99/98 - Revision history

Lucius Chiaraviglio: /* Etymology */ Add links to temperaments

2025-10-27T01:31:32Z

Etymology: Add links to temperaments

← Older revision		Revision as of 01:31, 27 October 2025
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	== Etymology ==		== Etymology ==
	This comma's name comes from a contraction of ''mothra'' and ''orwell'', two of the rank-2 temperaments that temper out the comma.		This comma's name comes from a contraction of ''[[mothra]]'' and ''[[orwell]]'', two of the rank-2 temperaments that temper out the comma.

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

FloraC: Make mothwell explicit

2025-10-20T13:21:55Z

Make mothwell explicit

← Older revision		Revision as of 13:21, 20 October 2025
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''99/98''', or the '''mothwellsma''', is a [[small comma\|small]] [[11-limit]] [[comma]] of 17.6 [[cent]]s in size. It represents the difference between the [[9/7]] and [[14/11]] supermajor thirds, or the difference between two [[7/6]] subminor thirds and one [[11/8]] semi-augmented fourth. Note that 11/8 = (7/6)<sup>2</sup>(99/98) and that 7/6 × 99/98 = [[33/28]], which is the fifth complement of 14/11.		'''99/98''', or the '''mothwellsma''', is a [[small comma\|small]] [[11-limit]] [[comma]] of 17.6 [[cent]]s in size. It represents the difference between the [[9/7]] and [[14/11]] supermajor thirds, or the difference between two [[7/6]] subminor thirds and one [[11/8]] semi-augmented fourth. Note that 11/8 = (7/6)<sup>2</sup>(99/98) and that (7/6)⋅(99/98) = [[33/28]], which is the fifth complement of 14/11.

	== Temperaments ==		== Temperaments ==
	Tempering out this comma alone in the 11-limit leads to the '''mothwellsmic temperament''' (→ [[Catalog of rank-4 temperaments #Mothwellsmic (99/98)]]) ~~and enables~~ [[mothwellsmic chords]]. It is related to 11-limit [[orwell]], as a generator between 7/6 and (11/8)<sup>1/2</sup> is befitting of orwell.		[[Tempering out]] this comma alone in the 11-limit leads to the rank-4 '''mothwellsmic temperament''' (→ [[Catalog of rank-4 temperaments #Mothwellsmic (99/98)]]), or in the 2.3.7.11 subgroup, the rank-3 '''mothwell''' temperament, enabling [[mothwellsmic chords]]. It is related to 11-limit [[orwell]], as a generator between 7/6 and (11/8)<sup>1/2</sup> is befitting of orwell.

	== Etymology ==		== Etymology ==

Lériendil at 14:56, 29 April 2025

2025-04-29T14:56:23Z

← Older revision		Revision as of 14:56, 29 April 2025
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	== Etymology ==		== Etymology ==
	This comma's name comes from a contraction of ''mothra'' and ''orwell'', the ~~two~~ rank-2 temperaments that temper out the comma.		This comma's name comes from a contraction of ''mothra'' and ''orwell'', two of the rank-2 temperaments that temper out the comma.

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

FloraC: +etymology

2025-01-29T09:56:17Z

+etymology

← Older revision		Revision as of 09:56, 29 January 2025
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma alone in the 11-limit leads to the '''mothwellsmic temperament''' (→ [[Catalog of rank-4 temperaments #Mothwellsmic (99/98)]]) and enables [[mothwellsmic chords]]. It is related to 11-limit [[orwell]], as a generator between 7/6 and (11/8)<sup>1/2</sup> is befitting of orwell.		Tempering out this comma alone in the 11-limit leads to the '''mothwellsmic temperament''' (→ [[Catalog of rank-4 temperaments #Mothwellsmic (99/98)]]) and enables [[mothwellsmic chords]]. It is related to 11-limit [[orwell]], as a generator between 7/6 and (11/8)<sup>1/2</sup> is befitting of orwell.

			== Etymology ==
			This comma's name comes from a contraction of ''mothra'' and ''orwell'', the two rank-2 temperaments that temper out the comma.

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

FloraC: Simplify the equation

2025-01-29T09:54:15Z

Simplify the equation

← Older revision		Revision as of 09:54, 29 January 2025
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''99/98''', or the '''mothwellsma''', is a [[small comma\|small]] [[11-limit]] [[comma]] of 17.6 [[cent]]s in size. It represents the difference between the [[9/7]] and [[14/11]] supermajor thirds, or the difference between two [[7/6]] subminor thirds and one [[11/8]] semi-augmented fourth. Note that (11/8)<sup>1/2</sup> ~~= (7/6)~~(99/98)~~<sup>1/2</sup>~~ and that 7/6 × 99/98 = [[33/28]], which is the fifth complement of 14/11.		'''99/98''', or the '''mothwellsma''', is a [[small comma\|small]] [[11-limit]] [[comma]] of 17.6 [[cent]]s in size. It represents the difference between the [[9/7]] and [[14/11]] supermajor thirds, or the difference between two [[7/6]] subminor thirds and one [[11/8]] semi-augmented fourth. Note that 11/8 = (7/6)<sup>2</sup>(99/98) and that 7/6 × 99/98 = [[33/28]], which is the fifth complement of 14/11.

	== Temperaments ==		== Temperaments ==

Godtone: multiplication sign

2025-01-27T20:11:24Z

multiplication sign

← Older revision		Revision as of 20:11, 27 January 2025
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''99/98''', or the '''mothwellsma''', is a [[small comma\|small]] [[11-limit]] [[comma]] of 17.6 [[cent]]s in size. It represents the difference between the [[9/7]] and [[14/11]] supermajor thirds, or the difference between two [[7/6]] subminor thirds and one [[11/8]] semi-augmented fourth. Note that (11/8)<sup>1/2</sup> = (7/6)(99/98)<sup>1/2</sup> and that 7/6 * 99/98 = [[33/28]], which is the fifth complement of 14/11.		'''99/98''', or the '''mothwellsma''', is a [[small comma\|small]] [[11-limit]] [[comma]] of 17.6 [[cent]]s in size. It represents the difference between the [[9/7]] and [[14/11]] supermajor thirds, or the difference between two [[7/6]] subminor thirds and one [[11/8]] semi-augmented fourth. Note that (11/8)<sup>1/2</sup> = (7/6)(99/98)<sup>1/2</sup> and that 7/6 × 99/98 = [[33/28]], which is the fifth complement of 14/11.

	== Temperaments ==		== Temperaments ==

Godtone: fix

2025-01-27T20:10:37Z

fix

← Older revision		Revision as of 20:10, 27 January 2025
Line 4:		Line 4:
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''99/98''', or the '''mothwellsma''', is a [[small comma\|small]] [[11-limit]] [[comma]] of 17.6 [[cent]]s in size. It represents the difference between the [[9/7]] and [[14/11]] supermajor thirds, or the difference between two [[7/6]] subminor thirds and one [[11/8]] semi-augmented fourth. Note that (11/8)<sup>1/2</sup> = (7/6)(99/98)<sup>1/2</sup> and that (7/6)99/98 = [[33/28]], which is the fifth complement of 14/11.		'''99/98''', or the '''mothwellsma''', is a [[small comma\|small]] [[11-limit]] [[comma]] of 17.6 [[cent]]s in size. It represents the difference between the [[9/7]] and [[14/11]] supermajor thirds, or the difference between two [[7/6]] subminor thirds and one [[11/8]] semi-augmented fourth. Note that (11/8)<sup>1/2</sup> = (7/6)(99/98)<sup>1/2</sup> and that 7/6 * 99/98 = [[33/28]], which is the fifth complement of 14/11.

	== Temperaments ==		== Temperaments ==

BudjarnLambeth at 13:16, 3 November 2024

2024-11-03T13:16:38Z

← Older revision		Revision as of 13:16, 3 November 2024
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	[[Category:Mothwellsmic]]		[[Category:Mothwellsmic]]
			[[Category:Commas named by combining multiple temperament names]]

FloraC: Integrate the link to small comma into the intro

2024-10-12T09:26:39Z

Integrate the link to small comma into the intro

← Older revision		Revision as of 09:26, 12 October 2024
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''99/98''', or the '''mothwellsma''' (17.6 [[cent]]s in size), represents the difference between the [[9/7]] and [[14/11]] supermajor thirds, or the difference between two [[7/6]] subminor thirds and one [[11/8]] semi-augmented fourth. Note that (11/8)<sup>1/2</sup> = (7/6)(99/98)<sup>1/2</sup> and that (7/6)99/98 = [[33/28]], which is the fifth complement of 14/11.		'''99/98''', or the '''mothwellsma''', is a [[small comma\|small]] [[11-limit]] [[comma]] of 17.6 [[cent]]s in size. It represents the difference between the [[9/7]] and [[14/11]] supermajor thirds, or the difference between two [[7/6]] subminor thirds and one [[11/8]] semi-augmented fourth. Note that (11/8)<sup>1/2</sup> = (7/6)(99/98)<sup>1/2</sup> and that (7/6)99/98 = [[33/28]], which is the fifth complement of 14/11.

	== Temperaments ==		== Temperaments ==
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	* [[99/49]] – the same interval but one octave higher		* [[99/49]] – the same interval but one octave higher
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[Small comma]]

	[[Category:Mothwellsmic]]		[[Category:Mothwellsmic]]

FloraC: Rework for the temperaments section

2024-10-12T09:25:04Z

Rework for the temperaments section

← Older revision		Revision as of 09:25, 12 October 2024
Line 4:		Line 4:
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''99/98''', or the '''mothwellsma''' (17.6 [[cent]]s in size), represents the difference between the [[9/7]] and [[14/11]] supermajor thirds, or the difference between two [[7/6]] subminor thirds and one [[11/8]] semi-augmented fourth. ~~If tempered, it leads to the [[Mothwellsmic triad]], and is related to~~ 11~~-limit [[orwell]], as a generator between~~ 7/6 ~~and~~ (11/8)<sup>1/2</sup> – is ~~befitting~~ of ~~orwell~~.		'''99/98''', or the '''mothwellsma''' (17.6 [[cent]]s in size), represents the difference between the [[9/7]] and [[14/11]] supermajor thirds, or the difference between two [[7/6]] subminor thirds and one [[11/8]] semi-augmented fourth. Note that (11/8)<sup>1/2</sup> = (7/6)(99/98)<sup>1/2</sup> and that (7/6)99/98 = [[33/28]], which is the fifth complement of 14/11.

	(~~Note that~~ (11/8)~~<sup>1/2</sup> =~~ 7/6 × (99/98)<sup>1/2</sup> ~~and that 7/6 × 99/98 = [[33/28]], which~~ is ~~the fifth complement~~ of ~~14/11~~.)		== Temperaments ==
			Tempering out this comma alone in the 11-limit leads to the '''mothwellsmic temperament''' (→ [[Catalog of rank-4 temperaments #Mothwellsmic (99/98)]]) and enables [[mothwellsmic chords]]. It is related to 11-limit [[orwell]], as a generator between 7/6 and (11/8)<sup>1/2</sup> is befitting of orwell.

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