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
- 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
- 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
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
- 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