Starling temperaments: Difference between revisions
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Valentine is very closely related to [[Carlos Alpha]], the rank one nonoctave temperament of Wendy Carlos, as the generator chain of valentine is the same thing as Carlos Alpha. Indeed, the way Carlos uses Alpha in ''Beauty in the Beast'' suggests that she really intended Alpha to be the same thing as valentine, and that it is misdescribed as a rank one temperament. Carlos tells us that "The melodic motions of Alpha are amazingly exotic and fresh, like you've never heard before", and since Alpha lives inside valentine this comment carries over and applies to it if you stick close melodically to generator steps, which is almost impossible not to do since the generator step is so small. MOS of 15, 16, 31 and 46 notes are available to explore these exotic and fresh melodies, or the less exotic ones you might cook up otherwise. | Valentine is very closely related to [[Carlos Alpha]], the rank one nonoctave temperament of Wendy Carlos, as the generator chain of valentine is the same thing as Carlos Alpha. Indeed, the way Carlos uses Alpha in ''Beauty in the Beast'' suggests that she really intended Alpha to be the same thing as valentine, and that it is misdescribed as a rank one temperament. Carlos tells us that "The melodic motions of Alpha are amazingly exotic and fresh, like you've never heard before", and since Alpha lives inside valentine this comment carries over and applies to it if you stick close melodically to generator steps, which is almost impossible not to do since the generator step is so small. MOS of 15, 16, 31 and 46 notes are available to explore these exotic and fresh melodies, or the less exotic ones you might cook up otherwise. | ||
[[Comma]]s: 1029/1024 | [[Comma]]s: 126/125, 1029/1024 | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
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[[Eigenmonzo]]s: 2, 9/7 | [[Eigenmonzo]]s: 2, 9/7 | ||
[[POTE_tuning|POTE generator]]: 77.864 | [[POTE_tuning|POTE generator]]: ~21/20 = 77.864 | ||
Algebraic generator: [[Algebraic_number|smaller root]] of x^2-89x+92, or (89-sqrt(7553))/2, at 77.8616 cents. | Algebraic generator: [[Algebraic_number|smaller root]] of x^2-89x+92, or (89-sqrt(7553))/2, at 77.8616 cents. | ||
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Map: [<1 1 2 3|, <0 9 5 -3|] | Map: [<1 1 2 3|, <0 9 5 -3|] | ||
[[ | Mapping [[generator]]s: 2, 21/20 | ||
EDOs: {{EDOs|15, 31, 46, 77, 185, 262cd}} | EDOs: {{EDOs|15, 31, 46, 77, 185, 262cd}} | ||
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Map: [<1 1 2 3 3|, <0 9 5 -3 7|] | Map: [<1 1 2 3 3|, <0 9 5 -3 7|] | ||
[[EDO]]s: {{EDOs|15, 31, 46, 77}} | [[EDO]]s: {{EDOs|15, 31, 46, 77, 262cdee, 339cdeee}} | ||
Badness: 0.0167 | Badness: 0.0167 | ||