Olympic clan: Difference between revisions
+sophia as requested by Scott Dakota, and +baffin for obvious reasons |
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== Baffin == | == Baffin == | ||
=== 7-limit (decovulture) === | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: 67108864/66976875 | |||
[[Mapping]]: [{{val| 1 0 0 13 }}, {{val| 0 2 0 -7 }}, {{val| 0 0 1 -2 }}] | |||
Mapping generators: ~2, ~8192/4725, ~5 | |||
Optimal tuning ([[POTE]]): ~8192/4725 = 951.0868, ~5/4 = 386.6183 | |||
{{Val list|legend=1| 10, 19d, 24, 34, 43, 53, 87, 130, 183, 217, 270, 593, 863, 1133, 1856cd, 2126cd, 2719cd, 2989bcd }} | |||
[[Badness]]: 0.865 × 10<sup>-3</sup> | |||
=== 11-limit === | |||
[[Subgroup]]: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
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[[Mapping]]: [{{val| 1 0 0 13 -9 }}, {{val| 0 2 0 -7 4 }}, {{val| 0 0 1 -2 4 }}] | [[Mapping]]: [{{val| 1 0 0 13 -9 }}, {{val| 0 2 0 -7 4 }}, {{val| 0 0 1 -2 4 }}] | ||
Optimal tuning ([[POTE]]): ~400/231 = 951.0585, ~5/4 = 386.7912 | Optimal tuning ([[POTE]]): ~400/231 = 951.0585, ~5/4 = 386.7912 | ||
{{Val list|legend=1| 34, 43, 53, 87, 130, 183, 270, 670, 940, 1210 }} | {{Val list|legend=1| 34, 43, 53, 87, 130, 183, 270, 670, 940, 1210, 2063c }} | ||
[[Badness]]: 0.976 × 10<sup>-3</sup> | [[Badness]]: 0.976 × 10<sup>-3</sup> | ||
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[[Mapping]]: [{{val| 1 0 2 3 11 }}, {{val| 0 1 0 0 -5 }}, {{val| 0 0 5 -3 6 }}] | [[Mapping]]: [{{val| 1 0 2 3 11 }}, {{val| 0 1 0 0 -5 }}, {{val| 0 0 5 -3 6 }}] | ||
Optimal tuning ([[POTE]]): ~3/2 = 702.3024, ~256/245 = 77.1952 | Optimal tuning ([[POTE]]): ~3/2 = 702.3024, ~256/245 = 77.1952 | ||
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Mapping: [{{val| 1 0 2 3 11 7 }}, {{val| 0 1 0 0 -5 -2 }}, {{val| 0 0 5 -3 6 -2 }}] | Mapping: [{{val| 1 0 2 3 11 7 }}, {{val| 0 1 0 0 -5 -2 }}, {{val| 0 0 5 -3 6 -2 }}] | ||
Optimal tuning (POTE): ~3/2 = 702.3319, ~117/112 = 77.2152 | |||
Optimal tuning (POTE): ~3/2 = 702.3319, ~ | |||
Optimal GPV sequence: {{Val list| 46, 77e, 94, 140, 171, 217, 311, 668, 979, 1290 }} | Optimal GPV sequence: {{Val list| 46, 77e, 94, 140, 171, 217, 311, 668, 979, 1290 }} | ||
Badness: 1.67 × 10<sup>-3</sup> | Badness: 1.67 × 10<sup>-3</sup> | ||
=== 17-limit === | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 595/594, 833/832, 1156/1155, 4096/4095 | |||
Mapping: [{{val| 1 0 2 3 11 7 7 }}, {{val| 0 1 0 0 -5 -2 -2 }}, {{val| 0 0 5 -3 6 -2 4 }}] | |||
Optimal tuning (POTE): ~3/2 = 702.3205, ~68/65 = 77.2255 | |||
Optimal GPV sequence: {{Val list| 46, 77e, 94, 140, 171, 217, 311, 668, 839e, 979g }} | |||
Badness: 0.989 × 10<sup>-3</sup> | |||
[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||
[[Category:Olympic clan| ]] <!-- main article --> | [[Category:Olympic clan| ]] <!-- main article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
Revision as of 21:03, 15 June 2022
The olympic clan of rank-3 temperaments tempers out the olympia, 131072/130977 = [17 -5 0 -2 -1⟩.
Temperaments discussed elsewhere are:
- Akea, {385/384, 2200/2187} → Hemifamity family
- Lux, {3025/3024, 130172/130977} → Lehmerismic temperaments
Considered below are baffin and sophia, in addition to the no-5 subgroup temperament, but we can begin by looking at the rank-4 temperament.
Baffin
7-limit (decovulture)
Subgroup: 2.3.5.7.11
Comma list: 67108864/66976875
Mapping: [⟨1 0 0 13], ⟨0 2 0 -7], ⟨0 0 1 -2]]
Mapping generators: ~2, ~8192/4725, ~5
Optimal tuning (POTE): ~8192/4725 = 951.0868, ~5/4 = 386.6183
Badness: 0.865 × 10-3
11-limit
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 131072/130977
Mapping: [⟨1 0 0 13 -9], ⟨0 2 0 -7 4], ⟨0 0 1 -2 4]]
Optimal tuning (POTE): ~400/231 = 951.0585, ~5/4 = 386.7912
Badness: 0.976 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 4096/4095
Mapping: [⟨1 0 0 13 -9 1], ⟨0 2 0 -7 4 3], ⟨0 0 1 -2 4 1]]
Optimal tuning (POTE): ~26/15 = 951.0882, ~5/4 = 386.7507
Optimal GPV sequence: Template:Val list
Badness: 0.604 × 10-3
Complexity spectrum: 15/13, 16/15, 13/12, 4/3, 16/13, 5/4, 18/13, 13/10, 6/5, 9/8, 11/10, 8/7, 7/5, 15/11, 10/9, 13/11, 15/14, 11/8, 7/6, 14/13, 12/11, 9/7, 11/9, 14/11
Sophia
Subgroup: 2.3.5.7.11
Comma list: 42875/42768, 131072/130977
Mapping: [⟨1 0 2 3 11], ⟨0 1 0 0 -5], ⟨0 0 5 -3 6]]
Optimal tuning (POTE): ~3/2 = 702.3024, ~256/245 = 77.1952
Badness: 3.78 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 4096/4095, 13720/13689
Mapping: [⟨1 0 2 3 11 7], ⟨0 1 0 0 -5 -2], ⟨0 0 5 -3 6 -2]]
Optimal tuning (POTE): ~3/2 = 702.3319, ~117/112 = 77.2152
Optimal GPV sequence: Template:Val list
Badness: 1.67 × 10-3
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 595/594, 833/832, 1156/1155, 4096/4095
Mapping: [⟨1 0 2 3 11 7 7], ⟨0 1 0 0 -5 -2 -2], ⟨0 0 5 -3 6 -2 4]]
Optimal tuning (POTE): ~3/2 = 702.3205, ~68/65 = 77.2255
Optimal GPV sequence: Template:Val list
Badness: 0.989 × 10-3