144/143 - Revision history

Overthink: /* Temperaments */ more neutral tone

2026-05-20T01:23:25Z

Temperaments: more neutral tone

← Older revision		Revision as of 01:23, 20 May 2026
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	== Temperaments ==		== Temperaments ==
	~~The best~~ 2.3.11.13 temperament that extends it is [[namo]], which sets the equated undecimal and tridecimal intervals to true neutral intervals. Namo is often used to extend temperaments with neutral thirds to the 13-limit, such as [[hemififths]] and [[squares]].		A natural 2.3.11.13 temperament that extends it is [[namo]], which sets the equated undecimal and tridecimal intervals to true neutral intervals. Namo is often used to extend temperaments with neutral thirds to the 13-limit, such as [[hemififths]] and [[squares]].

	[[Teff]] is a full 13-limit (and beyond) temperament of note that targets it, which also tempers out the syntonic comma [[81/80]].		[[Teff]] is a full 13-limit (and beyond) temperament of note that targets it, which also tempers out the syntonic comma [[81/80]].

Lucius Chiaraviglio: Fix typo

2025-12-19T09:04:18Z

Fix typo

← Older revision		Revision as of 09:04, 19 December 2025
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	}}		}}

	'''144/143''', the '''grossma''', is a [[13-limit]] [[small comma]]. It is the difference between the [[11/9]] and [[16/13]] neutral thirds, between the [[12/11]] and [[13/12]] neutral seconds, and between the [[11/8]] and [[18/13]] superfourths/subtritones. Since it ~~seperates~~ so many 2.3.11 and 2.3.13 intervals, the grossma is a very important interval in the 13-limit, with a function in the 2.3.11.13 subgroup akin to [[36/35]] in the 2.3.5.7 subgroup ([[7-limit]]), though the size of 144/143 is a quarter that of 36/35, so tempering it out is arguably more plausible.		'''144/143''', the '''grossma''', is a [[13-limit]] [[small comma]]. It is the difference between the [[11/9]] and [[16/13]] neutral thirds, between the [[12/11]] and [[13/12]] neutral seconds, and between the [[11/8]] and [[18/13]] superfourths/subtritones. Since it separates so many 2.3.11 and 2.3.13 intervals, the grossma is a very important interval in the 13-limit, with a function in the 2.3.11.13 subgroup akin to [[36/35]] in the 2.3.5.7 subgroup ([[7-limit]]), though the size of 144/143 is a quarter that of 36/35, so tempering it out is arguably more plausible.

	== Temperaments ==		== Temperaments ==

Overthink: /* Temperaments */ added note about teff being a meantone temperament

2025-10-14T16:25:57Z

Temperaments: added note about teff being a meantone temperament

← Older revision		Revision as of 16:25, 14 October 2025
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	The best 2.3.11.13 temperament that extends it is [[namo]], which sets the equated undecimal and tridecimal intervals to true neutral intervals. Namo is often used to extend temperaments with neutral thirds to the 13-limit, such as [[hemififths]] and [[squares]].		The best 2.3.11.13 temperament that extends it is [[namo]], which sets the equated undecimal and tridecimal intervals to true neutral intervals. Namo is often used to extend temperaments with neutral thirds to the 13-limit, such as [[hemififths]] and [[squares]].

	[[Teff]] is a full 13-limit (and beyond) temperament of note that targets it.		[[Teff]] is a full 13-limit (and beyond) temperament of note that targets it, which also tempers out the syntonic comma [[81/80]].

	== Sagittal notation ==		== Sagittal notation ==

Overthink: Expanded page

2025-10-14T16:25:06Z

Expanded page

← Older revision		Revision as of 16:25, 14 October 2025
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	}}		}}

	'''144/143''', the '''grossma''', is a [[13-limit]] [[small comma]]. It is the difference between the [[11/9]] and [[16/13]] neutral thirds, ~~and~~ between the [[12/11]] and [[13/12]] neutral seconds. [[Teff]] is a temperament of note that targets it.		'''144/143''', the '''grossma''', is a [[13-limit]] [[small comma]]. It is the difference between the [[11/9]] and [[16/13]] neutral thirds, between the [[12/11]] and [[13/12]] neutral seconds, and between the [[11/8]] and [[18/13]] superfourths/subtritones. Since it seperates so many 2.3.11 and 2.3.13 intervals, the grossma is a very important interval in the 13-limit, with a function in the 2.3.11.13 subgroup akin to [[36/35]] in the 2.3.5.7 subgroup ([[7-limit]]), though the size of 144/143 is a quarter that of 36/35, so tempering it out is arguably more plausible.

			== Temperaments ==
			The best 2.3.11.13 temperament that extends it is [[namo]], which sets the equated undecimal and tridecimal intervals to true neutral intervals. Namo is often used to extend temperaments with neutral thirds to the 13-limit, such as [[hemififths]] and [[squares]].

			[[Teff]] is a full 13-limit (and beyond) temperament of note that targets it.

	== Sagittal notation ==		== Sagittal notation ==

BudjarnLambeth at 23:14, 15 November 2024

2024-11-15T23:14:56Z

← Older revision		Revision as of 23:14, 15 November 2024
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	[[Category:Grossmic]]		[[Category:Grossmic]]
			[[Category:Commas with unknown etymology]]

Dave Keenan: /* Sagittal notation */ Changed "simplest ratio" to "simplest interval". Changed colons to slashes and dash. Gave the truly-simplest (2,3-free) interval in addition to the octave-reduced interval. Replaced hair-space with nbhsp template call.

2024-10-10T07:08:32Z

Sagittal notation: Changed "simplest ratio" to "simplest interval". Changed colons to slashes and dash. Gave the truly-simplest (2,3-free) interval in addition to the octave-reduced interval. Replaced hair-space with nbhsp template call.

← Older revision		Revision as of 07:08, 10 October 2024
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	== Sagittal notation ==		== Sagittal notation ==
	In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| )~! }} and is called the '''143 comma''', or '''143C''' for short, because the simplest ~~ratio~~ it notates is 128~~:143~~, as for example in C:D~~ ~~{{sagittal \| )~! }}. The upward version is called '''1/143C''' or '''143C up''' and is represented by {{sagittal\| )~\| }}~~. 143 = 11 × 13~~.		In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| )~! }} and is called the '''143 comma''', or '''143C''' for short, because the simplest interval it notates is 143/1 = 11×13 (equiv. 143/128), as for example in C-D{{nbhsp}}{{sagittal \| )~! }}. The upward version is called '''1/143C''' or '''143C up''' and is represented by {{sagittal\| )~\| }}.

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

Dave Keenan: /* Sagittal notation */ Added 143 = 11 × 13.

2024-10-09T12:22:16Z

Sagittal notation: Added 143 = 11 × 13.

← Older revision		Revision as of 12:22, 9 October 2024
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	== Sagittal notation ==		== Sagittal notation ==
	In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| )~! }} and is called the '''143 comma''', or '''143C''' for short, because the simplest ratio it notates is 128:143, as for example in C:D {{sagittal \| )~! }}. The upward version is called '''1/143C''' or '''143C up''' and is represented by {{sagittal\| )~\| }}.		In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| )~! }} and is called the '''143 comma''', or '''143C''' for short, because the simplest ratio it notates is 128:143, as for example in C:D {{sagittal \| )~! }}. The upward version is called '''1/143C''' or '''143C up''' and is represented by {{sagittal\| )~\| }}. 143 = 11 × 13.

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

Dave Keenan: /* Sagittal notation */ Added upward version

2024-10-09T12:20:01Z

Sagittal notation: Added upward version

← Older revision		Revision as of 12:20, 9 October 2024
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	== Sagittal notation ==		== Sagittal notation ==
	In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| )~! }} and is called the '''143 comma''', or '''143C''' for short, because the simplest ratio it notates is 128:143, as for example in C:D{{sagittal \| )~! }}.		In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| )~! }} and is called the '''143 comma''', or '''143C''' for short, because the simplest ratio it notates is 128:143, as for example in C:D {{sagittal \| )~! }}. The upward version is called '''1/143C''' or '''143C up''' and is represented by {{sagittal\| )~\| }}.

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

Cmloegcmluin: add section for this comma's use in Sagittal notation

2024-10-09T05:18:08Z

add section for this comma's use in Sagittal notation

← Older revision		Revision as of 05:18, 9 October 2024
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	'''144/143''', the '''grossma''', is a [[13-limit]] [[small comma]]. It is the difference between the [[11/9]] and [[16/13]] neutral thirds, and between the [[12/11]] and [[13/12]] neutral seconds. [[Teff]] is a temperament of note that targets it.		'''144/143''', the '''grossma''', is a [[13-limit]] [[small comma]]. It is the difference between the [[11/9]] and [[16/13]] neutral thirds, and between the [[12/11]] and [[13/12]] neutral seconds. [[Teff]] is a temperament of note that targets it.

			== Sagittal notation ==
			In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| )~! }} and is called the '''143 comma''', or '''143C''' for short, because the simplest ratio it notates is 128:143, as for example in C:D{{sagittal \| )~! }}.

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

Xenllium at 14:46, 18 July 2023

2023-07-18T14:46:22Z

← Older revision		Revision as of 14:46, 18 July 2023
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	* [[Small comma]]		* [[Small comma]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]
			* [[Grossmisma]], the difference by which a stack of seven 144/143s falls short of [[21/20]]

	[[Category:Grossmic]]		[[Category:Grossmic]]