57/56 - Revision history

FloraC: Move "hendrix" here

2026-03-31T13:06:26Z

Move "hendrix" here

← Older revision		Revision as of 13:06, 31 March 2026
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	57/56 is a comma of the 2.3.7.19 subgroup, and on that subgroup, patent vals tempering it out include those from 9, 12, 14, 17 and 26. The comma defines a rank three temperament on this subgroup, called [[hendrix]]. You can also temper it out in a rank-2 temperament in 2.3.19/7, called surprise.		57/56 is a comma of the 2.3.7.19 subgroup, and on that subgroup, patent vals tempering it out include those from 9, 12, 14, 17 and 26. The comma defines a rank three temperament on this subgroup, called [[hendrix]]. You can also temper it out in a rank-2 temperament in 2.3.19/7, called surprise.

			== Temperaments ==
			=== Hendrix ===
			This is the [[rank-3]] temperament tempering out the hendrix comma, 57/56. This is simply the most sensible name for this temperament.

			[[Subgroup]]: 2.3.7.19

			[[Comma list]]: 57/56

			{{Mapping\|legend=2\| 1 0 0 3 \| 0 1 0 -1 \| 0 0 1 1 }}
			: mapping generators: ~2, ~3, ~7

			[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1202.4345{{c}}, ~3/2 = 697.4314{{c}}, ~7/4 = 970.3487{{c}}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 697.3981{{c}}, ~7/4 = 972.1990{{c}}

			{{Optimal ET sequence\|legend=1\| 5, 9, 12, 14, 17, 26, 31h }}

			[[Badness]] (Sintel): 0.155

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

VectorGraphics at 22:11, 17 March 2025

2025-03-17T22:11:31Z

← Older revision		Revision as of 22:11, 17 March 2025
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	'''57/56''' is a [[superparticular]] interval of about 30.6¢ which makes the difference between [[4/3]] (about 498¢) and [[19/14]] (about 528.7¢) in [[19-limit]] [[just intonation]]; it is also the difference between [[19/16]] and [[7/6]]. It is also called the '''hendrix comma''', since by tempering it out, one can build an 8:10:14:19 [[hendrix chord]], which has steps of [[5/4]]-[[7/5]]-4/3. [[Patent val]]s which temper out the hendrix comma include those from {{EDOs\| 9, 10, 12, 16, 21, 22 and 26 }} edo.		'''57/56''' is a [[superparticular]] interval of about 30.6¢ which makes the difference between [[4/3]] (about 498¢) and [[19/14]] (about 528.7¢) in [[19-limit]] [[just intonation]]; it is also the difference between [[19/16]] and [[7/6]]. It is also called the '''hendrix comma''', since by tempering it out, one can build an 8:10:14:19 [[hendrix chord]], which has steps of [[5/4]]-[[7/5]]-4/3. [[Patent val]]s which temper out the hendrix comma include those from {{EDOs\| 9, 10, 12, 16, 21, 22 and 26 }} edo.

	57/56 is a comma of the 2.3.7.19 subgroup, and on that subgroup, patent vals tempering it out include those from 9, 12, 14, 17 and 26. The comma defines a rank three temperament on this subgroup.		57/56 is a comma of the 2.3.7.19 subgroup, and on that subgroup, patent vals tempering it out include those from 9, 12, 14, 17 and 26. The comma defines a rank three temperament on this subgroup, called [[hendrix]]. You can also temper it out in a rank-2 temperament in 2.3.19/7, called surprise.

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

BudjarnLambeth at 02:14, 4 November 2024

2024-11-04T02:14:33Z

← Older revision		Revision as of 02:14, 4 November 2024
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	[[Category:Hendrix]]		[[Category:Hendrix]]
	[[Category:Commas named after ~~individuals~~]]		[[Category:Commas named after composers]]

BudjarnLambeth at 07:51, 3 November 2024

2024-11-03T07:51:18Z

← Older revision		Revision as of 07:51, 3 November 2024
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	[[Category:Hendrix]]		[[Category:Hendrix]]
			[[Category:Commas named after individuals]]

TallKite at 07:13, 14 January 2023

2023-01-14T07:13:26Z

← Older revision		Revision as of 07:13, 14 January 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = hendrix comma		\| Name = hendrix comma
	\| Color name = 19or1, Noru comma		\| Color name = 19or1, noru 1sn,<br>Noru comma
	\| Comma = yes		\| Comma = yes
	}}		}}

TallKite: added color name

2022-12-04T02:40:10Z

added color name

← Older revision		Revision as of 02:40, 4 December 2022
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	{{Infobox Interval		{{Infobox Interval
	\| Name = hendrix comma		\| Name = hendrix comma
			\| Color name = 19or1, Noru comma
	\| Comma = yes		\| Comma = yes
	}}		}}

Plumtree: Normalising usage of Infobox Interval

2022-10-25T16:22:34Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 16:22, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| JI glyph =~~
	~~\| Ratio = 57/56~~
	~~\| Monzo = -3 1 0 -1 0 0 0 1~~
	~~\| Cents = 30.64211~~
	\| Name = hendrix comma		\| Name = hendrix comma
	\| ~~Color name =~~		\| Comma = yes
	~~\| FJS name = P1<sup>19</sup><sub>7</sub>~~
	~~\| Sound~~ =
	}}		}}

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	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	~~[[Category:19-limit]]~~
	~~[[Category:Small commas]]~~
	~~[[Category:Medium commas]]~~
	~~[[Category:Superparticular]]~~
	[[Category:Hendrix]]		[[Category:Hendrix]]

KingHyperio at 15:03, 4 October 2022

2022-10-04T15:03:28Z

← Older revision		Revision as of 15:03, 4 October 2022
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	}}		}}

	'''57/56''' is a [[superparticular]] interval of about 30.6¢ which makes the difference between [[4/3]] (about 498¢) and [[19/14]] (about 528.7¢) in [[19-limit]] [[just intonation]]; it is also the difference between [[19/16]] and [[7/6]]. It is also called the '''hendrix comma''', since by tempering it out, one can build an 8:10:12:19 [[hendrix chord]], which has steps of [[5/4]]-[[7/5]]-4/3. [[Patent val]]s which temper out the hendrix comma include those from {{EDOs\| 9, 10, 12, 16, 21, 22 and 26 }} edo.		'''57/56''' is a [[superparticular]] interval of about 30.6¢ which makes the difference between [[4/3]] (about 498¢) and [[19/14]] (about 528.7¢) in [[19-limit]] [[just intonation]]; it is also the difference between [[19/16]] and [[7/6]]. It is also called the '''hendrix comma''', since by tempering it out, one can build an 8:10:14:19 [[hendrix chord]], which has steps of [[5/4]]-[[7/5]]-4/3. [[Patent val]]s which temper out the hendrix comma include those from {{EDOs\| 9, 10, 12, 16, 21, 22 and 26 }} edo.

	57/56 is a comma of the 2.3.7.19 subgroup, and on that subgroup, patent vals tempering it out include those from 9, 12, 14, 17 and 26. The comma defines a rank three temperament on this subgroup.		57/56 is a comma of the 2.3.7.19 subgroup, and on that subgroup, patent vals tempering it out include those from 9, 12, 14, 17 and 26. The comma defines a rank three temperament on this subgroup.

Fredg999 category edits: Moving from Category:Small comma to Category:Small commas using Cat-a-lot

2022-03-20T21:59:57Z

Moving from Category:Small comma to Category:Small commas using Cat-a-lot

← Older revision		Revision as of 21:59, 20 March 2022
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	[[Category:19-limit]]		[[Category:19-limit]]
	[[Category:Small ~~comma~~]]		[[Category:Small commas]]
	[[Category:Medium commas]]		[[Category:Medium commas]]
	[[Category:Superparticular]]		[[Category:Superparticular]]
	[[Category:Hendrix]]		[[Category:Hendrix]]

Fredg999 category edits: Moving from Category:Medium comma to Category:Medium commas using Cat-a-lot

2022-03-20T21:53:42Z

Moving from Category:Medium comma to Category:Medium commas using Cat-a-lot

← Older revision		Revision as of 21:53, 20 March 2022
Line 21:		Line 21:
	[[Category:19-limit]]		[[Category:19-limit]]
	[[Category:Small comma]]		[[Category:Small comma]]
	[[Category:Medium ~~comma~~]]		[[Category:Medium commas]]
	[[Category:Superparticular]]		[[Category:Superparticular]]
	[[Category:Hendrix]]		[[Category:Hendrix]]