Biyatismic clan: Difference between revisions
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→Aphrodite: add 23-limit Eros; NOTE: do not rename "(13-limit) Eros" as it will break the link! |
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Badness: 1.456 × 10<sup>-3</sup> | Badness: 1.456 × 10<sup>-3</sup> | ||
==== Eros ==== | ==== (13-limit) Eros ==== | ||
This is the [[13-limit]] restriction of [[#Eros|23-limit Eros]], documented for readability in a separate section of this page. | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 1.150 × 10<sup>-3</sup> | Badness: 1.150 × 10<sup>-3</sup> | ||
Dirichlet badness: 1.075 | |||
==== Inanna ==== | ==== Inanna ==== | ||
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Badness: 1.151 × 10<sup>-3</sup> | Badness: 1.151 × 10<sup>-3</sup> | ||
== Eros == | |||
This temperament is an extension of [[#Aphrodite]], specifically [[#(13-limit) Eros|(13-limit) Eros]], into the 23-limit, in which it fairs impressively as a rank 3 temperament. | |||
Due to having natural extensions to such a high prime limit and due to its unusual efficiency, it is documented here in its own section to keep other extensions of Aphrodite more readable. | |||
=== 13-limit === | |||
Subgroup: [[13-limit]] | |||
Comma list: 121/120, 441/440, 352/351 | |||
Mapping: {{mapping| 1 0 1 3 2 7 | 0 1 1 0 1 -2 | 0 0 -4 -3 -2 -2 }} | |||
Optimal tuning ([[CTE]]): 2, ~3 = 1901.722, ~22/21 = 78.110 | |||
[[Patent val]] EDO tunings: [[29edo|29]], [[31edo|31]], [[46edo|46]], [[77edo|77]], [[92edo|92]] | |||
Dirichlet badness: 1.075 | |||
=== 17-limit === | |||
Note that there is one more patent val EDO tuning in the 17-limit than in the 19- and 23-limit corresponding to using 46 EDO with a better mapping for 19. 29 disappears as it requires the 29g val. | |||
Subgroup: [[17-limit]] | |||
Comma list: 121/120, 441/440, 352/351, 154/153 | |||
Mapping: {{mapping| 1 0 1 3 2 7 6 | 0 1 1 0 1 -2 -1 | 0 0 -4 -3 -2 -2 -5 }} | |||
Optimal tuning ([[CTE]]): 2, ~3 = 1901.930, ~22/21 = 78.254 | |||
[[Patent val]] EDO tunings: [[31edo|31]], [[46edo|46]], [[77edo|77]], [[92edo|92]] | |||
Dirichlet badness: 0.931 | |||
=== 19-limit === | |||
Subgroup: [[19-limit]] | |||
Comma list: 441/440, 1617/1600, 196/195, 154/153, 286/285 | |||
Mapping: {{mapping| 1 0 1 3 2 7 6 9 | 0 1 1 0 1 -2 -1 -3 | 0 0 -4 -3 -2 -2 -5 0 }} | |||
Optimal tuning ([[CTE]]): 2, ~3/2 = 1901.564, ~22/21 = 78.235 | |||
[[Patent val]] EDO tunings: [[31edo|31]], [[46edo|46]], [[77edo|77]] | |||
Dirichlet badness: 1.159 | |||
=== 23-limit === | |||
Subgroup: [[23-limit]] | |||
Comma list: 441/440, 1617/1600, 196/195, 154/153, 286/285, 161/160 | |||
Mapping: {{mapping| 1 0 1 3 2 7 6 9 3 | 0 1 1 0 1 -2 -1 -3 1 | 0 0 -4 -3 -2 -2 -5 0 -1 }} | |||
Optimal tuning ([[CTE]]): 2, ~3 = 1901.711, ~23/22 = 78.205 | |||
[[Patent val]] EDO tunings: [[31edo|31]], [[46edo|46]], [[77edo|77]] | |||
Dirichlet badness: 1.084 | |||
[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||