Lériendil: Lériendil moved page Chords of valentine to Valentine/Chords

2025-06-22T21:52:57Z

Lériendil moved page Chords of valentine to Valentine/Chords

← Older revision	Revision as of 21:52, 22 June 2025
(No difference)

FloraC: Cleanup

2025-01-22T11:38:55Z

Cleanup

← Older revision		Revision as of 11:38, 22 January 2025
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	Below are listed the [[dyadic chord]]s of 11-limit [[~~Valentine\|~~valentine ~~temperament~~]]. Typing the chords requires consideration of the fact that valentine conflates 12/11 and 11/10 and so also 11/6 and 20/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 11/10 and 20/11.		Below are listed the [[11-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[valentine]] temperament. Typing the chords requires consideration of the fact that valentine conflates 12/11 and 11/10 and so also 11/6 and 20/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 11/10 and 11/6.

	~~(Note that this preference for 20~~/~~11 over 11~~/~~6 is only true for the "transversal" column -- and there aren't any there. As the person who created the list of inversions~~, ~~I (Jake) would rather know about an 11~~/~~6 than a 20~~/11, ~~so the "as generated"~~ and ~~inversion columns show 11~~/6. ~~That sometimes required tempering out~~ 121/120 ~~where the original list didn't indicate the need~~. ~~All that being said~~, ~~the transversals are untouched from the original entry~~.)		If only [[126/125]] needs to be tempered out, the chord is labeled [[starling chords\|starling]], if [[121/120]], [[biyatismic chords\|biyatismic]], if [[176/175]], [[valinorsmic chords\|valinorsmic]], if [[385/384]], [[keenanismic chords\|keenanismic]], and if [[441/440]], [[werckismic chords\|werckismic]]. Chords which require any two of 121/120, 176/175 or 385/384 are labeled [[zeus chords\|zeus]], if they require any two of 126/125, 176/175 or 441/440, they are labeled [[thrush chords\|thrush]]. Finally, if they require any three independent commas among those discussed above, it is labeled [[valentine chords\|valentine]].

	~~If only [[126/125]] needs to be tempered out, the chord is labeled starling, if [[121/120]], biyatismic, if [[176/175]], valinorsmic, if [~~[~~385/384]], keenanismic, and if~~ [~~[441/440~~]], werckismic. Chords which require any two of 121/120, 176/175 or 385/384 are labeled zeus, if they require any two of 126/125, 176/175 or 441/440, they are labeled thrush. Finally, if they require any three independent commas among those discussed above, it is labeled valentine.		Valentine has [[mos scale]]s of size 15, 16, 31 and 46. It is readily observed from the list below that even the smallest of these is well-supplied with chords.

	~~Valentine has MOS~~ of size 15, 16, 31 and 46. It is readily observed from the list below that even the smallest of these is well-supplied with chords.

	== Relationship to Carlos Alpha ==		== Relationship to Carlos Alpha ==
			Because [[Carlos Alpha]] is the generator chain of valentine, the list below is also a list of chords of Carlos Alpha, so long as the transversals are adjusted so that the notes are in the correct octave. This means that a number in a chord listed under "chord" less than 16 corresponds to a note in the transversal which should be left unaltered, whereas the notes from 16 to 21 correspond to transversal notes which should be adjusted up an octave. Hence, tetrad 8, the 0–2–5–9 chord with transversal 1–6/5–11/8–3/2, is an essentially zeus chord of Carlos Alpha as well as valentine. On the other hand, tetrad 76, 0–10–13–18 with transversal 1–11/7–9/5–9/8, corresponds to the werckismic 1–11/7–9/5–9/4 chord of Carlos Alpha.
	Because [[Carlos Alpha]] is the generator chain of valentine ~~in the tuning with pure 3/2's~~, the list below is also a list of chords of Carlos Alpha, so long as the transversals are adjusted so that the notes are in the correct octave. This means that a number in a chord listed under "chord" less than 16 corresponds to a note in the transversal which should be left unaltered, whereas the notes from 16 to 21 correspond to transversal notes which should be adjusted up an octave. Hence, tetrad 8, the ~~0-2-5-9~~ chord with transversal ~~1-6~~/~~5-11~~/~~8-3~~/2, is an essentially zeus chord of Carlos Alpha as well as valentine. On the other hand, tetrad 76, ~~0-10-13-18~~ with transversal ~~1-11~~/~~7-9~~/~~5-9~~/8, corresponds to the werckismic ~~1-11~~/~~7-9~~/~~5-9~~/4 chord of Carlos Alpha.

	In other words, each chord here has an unlimited number of "voicings" in valentine temperament, but exactly one voicing in Carlos Alpha, because there are no octaves.		In other words, each chord here has an unlimited number of "voicings" in valentine temperament, but exactly one voicing in Carlos Alpha, because there are no octaves.

	== Chord ordering ==		== Chord ordering ==

	The chords are ordered by generator steps. This chord ordering is useful because you can tell how often it will occur in a scale of valentine.		The chords are ordered by generator steps. This chord ordering is useful because you can tell how often it will occur in a scale of valentine.

	Example 1: Triad #13 is generators ~~0-5-9~~ and is a traditional five-limit major chord, ~~1/1-~~5/~~4-3~~/2. It occurs for the first time on the ninth generation, and will therefore occur six times in ~~valentine~~[15] (because 15-9=6) .		Example 1: Triad #13 is generators 0–5–9 and is a traditional five-limit major chord, [[4:5:6\|1–5/4–3/2]]. It occurs for the first time on the ninth generation, and will therefore occur six times in Valentine[15] (because {{nowrap\| 15 - 9 {{=}} 6 }}).

	Example 2: Triad #38 is generators ~~0-8-13~~, which is 1/~~1-5/4-7~~/5, occurs for the first time on the thirteenth generation, and therefore appears only twice in ~~valentine~~[15] (because 15-13=2).		Example 2: Triad #38 is generators 0–8–13, which is 1–5/4–7/5, occurs for the first time on the thirteenth generation, and therefore appears only twice in Valentine[15] (because {{nowrap\| 15 - 13 {{=}} 2 }}).

	Each of the triads generated has three inversions, i.e., can be written starting on any one of the three tones in the triad. Traditional music theory uses a traditional chord, e.g., the major triad, as the basis for the other two inversions. In this list, that place is taken by the chord that gets generated after a certain number of generator steps is taken to reach the tones needed for the chord. This ordering makes it easy to see how often it will occur in a given ~~MOS~~, as noted in the examples above, but it may seem surprising if you~~'re~~ new to it: ~~For~~ example, triad #8 is 1/~~1-8/7-10~~/7, but it might seem more "natural" to use 1/~~1-5/4-7~~/4, which is listed as the second inversion. The same type of thinking goes into the list of tetrads, pentads, and hexads.		Each of the triads generated has three inversions, i.e., can be written starting on any one of the three tones in the triad. Traditional music theory uses a traditional chord, e.g., the major triad, as the basis for the other two inversions. In this list, that place is taken by the chord that gets generated after a certain number of generator steps is taken to reach the tones needed for the chord. This ordering makes it easy to see how often it will occur in a given mos, as noted in the examples above, but it may seem surprising if you are new to it: for example, triad #8 is 1–8/7–10/7, but it might seem more "natural" to use 1–5/4–7/4, which is listed as the second inversion. The same type of thinking goes into the list of tetrads, pentads, and hexads.

	Note that, unlike in traditional music theory, there is nothing canonical, key-centric, harmonically relevant, or otherwise musically important about these orderings and inversions. It's just how the math works out.		Note that, unlike in traditional music theory, there is nothing canonical, key-centric, harmonically relevant, or otherwise musically important about these orderings and inversions. It is just how the math works out.

	== Triads ==		== Triads ==
	{\| class="wikitable"		{\| class="wikitable center-1"
	\|-		\|-
	! ~~Number~~		! #
	! Chord		! Chord
	! Transversal		! Transversal
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	== Tetrads ==		== Tetrads ==
			{\| class="wikitable center-1"
	{\| class="wikitable"
	\|-		\|-
	! ~~Number~~		! #
	! Chord		! Chord
	! Transversal		! Transversal
Line 1,374:		Line 1,369:

	== Pentads ==		== Pentads ==
			{\| class="wikitable center-1"
	{\| class="wikitable"
	\|-		\|-
	! ~~Number~~		! #
	! Chord		! Chord
	! Transversal		! Transversal
Line 2,039:		Line 2,033:

	== Hexads ==		== Hexads ==
			{\| class="wikitable center-1"
	{\| class="wikitable"
	\|-		\|-
	! ~~Number~~		! #
	! Chord		! Chord
	! Transversal		! Transversal

FloraC: Recategorize

2023-05-23T11:39:51Z

Recategorize

← Older revision		Revision as of 11:39, 23 May 2023
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	[[Category:Lists of chords]]		[[Category:Lists of chords]]
	[[Category:Valentine]]		[[Category:Valentine]]
	[[Category:~~Triad~~]]		[[Category:Triads]]
	[[Category:~~Tetrad~~]]		[[Category:Tetrads]]
	[[Category:~~Pentad~~]]		[[Category:Pentads]]
	[[Category:~~Hexad~~]]		[[Category:Hexads]]

Fredg999 category edits: Moving from Category:Chords to Category:Lists of chords using Cat-a-lot

2023-04-28T03:50:20Z

Moving from Category:Chords to Category:Lists of chords using Cat-a-lot

← Older revision		Revision as of 03:50, 28 April 2023
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	\|}		\|}

	[[Category:~~Chords~~]]		[[Category:Lists of chords]]
	[[Category:Valentine]]		[[Category:Valentine]]
	[[Category:Triad]]		[[Category:Triad]]

Jdfreivald: /* Triads */ Fixes

2022-02-17T02:56:03Z

Triads: Fixes

← Older revision		Revision as of 02:56, 17 February 2022
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	\| 1/1-11/7-12/7		\| 1/1-11/7-12/7
	\| 1/1-11/10-14/11		\| 1/1-11/10-14/11
	\| 1/1-7/6-~~146~~/79		\| 1/1-7/6-11/6
	\|-		\|-
	\| 34		\| 34

Jdfreivald: /* Triads */ Fixes

2022-02-17T02:53:57Z

Triads: Fixes

← Older revision		Revision as of 02:53, 17 February 2022
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	\| 1/1-3/2-18/11		\| 1/1-3/2-18/11
	\| 1/1-11/10-4/3		\| 1/1-11/10-4/3
	\| 1/1-97/80-11/6		\| 1/1-11/9-11/6
	\|-		\|-
	\| 26		\| 26

Jdfreivald: /* Triads */ Fixes

2022-02-17T02:49:19Z

Triads: Fixes

← Older revision		Revision as of 02:49, 17 February 2022
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	\| 1/1-11/8-3/2		\| 1/1-11/8-3/2
	\| 1/1-11/10-16/11		\| 1/1-11/10-16/11
	\| 1/1-41/31-11/6		\| 1/1-4/3-11/6
	\|-		\|-
	\| 15		\| 15
Line 155:		Line 155:
	\| 1/1-11/10-11/7		\| 1/1-11/10-11/7
	\| 1/1-10/7-11/6		\| 1/1-10/7-11/6
	\| 1/1-68/53-7/5		\| 1/1-14/11-7/5
	\|-		\|-
	\| 16		\| 16

Jdfreivald: /* Hexads */

2022-02-17T02:45:50Z

Hexads

← Older revision		Revision as of 02:45, 17 February 2022
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	! Transversal		! Transversal
	! Type		! Type
	\| As generated		! As generated
	\| 1st inversion		! 1st inversion
	\| 2nd inversion		! 2nd inversion
	\| 3rd inversion		! 3rd inversion
	\| 4th inversion		! 4th inversion
	\| 5th inversion		! 5th inversion
	\|-		\|-
	\| 1		\| 1

Jdfreivald: /* Pentads */ Changed 12/11s to 11/10s.

2022-02-17T01:48:05Z

Pentads: Changed 12/11s to 11/10s.

← Older revision		Revision as of 01:48, 17 February 2022
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	\| 14		\| 14
	\| 0-2-4-9-12		\| 0-2-4-9-12
	\| 1-12/11-6/5-3/2-12/7		\| 1-11/10-6/5-3/2-12/7
	\| utonal		\| utonal
	\| 1/1-12/11-6/5-3/2-12/7		\| 1/1-11/10-6/5-3/2-12/7
	\| 1/1-11/10-11/8-11/7-11/6		\| 1/1-11/10-11/8-11/7-11/6
	\| 1/1-5/4-10/7-5/3-11/6		\| 1/1-5/4-10/7-5/3-11/6

Jdfreivald: /* Tetrads */ Changed 12/11s to 11/10s.

2022-02-17T01:47:30Z

Tetrads: Changed 12/11s to 11/10s.

← Older revision		Revision as of 01:47, 17 February 2022
Line 537:		Line 537:
	\| 5		\| 5
	\| 0-2-4-9		\| 0-2-4-9
	\| 1-12/11-6/5-3/2		\| 1-11/10-6/5-3/2
	\| utonal		\| utonal
	\| 1/1-12/11-6/5-3/2		\| 1/1-11/10-6/5-3/2
	\| 1/1-11/10-11/8-11/6		\| 1/1-11/10-11/8-11/6
	\| 1/1-5/4-5/3-11/6		\| 1/1-5/4-5/3-11/6
Line 699:		Line 699:
	\| 23		\| 23
	\| 0-2-9-11		\| 0-2-9-11
	\| 1-12/11-3/2-18/11		\| 1-11/10-3/2-18/11
	\| ambitonal		\| ambitonal
	\| 1/1-12/11-3/2-18/11		\| 1/1-11/10-3/2-18/11
	\| 1/1-11/8-3/2-11/6		\| 1/1-11/8-3/2-11/6
	\| 1/1-11/10-4/3-16/11		\| 1/1-11/10-4/3-16/11
Line 726:		Line 726:
	\| 26		\| 26
	\| 0-2-4-12		\| 0-2-4-12
	\| 1-12/11-6/5-12/7		\| 1-11/10-6/5-12/7
	\| utonal		\| utonal
	\| 1/1-12/11-6/5-12/7		\| 1/1-11/10-6/5-12/7
	\| 1/1-11/10-11/7-11/6		\| 1/1-11/10-11/7-11/6
	\| 1/1-10/7-5/3-11/6		\| 1/1-10/7-5/3-11/6
Line 816:		Line 816:
	\| 36		\| 36
	\| 0-2-9-12		\| 0-2-9-12
	\| 1-12/11-3/2-12/7		\| 1-11/10-3/2-12/7
	\| utonal		\| utonal
	\| 1/1-12/11-3/2-12/7		\| 1/1-11/10-3/2-12/7
	\| 1/1-11/8-11/7-11/6		\| 1/1-11/8-11/7-11/6
	\| 1/1-8/7-4/3-16/11		\| 1/1-8/7-4/3-16/11

Valentine/Chords - Revision history

Lériendil: Lériendil moved page Chords of valentine to Valentine/Chords

FloraC: Cleanup

FloraC: Recategorize

Fredg999 category edits: Moving from Category:Chords to Category:Lists of chords using Cat-a-lot

Jdfreivald: /* Triads */ Fixes

Jdfreivald: /* Triads */ Fixes

Jdfreivald: /* Triads */ Fixes

Jdfreivald: /* Hexads */

Jdfreivald: /* Pentads */ Changed 12/11s to 11/10s.

Jdfreivald: /* Tetrads */ Changed 12/11s to 11/10s.