Ragismic microtemperaments: Difference between revisions
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The ragisma is [[4375/4374]] with a [[monzo]] of |-1 -7 4 1>, the smallest 7-limit [[superparticular]] ratio. Since (10/9)^4 = 4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low [[complexity]] in temperaments tempering out the ragisma, though when looking at [[microtemperament]]s the word "relatively" should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low complexity, with the same caveat about "relatively"; however 27/25 is the period for ennealimmal. | The ragisma is [[4375/4374]] with a [[monzo]] of |-1 -7 4 1>, the smallest 7-limit [[superparticular]] ratio. Since (10/9)^4 = 4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low [[complexity]] in temperaments tempering out the ragisma, though when looking at [[microtemperament]]s the word "relatively" should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low complexity, with the same caveat about "relatively"; however 27/25 is the period for ennealimmal. | ||
Temperaments not discussed here include [[Jubilismic clan #Crepuscular|crepuscular]], [[Meantone family #Flattone|flattone]], [[Porcupine family #Hystrix|hystrix]], [[Starling temperaments #Sensi|sensi]], [[Gamelismic clan #Unidec|unidec]], [[Orwellismic temperaments #Quartonic|quartonic]], [[Kleismic family #Catakleismic|catakleismic]], [[Tetracot family #Modus|modus]], [[Schismatic family #Pontiac|pontiac]], [[Würschmidt family #Whirrschmidt|whirrschmidt]], [[Gravity family #Zarvo|zarvo]], [[Vishnuzmic family #Vishnu|vishnu]], and [[Vulture family #Vulture|vulture]]. | Temperaments not discussed here include [[Jubilismic clan #Crepuscular|crepuscular]], [[Meantone family #Flattone|flattone]], [[Porcupine family #Hystrix|hystrix]], [[Starling temperaments #Sensi|sensi]], [[Gamelismic clan #Unidec|unidec]], [[Orwellismic temperaments #Quartonic|quartonic]], [[Kleismic family #Catakleismic|catakleismic]], [[Tetracot family #Modus|modus]], [[Schismatic family #Pontiac|pontiac]], [[Tricot family|trillium]], [[Würschmidt family #Whirrschmidt|whirrschmidt]], [[Gravity family #Zarvo|zarvo]], [[Vishnuzmic family #Vishnu|vishnu]], and [[Vulture family #Vulture|vulture]]. | ||
= Ennealimmal = | = Ennealimmal = | ||
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[[Mapping]]: [<17 26 39 43|, <0 2 1 10|] | [[Mapping]]: [<17 26 39 43|, <0 2 1 10|] | ||
[[Wedgie]]: <<34 17 170 -52 174 347|| | |||
[[POTE tuning|POTE generators]]: ~25/24 = 70.5882, ~5/4 = 386.2936 | [[POTE tuning|POTE generators]]: ~25/24 = 70.5882, ~5/4 = 386.2936 | ||
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[[Mapping]]: [<1 2 10 -25|, <0 -2 -37 134|] | [[Mapping]]: [<1 2 10 -25|, <0 -2 -37 134|] | ||
[[Wedgie]]: <<2 37 -134 54 -218 -415|| | |||
[[POTE tuning|POTE generator]]: ~310078125/268435456 = 249.0207 | [[POTE tuning|POTE generator]]: ~310078125/268435456 = 249.0207 | ||