Valentine - Revision history

Overthink: update scale sizes

2026-02-13T00:21:17Z

update scale sizes

← Older revision		Revision as of 00:21, 13 February 2026
Line 8:		Line 8:
	\| MOS scales = …, [[1L 14s]], [[15L 1s]], [[15L 16s]]		\| MOS scales = …, [[1L 14s]], [[15L 1s]], [[15L 16s]]
	\| Pergen = (P8, P5/9)		\| Pergen = (P8, P5/9)
	\| Odd limit 1 = 7 \| Mistuning 1 = 4.60 \| Complexity 1 = 31		\| Odd limit 1 = 7 \| Mistuning 1 = 4.60 \| Complexity 1 = 15
	\| Odd limit 2 = 11-limit 21 \| Mistuning 2 = 9.01 \| Complexity 2 = 46		\| Odd limit 2 = 11-limit 21 \| Mistuning 2 = 9.01 \| Complexity 2 = 31
	}}		}}
	'''Valentine''' is a [[regular temperament]] that divides a tempered [[3/2]] into 9 equal [[generator]]s which are small semitones close to 78 cents; a stack of 3 generators is interpreted as [[8/7]] and a stack of 5 generators is interpreted as [[5/4]]. The generator serves as both [[21/20]] and [[25/24]]. It is a member of the [[starling temperaments]], by [[tempering out]] [[126/125]], and the [[gamelismic clan]], by tempering out [[1029/1024]]. It extends naturally to the [[11-limit]] by treating the generator as [[22/21]], tempering out [[121/120]], [[176/175]], [[385/384]], and [[441/440]].		'''Valentine''' is a [[regular temperament]] that divides a tempered [[3/2]] into 9 equal [[generator]]s which are small semitones close to 78 cents; a stack of 3 generators is interpreted as [[8/7]] and a stack of 5 generators is interpreted as [[5/4]]. The generator serves as both [[21/20]] and [[25/24]]. It is a member of the [[starling temperaments]], by [[tempering out]] [[126/125]], and the [[gamelismic clan]], by tempering out [[1029/1024]]. It extends naturally to the [[11-limit]] by treating the generator as [[22/21]], tempering out [[121/120]], [[176/175]], [[385/384]], and [[441/440]].

FloraC at 10:20, 9 February 2026

2026-02-09T10:20:15Z

← Older revision		Revision as of 10:20, 9 February 2026
Line 1:		Line 1:
	{{Infobox ~~Regtemp~~		{{Infobox regtemp
	\| Title = Valentine		\| Title = Valentine
	\| Subgroups = 2.3.5.7, 2.3.5.7.11		\| Subgroups = 2.3.5.7, 2.3.5.7.11
	\| Comma basis = [[126/125]], [[1029/1024]] (7-limit); <br /> [[121/120]], [[126/125]], [[176/175]] (11-limit)		\| Comma basis = [[126/125]], [[1029/1024]] (7-limit); <br>[[121/120]], [[126/125]], [[176/175]] (11-limit)
	\| Edo join 1 = 15 \| Edo join 2 = 16		\| Edo join 1 = 15 \| Edo join 2 = 16
	\| Mapping = 1; 9 5 -3 7		\| Mapping = 1; 9 5 -3 7

FloraC at 09:50, 9 February 2026

2026-02-09T09:50:05Z

← Older revision		Revision as of 09:50, 9 February 2026
Line 9:		Line 9:
	\| Pergen = (P8, P5/9)		\| Pergen = (P8, P5/9)
	\| Odd limit 1 = 7 \| Mistuning 1 = 4.60 \| Complexity 1 = 31		\| Odd limit 1 = 7 \| Mistuning 1 = 4.60 \| Complexity 1 = 31
	\| Odd limit 2 = (11-limit) 21 \| Mistuning 2 = 9.01 \| Complexity 2 = 46		\| Odd limit 2 = 11-limit 21 \| Mistuning 2 = 9.01 \| Complexity 2 = 46
	}}		}}
	'''Valentine''' is a [[regular temperament]] that divides a tempered [[3/2]] into 9 equal [[generator]]s which are small semitones close to 78 cents; a stack of 3 generators is interpreted as [[8/7]] and a stack of 5 generators is interpreted as [[5/4]]. The generator serves as both [[21/20]] and [[25/24]]. It is a member of the [[starling temperaments]], by [[tempering out]] [[126/125]], and the [[gamelismic clan]], by tempering out [[1029/1024]]. It extends naturally to the [[11-limit]] by treating the generator as [[22/21]], tempering out [[121/120]], [[176/175]], [[385/384]], and [[441/440]].		'''Valentine''' is a [[regular temperament]] that divides a tempered [[3/2]] into 9 equal [[generator]]s which are small semitones close to 78 cents; a stack of 3 generators is interpreted as [[8/7]] and a stack of 5 generators is interpreted as [[5/4]]. The generator serves as both [[21/20]] and [[25/24]]. It is a member of the [[starling temperaments]], by [[tempering out]] [[126/125]], and the [[gamelismic clan]], by tempering out [[1029/1024]]. It extends naturally to the [[11-limit]] by treating the generator as [[22/21]], tempering out [[121/120]], [[176/175]], [[385/384]], and [[441/440]].

FloraC: Cleanup on infobox

2026-02-09T09:49:57Z

Cleanup on infobox

← Older revision		Revision as of 09:49, 9 February 2026
Line 4:		Line 4:
	\| Comma basis = [[126/125]], [[1029/1024]] (7-limit); <br /> [[121/120]], [[126/125]], [[176/175]] (11-limit)		\| Comma basis = [[126/125]], [[1029/1024]] (7-limit); <br /> [[121/120]], [[126/125]], [[176/175]] (11-limit)
	\| Edo join 1 = 15 \| Edo join 2 = 16		\| Edo join 1 = 15 \| Edo join 2 = 16
	~~\| Generator = 21/20 \| Generator tuning = 77.9 \| Optimization method = CTE~~
	~~\| MOS scales = ..., [[1L 14s]], [[15L 1s]], [[15L 16s]]~~
	\| Mapping = 1; 9 5 -3 7		\| Mapping = 1; 9 5 -3 7
			\| Generators = 22/21 \| Generators tuning = 77.9 \| Optimization method = CWE
			\| MOS scales = …, [[1L 14s]], [[15L 1s]], [[15L 16s]]
	\| Pergen = (P8, P5/9)		\| Pergen = (P8, P5/9)
	\| Odd limit 1 = 7 \| Mistuning 1 = 4.60 \| Complexity 1 = 31		\| Odd limit 1 = 7 \| Mistuning 1 = 4.60 \| Complexity 1 = 31
	\| Odd limit 2 = (11-limit) 21 \| Mistuning 2 = 9.01 \| Complexity 2 = 46		\| Odd limit 2 = (11-limit) 21 \| Mistuning 2 = 9.01 \| Complexity 2 = 46
	}}		}}

	'''Valentine''' is a [[regular temperament]] that divides a tempered [[3/2]] into 9 equal [[generator]]s which are small semitones close to 78 cents; a stack of 3 generators is interpreted as [[8/7]] and a stack of 5 generators is interpreted as [[5/4]]. The generator serves as both [[21/20]] and [[25/24]]. It is a member of the [[starling temperaments]], by [[tempering out]] [[126/125]], and the [[gamelismic clan]], by tempering out [[1029/1024]]. It extends naturally to the [[11-limit]] by treating the generator as [[22/21]], tempering out [[121/120]], [[176/175]], [[385/384]], and [[441/440]].		'''Valentine''' is a [[regular temperament]] that divides a tempered [[3/2]] into 9 equal [[generator]]s which are small semitones close to 78 cents; a stack of 3 generators is interpreted as [[8/7]] and a stack of 5 generators is interpreted as [[5/4]]. The generator serves as both [[21/20]] and [[25/24]]. It is a member of the [[starling temperaments]], by [[tempering out]] [[126/125]], and the [[gamelismic clan]], by tempering out [[1029/1024]]. It extends naturally to the [[11-limit]] by treating the generator as [[22/21]], tempering out [[121/120]], [[176/175]], [[385/384]], and [[441/440]].

FloraC: /* Tunings */ formatting

2025-11-16T12:52:47Z

Tunings: formatting

← Older revision		Revision as of 12:52, 16 November 2025
Line 168:		Line 168:
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|
	! colspan="2" \| Euclidean		! colspan="3" \| Euclidean
	\|-		\|-
	! Constrained		! Constrained
Line 194:		Line 194:
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|
	! colspan="2" \| Euclidean		! colspan="3" \| Euclidean
	\|-		\|-
	! Constrained		! Constrained

FloraC: /* Tunings */ + destretched tunings

2025-11-16T12:52:20Z

Tunings: + destretched tunings

← Older revision		Revision as of 12:52, 16 November 2025
Line 170:		Line 170:
	! colspan="2" \| Euclidean		! colspan="2" \| Euclidean
	\|-		\|-
	! ~~Unskewed~~		! Constrained
	! ~~Skewed~~		! Constrained & skewed
			! Destretched
	\|-		\|-
	! Equilateral		! Equilateral
	\| CEE: ~15/14 = 77.7625{{c}}		\| CEE: ~21/20 = 77.7625{{c}}
	\| CSEE: ~15/14 = 77.7211{{c}}		\| CSEE: ~21/20 = 77.7211{{c}}
			\| POEE: ~21/20 = 77.7256{{c}}
	\|-		\|-
	! Tenney		! Tenney
	\| CTE: ~15/14 = 77.8776{{c}}		\| CTE: ~21/20 = 77.8776{{c}}
	\| CWE: ~15/14 = 77.8673{{c}}		\| CWE: ~21/20 = 77.8673{{c}}
			\| POTE: ~21/20 = 77.8638{{c}}
	\|-		\|-
	! Benedetti, <br>Wilson		! Benedetti, <br>Wilson
	\| CBE: ~15/14 = 77.9062{{c}}		\| CBE: ~21/20 = 77.9062{{c}}
	\| CSBE: ~15/14 = 77.9075{{c}}		\| CSBE: ~21/20 = 77.9075{{c}}
			\| POBE: ~21/20 = 77.9104{{c}}
	\|}		\|}

Line 192:		Line 196:
	! colspan="2" \| Euclidean		! colspan="2" \| Euclidean
	\|-		\|-
	! ~~Unskewed~~		! Constrained
	! ~~Skewed~~		! Constrained & skewed
			! Destretched
	\|-		\|-
	! Equilateral		! Equilateral
	\| CEE: ~15/14 = 78.0604{{c}}		\| CEE: ~22/21 = 78.0604{{c}}
	\| CSEE: ~15/14 = 77.9698{{c}}		\| CSEE: ~22/21 = 77.9698{{c}}
			\| POEE: ~22/21 = 77.8485{{c}}
	\|-		\|-
	! Tenney		! Tenney
	\| CTE: ~15/14 = 77.9633{{c}}		\| CTE: ~22/21 = 77.9633{{c}}
	\| CWE: ~15/14 = 77.9007{{c}}		\| CWE: ~22/21 = 77.9007{{c}}
			\| POTE: ~22/21 = 77.8813{{c}}
	\|-		\|-
	! Benedetti, <br>Wilson		! Benedetti, <br>Wilson
	\| CBE: ~15/14 = 77.9388{{c}}		\| CBE: ~22/21 = 77.9388{{c}}
	\| CSBE: ~15/14 = 77.9028{{c}}		\| CSBE: ~22/21 = 77.9028{{c}}
			\| POBE: ~22/21 = 77.9093{{c}}
	\|}		\|}

FloraC: /* Tunings */ terminology

2025-09-12T14:11:32Z

Tunings: terminology

← Older revision		Revision as of 14:11, 12 September 2025
Line 165:		Line 165:
	=== Norm-based tunings ===		=== Norm-based tunings ===
	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit ~~Prime~~-~~Optimized Tunings~~		\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit norm-based tunings
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|
Line 174:		Line 174:
	\|-		\|-
	! Equilateral		! Equilateral
	\| CEE: ~15/14 = 77.~~7625¢~~		\| CEE: ~15/14 = 77.7625{{c}}
	\| CSEE: ~15/14 = 77.~~7211¢~~		\| CSEE: ~15/14 = 77.7211{{c}}
	\|-		\|-
	! Tenney		! Tenney
	\| CTE: ~15/14 = 77.~~8776¢~~		\| CTE: ~15/14 = 77.8776{{c}}
	\| CWE: ~15/14 = 77.~~8673¢~~		\| CWE: ~15/14 = 77.8673{{c}}
	\|-		\|-
	! Benedetti, <br>Wilson		! Benedetti, <br>Wilson
	\| CBE: ~15/14 = 77.~~9062¢~~		\| CBE: ~15/14 = 77.9062{{c}}
	\| CSBE: ~15/14 = 77.~~9075¢~~		\| CSBE: ~15/14 = 77.9075{{c}}
	\|}		\|}

	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 11-limit ~~Prime~~-~~Optimized Tunings~~		\|+ style="font-size: 105%; white-space: nowrap;" \| 11-limit norm-based tunings
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|
Line 196:		Line 196:
	\|-		\|-
	! Equilateral		! Equilateral
	\| CEE: ~15/14 = 78.~~0604¢~~		\| CEE: ~15/14 = 78.0604{{c}}
	\| CSEE: ~15/14 = 77.~~9698¢~~		\| CSEE: ~15/14 = 77.9698{{c}}
	\|-		\|-
	! Tenney		! Tenney
	\| CTE: ~15/14 = 77.~~9633¢~~		\| CTE: ~15/14 = 77.9633{{c}}
	\| CWE: ~15/14 = 77.~~9007¢~~		\| CWE: ~15/14 = 77.9007{{c}}
	\|-		\|-
	! Benedetti, <br>Wilson		! Benedetti, <br>Wilson
	\| CBE: ~15/14 = 77.~~9388¢~~		\| CBE: ~15/14 = 77.9388{{c}}
	\| CSBE: ~15/14 = 77.~~9028¢~~		\| CSBE: ~15/14 = 77.9028{{c}}
	\|}		\|}

FloraC: Text replacement - "Prime-optimized" to "Norm-based"

2025-09-12T14:08:40Z

Text replacement - "Prime-optimized" to "Norm-based"

← Older revision		Revision as of 14:08, 12 September 2025
Line 163:		Line 163:

	== Tunings ==		== Tunings ==
	=== ~~Prime~~-~~optimized~~ tunings ===		=== Norm-based tunings ===
	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit Prime-Optimized Tunings		\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit Prime-Optimized Tunings

FloraC: /* Tunings */ excessive bold is no bold

2025-06-10T03:16:46Z

Tunings: excessive bold is no bold

← Older revision		Revision as of 03:16, 10 June 2025
Line 249:		Line 249:
	\| [[5/4]]		\| [[5/4]]
	\| 77.263		\| 77.263
	\| ~~'''~~Lower bound of 5-odd-limit diamond tradeoff~~'''~~		\| Lower bound of 5-odd-limit diamond tradeoff
	\|-		\|-
	\| '''[[31edo\|2\31]]'''		\| '''[[31edo\|2\31]]'''
Line 349:		Line 349:
	\| [[6/5]]		\| [[6/5]]
	\| 78.910		\| 78.910
	\| ~~'''~~Upper bound of 5-odd-limit diamond tradeoff~~'''~~		\| Upper bound of 5-odd-limit diamond tradeoff
	\|-		\|-
	\| '''[[15edo\|1\15]]'''		\| '''[[15edo\|1\15]]'''

Zhenlige: /* Tuning spectrum */

2025-06-10T03:01:21Z

Tuning spectrum

← Older revision		Revision as of 03:01, 10 June 2025
Line 249:		Line 249:
	\| [[5/4]]		\| [[5/4]]
	\| 77.263		\| 77.263
	\|		\| '''Lower bound of 5-odd-limit diamond tradeoff'''
	\|-		\|-
	\| '''[[31edo\|2\31]]'''		\| '''[[31edo\|2\31]]'''
Line 349:		Line 349:
	\| [[6/5]]		\| [[6/5]]
	\| 78.910		\| 78.910
	\|		\| '''Upper bound of 5-odd-limit diamond tradeoff'''
	\|-		\|-
	\| '''[[15edo\|1\15]]'''		\| '''[[15edo\|1\15]]'''