Valentine: Difference between revisions

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{{Infobox ~~Regtemp~~

{{Infobox regtemp

| Title = Valentine

| 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

~~| Generator = 21/20 | Generator tuning = 77.9 | Optimization method = CTE~~

~~| MOS scales = ..., [[1L 14s]], [[15L 1s]], [[15L 16s]]~~

| 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)

| 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]].

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== Tunings ==

=== ~~Prime~~-~~optimized~~ tunings ===

=== Norm-based tunings ===

{| 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" |

! colspan="2" | Euclidean

! colspan="3" | Euclidean

|-

! ~~Unskewed~~

! Constrained

! ~~Skewed~~

! Constrained & skewed

! Destretched

|-

! Equilateral

| CEE: ~15/14 = 77.~~7625¢~~

| CEE: ~21/20 = 77.7625{{c}}

| CSEE: ~15/14 = 77.~~7211¢~~

| CSEE: ~21/20 = 77.7211{{c}}

| POEE: ~21/20 = 77.7256{{c}}

|-

! Tenney

| CTE: ~15/14 = 77.~~8776¢~~

| CTE: ~21/20 = 77.8776{{c}}

| CWE: ~15/14 = 77.~~8673¢~~

| CWE: ~21/20 = 77.8673{{c}}

| POTE: ~21/20 = 77.8638{{c}}

|-

! Benedetti, <br>Wilson

| CBE: ~15/14 = 77.~~9062¢~~

| CBE: ~21/20 = 77.9062{{c}}

| CSBE: ~15/14 = 77.~~9075¢~~

| CSBE: ~21/20 = 77.9075{{c}}

| POBE: ~21/20 = 77.9104{{c}}

|}

{| 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" |

! colspan="2" | Euclidean

! colspan="3" | Euclidean

|-

! ~~Unskewed~~

! Constrained

! ~~Skewed~~

! Constrained & skewed

! Destretched

|-

! Equilateral

| CEE: ~15/14 = 78.~~0604¢~~

| CEE: ~22/21 = 78.0604{{c}}

| CSEE: ~15/14 = 77.~~9698¢~~

| CSEE: ~22/21 = 77.9698{{c}}

| POEE: ~22/21 = 77.8485{{c}}

|-

! Tenney

| CTE: ~15/14 = 77.~~9633¢~~

| CTE: ~22/21 = 77.9633{{c}}

| CWE: ~15/14 = 77.~~9007¢~~

| CWE: ~22/21 = 77.9007{{c}}

| POTE: ~22/21 = 77.8813{{c}}

|-

! Benedetti, <br>Wilson

| CBE: ~15/14 = 77.~~9388¢~~

| CBE: ~22/21 = 77.9388{{c}}

| CSBE: ~15/14 = 77.~~9028¢~~

| CSBE: ~22/21 = 77.9028{{c}}

| POBE: ~22/21 = 77.9093{{c}}

|}

@@ Line 1: / Line 1: @@
-{{Infobox Regtemp
+{{Infobox regtemp
 | Title = Valentine
 | 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
-| Generator = 21/20 | Generator tuning = 77.9 | Optimization method = CTE
-| MOS scales = ..., [[1L 14s]], [[15L 1s]], [[15L 16s]]
 | 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)
-| 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]].
@@ Line 163: / Line 162: @@
 == Tunings ==
-=== Prime-optimized tunings ===
+=== Norm-based tunings ===
 {| 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" |
-! colspan="2" | Euclidean
+! colspan="3" | Euclidean
 |-
-! Unskewed
+! Constrained
-! Skewed
+! Constrained & skewed
+! Destretched
 |-
 ! Equilateral
-| CEE: ~15/14 = 77.7625¢
+| CEE: ~21/20 = 77.7625{{c}}
-| CSEE: ~15/14 = 77.7211¢
+| CSEE: ~21/20 = 77.7211{{c}}
+| POEE: ~21/20 = 77.7256{{c}}
 |-
 ! Tenney
-| CTE: ~15/14 = 77.8776¢
+| CTE: ~21/20 = 77.8776{{c}}
-| CWE: ~15/14 = 77.8673¢
+| CWE: ~21/20 = 77.8673{{c}}
+| POTE: ~21/20 = 77.8638{{c}}
 |-
 ! Benedetti, <br>Wilson
-| CBE: ~15/14 = 77.9062¢
+| CBE: ~21/20 = 77.9062{{c}}
-| CSBE: ~15/14 = 77.9075¢
+| CSBE: ~21/20 = 77.9075{{c}}
+| POBE: ~21/20 = 77.9104{{c}}
 |}
 {| 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" |
-! colspan="2" | Euclidean
+! colspan="3" | Euclidean
 |-
-! Unskewed
+! Constrained
-! Skewed
+! Constrained & skewed
+! Destretched
 |-
 ! Equilateral
-| CEE: ~15/14 = 78.0604¢
+| CEE: ~22/21 = 78.0604{{c}}
-| CSEE: ~15/14 = 77.9698¢
+| CSEE: ~22/21 = 77.9698{{c}}
+| POEE: ~22/21 = 77.8485{{c}}
 |-
 ! Tenney
-| CTE: ~15/14 = 77.9633¢
+| CTE: ~22/21 = 77.9633{{c}}
-| CWE: ~15/14 = 77.9007¢
+| CWE: ~22/21 = 77.9007{{c}}
+| POTE: ~22/21 = 77.8813{{c}}
 |-
 ! Benedetti, <br>Wilson
-| CBE: ~15/14 = 77.9388¢
+| CBE: ~22/21 = 77.9388{{c}}
-| CSBE: ~15/14 = 77.9028¢
+| CSBE: ~22/21 = 77.9028{{c}}
+| POBE: ~22/21 = 77.9093{{c}}
 |}