847/845 - Revision history

Squib: Undo revision 229746 by Squib (talk)

2026-05-23T16:47:21Z

← Older revision		Revision as of 16:47, 23 May 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''847/845''', the '''cuthbert comma''', is a [[small comma\|small]] [[13-limit]] (also [[5.7.11.13 subgroup\|5.7.11.13-subgroup]]) [[comma]] measuring about 4.09{{cent}}. It is the difference between [[7/5]] and a stack of two [[13/11]]'s~~. It is also the difference between [[125/121]] and [[175/169]]~~.		'''847/845''', the '''cuthbert comma''', is a [[small comma\|small]] [[13-limit]] (also [[5.7.11.13 subgroup\|5.7.11.13-subgroup]]) [[comma]] measuring about 4.09{{cent}}. It is the difference between [[7/5]] and a stack of two [[13/11]]'s.

	In terms of full 13-limit commas, it is the difference between the following superparticular pairs:		In terms of full 13-limit commas, it is the difference between the following superparticular pairs:

Squib at 21:16, 20 May 2026

2026-05-20T21:16:10Z

← Older revision		Revision as of 21:16, 20 May 2026
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	[[Tempering out]] this comma in the 13-limit results in the rank-5 '''cuthbert''' temperament and enables the [[cuthbert chords]].		[[Tempering out]] this comma in the 13-limit results in the rank-5 '''cuthbert''' temperament and enables the [[cuthbert chords]].

	Tempering it out in the 5.7.11.13 subgroup leads to an extremely efficient rank-3 temperament, and tempering it out in the 7/5.11/5.13/5 subgroup leads to a rank-2 temperament containing the 5:7:11:13 chord~~. Both have a natural weak extension to prime 3 by tempering out 1575/1573, enabling 5:7:11:13:15~~.		Tempering it out in the 5.7.11.13 subgroup leads to an extremely efficient rank-3 temperament, and tempering it out in the 7/5.11/5.13/5 subgroup leads to a restriction of the rank-2 temperament [[edson]] containing the 5:7:11:13 chord.

	[[Category:Cuthbert]]		[[Category:Cuthbert]]
	[[Category:Commas with unknown etymology]]		[[Category:Commas with unknown etymology]]

Squib: Undo revision 227521 by FloraC (talk) important result of tempering this out is that these two larger intervals are equated

2026-05-06T11:15:53Z

Undo revision 227521 by FloraC (talk) important result of tempering this out is that these two larger intervals are equated

← Older revision		Revision as of 11:15, 6 May 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''847/845''', the '''cuthbert comma''', is a [[small comma\|small]] [[13-limit]] (also [[5.7.11.13 subgroup\|5.7.11.13-subgroup]]) [[comma]] measuring about 4.09{{cent}}. It is the difference between [[7/5]] and a stack of two [[13/11]]'s.		'''847/845''', the '''cuthbert comma''', is a [[small comma\|small]] [[13-limit]] (also [[5.7.11.13 subgroup\|5.7.11.13-subgroup]]) [[comma]] measuring about 4.09{{cent}}. It is the difference between [[7/5]] and a stack of two [[13/11]]'s. It is also the difference between [[125/121]] and [[175/169]].

	In terms of full 13-limit commas, it is the difference between the following superparticular pairs:		In terms of full 13-limit commas, it is the difference between the following superparticular pairs:

Squib: /* Temperaments */

2026-04-14T02:21:27Z

Temperaments

← Older revision		Revision as of 02:21, 14 April 2026
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	[[Tempering out]] this comma in the 13-limit results in the rank-5 '''cuthbert''' temperament and enables the [[cuthbert chords]].		[[Tempering out]] this comma in the 13-limit results in the rank-5 '''cuthbert''' temperament and enables the [[cuthbert chords]].

	Tempering it out in the 5.7.11.13 subgroup leads to an extremely efficient rank-3 temperament.		Tempering it out in the 5.7.11.13 subgroup leads to an extremely efficient rank-3 temperament, and tempering it out in the 7/5.11/5.13/5 subgroup leads to a rank-2 temperament containing the 5:7:11:13 chord. Both have a natural weak extension to prime 3 by tempering out 1575/1573, enabling 5:7:11:13:15.

	~~Tempering~~ it out in the 7/5.11/5.13/5 subgroup leads to a rank-2 temperament containing the 5:7:11:13 chord.

	[[Category:Cuthbert]]		[[Category:Cuthbert]]
	[[Category:Commas with unknown etymology]]		[[Category:Commas with unknown etymology]]

Squib: /* Temperaments */

2026-04-13T00:42:09Z

Temperaments

← Older revision		Revision as of 00:42, 13 April 2026
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	Tempering it out in the 5.7.11.13 subgroup leads to an extremely efficient rank-3 temperament.		Tempering it out in the 5.7.11.13 subgroup leads to an extremely efficient rank-3 temperament.

			Tempering it out in the 7/5.11/5.13/5 subgroup leads to a rank-2 temperament containing the 5:7:11:13 chord.

	[[Category:Cuthbert]]		[[Category:Cuthbert]]
	[[Category:Commas with unknown etymology]]		[[Category:Commas with unknown etymology]]

FloraC: - the second identity. as it contains intervals of 125 but this comma only has two factors of 5 in it

2026-04-09T09:03:23Z

- the second identity. as it contains intervals of 125 but this comma only has two factors of 5 in it

← Older revision		Revision as of 09:03, 9 April 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''847/845''', the '''cuthbert comma''', is a [[small comma\|small]] [[13-limit]] (also [[5.7.11.13 subgroup\|5.7.11.13-subgroup]]) [[comma]] measuring about 4.09{{cent}}. It is the difference between [[7/5]] and a stack of two [[13/11]]'s~~. It is also the difference between [[125/121]] and [[175/169]]~~.		'''847/845''', the '''cuthbert comma''', is a [[small comma\|small]] [[13-limit]] (also [[5.7.11.13 subgroup\|5.7.11.13-subgroup]]) [[comma]] measuring about 4.09{{cent}}. It is the difference between [[7/5]] and a stack of two [[13/11]]'s.

	In terms of full 13-limit commas, it is the difference between the following superparticular pairs:		In terms of full 13-limit commas, it is the difference between the following superparticular pairs:

FloraC: Cleanup

2026-04-09T09:02:27Z

Cleanup

← Older revision		Revision as of 09:02, 9 April 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''847/845''', the '''cuthbert comma''', is a [[13-limit]] (also [[5.7.11.13 subgroup]]) [[comma]] measuring about 4.09{{cent}}. It is the difference between [[7/5]] and a stack of two [[13/11]]'s. It is also the difference between [[125/121]] and [[175/169]].		'''847/845''', the '''cuthbert comma''', is a [[small comma\|small]] [[13-limit]] (also [[5.7.11.13 subgroup\|5.7.11.13-subgroup]]) [[comma]] measuring about 4.09{{cent}}. It is the difference between [[7/5]] and a stack of two [[13/11]]'s. It is also the difference between [[125/121]] and [[175/169]].

	In the 5.7.11.13 subgroup, it is the simplest comma of its size (and the smallest of its complexity) by an extremely large margin. For comparison, [[637/625]] is about as simple but much larger, and [[2941225/2924207]] is significantly more complex yet still twice as large.

	In terms of full 13-limit commas, it is the difference between the following superparticular pairs:		In terms of full 13-limit commas, it is the difference between the following superparticular pairs:
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	* [[385/384]] and [[4225/4224]]		* [[385/384]] and [[4225/4224]]

	Meanwhile, it can be factorized as [[1001/1000]] × [[2200/2197]] or [[441/440]] × [[10648/10647]].		Meanwhile, it can be factorized as ([[1001/1000]])⋅([[2200/2197]]) or ([[441/440]])⋅([[10648/10647]]).

			In the 5.7.11.13 subgroup, it is the simplest comma of its size (and the smallest of its complexity) by an extremely large margin. For comparison, [[637/625]] is about as simple but much larger, and [[2941225/2924207]] is significantly more complex yet still twice as large.

	== Temperaments ==		== Temperaments ==
	[[Tempering out]] this comma in the 13-limit results in the rank-5 cuthbert temperament and enables the [[cuthbert chords]].		[[Tempering out]] this comma in the 13-limit results in the rank-5 '''cuthbert''' temperament and enables the [[cuthbert chords]].

	Tempering it out in the 5.7.11.13 subgroup leads to an extremely efficient rank-3 temperament.		Tempering it out in the 5.7.11.13 subgroup leads to an extremely efficient rank-3 temperament.

	~~== See also ==~~
	* [[Small comma]]

	[[Category:Cuthbert]]		[[Category:Cuthbert]]
	[[Category:Commas with unknown etymology]]		[[Category:Commas with unknown etymology]]

Squib: in the 5.7.11.13 subgroup

2026-04-08T21:57:46Z

in the 5.7.11.13 subgroup

← Older revision		Revision as of 21:57, 8 April 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''847/845''', the '''cuthbert comma''', is a [[13-limit]] (also 5.7.11.13 [[subgroup]]) [[comma]] measuring about 4.09{{cent}}. It is the difference between [[7/5]] and a stack of two [[13/11]]'s. It is also the difference between [[125/121]] and [[175/169]].		'''847/845''', the '''cuthbert comma''', is a [[13-limit]] (also [[5.7.11.13 subgroup]]) [[comma]] measuring about 4.09{{cent}}. It is the difference between [[7/5]] and a stack of two [[13/11]]'s. It is also the difference between [[125/121]] and [[175/169]].

			In the 5.7.11.13 subgroup, it is the simplest comma of its size (and the smallest of its complexity) by an extremely large margin. For comparison, [[637/625]] is about as simple but much larger, and [[2941225/2924207]] is significantly more complex yet still twice as large.

	In terms of full 13-limit commas, it is the difference between the following superparticular pairs:		In terms of full 13-limit commas, it is the difference between the following superparticular pairs:
Line 16:		Line 18:
	== Temperaments ==		== Temperaments ==
	[[Tempering out]] this comma in the 13-limit results in the rank-5 cuthbert temperament and enables the [[cuthbert chords]].		[[Tempering out]] this comma in the 13-limit results in the rank-5 cuthbert temperament and enables the [[cuthbert chords]].

			Tempering it out in the 5.7.11.13 subgroup leads to an extremely efficient rank-3 temperament.

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

Squib at 01:04, 13 March 2026

2026-03-13T01:04:55Z

← Older revision		Revision as of 01:04, 13 March 2026
Line 4:		Line 4:
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''847/845''', the '''cuthbert comma''', is a [[13-limit]] (also 5.7.11.13 [[subgroup]]) [[comma]] measuring about 4.09{{cent}}. It is the difference between [[7/5]] and a stack of two [[13/11]]'s. In terms of commas, it is the difference between the following superparticular pairs:		'''847/845''', the '''cuthbert comma''', is a [[13-limit]] (also 5.7.11.13 [[subgroup]]) [[comma]] measuring about 4.09{{cent}}. It is the difference between [[7/5]] and a stack of two [[13/11]]'s. It is also the difference between [[125/121]] and [[175/169]].

			In terms of full 13-limit commas, it is the difference between the following superparticular pairs:
	* [[66/65]] and [[78/77]]		* [[66/65]] and [[78/77]]
	* [[121/120]] and [[169/168]]		* [[121/120]] and [[169/168]]

Tristanbay: Corrected a bit of math (847/845 was the product of one of the pairs of superparticulars listed, not the difference)

2024-12-07T21:16:54Z

Corrected a bit of math (847/845 was the product of one of the pairs of superparticulars listed, not the difference)

← Older revision		Revision as of 21:16, 7 December 2024
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	* [[352/351]] and [[2080/2079]]		* [[352/351]] and [[2080/2079]]
	* [[385/384]] and [[4225/4224]]		* [[385/384]] and [[4225/4224]]
	* [[441/440]] and [[10648/10647]]

	Meanwhile, it can be factorized as [[1001/1000]] × [[2200/2197]].		Meanwhile, it can be factorized as [[1001/1000]] × [[2200/2197]] or [[441/440]] × [[10648/10647]].

	== Temperaments ==		== Temperaments ==