Starling chords - Revision history

FloraC: Linking, recategorize

2024-10-09T09:41:05Z

Linking, recategorize

← Older revision		Revision as of 09:41, 9 October 2024
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	Starling chords come to triads: 3, tetrads: 6, pentads: 1, for a total of 10.		Starling chords come to triads: 3, tetrads: 6, pentads: 1, for a total of 10.

	[[~~EDO\|~~Equal ~~temperaments~~]] with starling chords include {{EDOs\| 19, 27, 31, 43, 46, 50, 58, 77, 185, and 265c }}, and using the [[patent val]] tuning, [[34edo\|34]] and [[65edo\|65]].		[[Equal temperament]]s with starling chords include {{EDOs\| 19, 27, 31, 43, 46, 50, 58, 77, 185, and 265c }}, and using the [[patent val]] tuning, [[34edo\|34]] and [[65edo\|65]].

	[[Category:7-odd-limit]]		[[Category:7-odd-limit chords]]
	[[Category:9-odd-limit]]		[[Category:9-odd-limit chords]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Triads]]		[[Category:Triads]]

FloraC: Readability

2024-08-24T09:08:05Z

Readability

← Older revision		Revision as of 09:08, 24 August 2024
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	'''Starling chords''' are [[Dyadic chord #Essentially tempered dyadic chords\|essentially tempered dyadic chords]] tempered by the starling comma, [[126/125]].		'''Starling chords''' are [[Dyadic chord #Essentially tempered dyadic chords\|essentially tempered dyadic chords]] tempered by the starling comma, [[126/125]].

	The starling [[tetrad]] is an 126/125-tempered [[chord]] which in close position ([[octave reduction\|reduced to an octave]]) consists of a chain of three approximate [[6/5]] minor thirds and an approximate [[7/6]] subminor third, in a tuning which [[~~Tempering~~ out\|tempers out]] the starling comma, 126/125, and hence causes it to close on the [[octave]]. That is, it is a starling-tempered 6/5-6/5-6/5~~-7/6~~, ~~which may also be regarded as a tempered 1-~~6/5~~-10/~~7~~-12~~/7; it is also known as the septimal semicomma diminished seventh chord. In a [[meantone]] tuning the starling tetrad is three minor thirds and an augmented second, which is the traditional diminished seventh chord of common practice music in the meantone era.		The starling [[tetrad]] is an 126/125-tempered [[chord]] which in close position ([[octave reduction\|reduced to an octave]]) consists of a chain of three approximate [[6/5]] minor thirds and an approximate [[7/6]] subminor third, in a tuning which [[tempering out\|tempers out]] the starling comma, 126/125, and hence causes it to close on the [[octave]]. That is, it is a starling-tempered
			* 1–6/5–10/7–12/7, with steps 6/5, 6/5, 6/5, 7/6.

	~~Also familiar from the music of common practice~~ is the diminished ~~[[triad]],~~ a ~~tempering of 1-6/5-10/7 with steps 6/5-6/5-7/5 when understood~~ [[~~7-limit\|septimally~~]]~~. Other essentially tempered~~ starling ~~triads are~~ the ~~1-5/4-7/5~~ chord ~~with steps 5/4-10/9-10/7 and its inversion, 1-5/4-9/5 with steps 5/4-10/7-10/9~~.		It is also known as the septimal semicomma diminished seventh chord. In a [[meantone]] tuning the starling tetrad is three minor thirds and an augmented second, which is the traditional diminished seventh chord of common practice music in the meantone era.

	~~For starling tetrads~~, ~~we also have the 1-5~~/~~4-3~~/~~2-9/5 chord~~ with steps ~~5/4-~~6/5-6/5~~-10/9 and its inversion~~, ~~1-6/5-3/2-5/3; the 1-5/4-~~7/5~~-7/4 chord with steps of 5/4-10/9-5/4-8/7; the 1-5/4-7/5-9/5 chord with steps of 5/4-10/9-9/7-10/9; and the 1-9/8-5/4-9/5 chord with steps of 9/8-10/9-10/7-10/9.~~		Also familiar from the music of common practice is the diminished [[triad]], a tempering of
			* 1–6/5–10/7 with steps 6/5, 6/5, 7/5,

	There is also a unique starling [[pentad]], ~~1-9~~/~~8-5~~/~~4-3~~/~~2-9~~/5, with steps of 9/8-10/9-6/5-6/5-10/9, ~~a modified complete ninth chord.~~ In the transposition ~~1-6~~/~~5-4~~/~~3-3~~/~~2-5~~/3 with steps 6/5-10/9-9/8-10/9-6/5 we can more easily see that the steps are symmetrical around 9/8.		when understood [[7-limit\|septimally]]. Other essentially tempered starling triads are
			* 1–5/4–7/5 with steps 5/4, 10/9, 10/7 and its inversion,
			* 1–5/4–9/5 with steps 5/4, 10/7, 10/9.

			For starling tetrads, we also have
			* 1–5/4–3/2–9/5 with steps 5/4, 6/5, 6/5, 10/9 and its inversion,
			* 1–6/5–3/2–5/3 with steps 6/5, 5/4, 10/9, 6/5;
			* 1–5/4–7/5–7/4 with steps 5/4, 10/9, 5/4, 8/7;
			* 1–5/4–7/5–9/5 with steps 5/4, 10/9, 9/7, 10/9;
			* 1–9/8–5/4–9/5 with steps 9/8, 10/9, 10/7, 10/9.

			There is also a unique starling [[pentad]], a modified complete ninth chord,
			* 1–9/8–5/4–3/2–9/5, with steps 9/8, 10/9, 6/5, 6/5, 10/9,

			In the transposition 1–6/5–4/3–3/2–5/3 with steps 6/5, 10/9, 9/8, 10/9, 6/5 we can more easily see that the steps are symmetrical around 9/8.

	Starling chords come to triads: 3, tetrads: 6, pentads: 1, for a total of 10.		Starling chords come to triads: 3, tetrads: 6, pentads: 1, for a total of 10.

	[[EDO\|Equal temperaments]] with starling chords include ~~[[19edo~~\|19]], ~~[[27edo\|~~27]], ~~[[31edo\|~~31]], ~~[[43edo\|~~43]], ~~[[46edo\|~~46]], ~~[[50edo\|~~50]], ~~[[58edo\|~~58]], ~~[[77edo\|~~77]], ~~[[185edo\|~~185]] and ~~[[265edo\|~~265c]], and using the [[patent val]] tuning, [[34edo\|34]] and [[65edo\|65]].		[[EDO\|Equal temperaments]] with starling chords include {{EDOs\| 19, 27, 31, 43, 46, 50, 58, 77, 185, and 265c }}, and using the [[patent val]] tuning, [[34edo\|34]] and [[65edo\|65]].

	[[Category:7-odd-limit]]		[[Category:7-odd-limit]]

FloraC: Recategorize

2023-05-23T11:47:05Z

Recategorize

← Older revision		Revision as of 11:47, 23 May 2023
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	[[Category:9-odd-limit]]		[[Category:9-odd-limit]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:~~Triad~~]]		[[Category:Triads]]
	[[Category:~~Tetrad~~]]		[[Category:Tetrads]]
	[[Category:~~Pentad~~]]		[[Category:Pentads]]
	[[Category:Starling]]		[[Category:Starling]]

FloraC: Re-add the odd-limit categories

2023-04-28T07:03:24Z

Re-add the odd-limit categories

← Older revision		Revision as of 07:03, 28 April 2023
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	[[EDO\|Equal temperaments]] with starling chords include [[19edo\|19]], [[27edo\|27]], [[31edo\|31]], [[43edo\|43]], [[46edo\|46]], [[50edo\|50]], [[58edo\|58]], [[77edo\|77]], [[185edo\|185]] and [[265edo\|265c]], and using the [[patent val]] tuning, [[34edo\|34]] and [[65edo\|65]].		[[EDO\|Equal temperaments]] with starling chords include [[19edo\|19]], [[27edo\|27]], [[31edo\|31]], [[43edo\|43]], [[46edo\|46]], [[50edo\|50]], [[58edo\|58]], [[77edo\|77]], [[185edo\|185]] and [[265edo\|265c]], and using the [[patent val]] tuning, [[34edo\|34]] and [[65edo\|65]].

			[[Category:7-odd-limit]]
			[[Category:9-odd-limit]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Triad]]		[[Category:Triad]]

FloraC: Recategorize

2023-04-28T06:58:30Z

Recategorize

← Older revision		Revision as of 06:58, 28 April 2023
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	'''Starling chords''' are [[Dyadic chord#Essentially tempered dyadic chords\|essentially tempered dyadic chords]] tempered by the ~~[[Starling family\|~~starling~~]] [[~~comma]], [[126/125]].		'''Starling chords''' are [[Dyadic chord #Essentially tempered dyadic chords\|essentially tempered dyadic chords]] tempered by the starling comma, [[126/125]].

	The starling [[tetrad]] is an 126/125-tempered [[chord]] which in close position ([[octave reduction\|reduced to an octave]]) consists of a chain of three approximate [[6/5]] minor thirds and an approximate [[7/6]] subminor third, in a tuning which [[Tempering out\|tempers out]] the starling comma, 126/125, and hence causes it to close on the [[octave]]. That is, it is a starling-tempered 6/5-6/5-6/5-7/6, which may also be regarded as a tempered 1-6/5-10/7-12/7; it is also known as the septimal semicomma diminished seventh chord. In a [[meantone]] tuning the starling tetrad is three minor thirds and an augmented second, which is the traditional diminished seventh chord of common practice music in the meantone era.		The starling [[tetrad]] is an 126/125-tempered [[chord]] which in close position ([[octave reduction\|reduced to an octave]]) consists of a chain of three approximate [[6/5]] minor thirds and an approximate [[7/6]] subminor third, in a tuning which [[Tempering out\|tempers out]] the starling comma, 126/125, and hence causes it to close on the [[octave]]. That is, it is a starling-tempered 6/5-6/5-6/5-7/6, which may also be regarded as a tempered 1-6/5-10/7-12/7; it is also known as the septimal semicomma diminished seventh chord. In a [[meantone]] tuning the starling tetrad is three minor thirds and an augmented second, which is the traditional diminished seventh chord of common practice music in the meantone era.
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	[[EDO\|Equal temperaments]] with starling chords include [[19edo\|19]], [[27edo\|27]], [[31edo\|31]], [[43edo\|43]], [[46edo\|46]], [[50edo\|50]], [[58edo\|58]], [[77edo\|77]], [[185edo\|185]] and [[265edo\|265c]], and using the [[patent val]] tuning, [[34edo\|34]] and [[65edo\|65]].		[[EDO\|Equal temperaments]] with starling chords include [[19edo\|19]], [[27edo\|27]], [[31edo\|31]], [[43edo\|43]], [[46edo\|46]], [[50edo\|50]], [[58edo\|58]], [[77edo\|77]], [[185edo\|185]] and [[265edo\|265c]], and using the [[patent val]] tuning, [[34edo\|34]] and [[65edo\|65]].

	~~[[Category:7-odd-limit]]~~
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	~~[[Category:Dyadic]]~~
	~~[[Category:Starling]]~~
	[[Category:Triad]]		[[Category:Triad]]
	[[Category:Tetrad]]		[[Category:Tetrad]]
	[[Category:Pentad]]		[[Category:Pentad]]
			[[Category:Starling]]

Fredg999 category edits: Removing from Category:Chords using Cat-a-lot

2023-04-28T03:51:55Z

Removing from Category:Chords using Cat-a-lot

← Older revision		Revision as of 03:51, 28 April 2023
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	[[Category:7-odd-limit]]		[[Category:7-odd-limit]]
	~~[[Category:Chords]]~~
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Dyadic]]		[[Category:Dyadic]]

BudjarnLambeth: Added links (as requested by the to:do notice)

2023-04-20T07:57:28Z

Added links (as requested by the to:do notice)

← Older revision		Revision as of 07:57, 20 April 2023
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	'''Starling chords''' are [[Dyadic chord#Essentially tempered dyadic chords\|essentially tempered dyadic chords]] tempered by the ~~starling comma,~~ [[~~126/125]]. The~~ starling ~~[[tetrad~~]] ~~is an 126/125-tempered~~ [[~~chord~~]] ~~which in close position (~~[[~~octave reduction\|reduced to an octave]]) consists of a chain of three approximate [[6/5]] minor thirds and an approximate [[7/6]] subminor third, in a tuning which tempers out the starling comma,~~ 126/125, and hence causes it to close on the octave; that is, it is a starling-tempered 6/5-6/5-6/5-7/6, which may also be regarded as a tempered 1-6/5-10/7-12/7; it is also known as the septimal semicomma diminished seventh chord. In a meantone tuning the starling tetrad is three minor thirds and an augmented second, which is the traditional diminished seventh chord of common practice music in the meantone era. Also familiar from the music of common practice is the diminished [[triad]]~~, a tempering of 1-6/5-10/7 with steps 6/5-6/5-7/5 when understood septimally~~.		'''Starling chords''' are [[Dyadic chord#Essentially tempered dyadic chords\|essentially tempered dyadic chords]] tempered by the [[Starling family\|starling]] [[comma]], [[126/125]].

	~~Other essentially~~ tempered starling [[triad]]s are the 1-5/4-7/5 chord with steps 5/4-10/9-10/7 and its inversion, 1-5/4-9/5 with steps 5/4-10/7-10/9. For starling tetrads, we also have the 1-5/4-3/2-9/5 chord with steps 5/4-6/5-6/5-10/9 and its inversion, 1-6/5-3/2-5/3; the 1-5/4-7/5-7/4 chord with steps of 5/4-10/9-5/4-8/7; the 1-5/4-7/5-9/5 chord with steps of 5/4-10/9-9/7-10/9; and the 1-9/8-5/4-9/5 chord with steps of 9/8-10/9-10/7-10/9.		The starling [[tetrad]] is an 126/125-tempered [[chord]] which in close position ([[octave reduction\|reduced to an octave]]) consists of a chain of three approximate [[6/5]] minor thirds and an approximate [[7/6]] subminor third, in a tuning which [[Tempering out\|tempers out]] the starling comma, 126/125, and hence causes it to close on the [[octave]]. That is, it is a starling-tempered 6/5-6/5-6/5-7/6, which may also be regarded as a tempered 1-6/5-10/7-12/7; it is also known as the septimal semicomma diminished seventh chord. In a [[meantone]] tuning the starling tetrad is three minor thirds and an augmented second, which is the traditional diminished seventh chord of common practice music in the meantone era.

			Also familiar from the music of common practice is the diminished [[triad]], a tempering of 1-6/5-10/7 with steps 6/5-6/5-7/5 when understood [[7-limit\|septimally]]. Other essentially tempered starling triads are the 1-5/4-7/5 chord with steps 5/4-10/9-10/7 and its inversion, 1-5/4-9/5 with steps 5/4-10/7-10/9.

			For starling tetrads, we also have the 1-5/4-3/2-9/5 chord with steps 5/4-6/5-6/5-10/9 and its inversion, 1-6/5-3/2-5/3; the 1-5/4-7/5-7/4 chord with steps of 5/4-10/9-5/4-8/7; the 1-5/4-7/5-9/5 chord with steps of 5/4-10/9-9/7-10/9; and the 1-9/8-5/4-9/5 chord with steps of 9/8-10/9-10/7-10/9.

	There is also a unique starling [[pentad]], 1-9/8-5/4-3/2-9/5, with steps of 9/8-10/9-6/5-6/5-10/9, a modified complete ninth chord. In the transposition 1-6/5-4/3-3/2-5/3 with steps 6/5-10/9-9/8-10/9-6/5 we can more easily see that the steps are symmetrical around 9/8.		There is also a unique starling [[pentad]], 1-9/8-5/4-3/2-9/5, with steps of 9/8-10/9-6/5-6/5-10/9, a modified complete ninth chord. In the transposition 1-6/5-4/3-3/2-5/3 with steps 6/5-10/9-9/8-10/9-6/5 we can more easily see that the steps are symmetrical around 9/8.
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	Starling chords come to triads: 3, tetrads: 6, pentads: 1, for a total of 10.		Starling chords come to triads: 3, tetrads: 6, pentads: 1, for a total of 10.

	Equal temperaments with starling chords include 19, 27, 31, 43, 46, 50, 58, 77, 185 and 265c, and using the patent val tuning, 34 and 65.		[[EDO\|Equal temperaments]] with starling chords include [[19edo\|19]], [[27edo\|27]], [[31edo\|31]], [[43edo\|43]], [[46edo\|46]], [[50edo\|50]], [[58edo\|58]], [[77edo\|77]], [[185edo\|185]] and [[265edo\|265c]], and using the [[patent val]] tuning, [[34edo\|34]] and [[65edo\|65]].

	[[Category:7-odd-limit]]		[[Category:7-odd-limit]]
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	[[Category:Tetrad]]		[[Category:Tetrad]]
	[[Category:Pentad]]		[[Category:Pentad]]

	~~[[Category:Todo:add links]]~~

Fredg999: Fixed typo

2022-01-08T00:54:49Z

Fixed typo

← Older revision		Revision as of 00:54, 8 January 2022
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	'''Starling chords''' are [[Dyadic chord#Essentially tempered dyadic chords\|essentially tempered dyadic chords]] tempered by the ~~staring~~ comma, [[126/125]]. The starling [[tetrad]] is an 126/125-tempered [[chord]] which in close position ([[octave reduction\|reduced to an octave]]) consists of a chain of three approximate [[6/5]] minor thirds and an approximate [[7/6]] subminor third, in a tuning which tempers out the starling comma, 126/125, and hence causes it to close on the octave; that is, it is a starling-tempered 6/5-6/5-6/5-7/6, which may also be regarded as a tempered 1-6/5-10/7-12/7; it is also known as the septimal semicomma diminished seventh chord. In a meantone tuning the starling tetrad is three minor thirds and an augmented second, which is the traditional diminished seventh chord of common practice music in the meantone era. Also familiar from the music of common practice is the diminished [[triad]], a tempering of 1-6/5-10/7 with steps 6/5-6/5-7/5 when understood septimally.		'''Starling chords''' are [[Dyadic chord#Essentially tempered dyadic chords\|essentially tempered dyadic chords]] tempered by the starling comma, [[126/125]]. The starling [[tetrad]] is an 126/125-tempered [[chord]] which in close position ([[octave reduction\|reduced to an octave]]) consists of a chain of three approximate [[6/5]] minor thirds and an approximate [[7/6]] subminor third, in a tuning which tempers out the starling comma, 126/125, and hence causes it to close on the octave; that is, it is a starling-tempered 6/5-6/5-6/5-7/6, which may also be regarded as a tempered 1-6/5-10/7-12/7; it is also known as the septimal semicomma diminished seventh chord. In a meantone tuning the starling tetrad is three minor thirds and an augmented second, which is the traditional diminished seventh chord of common practice music in the meantone era. Also familiar from the music of common practice is the diminished [[triad]], a tempering of 1-6/5-10/7 with steps 6/5-6/5-7/5 when understood septimally.

	Other essentially tempered starling [[triad]]s are the 1-5/4-7/5 chord with steps 5/4-10/9-10/7 and its inversion, 1-5/4-9/5 with steps 5/4-10/7-10/9. For starling tetrads, we also have the 1-5/4-3/2-9/5 chord with steps 5/4-6/5-6/5-10/9 and its inversion, 1-6/5-3/2-5/3; the 1-5/4-7/5-7/4 chord with steps of 5/4-10/9-5/4-8/7; the 1-5/4-7/5-9/5 chord with steps of 5/4-10/9-9/7-10/9; and the 1-9/8-5/4-9/5 chord with steps of 9/8-10/9-10/7-10/9.		Other essentially tempered starling [[triad]]s are the 1-5/4-7/5 chord with steps 5/4-10/9-10/7 and its inversion, 1-5/4-9/5 with steps 5/4-10/7-10/9. For starling tetrads, we also have the 1-5/4-3/2-9/5 chord with steps 5/4-6/5-6/5-10/9 and its inversion, 1-6/5-3/2-5/3; the 1-5/4-7/5-7/4 chord with steps of 5/4-10/9-5/4-8/7; the 1-5/4-7/5-9/5 chord with steps of 5/4-10/9-9/7-10/9; and the 1-9/8-5/4-9/5 chord with steps of 9/8-10/9-10/7-10/9.

Xenwolf: recat

2021-05-20T07:41:41Z

recat

← Older revision		Revision as of 07:41, 20 May 2021
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	Equal temperaments with starling chords include 19, 27, 31, 43, 46, 50, 58, 77, 185 and 265c, and using the patent val tuning, 34 and 65.		Equal temperaments with starling chords include 19, 27, 31, 43, 46, 50, 58, 77, 185 and 265c, and using the patent val tuning, 34 and 65.

	[[Category:7-limit]]		[[Category:7-odd-limit]]
	[[Category:Chords]]		[[Category:Chords]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]

Xenwolf: +cat

2021-05-20T07:02:40Z

+cat

← Older revision		Revision as of 07:02, 20 May 2021
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	[[Category:7-limit]]		[[Category:7-limit]]
	[[Category:Chords]]		[[Category:Chords]]
			[[Category:Essentially tempered chords]]
	[[Category:Dyadic]]		[[Category:Dyadic]]
	[[Category:Starling]]		[[Category:Starling]]