Sensibeta temperaments

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

This is a collection of rank-2 temperaments tempering out the sensibeta comma, 1071875/1062882 = [-1 -12 5 3⟩.

Temperament considered below is elven. Discussed elsewhere are:

• Sensi (+126/125 or +245/243) → Sensipent family
• Betic (+225/224) → Sycamore family
• Slithy (+4000/3969 or +420175/419904) → Octagar temperaments
• Ketchup (+5120/5103) → Hemifamity temperaments
• Polypyth (+6144/6125) → Porwell temperaments
• Marfifths (+10976/10935 or +15625/15552) → Kleismic family

Elven

See also: 11th-octave temperaments

Subgroup: 2.3.5.7

Comma list: 1071875/1062882, 9765625/9680832

Mapping: [⟨11 2 7 0], ⟨0 5 6 10]]

Mapping generators: ~729/686, ~756/625

Optimal tunings:

• WE: ~729/686 = 109.100¢, ~756/625 = 336.888¢
• CWE: ~729/686 = 109.091¢, ~49/48 = 336.875¢

Optimal ET sequence: 121, 253, 374

Badness (Sintel): 11.372

11-limit

Subgroup: 2.3.5.7.11

Comma list: 1375/1372, 4375/4356, 59290/59049

Mapping: [⟨11 2 7 0 1], ⟨0 5 6 10 12]]

Optimal tunings:

• WE: ~729/686 = 109.101¢, ~297/245 = 336.877¢
• CWE: ~729/686 = 109.091¢, ~297/245 = 336.863¢

Optimal ET sequence: 121, 253, 374

Badness (Sintel): 3.675

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 1375/1372, 1575/1573, 2200/2197

Mapping: [⟨11 2 7 0 1 16], ⟨0 5 6 10 12 8]]

Optimal tunings:

• WE: ~125/117 = 109.100¢, ~91/75 = 336.876¢
• CWE: ~125/117 = 109.091¢, ~91/75 = 336.863¢

Optimal ET sequence: 121, 253, 374

Badness (Sintel): 2.019

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 325/324, 375/374, 595/594, 1275/1274, 2200/2197

Mapping: [⟨11 2 7 0 1 16 11], ⟨0 5 6 10 12 8 11]]

Optimal tunings:

• WE: ~125/117 = 109.099¢, ~17/14 = 336.867¢
• CWE: ~125/117 = 109.091¢, ~17/14 = 336.856¢

Optimal ET sequence: 121, 253, 374

Badness (Sintel): 1.495