Akjaysma - Revision history

FloraC at 09:04, 30 May 2026

2026-05-30T09:04:21Z

← Older revision		Revision as of 09:04, 30 May 2026
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	== Temperaments ==		== Temperaments ==
	[[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]].		[[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]].

	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 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.		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.

FloraC: - duplicate data & cleanup

2026-05-30T09:03:20Z

- duplicate data & cleanup

← Older revision		Revision as of 09:03, 30 May 2026
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	\| Color name = Trisa-seprugu comma		\| Color name = Trisa-seprugu comma
	}}		}}
	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]]

FloraC: +category

2025-04-25T12:06:09Z

+category

← Older revision		Revision as of 12:06, 25 April 2025
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	[[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]]

Godtone: /* Temperaments */ all the noted akjaysmic temps follow the natural mapping of 39/32

2025-03-11T21:48:04Z

Temperaments: all the noted akjaysmic temps follow the natural mapping of 39/32

← Older revision		Revision as of 21:48, 11 March 2025
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	== 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–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.

	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.		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.

ArrowHead294 at 01:58, 4 December 2024

2024-12-04T01:58:06Z

← Older revision		Revision as of 01:58, 4 December 2024
Line 7:		Line 7:

	== 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–chromatic equivalence continuum\|absurdity]], [[Ragismic microtemperaments #Brahmagupta\|brahmagupta]], and [[Mistismic temperaments\|neutron]].

	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.		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.

BudjarnLambeth at 02:22, 4 November 2024

2024-11-04T02:22:00Z

← Older revision		Revision as of 02:22, 4 November 2024
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	[[Category:Akjaysmic]]		[[Category:Akjaysmic]]
	[[Category:Commas named after ~~individuals~~]]		[[Category:Commas named after composers]]
			[[Category:Commas named after music theorists]]

BudjarnLambeth at 23:37, 3 November 2024

2024-11-03T23:37:31Z

← Older revision		Revision as of 23:37, 3 November 2024
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	[[Category:Akjaysmic]]		[[Category:Akjaysmic]]
			[[Category:Commas named after individuals]]

FloraC: +naming

2023-07-20T08:49:36Z

+naming

← Older revision		Revision as of 08:49, 20 July 2023
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	\| Color name = Trisa-seprugu comma		\| Color name = Trisa-seprugu comma
	}}		}}
	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 ==
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	=== Akjaysmic ===		=== 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

	{{Optimal ET sequence\|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 }}

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

			== Notes ==

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

Eliora: /* Temperaments */ elaborate

2023-06-14T00:17:26Z

Temperaments: elaborate

← Older revision		Revision as of 00:17, 14 June 2023
Line 7:		Line 7:

	== 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-chromatic equivalence continuum\|absurdity]], [[Ragismic microtemperaments #Brahmagupta\|brahmagupta]], and [[Mistismic temperaments\|neutron]].

	In addition, ~~tempering~~ it out offers aptly named 441 & 1407 [[akjayland]] temperament, ~~where it is also tempered along with the landscape comma which splits the octave in three and therefore produces a temperament~~ that divides the octave into 7 x 3 = 21 parts.		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 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 ===		=== Akjaysmic ===
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	{{Optimal ET sequence\|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 }}

			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]].

	== See also ==		== See also ==

Eliora: /* Temperaments */ move 11-limit into 7th-octave temperaments, in the context of comma only the existing limit is relevant

2023-06-14T00:14:23Z

Temperaments: move 11-limit into 7th-octave temperaments, in the context of comma only the existing limit is relevant

← Older revision		Revision as of 00:14, 14 June 2023
Line 13:		Line 13:
	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.

	=== Akjaysmic ~~(441&1848&2954)~~ ===		=== Akjaysmic ===
	Subgroup: 2.3.5.7		Subgroup: 2.3.5.7

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	{{Optimal ET sequence\|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&1848&2954 ===~~
	~~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~~

	~~POTE generators: ~3/2 = 701.968, ~5/4 = 386.332~~

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

	== See also ==		== See also ==