Biyatismic clan: Difference between revisions
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[[Badness]] (Sintel): 0.701 | [[Badness]] (Sintel): 0.701 | ||
=== Eros === | |||
Eros fairs impressively into the 23-limit as a rank-3 temperament; not only is it fairly simple (considering this is a subgroup as complex as the full 23-limit, with many challenges) but has the pleasing property that all the harmonics are on the negative side of the last generator. Specifically, -3 to 2 fifths and -5 to 0 [[~]][[23/22]]'s will provide odd harmonics 1–23 up to octave equivalence; you can think of this as a 6×6 grid, which is a recommendable place to start looking at its structure. | Eros fairs impressively into the 23-limit as a rank-3 temperament; not only is it fairly simple (considering this is a subgroup as complex as the full 23-limit, with many challenges) but has the pleasing property that all the harmonics are on the negative side of the last generator. Specifically, -3 to 2 fifths and -5 to 0 [[~]][[23/22]]'s will provide odd harmonics 1–23 up to octave equivalence; you can think of this as a 6×6 grid, which is a recommendable place to start looking at its structure. | ||
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Badness (Sintel): 1.08 | Badness (Sintel): 1.08 | ||
==== 17-limit ==== | |||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
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Badness (Sintel): 0.931 | Badness (Sintel): 0.931 | ||
==== 19-limit ==== | |||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
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Badness (Sintel): 1.16 | Badness (Sintel): 1.16 | ||
==== 23-limit ==== | |||
Subgroup: 2.3.5.7.11.13.17.19.23 | Subgroup: 2.3.5.7.11.13.17.19.23 | ||
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Badness (Sintel): 1.08 | Badness (Sintel): 1.08 | ||
==== Inanna | === Astarte === | ||
This extension is catalogued as tridecimal aphrodite in [[Graham Breed]]'s temperament finder. | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 121/120, 351/350, 441/440 | |||
Mapping: {{mapping| 1 0 1 3 2 6 | 0 1 1 0 1 -1 | 0 0 -4 -3 -2 -11 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1201.0656{{c}}, ~3/2 = 700.7374{{c}}, ~22/21 = 78.5908{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.7005{{c}}, ~22/21 = 78.3253{{c}} | |||
{{Optimal ET sequence|legend=0| 14cf, 29ff, 31, 45ef, 46, 77, 122ee, 137def, 168deef }} | |||
Badness (Sintel): 1.36 | |||
=== Inanna === | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness (Sintel): 1.01 | Badness (Sintel): 1.01 | ||
=== Ishtar === | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||