all of which also temper out ([[128/105]])/([[39/32]]) = [[4096/4095]] in the 13-limit.


=== Akjaysmic ===
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 21 parts.  
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: {{monzo| 47 -7 -7 -7 }}
 
{{Mapping|legend=1| 7 0 0 47 | 0 1 0 -1 | 0 0 1 -1 }}
 
: mapping generators: ~1157625/1048576, ~3, ~5
 
[[Optimal tuning]] ([[POTE]]): ~1157625/1048576 = 1\7, ~3/2 = 701.965, ~5/4 = 386.330
 
{{Optimal ET sequence|legend=1| 140, 224, 301, 441, 665, 742, 966, 1106, 1407, 1547, 1848, 2289, 2513, 2954, 3395, 4802 }}
 
In higher limits, akjaysmic rank-3 temperament can be described as the 441 & 1848 & 2954 temperament, and it tempers out 184549376/184528125 and 199297406/199290375 in the 11-limit. See [[7th-octave temperaments]].


== Etymology ==
== 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>.  
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>.  


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


[[Category:Akjaysmic]]
[[Category:Akjaysmic]]
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