Olympic clan

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.

For the rank-4 olympic temperament, see Rank-4 temperament #Olympic (131072/130977).

No-5 olympic

Subgroup: 2.3.7.11

Comma list: 131072/130977

Mapping: [⟨1 0 0 17], ⟨0 1 0 -5], ⟨0 0 1 -2]]

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