Augmented chords in just intonation, some - Revision history

Fredg999: Categories

2024-12-22T22:13:04Z

BudjarnLambeth at 06:51, 4 December 2024

2024-12-04T06:51:18Z

← Older revision		Revision as of 06:51, 4 December 2024
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	~~{{todo \| cleanup \| discuss title \| inline=1}}~~

	== Harmonic augmented 7th chords based on 8:10:13 ==		== Harmonic augmented 7th chords based on 8:10:13 ==

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	20 : 11 ~ 1035 cents		20 : 11 ~ 1035 cents


			{{todo \| intro \| discuss title \| review \| inline=1}}

	[[Category:Chords]]		[[Category:Chords]]
	[[Category:Just intonation]]		[[Category:Just intonation]]
	[[Category:13-limit chords]]		[[Category:13-limit chords]]

BudjarnLambeth: Capitalisation

2024-12-04T06:47:33Z

Capitalisation

← Older revision		Revision as of 06:47, 4 December 2024
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	{{todo \| cleanup \| discuss title \| inline=1}}		{{todo \| cleanup \| discuss title \| inline=1}}

	== ~~harmonic~~ augmented 7th chords based on 8:10:13 ==		== Harmonic augmented 7th chords based on 8:10:13 ==

	The central [[triad]] in all three [[chord]]s is 8:10:13, but each uses a different 7th degree, to come as close as possible to the familiar aug7 (without straying into [[17-limit\|high harmonics]]).		The central [[triad]] in all three [[chord]]s is 8:10:13, but each uses a different 7th degree, to come as close as possible to the familiar aug7 (without straying into [[17-limit\|high harmonics]]).
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	24 : 13 ~ 1061 cents		24 : 13 ~ 1061 cents

	== ~~augmented~~ 7th chords based on 9:11:13 ==		== Augmented 7th chords based on 9:11:13 ==

	Interestingly, none of these chords has a [[5/4\|5:4]]. Someone might argue that a chord with a [[neutral third scale\|neutral third]] is not properly augmented, but they certainly sound closer to augmented than they do to anything else in Western music.		Interestingly, none of these chords has a [[5/4\|5:4]]. Someone might argue that a chord with a [[neutral third scale\|neutral third]] is not properly augmented, but they certainly sound closer to augmented than they do to anything else in Western music.

BudjarnLambeth: Category, links, clarify wording slightly

2024-12-04T06:47:13Z

Category, links, clarify wording slightly

← Older revision		Revision as of 06:47, 4 December 2024
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	== harmonic augmented 7th chords based on 8:10:13 ==		== harmonic augmented 7th chords based on 8:10:13 ==

	The central triad in all three ~~chords~~ is 8:10:13,		The central [[triad]] in all three [[chord]]s is 8:10:13, but each uses a different 7th degree, to come as close as possible to the familiar aug7 (without straying into [[17-limit\|high harmonics]]).
	but each uses a different 7th degree,
	to come as close as possible to the familiar aug7
	(without straying into high harmonics).

	Some of the ~~intervals~~ are listed below in terms of cents.		Some of the [[interval]]s are listed below in terms of [[cents]].


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	10 : 13 : 16 : 18 \| aug 7		10 : 13 : 16 : 18 \| aug 7

	13 : 16 : 20 : 24 \| aug neutral 7		13 : 16 : 20 : 24 \| aug [[neutral]] 7



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	== augmented 7th chords based on 9:11:13 ==		== augmented 7th chords based on 9:11:13 ==

	Interestingly, none of these chords has a 5:4.		Interestingly, none of these chords has a [[5/4\|5:4]]. Someone might argue that a chord with a [[neutral third scale\|neutral third]] is not properly augmented, but they certainly sound closer to augmented than they do to anything else in Western music.
	Someone might argue that a chord with a neutral third is not properly augmented,
	but they certainly sound closer to augmented than anything else in Western music.
	Some of the intervals are listed below in terms of cents.		Some of the intervals are listed below in terms of cents.

	The central triad in all three chords is 7:9:11,		The central triad in all three chords is 7:9:11, but each uses a different 7th degree, to come as close as possible to aug7 (without straying into high harmonics).
	but each uses a different 7th degree,
	to come as close as possible to aug7 (without straying into high harmonics).


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	[[Category:Chords]]		[[Category:Chords]]
	[[Category:Just intonation]]		[[Category:Just intonation]]
			[[Category:13-limit chords]]

BudjarnLambeth: Todo

2024-12-04T06:34:15Z

Todo

← Older revision		Revision as of 06:34, 4 December 2024
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	{{todo \| cleanup \| inline=1}}		{{todo \| cleanup \| discuss title \| inline=1}}

	== harmonic augmented 7th chords based on 8:10:13 ==		== harmonic augmented 7th chords based on 8:10:13 ==

BudjarnLambeth: Todo cleanup

2024-09-18T23:19:05Z

Todo cleanup

← Older revision		Revision as of 23:19, 18 September 2024
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			{{todo \| cleanup \| inline=1}}

	== harmonic augmented 7th chords based on 8:10:13 ==		== harmonic augmented 7th chords based on 8:10:13 ==

Aura: Fixed typos

2024-06-16T14:23:06Z

Fixed typos

← Older revision		Revision as of 14:23, 16 June 2024
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	== harmonic ~~augmneted~~ 7th chords based on 8:10:13 ==		== harmonic augmented 7th chords based on 8:10:13 ==

	The central triad in all three chords is 8:10:13,		The central triad in all three chords is 8:10:13,
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	24 : 13 ~ 1061 cents		24 : 13 ~ 1061 cents

	== ~~agumented~~ 7th chords based on 9:11:13 ==		== augmented 7th chords based on 9:11:13 ==

	Interestingly, none of these chords has a 5:4.		Interestingly, none of these chords has a 5:4.

Fredg999: Categories

2024-06-16T04:23:41Z

Jeff Brown: whitespace

2024-06-15T21:39:36Z

whitespace

← Older revision		Revision as of 21:39, 15 June 2024
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	but each uses a different 7th degree,		but each uses a different 7th degree,
	to come as close as possible to aug7 (without straying into high harmonics).		to come as close as possible to aug7 (without straying into high harmonics).


	The inversions:		The inversions:

Jeff Brown: whitespace

2024-06-15T21:39:14Z

whitespace

← Older revision		Revision as of 21:39, 15 June 2024
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	Some of the intervals are listed below in terms of cents.		Some of the intervals are listed below in terms of cents.


			The chords:

	8 : 10 : 13 : 14 \| aug 7		8 : 10 : 13 : 14 \| aug 7
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	16 : 13 ~ 359 cents		16 : 13 ~ 359 cents


	The sevenths (as reduced fractions):		The sevenths (as reduced fractions):

← Older revision		Revision as of 22:13, 22 December 2024
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	{{todo \| intro \| discuss title \| review \| inline=1}}		{{todo \| intro \| discuss title \| review \| inline=1}}

	~~[[Category:Chords]]~~		[[Category:Just intonation chords]]
	[[Category:Just intonation]]
	[[Category:13-limit chords]]		[[Category:13-limit chords]]

← Older revision		Revision as of 04:23, 16 June 2024
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	20 : 11 ~ 1035 cents		20 : 11 ~ 1035 cents

			[[Category:Chords]]
			[[Category:Just intonation]]