Valentine: Difference between revisions

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| 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 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]].

@@ Line 4: / Line 4: @@
 | 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 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]].