Valentine: Difference between revisions

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'''Valentine''' is a [[regular temperament]] that divides a tempered 3/2 into 9 equal ~~generators~~ 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]].

Valentine can be viewed as a counterpart of [[miracle]] in several ways. Miracle splits the generator of [[slendric]] in two while valentine splits it in three. Miracle is generated by [[15/14]][[~]][[16/15]], the classical diatonic semitone tempered together with the septimal major semitone, while valentine is generated by 21/20~25/24, the classical chromatic semitone tempered together with the septimal minor semitone. Miracle is known for its efficiency; the same is true of valentine. The [[11-odd-limit]] [[tonality diamond]] is covered by miracle with 22 generator steps, and by valentine with 21 generator steps.

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== Chords ==

== Tunings ==

=== Prime-optimized tunings ===

{| class="wikitable mw-collapsible mw-collapsed"

|+ style="font-size: 105%; white-space: nowrap;" | 7-limit Prime-Optimized Tunings

|-

! rowspan="2" |

! colspan="2" | Euclidean

|-

! Unskewed

! Skewed

|-

! Equilateral

| CEE: ~15/14 = 77.7625¢

| CSEE: ~15/14 = 77.7211¢

|-

! Tenney

| CTE: ~15/14 = 77.8776¢

| CWE: ~15/14 = 77.8673¢

|-

! Benedetti, <br>Wilson

| CBE: ~15/14 = 77.9062¢

| CSBE: ~15/14 = 77.9075¢

|}

{| class="wikitable mw-collapsible mw-collapsed"

|+ style="font-size: 105%; white-space: nowrap;" | 11-limit Prime-Optimized Tunings

|-

! rowspan="2" |

! colspan="2" | Euclidean

|-

! Unskewed

! Skewed

|-

! Equilateral

| CEE: ~15/14 = 78.0604¢

| CSEE: ~15/14 = 77.9698¢

|-

! Tenney

| CTE: ~15/14 = 77.9633¢

| CWE: ~15/14 = 77.9007¢

|-

! Benedetti, <br>Wilson

| CBE: ~15/14 = 77.9388¢

| CSBE: ~15/14 = 77.9028¢

|}

=== Tuning spectrum ===

{| class="wikitable center-all left-4"

@@ Line 1: / Line 1: @@
-'''Valentine''' is a [[regular temperament]] that divides a tempered 3/2 into 9 equal generators 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]].
 Valentine can be viewed as a counterpart of [[miracle]] in several ways. Miracle splits the generator of [[slendric]] in two while valentine splits it in three. Miracle is generated by [[15/14]][[~]][[16/15]], the classical diatonic semitone tempered together with the septimal major semitone, while valentine is generated by 21/20~25/24, the classical chromatic semitone tempered together with the septimal minor semitone. Miracle is known for its efficiency; the same is true of valentine. The [[11-odd-limit]] [[tonality diamond]] is covered by miracle with 22 generator steps, and by valentine with 21 generator steps.
@@ Line 147: / Line 147: @@
 == Chords ==
-{{main| Chords of valentine }}
+{{Main| Chords of valentine }}
 == Tunings ==
+=== Prime-optimized tunings ===
+{| class="wikitable mw-collapsible mw-collapsed"
+|+ style="font-size: 105%; white-space: nowrap;" | 7-limit Prime-Optimized Tunings
+|-
+! rowspan="2" |
+! colspan="2" | Euclidean
+|-
+! Unskewed
+! Skewed
+|-
+! Equilateral
+| CEE: ~15/14 = 77.7625¢
+| CSEE: ~15/14 = 77.7211¢
+|-
+! Tenney
+| CTE: ~15/14 = 77.8776¢
+| CWE: ~15/14 = 77.8673¢
+|-
+! Benedetti, <br>Wilson
+| CBE: ~15/14 = 77.9062¢
+| CSBE: ~15/14 = 77.9075¢
+|}
+{| class="wikitable mw-collapsible mw-collapsed"
+|+ style="font-size: 105%; white-space: nowrap;" | 11-limit Prime-Optimized Tunings
+|-
+! rowspan="2" |
+! colspan="2" | Euclidean
+|-
+! Unskewed
+! Skewed
+|-
+! Equilateral
+| CEE: ~15/14 = 78.0604¢
+| CSEE: ~15/14 = 77.9698¢
+|-
+! Tenney
+| CTE: ~15/14 = 77.9633¢
+| CWE: ~15/14 = 77.9007¢
+|-
+! Benedetti, <br>Wilson
+| CBE: ~15/14 = 77.9388¢
+| CSBE: ~15/14 = 77.9028¢
+|}
 === Tuning spectrum ===
 {| class="wikitable center-all left-4"