936/935 - Revision history

FloraC: Update data

2026-03-22T15:31:54Z

Update data

← Older revision		Revision as of 15:31, 22 March 2026
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[~~CTE~~]]: ~2 = ~~1200~~.~~0000~~{{c}}, ~3/2 = 701.~~7942~~{{c}}, ~5/4 = 386.~~4863~~{{c}}, ~11/8 = 551.~~7011~~{{c}}, ~13/8 = 840.~~0893~~{{c}}		* [[WE]]: ~2 = 1199.9169{{c}}, ~3/2 = 701.8989{{c}}, ~5/4 = 386.6292{{c}}, ~11/8 = 551.8987{{c}}, ~13/8 = 840.3976{{c}}
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8763{{c}}, ~5/4 = 386.5772{{c}}, ~11/8 = 551.8274{{c}}, ~13/8 = 840.2857{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8763{{c}}, ~5/4 = 386.5772{{c}}, ~11/8 = 551.8274{{c}}, ~13/8 = 840.2857{{c}}

	{{Optimal ET sequence\|legend=1\| 22, 24, 31, 34, 46, 53, 58, 65, 72, 87, 111, 137, 183, 304, 320, 354, 400, 407, 441, 537, 552g, 624 }}		{{Optimal ET sequence\|legend=1\| 22, 24, 31, 34, 46, 53, 58, 65, 72, 87, 111, 137, 183, 304, 320, 354, 400, 407, 441, 537, 552g, 624 }}

			[[Badness]] (Sintel): 0.119

	=== Ainismic ===		=== Ainismic ===
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[~~CTE~~]]: ~2 = ~~1200~~.~~0000~~{{c}}, ~3/2 = 701.~~7942~~{{c}}, ~5/4 = 386.~~4863~~{{c}}, ~7/4 = 968.~~8259~~{{c}}, ~11/8 = 551.~~7011~~{{c}}, ~13/8 = 840.~~0893~~{{c}}		* [[WE]]: ~2 = 1199.9169{{c}}, ~3/2 = 701.8989{{c}}, ~5/4 = 386.6292{{c}}, ~7/4 = 968.9921{{c}}, ~11/8 = 551.8987{{c}}, ~13/8 = 840.3976{{c}}
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8763{{c}}, ~5/4 = 386.5773{{c}}, ~7/4 = 968.9509{{c}}, ~11/8 = 551.8275{{c}}, ~13/8 = 840.2857{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8763{{c}}, ~5/4 = 386.5773{{c}}, ~7/4 = 968.9509{{c}}, ~11/8 = 551.8275{{c}}, ~13/8 = 840.2857{{c}}

	{{Optimal ET sequence\|legend=1\| 22, 26, 31, 38df, 41, 46, 58, 72, 103, 111, 121, 149, 159, 171, 183, 217, 224, 270, 354, 400, 441, 552g, 624, 1393ceegg, 1576cdegg }}		{{Optimal ET sequence\|legend=1\| 22, 26, 31, 38df, 41, 46, 58, 72, 103, 111, 121, 149, 159, 171, 183, 217, 224, 270, 354, 400, 441, 552g, 624, 1393ceegg, 1576cdegg }}

			[[Badness]] (Sintel): 0.322

	== Etymology ==		== Etymology ==

FloraC: Cleanup

2026-03-22T15:27:58Z

Cleanup

← Older revision		Revision as of 15:27, 22 March 2026
Line 4:		Line 4:
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''936/935''', the '''ainisma''' or '''ainic comma''', is a [[17-limit]] [[~~unnoticeable~~ comma]] with a size of roughly 1.85 [[cent]]s. It arises as the amount by which a stack consisting of [[18/17]] and [[13/11]] exceeds [[5/4]], as well as the amount by which a stack consisting of [[10/9]] and [[17/16]] falls short of 13/11. Moreover, it is also the interval that differentiates the [[273/272\|tannisma (273/272)]] from the [[385/384\|keenanisma (385/384)]], and the [[256/255\|septendecimal kleisma (256/255)]] from the [[352/351\|major minthma (352/351)]]. Thus, tempering out this comma is a good way to extend minthmic and gentle harmonies to the 17-limit, as well as a good way to bring keenanismic and tannismic harmonies together. See [[#Commatic relations]] for more.		'''936/935''', the '''ainisma''' or '''ainic comma''', is an [[unnoticeable comma\|unnoticeable]] [[17-limit]] [[comma]] with a size of roughly 1.85 [[cent]]s. It arises as the amount by which a stack consisting of [[18/17]] and [[13/11]] exceeds [[5/4]], as well as the amount by which a stack consisting of [[10/9]] and [[17/16]] falls short of 13/11. Moreover, it is also the interval that differentiates the [[273/272\|tannisma (273/272)]] from the [[385/384\|keenanisma (385/384)]], and the [[256/255\|septendecimal kleisma (256/255)]] from the [[352/351\|major minthma (352/351)]]. Thus, tempering out this comma is a good way to extend minthmic and gentle harmonies to the 17-limit, as well as a good way to bring keenanismic and tannismic harmonies together. See [[#Commatic relations]] for more.

	== Commatic relations ==		== Commatic relations ==
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	== Temperaments ==		== Temperaments ==
	When tempered out in the full 17-limit, the resulting rank-6 temperament is called the '''ainismic ~~temperament~~''', or in the 2.3.5.11.13.17 subgroup, the rank-5 '''ainic ~~temperament~~'''. Both are characterized by the presence of [[~~Dyadic chord\|~~essentially tempered chord]]s called [[ainismic chords]].		When tempered out in the full 17-limit, the resulting rank-6 temperament is called the '''ainismic''' temperament, or in the 2.3.5.11.13.17 subgroup, the rank-5 '''ainic''' temperament. Both are characterized by the presence of [[essentially tempered chord]]s called [[ainismic chords]].

	=== Ainic ===		=== Ainic ===
	[[Subgroup]]: 2.3.5.11.13.17		[[Subgroup]]: 2.3.5.11.13.17

	[[~~Comma list]]: 936/935~~		[[Subgroup val\|Subgroup-val]] [[mapping]]:<br>

	~~[[Sval~~]] [[mapping]]:<br>
	{\| class="right-all"		{\| class="right-all"
	\|-		\|-
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	\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 1 \|\| ]]		\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 1 \|\| ]]
	\|}		\|}
	: ~~sval~~ mapping generators: ~2, ~3, ~5, ~11, ~13		: mapping generators: ~2, ~3, ~5, ~11, ~13

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~2 = ~~1\1~~, ~3/2 = 701.7942, ~5/4 = 386.4863, ~11/8 = 551.7011, ~13/8 = 840.0893		* [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7942{{c}}, ~5/4 = 386.4863{{c}}, ~11/8 = 551.7011{{c}}, ~13/8 = 840.0893{{c}}
	* [[CWE]]: ~2 = ~~1\1~~, ~3/2 = 701.8763, ~5/4 = 386.5772, ~11/8 = 551.8274, ~13/8 = 840.2857		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8763{{c}}, ~5/4 = 386.5772{{c}}, ~11/8 = 551.8274{{c}}, ~13/8 = 840.2857{{c}}

	{{Optimal ET sequence\|legend=1\| 22, 24, 31, 34, 46, 53, 58, 65, 72, 87, 111, 137, 183, 304, 320, 354, 400, 407, 441, 537, 552g, 624 }}		{{Optimal ET sequence\|legend=1\| 22, 24, 31, 34, 46, 53, 58, 65, 72, 87, 111, 137, 183, 304, 320, 354, 400, 407, 441, 537, 552g, 624 }}
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	=== Ainismic ===		=== Ainismic ===
	[[Subgroup]]: 2.3.5.7.11.13.17		[[Subgroup]]: 2.3.5.7.11.13.17

	~~[[Comma list]]: 936/935~~

	[[Mapping]]:<br>		[[Mapping]]:<br>
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~2 = ~~1\1~~, ~3/2 = 701.7942, ~5/4 = 386.4863, ~7/4 = 968.8259, ~11/8 = 551.7011, ~13/8 = 840.0893		* [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7942{{c}}, ~5/4 = 386.4863{{c}}, ~7/4 = 968.8259{{c}}, ~11/8 = 551.7011{{c}}, ~13/8 = 840.0893{{c}}
	* [[CWE]]: ~2 = ~~1\1~~, ~3/2 = 701.8763, ~5/4 = 386.5773, ~7/4 = 968.9509, ~11/8 = 551.8275, ~13/8 = 840.2857		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8763{{c}}, ~5/4 = 386.5773{{c}}, ~7/4 = 968.9509{{c}}, ~11/8 = 551.8275{{c}}, ~13/8 = 840.2857{{c}}

	{{Optimal ET sequence\|legend=1\| 22, 26, 31, 38df, 41, 46, 58, 72, 103, 111, 121, 149, 159, 171, 183, 217, 224, 270, 354, 400, 441, 552g, 624, 1393ceegg, 1576cdegg }}		{{Optimal ET sequence\|legend=1\| 22, 26, 31, 38df, 41, 46, 58, 72, 103, 111, 121, 149, 159, 171, 183, 217, 224, 270, 354, 400, 441, 552g, 624, 1393ceegg, 1576cdegg }}
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	== See also ==		== See also ==
	* [[Unnoticeable comma]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	[[Category:Ainismic]]		[[Category:Ainismic]]
	[[Category:Commas named by translating something into another language]]		[[Category:Commas named by translating something into another language]]

Squib: it's the ''major'' minthma

2026-02-13T16:06:06Z

it's the ''major'' minthma

← Older revision		Revision as of 16:06, 13 February 2026
Line 4:		Line 4:
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''936/935''', the '''ainisma''' or '''ainic comma''', is a [[17-limit]] [[unnoticeable comma]] with a size of roughly 1.85 [[cent]]s. It arises as the amount by which a stack consisting of [[18/17]] and [[13/11]] exceeds [[5/4]], as well as the amount by which a stack consisting of [[10/9]] and [[17/16]] falls short of 13/11. Moreover, it is also the interval that differentiates the [[273/272\|tannisma (273/272)]] from the [[385/384\|keenanisma (385/384)]], and the [[256/255\|septendecimal kleisma (256/255)]] from the [[352/351\|minthma (352/351)]]. Thus, tempering out this comma is a good way to extend minthmic and gentle harmonies to the 17-limit, as well as a good way to bring keenanismic and tannismic harmonies together. See [[#Commatic relations]] for more.		'''936/935''', the '''ainisma''' or '''ainic comma''', is a [[17-limit]] [[unnoticeable comma]] with a size of roughly 1.85 [[cent]]s. It arises as the amount by which a stack consisting of [[18/17]] and [[13/11]] exceeds [[5/4]], as well as the amount by which a stack consisting of [[10/9]] and [[17/16]] falls short of 13/11. Moreover, it is also the interval that differentiates the [[273/272\|tannisma (273/272)]] from the [[385/384\|keenanisma (385/384)]], and the [[256/255\|septendecimal kleisma (256/255)]] from the [[352/351\|major minthma (352/351)]]. Thus, tempering out this comma is a good way to extend minthmic and gentle harmonies to the 17-limit, as well as a good way to bring keenanismic and tannismic harmonies together. See [[#Commatic relations]] for more.

	== Commatic relations ==		== Commatic relations ==

Squib: /* Commatic relations */

2025-12-13T17:10:44Z

Commatic relations

← Older revision		Revision as of 17:10, 13 December 2025
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	== Commatic relations ==		== Commatic relations ==
	This comma is the difference between the following superparticular pairs:		This comma is the difference between the following superparticular pairs:
			* [[52/51]] and [[55/54]]
	* [[78/77]] and [[85/84]]		* [[78/77]] and [[85/84]]
	* [[144/143]] and [[170/169]]		* [[144/143]] and [[170/169]]

BudjarnLambeth at 01:54, 16 November 2024

2024-11-16T01:54:04Z

← Older revision		Revision as of 01:54, 16 November 2024
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	[[Category:Ainismic]]		[[Category:Ainismic]]
			[[Category:Commas named by translating something into another language]]

FloraC: +temperaments

2024-03-28T09:49:15Z

+temperaments

@@ Line 4: / Line 4: @@
 | Comma = yes
 }}
 '''936/935''', the '''ainisma''' or '''ainic comma''', is a [[17-limit]] [[unnoticeable comma]] with a size of roughly 1.85 [[cent]]s. It arises as the amount by which a stack consisting of [[18/17]] and [[13/11]] exceeds [[5/4]], as well as the amount by which a stack consisting of [[10/9]] and [[17/16]] falls short of 13/11. Moreover, it is also the interval that differentiates the [[273/272|tannisma (273/272)]] from the [[385/384|keenanisma (385/384)]], and the [[256/255|septendecimal kleisma (256/255)]] from the [[352/351|minthma (352/351)]]. Thus, tempering out this comma is a good way to extend minthmic and gentle harmonies to the 17-limit, as well as a good way to bring keenanismic and tannismic harmonies together. See [[#Commatic relations]] for more.
@@ Line 30: / Line 29: @@
 == Temperaments ==
-When tempered out in the full 17-limit, the resulting temperament is called the '''ainismic temperament''', or in the 2.3.5.11.13.17 subgroup, the '''ainic temperament'''. Both are characterized by the presence of [[Dyadic chord|essentially tempered chord]]s called [[ainismic chords]].
+When tempered out in the full 17-limit, the resulting rank-6 temperament is called the '''ainismic temperament''', or in the 2.3.5.11.13.17 subgroup, the rank-5 '''ainic temperament'''. Both are characterized by the presence of [[Dyadic chord|essentially tempered chord]]s called [[ainismic chords]].
 == Etymology ==

Francium: Added color name

2023-09-07T18:38:39Z

Added color name

← Older revision		Revision as of 18:38, 7 September 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = ainisma, ainic comma		\| Name = ainisma, ainic comma
			\| Color name = 17u3o1ug1, sutholugu unison
	\| Comma = yes		\| Comma = yes
	}}		}}

FloraC: Aura and I agreed we should follow the construction of the term "xenisma"

2023-08-15T16:59:45Z

Aura and I agreed we should follow the construction of the term "xenisma"

← Older revision		Revision as of 16:59, 15 August 2023
Line 1:		Line 1:
	{{Infobox Interval		{{Infobox Interval
	\| Name = ~~ainos~~, ainic comma		\| Name = ainisma, ainic comma
	\| Comma = yes		\| Comma = yes
	}}		}}

	'''936/935''', the '''~~ainos~~''' or '''ainic comma''', is a [[17-limit]] [[unnoticeable comma]] with a size of roughly 1.85 [[cent]]s. It arises as the amount by which a stack consisting of [[18/17]] and [[13/11]] exceeds [[5/4]], as well as the amount by which a stack consisting of [[10/9]] and [[17/16]] falls short of 13/11. Moreover, it is also the interval that differentiates the [[273/272\|tannisma (273/272)]] from the [[385/384\|keenanisma (385/384)]], and the [[256/255\|septendecimal kleisma (256/255)]] from the [[352/351\|minthma (352/351)]]. Thus, tempering out this comma is a good way to extend minthmic and gentle harmonies to the 17-limit, as well as a good way to bring keenanismic and tannismic harmonies together. See [[#Commatic relations]] for more.		'''936/935''', the '''ainisma''' or '''ainic comma''', is a [[17-limit]] [[unnoticeable comma]] with a size of roughly 1.85 [[cent]]s. It arises as the amount by which a stack consisting of [[18/17]] and [[13/11]] exceeds [[5/4]], as well as the amount by which a stack consisting of [[10/9]] and [[17/16]] falls short of 13/11. Moreover, it is also the interval that differentiates the [[273/272\|tannisma (273/272)]] from the [[385/384\|keenanisma (385/384)]], and the [[256/255\|septendecimal kleisma (256/255)]] from the [[352/351\|minthma (352/351)]]. Thus, tempering out this comma is a good way to extend minthmic and gentle harmonies to the 17-limit, as well as a good way to bring keenanismic and tannismic harmonies together. See [[#Commatic relations]] for more.

	== Commatic relations ==		== Commatic relations ==
Line 29:		Line 29:

	== Temperaments ==		== Temperaments ==
	When tempered out in the full 17-limit, the resulting temperament is called the '''~~ainic~~ temperament''', or in the 2.3.5.11.13.17 subgroup, the '''~~ainian~~ temperament'''. Both are characterized by the presence of [[Dyadic chord\|essentially tempered chord]]s called [[~~ainic~~ chords]].		When tempered out in the full 17-limit, the resulting temperament is called the '''ainismic temperament''', or in the 2.3.5.11.13.17 subgroup, the '''ainic temperament'''. Both are characterized by the presence of [[Dyadic chord\|essentially tempered chord]]s called [[ainismic chords]].

	== Etymology ==		== Etymology ==
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	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	[[Category:~~Ainic~~]]		[[Category:Ainismic]]

FloraC: +commatic relations

2023-05-23T07:53:50Z

+commatic relations

@@ Line 4: / Line 4: @@
 }}
-'''936/935''', the '''ainos''' or '''ainic comma''', is a [[17-limit]] [[unnoticeable comma]] with a size of roughly 1.85 [[cent]]s. It arises as the amount by which a stack consisting of [[18/17]] and [[13/11]] exceeds [[5/4]], as well as the amount by which a stack consisting of [[10/9]] and [[17/16]] falls short of 13/11. Moreover, it is also the interval that differentiates the [[273/272|tannisma (273/272)]] from the [[385/384|keenanisma (385/384)]], and the [[256/255|septendecimal kleisma (256/255)]] from the [[352/351|minthma (352/351)]]. Thus, tempering out this comma is a good way to extend minthmic and gentle harmonies to the 17-limit, as well as a good way to bring keenanismic and tannismic harmonies together.
+'''936/935''', the '''ainos''' or '''ainic comma''', is a [[17-limit]] [[unnoticeable comma]] with a size of roughly 1.85 [[cent]]s. It arises as the amount by which a stack consisting of [[18/17]] and [[13/11]] exceeds [[5/4]], as well as the amount by which a stack consisting of [[10/9]] and [[17/16]] falls short of 13/11. Moreover, it is also the interval that differentiates the [[273/272|tannisma (273/272)]] from the [[385/384|keenanisma (385/384)]], and the [[256/255|septendecimal kleisma (256/255)]] from the [[352/351|minthma (352/351)]]. Thus, tempering out this comma is a good way to extend minthmic and gentle harmonies to the 17-limit, as well as a good way to bring keenanismic and tannismic harmonies together. See [[#Commatic relations]] for more.
 == Commatic relations ==
-It factors into two superparticular intervals: [[1701/1700]] × [[2080/2079]].
+This comma is the difference between the following superparticular pairs:
 == Temperaments ==

FloraC: Rework

2023-05-23T07:34:30Z

Rework

← Older revision		Revision as of 07:34, 23 May 2023
Line 4:		Line 4:
	}}		}}

	'''936/935''', the '''ainos''' or '''ainic comma''', is a [[17-limit]] [[unnoticeable comma]] with a size of roughly 1.85 ~~cents~~. It arises as the amount by which a stack consisting of [[18/17]] and [[13/11]] exceeds [[5/4]], as well as the amount by which a stack consisting of [[10/9]] and [[17/16]] falls short of 13/11. Moreover, it is also the interval that differentiates the [[273/272\|tannisma (273/272)]] from the [[385/384\|keenanisma (385/384)]], and the [[256/255\|septendecimal kleisma (256/255)]] from the [[352/351\|minthma (352/351)]]. Thus, tempering out this comma is a good way to extend minthmic and gentle harmonies to the 17-limit, as well as a good way to bring keenanismic and tannismic harmonies together. When tempered out in a linearly independent fashion, the resulting temperaments are called "'''ainos temperaments'''", and are characterized by the presence of [[Dyadic chord\|essentially tempered chord]]s called "[[ainic chords]]".		'''936/935''', the '''ainos''' or '''ainic comma''', is a [[17-limit]] [[unnoticeable comma]] with a size of roughly 1.85 [[cent]]s. It arises as the amount by which a stack consisting of [[18/17]] and [[13/11]] exceeds [[5/4]], as well as the amount by which a stack consisting of [[10/9]] and [[17/16]] falls short of 13/11. Moreover, it is also the interval that differentiates the [[273/272\|tannisma (273/272)]] from the [[385/384\|keenanisma (385/384)]], and the [[256/255\|septendecimal kleisma (256/255)]] from the [[352/351\|minthma (352/351)]]. Thus, tempering out this comma is a good way to extend minthmic and gentle harmonies to the 17-limit, as well as a good way to bring keenanismic and tannismic harmonies together.

	~~This comma's names come from the Ancient Greek word "aînos" (meaning "tale", "story" or "fable"<ref>~~[[~~Wiktionary: αἶνος #Ancient Greek~~]]</~~ref>), which is fitting due to~~ the ~~comma serving as a viable~~ 17-limit ~~extension to minthmic temperaments~~, ~~among others~~. ~~Funny enough~~, ~~this same Greek word is~~ the ~~source~~ of ~~the Ancient Greek word "aínigma" (meaning "riddle"<ref>~~[[~~Wiktionary: αἴνιγμα #Ancient Greek~~]]</ref>), from which we ultimately get our word "enigma", and this is also fitting due to the sheer difficulty that was involved in the initial process of working out both the name and the uses of this comma in a short span of time.		== Commatic relations ==
			It factors into two superparticular intervals: [[1701/1700]] × [[2080/2079]].

			== Temperaments ==
			When tempered out in the full 17-limit, the resulting temperament is called the '''ainic temperament''', or in the 2.3.5.11.13.17 subgroup, the '''ainian temperament'''. Both are characterized by the presence of [[Dyadic chord\|essentially tempered chord]]s called [[ainic chords]].

	~~It factors into two superparticular intervals:~~ [[~~1701/1700~~]] × [[~~2080/2079~~]].		== Etymology ==
			This comma was named by [[Aura]] in 2020. Its names come from the Ancient Greek word [[Wiktionary: αἶνος #Ancient Greek\|''aînos'']] ("tale", "story" or "fable"), which is fitting due to the comma serving as a viable 17-limit extension to minthmic temperaments, among others. Funny enough, this same Greek word is the source of the Ancient Greek word [[Wiktionary: αἴνιγμα #Ancient Greek\|''aínigma'']] ("riddle"), from which we ultimately get our word "enigma", and this is also fitting due to the sheer difficulty that was involved in the initial process of working out both the name and the uses of this comma in a short span of time.

	== See also ==		== See also ==
	* [[Ainic chords]]
	* [[Unnoticeable comma]]		* [[Unnoticeable comma]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	~~== References ==~~		[[Category:Ainic]]
	~~<references/>~~

	[[Category:~~Ainos~~]]