Valentine extensions - Revision history

FloraC: FloraC moved page Valentine/Extensions to Valentine extensions over a redirect without leaving a redirect: Reversion for creating broken redirects with no clear gain

2025-08-06T12:07:29Z

FloraC moved page Valentine/Extensions to Valentine extensions over a redirect without leaving a redirect: Reversion for creating broken redirects with no clear gain

← Older revision	Revision as of 12:07, 6 August 2025
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Lériendil: Lériendil moved page Valentine extensions to Valentine/Extensions

2025-06-04T17:00:06Z

Lériendil moved page Valentine extensions to Valentine/Extensions

← Older revision	Revision as of 17:00, 4 June 2025
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Lériendil at 00:09, 20 April 2025

2025-04-20T00:09:15Z

← Older revision		Revision as of 00:09, 20 April 2025
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			{{Breadcrumb\|Valentine}}

	[[Valentine]] has various competing [[extension]]s to the [[13-limit]]. The following temperaments are discussed in this article:		[[Valentine]] has various competing [[extension]]s to the [[13-limit]]. The following temperaments are discussed in this article:
	* '''Valentino''' (31 & 46) – tempering out 121/120, 126/125, 176/175, and 196/195;		* '''Valentino''' (31 & 46) – tempering out 121/120, 126/125, 176/175, and 196/195;
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	[[Category:Valentine]]		[[Category:Valentine]]
	[[Category:Temperament extensions]]		[[Category:Temperament extensions]]
			[[Category:Rank-2 temperaments]]

FloraC: +link to data page

2025-04-08T19:55:00Z

+link to data page

← Older revision		Revision as of 19:55, 8 April 2025
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	Another path that relates a sense of compromise is to temper out [[169/168]], leading to [[semivalentine]]. This has the effect of slicing the period in two, and is supported by [[30edo\|30]], [[46edo\|46]], and [[62edo\|62]]. Yet another possibility is given by [[hemivalentine]], with the effect of slicing the generator of 21/20~25/24 into two [[40/39]]'s. Finally, tempering out [[676/675]] leads to [[demivalentine]], with the effect of slicing the generator of 21/10~25/12 (one octave above 21/20~25/24) into two [[13/9]]'s, and is supported by 62 and 77.		Another path that relates a sense of compromise is to temper out [[169/168]], leading to [[semivalentine]]. This has the effect of slicing the period in two, and is supported by [[30edo\|30]], [[46edo\|46]], and [[62edo\|62]]. Yet another possibility is given by [[hemivalentine]], with the effect of slicing the generator of 21/20~25/24 into two [[40/39]]'s. Finally, tempering out [[676/675]] leads to [[demivalentine]], with the effect of slicing the generator of 21/10~25/12 (one octave above 21/20~25/24) into two [[13/9]]'s, and is supported by 62 and 77.

			See [[Gamelismic clan #Valentino]], [[Gamelismic clan #Lupercalia\|#Lupercalia]], and [[Gamelismic clan #Dwynwen\|#Dwynwen]] for technical data.

	== Interval chain ==		== Interval chain ==

FloraC: Address semivalentine, hemivalentine, and demivalentine

2025-01-25T10:40:17Z

Address semivalentine, hemivalentine, and demivalentine

← Older revision		Revision as of 10:40, 25 January 2025
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	The most important of these is valentino, which tempers out [[196/195]] and may also be characterized by tempering out [[351/350]] or [[352/351]] instead. It is [[support]]ed by [[77edo\|77]]. However, it does come at the cost of a way increased complexity level. A low-complexity low-accuracy mapping is given by lupercalia, where the ~13/8 is conflated with the ~18/11. Dwynwen is a more perculiar case: the mapping is not very simple to start with, and the approximation is not ideal if we just use the tunings optimized for valentine or valentino. However, a sharper tuning especially from those sharper than [[46edo]] may do the trick.		The most important of these is valentino, which tempers out [[196/195]] and may also be characterized by tempering out [[351/350]] or [[352/351]] instead. It is [[support]]ed by [[77edo\|77]]. However, it does come at the cost of a way increased complexity level. A low-complexity low-accuracy mapping is given by lupercalia, where the ~13/8 is conflated with the ~18/11. Dwynwen is a more perculiar case: the mapping is not very simple to start with, and the approximation is not ideal if we just use the tunings optimized for valentine or valentino. However, a sharper tuning especially from those sharper than [[46edo]] may do the trick.

			Another path that relates a sense of compromise is to temper out [[169/168]], leading to [[semivalentine]]. This has the effect of slicing the period in two, and is supported by [[30edo\|30]], [[46edo\|46]], and [[62edo\|62]]. Yet another possibility is given by [[hemivalentine]], with the effect of slicing the generator of 21/20~25/24 into two [[40/39]]'s. Finally, tempering out [[676/675]] leads to [[demivalentine]], with the effect of slicing the generator of 21/10~25/12 (one octave above 21/20~25/24) into two [[13/9]]'s, and is supported by 62 and 77.

	== Interval chain ==		== Interval chain ==

FloraC: Expand

2025-01-23T09:59:02Z

Expand

← Older revision		Revision as of 09:59, 23 January 2025
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	[[Valentine]] has various competing [[extension]]s to the [[13-limit]].		[[Valentine]] has various competing [[extension]]s to the [[13-limit]]. The following temperaments are discussed in this article:
			* '''Valentino''' (31 & 46) – tempering out 121/120, 126/125, 176/175, and 196/195;
			* '''Lupercalia''' (31 & 46f) – tempering out 66/65, 105/104, 121/120, and 126/125;
			* '''Dwynwen''' (31f & 46) – tempering out 91/90, 121/120, 126/125, and 176/175.

			The most important of these is valentino, which tempers out [[196/195]] and may also be characterized by tempering out [[351/350]] or [[352/351]] instead. It is [[support]]ed by [[77edo\|77]]. However, it does come at the cost of a way increased complexity level. A low-complexity low-accuracy mapping is given by lupercalia, where the ~13/8 is conflated with the ~18/11. Dwynwen is a more perculiar case: the mapping is not very simple to start with, and the approximation is not ideal if we just use the tunings optimized for valentine or valentino. However, a sharper tuning especially from those sharper than [[46edo]] may do the trick.

	== Interval chain ==		== Interval chain ==

FloraC: Created page with "Valentine has various competing extensions to the 13-limit. == Interval chain == In the following table, odd harmonics and subharmonics 1–21 are in '''bold'''..."

2025-01-23T08:45:45Z

Created page with "Valentine has various competing extensions to the 13-limit. == Interval chain == In the following table, odd harmonics and subharmonics 1–21 are in '''bold'''..."

New page

[[Valentine]] has various competing [[extension]]s to the [[13-limit]].

== Interval chain ==
In the following table, odd harmonics and subharmonics 1–21 are in '''bold'''.

{| class="wikitable center-1 right-2"
|-
! rowspan="3" | #
! rowspan="3" | Cents*
! colspan="4" | Approximate ratios
|-
! rowspan="2" | 11-limit
! colspan="3" | 13-limit extensions
|-
! Valentino
! Lupercalia
! Dwynwen
|-
| 0
| 0.0
| '''1/1'''
|
|
|
|-
| 1
| 77.9
| 21/20, 22/21, 25/24
|
| 26/25
| 27/26
|-
| 2
| 155.8
| 12/11, 11/10, 35/32
|
| 13/12
|
|-
| 3
| 233.7
| '''8/7'''
|
| 15/13
|
|-
| 4
| 311.6
| 6/5
|
| 13/11
|
|-
| 5
| 389.5
| '''5/4'''
|
| 26/21, 33/26
|
|-
| 6
| 467.4
| '''21/16'''
|
| 13/10
|
|-
| 7
| 545.3
| '''11/8''', 15/11
|
| 18/13
|
|-
| 8
| 623.2
| 10/7
| 56/39
|
| 13/9
|-
| 9
| 701.1
| '''3/2'''
|
| 52/35
|
|-
| 10
| 779.0
| 11/7, 25/16
|
|
| 52/33
|-
| 11
| 856.9
| 18/11
| 64/39
| '''13/8'''
|
|-
| 12
| 934.8
| 12/7
|
|
| 26/15
|-
| 13
| 1012.7
| 9/5, 25/14
|
|
|
|-
| 14
| 1090.6
| '''15/8'''
|
| 13/7
|
|-
| 15
| 1168.5
| 55/28, 63/32, 96/49, <br>108/55, 125/64
|
| 39/20
|
|-
| 16
| 46.4
| 33/32, 36/35, 50/49
| 40/39
| 27/26
| 26/25
|-
| 17
| 124.3
| 15/14, 27/25
| 14/13
|
| 13/12
|-
| 18
| 202.2
| '''9/8'''
|
|
|
|-
| 19
| 280.1
| 33/28
|
|
| 13/11
|-
| 20
| 358.0
| 27/22
| '''16/13'''
| 39/32
| 26/21
|-
| 21
| 435.9
| 9/7
|
|
| 13/10
|-
| 22
| 513.8
| 27/20
| 35/26
|
|
|-
| 23
| 591.7
| 45/32
|
| 39/28
|
|-
| 24
| 669.6
| 72/49
|
|
| 52/35
|-
| 25
| 747.5
| 54/35
| 20/13
|
|
|-
| 26
| 825.4
| 45/28
| 21/13
|
| '''13/8'''
|-
| 27
| 903.3
| 27/16
| 22/13
|
|
|-
| 28
| 981.2
| 99/56
|
|
|
|-
| 29
| 1059.1
| 90/49
| 24/13
|
| 13/7
|-
| 30
| 1137.0
| 27/14
| 25/13
|
| 39/20
|-
| 31
| 14.9
| 81/80, 99/98
|
|
|
|}
<nowiki/>* In 11-limit [[CWE tuning]]

[[Category:Valentine]]
[[Category:Temperament extensions]]