65th-octave temperaments: Difference between revisions
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{{ | {{Infobox fractional-octave|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. | ||
===Terbium=== | |||
=== Terbium === | |||
The name of terbium temperament comes from Terbium, the 65th element. | The name of terbium temperament comes from Terbium, the 65th element. | ||
| Line 18: | Line 20: | ||
[[Badness]]: 0.169778 | [[Badness]]: 0.169778 | ||
====11-limit==== | |||
==== 11-limit ==== | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 30: | Line 33: | ||
Badness: 0.059966 | Badness: 0.059966 | ||
====13-limit==== | |||
==== 13-limit ==== | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
Latest revision as of 03:44, 14 February 2025
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