Akjaysma: Difference between revisions
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| Color name = Trisa-seprugu comma | | Color name = Trisa-seprugu comma | ||
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The '''akjaysma''' is an [[ | 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 | [[Tempering out]] this comma leads to the [[akjaysmic]] temperament, which splits the octave into 7 equal parts and maps the 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]]. | ||
Akjaysmic 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. | |||
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. | |||
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== 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>. | ||
== | == References == | ||
[[Category:Akjaysmic]] | [[Category:Akjaysmic]] | ||
[[Category:Commas named after composers]] | [[Category:Commas named after composers]] | ||
[[Category:Commas named after music theorists]] | [[Category:Commas named after music theorists]] | ||
[[Category:Commas someone named after themselves]] | |||
Latest revision as of 09:04, 30 May 2026
| Interval information |
5/7-octave comma
reduced subharmonic
The akjaysma (monzo: [47 -7 -7 -7⟩) is an 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
Tempering out this comma leads to the akjaysmic temperament, which splits the octave into 7 equal parts and maps the 105th harmonic to 5\7. For edos N up to 37316, this comma is tempered out only if 7 divides N. Examples are 7edo, 77edo, 217edo, 224edo, 441edo and 665edo.
Akjaysmic 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.
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.
Etymology
This comma was named by Aaron Krister Johnson in 2011 after himself[1].