Archytas clan: Difference between revisions

Xenllium (talk | contribs)
-passion (weak extesion of archy, has its own family)
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Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, 2430/2401 gives quasisuper, and 4375/4374 gives modus.  
Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, 2430/2401 gives quasisuper, and 4375/4374 gives modus.  


Discussed under their respective 5-limit families are [[Father family #Mother|mother]], [[Meantone family #Dominant|dominant]], [[Augmented family #Augene|augene]], [[Porcupine family #Porcupine|porcupine]], [[Diaschismic family #Pajara|pajara]], [[Kleismic family #Catalan|catalan]], [[Tetracot family #Modus|modus]], and [[Immunity family #Immunized|immunized]]. The rest are considered below.
Discussed under their respective 5-limit families are [[Father family #Mother|mother]], [[Meantone family #Dominant|dominant]], [[Augmented family #Augene|augene]], [[Porcupine family #Porcupine|porcupine]], [[Diaschismic family #Pajara|pajara]], [[Kleismic family #Catalan|catalan]], [[Tetracot family #Modus|modus]], [[Passion family #Septimal passion|passion]], and [[Immunity family #Immunized|immunized]]. The rest are considered below.


== Archy ==
== Archy ==
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Badness: 0.033971
Badness: 0.033971
== Passion ==
Passion tempers out 262144/253125 (saquingu) in the 5-limit. This temperament can be described as 12&49 temperament, which tempers out 64/63 and the gariboh (3125/3087). Alternative extensions [[Marvel temperaments #Passive|passive]] (1&11) and [[Starling temperaments #Passionate|passionate]] (12&61) temper out the same 5-limit comma as the passion, but with the marvel (225/224) or the starling (126/125) rather than 64/63 tempered out respectively.
Subgroup: 2.3.5
[[Comma]]: 262144/253125
[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -5 4 }}]
Mapping generators: 2, 16/15
[[POTE generator]]: ~16/15 = 98.670
{{Val list|legend=1| 12, 49, 61, 73 }}
[[Badness]]: 0.168550
=== 7-limit ===
Subgroup: 2.3.5.7
[[Comma list]]: 64/63, 3125/3087
[[Mapping]]: [{{val| 1 2 2 2 }}, {{val| 0 -5 4 10 }}]
Mapping generators: 2, 16/15
{{Multival|legend=1| 5 -4 -10 -18 -30 -12 }}
[[POTE generator]]: ~16/15 = 98.153
{{Val list|legend=1| 12, 37, 49, 110bcd }}
[[Badness]]: 0.062327
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 64/63, 100/99, 1375/1372
Mapping: [{{val| 1 2 2 2 2 }}, {{val| 0 -5 4 10 18 }}]
POTE generator: ~16/15 = 98.019
Vals: {{Val list| 12, 37, 49 }}
Badness: 0.040809
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 64/63, 100/99, 196/195, 275/273
Mapping: [{{val| 1 2 2 2 2 2 }}, {{val| 0 -5 4 10 18 21 }}]
POTE generator: ~16/15 = 97.910
Vals: {{Val list| 12f, 25f, 37, 49f }}
Badness: 0.030886


== Fervor ==
== Fervor ==