Mistismic temperaments: Difference between revisions
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These are rank | {{Technical data page}} | ||
These are [[rank 2 temperament]]s that temper out the [[mistisma]], 458752/455625 = {{monzo| 16 -6 -4 1 }}. | |||
Temperaments dicussed elsewhere include [[Escapade family #Escaped|escaped]], [[Schismatic family #Grackle|grackle]], [[Porwell temperaments #Hendecatonic|hendecatonic]], [[Kleismic family #Metakleismic|metakleismic]], [[Misty family|misty]], [[pajara]], [[Quintaleap family #Quintupole|quintupole]], [[Gamelismic clan #Restles|restles]], and [[Würschmidt family #Whirrschmidt|whirrschmidt]]. | Temperaments dicussed elsewhere include [[Escapade family #Escaped|escaped]], [[Schismatic family #Grackle|grackle]], [[Porwell temperaments #Hendecatonic|hendecatonic]], [[Kleismic family #Metakleismic|metakleismic]], [[Misty family|misty]], [[pajara]], [[Quintaleap family #Quintupole|quintupole]], [[Gamelismic clan #Restles|restles]], and [[Würschmidt family #Whirrschmidt|whirrschmidt]]. | ||
== Neutron == | == Neutron == | ||
Main article: [[Neutron]]. | |||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[Mapping]]: [{{val| 7 12 15 20 }}, {{val| 0 -5 7 -2 }}] | [[Mapping]]: [{{val| 7 12 15 20 }}, {{val| 0 -5 7 -2 }}] | ||
[[POTE generator]]: ~49/48 = 30.845 | [[POTE generator]]: ~49/48 = 30.845 | ||
{{ | {{Optimal ET sequence|legend=1| 35c, 42c, 77, 196, 273, 350d }} | ||
[[Badness]]: 0.650041 | [[Badness]]: 0.650041 | ||
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POTE generator: ~49/48 = 30.773 | POTE generator: ~49/48 = 30.773 | ||
{{Optimal ET sequence|legend=1| 77, 119, 196, 315b, 511bbcd }} | |||
Badness: 0.212279 | Badness: 0.212279 | ||
Badness (Dirichet): 7.018 | |||
=== 13-limit === | |||
Note that [[119edo]] is a possible patent val tuning not appearing in the optimal ET sequence. | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 385/384, 352/351, 10192/10125, 50421/50336 | |||
Mapping: [{{val| 7 12 15 20 26 -10 }}, {{val| 0 -5 7 -2 -10 5 }}] | |||
[[CTE]] generator: ~49/48 = 30.781 | |||
{{Optimal ET sequence|legend=1| 77, 196, 273 }} | |||
Badness (Sintel): 4.223 | |||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
[[Category:Pages with mostly numerical content]] | |||
Latest revision as of 00:30, 24 June 2025
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
These are rank 2 temperaments that temper out the mistisma, 458752/455625 = [16 -6 -4 1⟩.
Temperaments dicussed elsewhere include escaped, grackle, hendecatonic, metakleismic, misty, pajara, quintupole, restles, and whirrschmidt.
Neutron
Main article: Neutron.
Subgroup: 2.3.5.7
Comma list: 458752/455625, 40353607/39813120
Mapping: [⟨7 12 15 20], ⟨0 -5 7 -2]]
POTE generator: ~49/48 = 30.845
Optimal ET sequence: 35c, 42c, 77, 196, 273, 350d
Badness: 0.650041
11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 166012/164025, 585640/583443
Mapping: [⟨7 12 15 20 26], ⟨0 -5 7 -2 -10]]
POTE generator: ~49/48 = 30.773
Optimal ET sequence: 77, 119, 196, 315b, 511bbcd
Badness: 0.212279
Badness (Dirichet): 7.018
13-limit
Note that 119edo is a possible patent val tuning not appearing in the optimal ET sequence.
Subgroup: 2.3.5.7.11.13
Comma list: 385/384, 352/351, 10192/10125, 50421/50336
Mapping: [⟨7 12 15 20 26 -10], ⟨0 -5 7 -2 -10 5]]
CTE generator: ~49/48 = 30.781
Optimal ET sequence: 77, 196, 273
Badness (Sintel): 4.223