Mistismic temperaments: Difference between revisions
m →Neutron: figuring out the number of periods for 13 proved difficult... but im pretty sure it's correct |
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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 (Dirichlet): 4.223 | |||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
Revision as of 21:46, 11 March 2025
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]]
Wedgie: ⟨⟨ 35 -49 14 -159 -76 170 ]]
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 (Dirichlet): 4.223