Moctdelismic clan

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.

The moctdelismic clan of rank-3 temperaments tempers out the moctdel comma, 1375/1372, the amount by which a stack of three 7/5s falls short of 11/4, one octave above 11/8.

The second comma in the comma list determines how we extend the no-3 subgroup temperament to include the harmonic 3. Indra adds 540/539 as well as 3025/3024, prodigy adds 225/224 as well as 441/440, and agni adds 385/384 as well as 2401/2400. Dimcomp adds 6250/6237 as well as 9801/9800, splitting the octave in four.

Discussed elsewhere are:

• Prodigy (+225/224 or 441/440) → Marvel family
• Agni (+385/384 or 2401/2400) → Breed family
• Indra (+540/539 or 441/440) → Mirkwai family
• Dimcomp (+6250/6237 or 9801/9800) → Dimcomp family

Considered below are mendel (12 & 31 & 152) and moctpine (29 & 72 & 80), besides the no-3 subgroup temperament.

Moctdelic

Subgroup: 2.5.7.11

Comma list: 1375/1372

Subgroup-val mapping: [⟨1 0 0 2], ⟨0 1 0 -3], ⟨0 0 1 3]]

Sval mapping generators: ~2, ~5, ~7

Optimal tunings:

• WE: ~2 = 1200.056¢, ~5 = 2785.862¢, ~7 = 3369.486¢
• CWE: ~2 = 1200.000¢, ~5 = 2785.789¢, ~7 = 3369.416¢

Optimal ET sequence: 25, 29, 31, 37

Badness (Sintel): 0.110

Mendel

Subgroup: 2.3.5.7.11

Comma list: 1375/1372, 5632/5625

Mapping: [⟨1 0 2 1 -1], ⟨0 1 1 3 6], ⟨0 0 -3 -7 -12]]

Mapping generators: ~2, ~3, ~75/56

Optimal tunings:

• WE: ~2 = 1199.840¢, ~3 = 1902.091¢, ~75/56 = 505.185¢
• CWE: ~2 = 1200.000¢, ~3 = 1902.281¢, ~75/56 = 505.243¢

Optimal ET sequence: 12, 19e, 31, 90e, 109, 121, 140, 152, 292

Badness (Sintel): 1.202

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 625/624, 1375/1372

Mapping: [⟨1 0 2 1 -1 4], ⟨0 1 1 3 6 3], ⟨0 0 -3 -7 -12 -12]]

Optimal tunings:

• WE: ~2 = 1199.748¢, ~3 = 1902.479¢, ~75/56 = 505.405¢
• CWE: ~2 = 1200.000¢, ~3 = 1902.813¢, ~75/56 = 505.516¢

Optimal ET sequence: 12f, 19e, 31, 90e, 109, 121, 140, 152f, 261, 292

Badness (Sintel): 1.339

Moctpine

Subgroup: 2.3.5.7.11

Comma list: 1375/1372, 4000/3993

Mapping: [⟨1 2 1 1 2], ⟨0 -3 -1 -1 0], ⟨0 0 3 4 3]]

Mapping generators: ~2, ~11/10, ~7/5

Optimal tunings:

• WE: ~2 = 1199.975¢, ~11/10 = 165.985¢, ~7/5 = 583.872¢
• CWE: ~2 = 1200.000¢, ~11/10 = 165.994¢, ~7/5 = 583.877¢

Optimal ET sequence: 29, 37, 43, 72, 152, 224

Badness (Sintel): 1.275