65th-octave temperaments

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65th-octave temperaments

65edo is accurate for harmonics 3, 5, and 11, so various 65th-octave temperaments actually make sense.

Terbium

The name of terbium temperament comes from Terbium, the 65th element.

Subgroup: 2.3.5.7

Comma list: 32805/32768, 78732/78125

Mapping: [65 103 151 0], 0 0 0 1]]

Mapping generators: ~81/80, ~7

Optimal tuning (POTE): ~7/4 = 969.1359

Optimal ET sequence65, 130

Badness: 0.169778

11-limit

Subgroup: 2.3.5.7.11

Comma list: 243/242, 4000/3993, 5632/5625

Mapping: [65 103 151 0 225], 0 0 0 1 0]]

Optimal tuning (POTE): ~7/4 = 969.5715

Optimal ET sequence65d, 130

Badness: 0.059966

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 351/350, 2080/2079, 3584/3575

Mapping: [65 103 151 0 225 58], 0 0 0 1 0 1]]

Optimal tuning (POTE): ~7/4 = 969.9612

Optimal ET sequence65d, 130

Badness: 0.036267