243/242 - Revision history

Eufalesio: Added sqrt(rastma) as comma for Neutral FJS

2025-11-28T11:47:17Z

Added sqrt(rastma) as comma for Neutral FJS

← Older revision		Revision as of 11:47, 28 November 2025
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	'''243/242''', the '''rastma''' or the '''neutral third comma''', is a [[small comma\|small]] [[11-limit]] (also [[2.3.11 subgroup\|2.3.11-subgroup]]) [[comma]] with a value of roughly 7.1 [[cent]]s. It is significant in [[just intonation]] as the amount by which a stack of two [[11/9]] neutral thirds (that is an Alpharabian narrow fifth		'''243/242''', the '''rastma''' or the '''neutral third comma''', is a [[small comma\|small]] [[11-limit]] (also [[2.3.11 subgroup\|2.3.11-subgroup]]) [[comma]] with a value of roughly 7.1 [[cent]]s. It is significant in [[just intonation]] as the amount by which a stack of two [[11/9]] neutral thirds (that is an Alpharabian narrow fifth
	[[121/81]]) fall short of [[3/2]] just perfect fifth as well as the amount by which a stack of two [[27/22]] neutral thirds (that is an Alpharabian wide fifth [[729/484]]) exceeds a 3/2 just perfect fifth, the amount by which a stack of two [[33/32]] quartertones falls short of an [[2187/2048\|apotome (2187/2048)]] as well as the difference between 11/9 and 27/22, and the difference between [[45/44]] and [[55/54]]. The last makes the theory where the rastma serves as the [[subchromatic\|subchroma]] that separates greater and lesser 11-limit chromas – a theory that becomes especially useful when one works extensively with high-fidelity renditions of the 11-limit.		[[121/81]]) fall short of [[3/2]] just perfect fifth as well as the amount by which a stack of two [[27/22]] neutral thirds (that is an Alpharabian wide fifth [[729/484]]) exceeds a 3/2 just perfect fifth, the amount by which a stack of two [[33/32]] quartertones falls short of an [[2187/2048\|apotome (2187/2048)]] as well as the difference between 11/9 and 27/22, and the difference between [[45/44]] and [[55/54]]. The last makes the theory where the rastma serves as the [[subchromatic\|subchroma]] that separates greater and lesser 11-limit chromas – a theory that becomes especially useful when one works extensively with high-fidelity renditions of the 11-limit.

			Its square rooted value, about 3.57 cents, is also a tiny comma that is used in [[Neutral FJS]] as the formal comma of prime 11; the difference between [[11/8]] and the half-augmented fourth sqrt(243/128), or between 11/9 or 27/22 and the hemipythagorean neutral third [[sqrt(3/2)]].

	== Temperaments ==		== Temperaments ==

FloraC: Fix linking

2025-08-27T13:56:51Z

Fix linking

← Older revision		Revision as of 13:56, 27 August 2025
Line 1:		Line 1:
	{{interwiki		{{interwiki
			\| en = 243/242
	\| de = 243/242		\| de = 243/242
	~~\| en = 243/242~~
	\| es =		\| es =
	\| ja =		\| ja =
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	[[Tempering out]] this comma in the full 11-limit leads to the [[rastmic]] rank-4 temperament, or in the 2.3.11 subgroup, the [[neutral (temperament)\|neutral]] temperament, enabling [[rastmic chords]] in either case.		[[Tempering out]] this comma in the full 11-limit leads to the [[rastmic]] rank-4 temperament, or in the 2.3.11 subgroup, the [[neutral (temperament)\|neutral]] temperament, enabling [[rastmic chords]] in either case.

	See [[Rastmic clan]] for the clan of rank-2 temperaments where it is tempered out. See [[~~Rastmic rank three clan\|~~Rastmic rank-3 clan]] for the clan of rank-3 temperaments where it is tempered out.		See [[Rastmic clan]] for the clan of rank-2 temperaments where it is tempered out. See [[Rastmic rank-3 clan]] for the clan of rank-3 temperaments where it is tempered out.

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

Lucius Chiaraviglio: /* Temperaments */ Specify Rastmic as rank-4 temperament

2025-07-13T14:14:13Z

Temperaments: Specify Rastmic as rank-4 temperament

← Older revision		Revision as of 14:14, 13 July 2025
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	== Temperaments ==		== Temperaments ==
	[[Tempering out]] this comma in the full 11-limit leads to the [[rastmic]] temperament, or in the 2.3.11 subgroup, the [[neutral (temperament)\|neutral]] temperament, enabling [[rastmic chords]] in either case.		[[Tempering out]] this comma in the full 11-limit leads to the [[rastmic]] rank-4 temperament, or in the 2.3.11 subgroup, the [[neutral (temperament)\|neutral]] temperament, enabling [[rastmic chords]] in either case.

	See [[Rastmic clan]] for the clan of rank-2 temperaments where it is tempered out. See [[Rastmic rank three clan\|Rastmic rank-3 clan]] for the clan of rank-3 temperaments where it is tempered out.		See [[Rastmic clan]] for the clan of rank-2 temperaments where it is tempered out. See [[Rastmic rank three clan\|Rastmic rank-3 clan]] for the clan of rank-3 temperaments where it is tempered out.

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

FloraC: The link has been fixed

2025-07-13T11:24:41Z

The link has been fixed

← Older revision		Revision as of 11:24, 13 July 2025
Line 14:		Line 14:

	== Temperaments ==		== Temperaments ==
	[[Tempering out]] this comma in the full 11-limit leads to the rastmic temperament, or in the 2.3.11 subgroup, the [[neutral (temperament)\|neutral]] temperament, enabling [[rastmic chords]] in either case.		[[Tempering out]] this comma in the full 11-limit leads to the [[rastmic]] temperament, or in the 2.3.11 subgroup, the [[neutral (temperament)\|neutral]] temperament, enabling [[rastmic chords]] in either case.

	See [[Rastmic clan]] for the clan of rank-2 temperaments where it is tempered out. See [[Rastmic rank three clan\|Rastmic rank-3 clan]] for the clan of rank-3 temperaments where it is tempered out.		See [[Rastmic clan]] for the clan of rank-2 temperaments where it is tempered out. See [[Rastmic rank three clan\|Rastmic rank-3 clan]] for the clan of rank-3 temperaments where it is tempered out.

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

Lucius Chiaraviglio: /* Temperaments */ Remove circular link

2025-07-13T05:35:16Z

Temperaments: Remove circular link

← Older revision		Revision as of 05:35, 13 July 2025
Line 14:		Line 14:

	== Temperaments ==		== Temperaments ==
	[[Tempering out]] this comma in the full 11-limit leads to the [[rastmic]] temperament, or in the 2.3.11 subgroup, the [[neutral (temperament)\|neutral]] temperament, enabling [[rastmic chords]] in either case.		[[Tempering out]] this comma in the full 11-limit leads to the rastmic temperament, or in the 2.3.11 subgroup, the [[neutral (temperament)\|neutral]] temperament, enabling [[rastmic chords]] in either case.

	See [[Rastmic clan]] for the clan of rank-2 temperaments where it is tempered out. See [[Rastmic rank three clan\|Rastmic rank-3 clan]] for the clan of rank-3 temperaments where it is tempered out.		See [[Rastmic clan]] for the clan of rank-2 temperaments where it is tempered out. See [[Rastmic rank three clan\|Rastmic rank-3 clan]] for the clan of rank-3 temperaments where it is tempered out.

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

Dummy index: link target changed

2025-06-03T14:36:36Z

link target changed

← Older revision		Revision as of 14:36, 3 June 2025
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	}}		}}
	'''243/242''', the '''rastma''' or the '''neutral third comma''', is a [[small comma\|small]] [[11-limit]] (also [[2.3.11 subgroup\|2.3.11-subgroup]]) [[comma]] with a value of roughly 7.1 [[cent]]s. It is significant in [[just intonation]] as the amount by which a stack of two [[11/9]] neutral thirds (that is an Alpharabian narrow fifth		'''243/242''', the '''rastma''' or the '''neutral third comma''', is a [[small comma\|small]] [[11-limit]] (also [[2.3.11 subgroup\|2.3.11-subgroup]]) [[comma]] with a value of roughly 7.1 [[cent]]s. It is significant in [[just intonation]] as the amount by which a stack of two [[11/9]] neutral thirds (that is an Alpharabian narrow fifth
	[[121/81]]) fall short of [[3/2]] just perfect fifth as well as the amount by which a stack of two [[27/22]] neutral thirds (that is an Alpharabian wide fifth [[729/484]]) exceeds a 3/2 just perfect fifth, the amount by which a stack of two [[33/32]] quartertones falls short of an [[2187/2048\|apotome (2187/2048)]] as well as the difference between 11/9 and 27/22, and the difference between [[45/44]] and [[55/54]]. The last makes the theory where the rastma serves as the [[~~diatonic, chromatic, enharmonic,~~ subchromatic\|subchroma]] that separates greater and lesser 11-limit chromas – a theory that becomes especially useful when one works extensively with high-fidelity renditions of the 11-limit.		[[121/81]]) fall short of [[3/2]] just perfect fifth as well as the amount by which a stack of two [[27/22]] neutral thirds (that is an Alpharabian wide fifth [[729/484]]) exceeds a 3/2 just perfect fifth, the amount by which a stack of two [[33/32]] quartertones falls short of an [[2187/2048\|apotome (2187/2048)]] as well as the difference between 11/9 and 27/22, and the difference between [[45/44]] and [[55/54]]. The last makes the theory where the rastma serves as the [[subchromatic\|subchroma]] that separates greater and lesser 11-limit chromas – a theory that becomes especially useful when one works extensively with high-fidelity renditions of the 11-limit.

	== Temperaments ==		== Temperaments ==

Aura at 00:48, 14 April 2025

2025-04-14T00:48:21Z

← Older revision		Revision as of 00:48, 14 April 2025
Line 10:		Line 10:
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''243/242''', the '''rastma''' or the '''neutral third comma''', is a [[small comma\|small]] [[11-limit]] (also [[2.3.11 subgroup\|2.3.11-subgroup]]) [[comma]] with a value of roughly 7.1 [[cent]]s. It is significant in [[just intonation]] as the amount by which a stack of two [[11/9]] neutral thirds fall short of [[3/2]] just perfect fifth as well as the amount by which a stack of two [[27/22]] neutral thirds (~~which equals~~ an Alpharabian wide fifth [[729/484]]) exceeds a 3/2 just perfect fifth, the amount by which a stack of two [[33/32]] quartertones falls short of an [[2187/2048\|apotome (2187/2048)]] as well as the difference between 11/9 and 27/22, and the difference between [[45/44]] and [[55/54]]. The last makes the theory where the rastma serves as the [[diatonic, chromatic, enharmonic, subchromatic\|subchroma]] that separates greater and lesser 11-limit chromas – a theory that becomes especially useful when one works extensively with high-fidelity renditions of the 11-limit.		'''243/242''', the '''rastma''' or the '''neutral third comma''', is a [[small comma\|small]] [[11-limit]] (also [[2.3.11 subgroup\|2.3.11-subgroup]]) [[comma]] with a value of roughly 7.1 [[cent]]s. It is significant in [[just intonation]] as the amount by which a stack of two [[11/9]] neutral thirds (that is an Alpharabian narrow fifth
			[[121/81]]) fall short of [[3/2]] just perfect fifth as well as the amount by which a stack of two [[27/22]] neutral thirds (that is an Alpharabian wide fifth [[729/484]]) exceeds a 3/2 just perfect fifth, the amount by which a stack of two [[33/32]] quartertones falls short of an [[2187/2048\|apotome (2187/2048)]] as well as the difference between 11/9 and 27/22, and the difference between [[45/44]] and [[55/54]]. The last makes the theory where the rastma serves as the [[diatonic, chromatic, enharmonic, subchromatic\|subchroma]] that separates greater and lesser 11-limit chromas – a theory that becomes especially useful when one works extensively with high-fidelity renditions of the 11-limit.

	== Temperaments ==		== Temperaments ==

Lucius Chiaraviglio: Add that stack of two 27/22 neutral thirds is Alpharabian wide fifth

2025-04-13T21:07:51Z

Add that stack of two 27/22 neutral thirds is Alpharabian wide fifth

← Older revision		Revision as of 21:07, 13 April 2025
Line 10:		Line 10:
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''243/242''', the '''rastma''' or the '''neutral third comma''', is a [[small comma\|small]] [[11-limit]] (also [[2.3.11 subgroup\|2.3.11-subgroup]]) [[comma]] with a value of roughly 7.1 [[cent]]s. It is significant in [[just intonation]] as the amount by which a stack of two [[11/9]] neutral thirds fall short of [[3/2]] just perfect fifth as well as the amount by which a stack of two [[27/22]] neutral thirds exceeds a 3/2 just perfect fifth, the amount by which a stack of two [[33/32]] quartertones falls short of an [[2187/2048\|apotome (2187/2048)]] as well as the difference between 11/9 and 27/22, and the difference between [[45/44]] and [[55/54]]. The last makes the theory where the rastma serves as the [[diatonic, chromatic, enharmonic, subchromatic\|subchroma]] that separates greater and lesser 11-limit chromas – a theory that becomes especially useful when one works extensively with high-fidelity renditions of the 11-limit.		'''243/242''', the '''rastma''' or the '''neutral third comma''', is a [[small comma\|small]] [[11-limit]] (also [[2.3.11 subgroup\|2.3.11-subgroup]]) [[comma]] with a value of roughly 7.1 [[cent]]s. It is significant in [[just intonation]] as the amount by which a stack of two [[11/9]] neutral thirds fall short of [[3/2]] just perfect fifth as well as the amount by which a stack of two [[27/22]] neutral thirds (which equals an Alpharabian wide fifth [[729/484]]) exceeds a 3/2 just perfect fifth, the amount by which a stack of two [[33/32]] quartertones falls short of an [[2187/2048\|apotome (2187/2048)]] as well as the difference between 11/9 and 27/22, and the difference between [[45/44]] and [[55/54]]. The last makes the theory where the rastma serves as the [[diatonic, chromatic, enharmonic, subchromatic\|subchroma]] that separates greater and lesser 11-limit chromas – a theory that becomes especially useful when one works extensively with high-fidelity renditions of the 11-limit.

	== Temperaments ==		== Temperaments ==

Aura: Broke the Alpharabian wide fifth into its two component 27/22 neutral thirds

2025-04-13T10:39:30Z

Broke the Alpharabian wide fifth into its two component 27/22 neutral thirds

← Older revision		Revision as of 10:39, 13 April 2025
Line 10:		Line 10:
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''243/242''', the '''rastma''' or the '''neutral third comma''', is a [[small comma\|small]] [[11-limit]] (also [[2.3.11 subgroup\|2.3.11-subgroup]]) [[comma]] with a value of roughly 7.1 [[cent]]s. It is significant in [[just intonation]] as the amount by which a stack of two [[11/9]] neutral thirds fall short of [[3/2]] just perfect fifth as well as the ~~difference between an Alpharabian wide fifth (~~[[~~729~~/~~484~~]]) exceeds a just perfect fifth, the amount by which a stack of two [[33/32]] quartertones falls short of an [[2187/2048\|apotome (2187/2048)]] as well as the difference between [[11/9]] and [[27/22]], and the difference between [[45/44]] and [[55/54]]. The last makes the theory where the rastma serves as the [[diatonic, chromatic, enharmonic, subchromatic\|subchroma]] that separates greater and lesser 11-limit chromas – a theory that becomes especially useful when one works extensively with high-fidelity renditions of the 11-limit.		'''243/242''', the '''rastma''' or the '''neutral third comma''', is a [[small comma\|small]] [[11-limit]] (also [[2.3.11 subgroup\|2.3.11-subgroup]]) [[comma]] with a value of roughly 7.1 [[cent]]s. It is significant in [[just intonation]] as the amount by which a stack of two [[11/9]] neutral thirds fall short of [[3/2]] just perfect fifth as well as the amount by which a stack of two [[27/22]] neutral thirds exceeds a 3/2 just perfect fifth, the amount by which a stack of two [[33/32]] quartertones falls short of an [[2187/2048\|apotome (2187/2048)]] as well as the difference between 11/9 and 27/22, and the difference between [[45/44]] and [[55/54]]. The last makes the theory where the rastma serves as the [[diatonic, chromatic, enharmonic, subchromatic\|subchroma]] that separates greater and lesser 11-limit chromas – a theory that becomes especially useful when one works extensively with high-fidelity renditions of the 11-limit.

	== Temperaments ==		== Temperaments ==

Lucius Chiaraviglio: Add Alpharabian wide fifth vs 3/2

2025-04-13T10:31:36Z

Add Alpharabian wide fifth vs 3/2

← Older revision		Revision as of 10:31, 13 April 2025
Line 10:		Line 10:
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''243/242''', the '''rastma''' or the '''neutral third comma''', is a [[small comma\|small]] [[11-limit]] (also [[2.3.11 subgroup\|2.3.11-subgroup]]) [[comma]] with a value of roughly 7.1 [[cent]]s. It is significant in [[just intonation]] as the amount by which a stack of two [[11/9]] neutral thirds fall short of [[3/2]] just perfect fifth, by which a stack of two [[33/32]] quartertones falls short of an [[2187/2048\|apotome (2187/2048)]] as well as the difference between [[11/9]] and [[27/22]], and, the difference between [[45/44]] and [[55/54]]. The last makes the theory where the rastma serves as the [[diatonic, chromatic, enharmonic, subchromatic\|subchroma]] that separates greater and lesser 11-limit chromas – a theory that becomes especially useful when one works extensively with high-fidelity renditions of the 11-limit.		'''243/242''', the '''rastma''' or the '''neutral third comma''', is a [[small comma\|small]] [[11-limit]] (also [[2.3.11 subgroup\|2.3.11-subgroup]]) [[comma]] with a value of roughly 7.1 [[cent]]s. It is significant in [[just intonation]] as the amount by which a stack of two [[11/9]] neutral thirds fall short of [[3/2]] just perfect fifth as well as the difference between an Alpharabian wide fifth ([[729/484]]) exceeds a just perfect fifth, the amount by which a stack of two [[33/32]] quartertones falls short of an [[2187/2048\|apotome (2187/2048)]] as well as the difference between [[11/9]] and [[27/22]], and the difference between [[45/44]] and [[55/54]]. The last makes the theory where the rastma serves as the [[diatonic, chromatic, enharmonic, subchromatic\|subchroma]] that separates greater and lesser 11-limit chromas – a theory that becomes especially useful when one works extensively with high-fidelity renditions of the 11-limit.

	== Temperaments ==		== Temperaments ==