65th-octave temperaments: Difference between revisions
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{{Fractional-octave navigation|65}} | |||
==65th-octave temperaments== | ==65th-octave temperaments== | ||
[[65edo]] is accurate for harmonics 3, 5, and 11, so various 65th-octave temperaments actually make sense. | [[65edo]] is accurate for harmonics 3, 5, and 11, so various 65th-octave temperaments actually make sense. | ||
Revision as of 12:13, 17 September 2023
Template:Fractional-octave navigation
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
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
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
Badness: 0.036267