Olympic clan: Difference between revisions
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* ''[[Hera]]'', {6144/6125, 8019/8000} → [[Porwell family #Hera|Porwell family]] | * ''[[Hera]]'', {6144/6125, 8019/8000} → [[Porwell family #Hera|Porwell family]] | ||
Considered below are | Considered below are olympian, no-5 subgroup temperament, in addition to baffin and sophia. | ||
For the rank-4 olympic temperament, see [[Rank-4 temperament #Olympic (131072/130977)]]. | For the rank-4 olympic temperament, see [[Rank-4 temperament #Olympic (131072/130977)]]. | ||
== | == Olympian == | ||
[[Subgroup]]: 2.3.7.11 | [[Subgroup]]: 2.3.7.11 | ||
[[Comma list]]: 131072/130977 | [[Comma list]]: 131072/130977 | ||
[[ | [[Sval]] [[mapping]]: [{{val| 1 0 0 17 }}, {{val| 0 1 0 -5 }}, {{val| 0 0 1 -2 }}] | ||
: sval mapping generators: ~2, ~3, ~7 | |||
Optimal tuning ([[POTE]]): ~3/2 = 702.0805, ~7/4 = 969.0275 | [[Optimal tuning]] ([[POTE]]): ~3/2 = 702.0805, ~7/4 = 969.0275 | ||
{{Val list|legend=1| 41, 87, 89, 94, 130, 135, 359, 400, 494, 535, 670, 805, 1164, 1299, 1834, 1969, 5102bde, 5237bde, 7206bddee, 10339bbdddeee }} | {{Val list|legend=1| 41, 87, 89, 94, 130, 135, 359, 400, 494, 535, 670, 805, 1164, 1299, 1834, 1969, 5102bde, 5237bde, 7206bddee, 10339bbdddeee }} | ||
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[[Mapping]]: [{{val| 1 0 0 13 }}, {{val| 0 2 0 -7 }}, {{val| 0 0 1 -2 }}] | [[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 | [[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 }} | {{Val list|legend=1| 10, 19d, 24, 34, 43, 53, 87, 130, 183, 217, 270, 593, 863, 1133, 1856cd, 2126cd, 2719cd, 2989bcd }} | ||
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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, 2063c }} | {{Val list|legend=1| 34, 43, 53, 87, 130, 183, 270, 670, 940, 1210, 2063c }} | ||
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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 | ||
{{Val list|legend=1| 46, 94, 140, 171, 217, 311, 979, 1290 }} | {{Val list|legend=1| 46, 94, 140, 171, 217, 311, 979, 1290 }} | ||
Revision as of 11:18, 3 May 2023
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, 131072/130977} → Lehmerismic temperaments
- Hera, {6144/6125, 8019/8000} → Porwell family
Considered below are olympian, no-5 subgroup temperament, in addition to baffin and sophia.
For the rank-4 olympic temperament, see Rank-4 temperament #Olympic (131072/130977).
Olympian
Subgroup: 2.3.7.11
Comma list: 131072/130977
Sval mapping: [⟨1 0 0 17], ⟨0 1 0 -5], ⟨0 0 1 -2]]
- sval mapping generators: ~2, ~3, ~7
Optimal tuning (POTE): ~3/2 = 702.0805, ~7/4 = 969.0275
Badness: 0.0183 × 10-3
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