Hendrix chord - Revision history

Sintel: /* JI interpretations */ Don't put instructions for editors in main text

2025-05-29T13:18:06Z

JI interpretations: Don't put instructions for editors in main text

← Older revision		Revision as of 13:18, 29 May 2025
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	Interpretations as a [[just intonation]] chord.		Interpretations as a [[just intonation]] chord.

	''The only interpretations allowed in this section are ones where all 'intervals from root'		<!-- ''The only interpretations allowed in this section are ones where all 'intervals from root'
	''have a denominator of 8 or less (to prevent the section becoming too long).''		''have a denominator of 8 or less (to prevent the section becoming too long).'' -->

	=== 5-limit ===		=== 5-limit ===

BudjarnLambeth: /* 5-limit */

2025-04-27T03:15:33Z

5-limit

← Older revision		Revision as of 03:15, 27 April 2025
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	In the [[5-limit]] it may be tuned as '''10:20:25:36:40:48''', an extended [[20:25:30:36\|major-minor seventh chord]].		In the [[5-limit]] it may be tuned as '''10:20:25:36:40:48''', an extended [[20:25:30:36\|major-minor seventh chord]].

	This chord appears in [[~~5afdo~~]] and all higher [[AFDO]]s.		This chord appears in [[20afdo]] and all higher [[AFDO]]s.

	According to this interpretation, the 12edo hendrix chord has 30.2 [[cents]] of total error and no more than 17.6 cents error on any single interval.		According to this interpretation, the 12edo hendrix chord has 30.2 [[cents]] of total error and no more than 17.6 cents error on any single interval.

BudjarnLambeth: /* JI interpretations */

2025-04-27T03:15:06Z

JI interpretations

← Older revision		Revision as of 03:15, 27 April 2025
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	=== 5-limit ===		=== 5-limit ===
	{{Infobox Chord\|10:20:25:36:40:48\|ColorName=yo gu-7 guqu-9 no-5 or y,g7gq9no5\|Root=20}}		{{Infobox Chord\|10:20:25:36:40:48\|ColorName=yo gu-7 guqu-9 no-5 or y,g7gq9no5\|Root=20}}
	In the [[5-limit]] it may be tuned as 10:20:25:36:40:48, an extended [[20:25:30:36\|major-minor seventh chord]].		In the [[5-limit]] it may be tuned as '''10:20:25:36:40:48''', an extended [[20:25:30:36\|major-minor seventh chord]].

	This chord appears in [[5afdo]] and all higher [[AFDO]]s.		This chord appears in [[5afdo]] and all higher [[AFDO]]s.
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	=== 7-limit ===		=== 7-limit ===
	{{Infobox Chord\|6:12:15:21:24:28\|ColorName=har-7 zoqu-9 no-5 or h7zq9no5\|Root=12}}		{{Infobox Chord\|6:12:15:21:24:28\|ColorName=har-7 zoqu-9 no-5 or h7zq9no5\|Root=12}}
	In the [[7-limit]] it may be tuned as 6:12:15:21:24:28, an extended [[4:5:6:7\|harmonic seventh chord]].		In the [[7-limit]] it may be tuned as '''6:12:15:21:24:28''', an extended [[4:5:6:7\|harmonic seventh chord]].

	This chord appears in [[12afdo]] and all higher [[AFDO]]s.		This chord appears in [[12afdo]] and all higher [[AFDO]]s.
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	=== 19-limit ===		=== 19-limit ===
	{{Infobox Chord\|4:8:10:14:16:19\|ColorName=har-7 noqu-9 no-5 or h7,19oq9no5\|Root=8}}		{{Infobox Chord\|4:8:10:14:16:19\|ColorName=har-7 noqu-9 no-5 or h7,19oq9no5\|Root=8}}
	In the [[19-limit]] it may be tuned as 4:8:10:14:16:19, an extended [[4:5:6:7\|harmonic seventh chord]].		In the [[19-limit]] it may be tuned as '''4:8:10:14:16:19''', an extended [[4:5:6:7\|harmonic seventh chord]].

	This chord appears in [[8afdo]] and all higher [[AFDO]]s.		This chord appears in [[8afdo]] and all higher [[AFDO]]s.

BudjarnLambeth: /* JI interpretations */

2025-04-27T03:14:30Z

JI interpretations

← Older revision		Revision as of 03:14, 27 April 2025
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	=== 5-limit ===		=== 5-limit ===
	{{Infobox Chord\|10:20:25:36:40:48\|ColorName=yo gu-7 guqu-9 no-5 or y,g7gq9no5\|Root=20}}		{{Infobox Chord\|10:20:25:36:40:48\|ColorName=yo gu-7 guqu-9 no-5 or y,g7gq9no5\|Root=20}}
	In the [[5-limit]] it may be tuned as 10:20:25:36:40:48, an extended [[20:25:30:36\|major-minor seventh chord]].		In the [[5-limit]] it may be tuned as 10:20:25:36:40:48, an extended [[20:25:30:36\|major-minor seventh chord]].

			This chord appears in [[5afdo]] and all higher [[AFDO]]s.

	According to this interpretation, the 12edo hendrix chord has 30.2 [[cents]] of total error and no more than 17.6 cents error on any single interval.		According to this interpretation, the 12edo hendrix chord has 30.2 [[cents]] of total error and no more than 17.6 cents error on any single interval.
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	{{Infobox Chord\|6:12:15:21:24:28\|ColorName=har-7 zoqu-9 no-5 or h7zq9no5\|Root=12}}		{{Infobox Chord\|6:12:15:21:24:28\|ColorName=har-7 zoqu-9 no-5 or h7zq9no5\|Root=12}}
	In the [[7-limit]] it may be tuned as 6:12:15:21:24:28, an extended [[4:5:6:7\|harmonic seventh chord]].		In the [[7-limit]] it may be tuned as 6:12:15:21:24:28, an extended [[4:5:6:7\|harmonic seventh chord]].

			This chord appears in [[12afdo]] and all higher [[AFDO]]s.

	According to this interpretation, the 12edo hendrix chord has 78.0 [[cents]] of total error and no more than 33.1 cents error on any single interval.		According to this interpretation, the 12edo hendrix chord has 78.0 [[cents]] of total error and no more than 33.1 cents error on any single interval.
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	{{Infobox Chord\|4:8:10:14:16:19\|ColorName=har-7 noqu-9 no-5 or h7,19oq9no5\|Root=8}}		{{Infobox Chord\|4:8:10:14:16:19\|ColorName=har-7 noqu-9 no-5 or h7,19oq9no5\|Root=8}}
	In the [[19-limit]] it may be tuned as 4:8:10:14:16:19, an extended [[4:5:6:7\|harmonic seventh chord]].		In the [[19-limit]] it may be tuned as 4:8:10:14:16:19, an extended [[4:5:6:7\|harmonic seventh chord]].

			This chord appears in [[8afdo]] and all higher [[AFDO]]s.

	According to this interpretation, the 12edo hendrix chord has 47.4 [[cents]] of total error and no more than 33.1 cents error on any single interval.		According to this interpretation, the 12edo hendrix chord has 47.4 [[cents]] of total error and no more than 33.1 cents error on any single interval.

BudjarnLambeth: /* JI interpretations */

2025-04-27T03:12:15Z

JI interpretations

← Older revision		Revision as of 03:12, 27 April 2025
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	''The only interpretations allowed in this section are ones where all 'intervals from root'		''The only interpretations allowed in this section are ones where all 'intervals from root'
	''have a denominator of 8 or less (to prevent the section becoming too long.''		''have a denominator of 8 or less (to prevent the section becoming too long).''

	=== 5-limit ===		=== 5-limit ===

BudjarnLambeth: /* JI interpretations */

2025-04-27T03:12:03Z

JI interpretations

← Older revision		Revision as of 03:12, 27 April 2025
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	''The only interpretations allowed in this section are ones where all 'intervals from root'		''The only interpretations allowed in this section are ones where all 'intervals from root'
	have a denominator of 8 or less (to prevent the section becoming too long.''		''have a denominator of 8 or less (to prevent the section becoming too long.''

	=== 5-limit ===		=== 5-limit ===

BudjarnLambeth: /* Essentially tempered */

2025-04-27T03:10:09Z

Essentially tempered

← Older revision		Revision as of 03:10, 27 April 2025
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	This chord tempers out the ''hendrix comma'' of [[57/56]].		This chord tempers out the ''hendrix comma'' of [[57/56]].

	[[EDO]]s including this chord are {{EDOs\|9, 10, 14, 16, 17, 21, 22, 26, and 31}}.		[[EDO]]s including this chord are {{EDOs\|9, 10, 12, 14, 16, 17, 21, 22, 26, and 31}}.

	{{Todo\|review\|inline=1\|text=The section about tempering 57/56 needs more explanation, and may be incorrect.}}		{{Todo\|review\|inline=1\|text=The section about tempering 57/56 needs more explanation, and may be incorrect.}}

BudjarnLambeth at 03:08, 27 April 2025

2025-04-27T03:08:40Z

← Older revision		Revision as of 03:08, 27 April 2025
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	=== Essentially tempered ===		=== Essentially tempered ===
	It can also be tuned as an [[essentially tempered chord]] that splits the difference between the [[19/16\|19/8]] 10th and the [[7/3]] 10th. This chord tempers out the ''hendrix comma'' of [[57/56]].		It can also be tuned as an [[essentially tempered chord]] that splits the difference between the [[19/16\|19/8]] 10th and the [[7/3]] 10th.
	{{Todo\|review\|inline=1\|text=The ~~paragraph~~ about tempering 57/56 needs more explanation, and may be incorrect.}}
			This chord tempers out the ''hendrix comma'' of [[57/56]].

			[[EDO]]s including this chord are {{EDOs\|9, 10, 14, 16, 17, 21, 22, 26, and 31}}.

			{{Todo\|review\|inline=1\|text=The section about tempering 57/56 needs more explanation, and may be incorrect.}}

	[[Category:Hendrix\| ]] <!-- main article -->		[[Category:Hendrix\| ]] <!-- main article -->
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Just intonation chords]]		[[Category:Just intonation chords]]

BudjarnLambeth: /* Tempered interpretations */

2025-04-27T03:06:44Z

Tempered interpretations

← Older revision		Revision as of 03:06, 27 April 2025
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	It can also be tuned as an [[essentially tempered chord]] that splits the difference between the [[19/16\|19/8]] 10th and the [[7/3]] 10th. This chord tempers out the ''hendrix comma'' of [[57/56]].		It can also be tuned as an [[essentially tempered chord]] that splits the difference between the [[19/16\|19/8]] 10th and the [[7/3]] 10th. This chord tempers out the ''hendrix comma'' of [[57/56]].
	{{Todo\|review\|inline=1\|text=The paragraph about tempering 57/56 needs more explanation, and may be incorrect.}}		{{Todo\|review\|inline=1\|text=The paragraph about tempering 57/56 needs more explanation, and may be incorrect.}}

	~~=== In EDOs ===~~
	~~[[EDO]]s with hendrix chords include the {{EDOs\|9, 10, 14, 16, 17, 21, 22, 26, and 31}}.~~
	~~{{Todo\|complete section\|inline=1\|text=Explain the reasoning for exactly when an EDO is considered to "have" a Hendrix chord and when not.}}~~

	[[Category:Hendrix\| ]] <!-- main article -->		[[Category:Hendrix\| ]] <!-- main article -->
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Just intonation chords]]		[[Category:Just intonation chords]]

BudjarnLambeth: /* JI interpretations */ add EDO approximations

2025-04-27T03:06:28Z

JI interpretations: add EDO approximations

← Older revision		Revision as of 03:06, 27 April 2025
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	In the [[5-limit]] it may be tuned as 10:20:25:36:40:48, an extended [[20:25:30:36\|major-minor seventh chord]].		In the [[5-limit]] it may be tuned as 10:20:25:36:40:48, an extended [[20:25:30:36\|major-minor seventh chord]].

	According to this interpretation, the 12edo hendrix chord has 30.2 [[cents]] of error ~~relative~~ to JI.		According to this interpretation, the 12edo hendrix chord has 30.2 [[cents]] of total error and no more than 17.6 cents error on any single interval.

			[[EDO]]s with less than 20 cents error on any one interval include: {{EDOs\|12, 15, 18, 19, 22, 24, 26, 27, 28...}} and everything bigger than 28.

			[[EDO]]s up to 100 with successively lower error include: {{EDOs\|4, 5, 6, 7, 12, 19, 34, 46, 53}}.
	{{clear}}		{{clear}}

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	In the [[7-limit]] it may be tuned as 6:12:15:21:24:28, an extended [[4:5:6:7\|harmonic seventh chord]].		In the [[7-limit]] it may be tuned as 6:12:15:21:24:28, an extended [[4:5:6:7\|harmonic seventh chord]].

	According to this interpretation, the 12edo hendrix chord has 78.0 [[cents]] of error ~~relative~~ to JI.		According to this interpretation, the 12edo hendrix chord has 78.0 [[cents]] of total error and no more than 33.1 cents error on any single interval.

			[[EDO]]s with less than 35 cents error on any one interval include: {{EDOs\|10, 12, 15, 16, 17...}} and everything bigger than 17.

			[[EDO]]s up to 100 with successively lower error include: {{EDOs\|4, 6, 9, 10, 19, 21, 22, 31, 68, 99}}.
	{{clear}}		{{clear}}

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	In the [[19-limit]] it may be tuned as 4:8:10:14:16:19, an extended [[4:5:6:7\|harmonic seventh chord]].		In the [[19-limit]] it may be tuned as 4:8:10:14:16:19, an extended [[4:5:6:7\|harmonic seventh chord]].

	According to this interpretation, the 12edo hendrix chord has 47.4 [[cents]] of error ~~relative~~ to JI.		According to this interpretation, the 12edo hendrix chord has 47.4 [[cents]] of total error and no more than 33.1 cents error on any single interval.

			[[EDO]]s with less than 35 cents error on any one interval include: {{EDOs\|12, 15, 16, 17...}} and everything bigger than 17.

			[[EDO]]s up to 100 with successively lower error include: {{EDOs\|4, 7, 9, 12, 15, 16, 25, 37, 53, 56, 68, 93}}.
	{{clear}}		{{clear}}