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 7/5's falls short of 11/4, one octave above 11/8.
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]]
- Mapping generators: ~2, ~5, ~7
- WE: ~2 = 1200.0558 ¢, ~5/4 = 385.7504 ¢, ~7/4 = 969.3743 ¢
- error map: ⟨+0.056 -0.452 +0.660 -0.334]
- CWE: ~2 = 1200.0000 ¢, ~5/4 = 385.7894 ¢, ~7/4 = 969.4163 ¢
- error map: ⟨0.000 -0.524 +0.590 -0.437]
Optimal ET sequence: 25, 29, 31, 37, 72, 103, 109, 255, 364, 734, 843, 952
Badness (Sintel): 0.110
Overview to extensions
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) → Mirkwai family
- Dimcomp (+6250/6237 or 9801/9800) → Dimcomp family
Considered below are mendel, moctpine, and compass, besides the no-3 subgroup temperament.
Mendel
- For the 7-limit version of this temperament, see Miscellaneous 7-limit temperaments #Metric.
Named by Xenllium in 2026, mendel tempers out the vishdel comma, 5632/5625, as well as meter (703125/702464). It can be extended to the 13-limit by adding 352/351 or 625/624 to the comma basis.
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 5632/5625
Mapping: [⟨1 0 -1 -6 -13], ⟨0 1 1 3 6], ⟨0 0 3 7 12]]
- Mapping generators: ~2, ~3, ~112/75
- WE: ~2 = 1199.8401 ¢, ~3 = 702.2508 ¢, ~112/75 = 694.6555 ¢
- error map: ⟨-0.160 +0.136 -0.097 +0.994 -0.828]
- CWE: ~2 = 1200.0000 ¢, ~3 = 702.2809 ¢, ~112/75 = 694.7567 ¢
- error map: ⟨0.000 +0.326 +0.237 +1.314 -0.552]
Optimal ET sequence: 12, 19e, 31, 90e, 109, 121, 140, 152, 292, 323, 444d, 475d, 627d
Badness (Sintel): 1.20
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 625/624, 1375/1372
Mapping: [⟨1 0 -1 -6 -13 -8], ⟨0 1 1 3 6 3], ⟨0 0 3 7 12 12]]
Optimal tunings:
- WE: ~2 = 1199.7481 ¢, ~3 = 702.7304 ¢, ~112/75 = 694.3426 ¢
- CWE: ~2 = 1200.0000 ¢, ~3 = 702.8125 ¢, ~112/75 = 694.4843 ¢
Optimal ET sequence: 12f, 19e, 31, 78f, 90e, 109, 121, 140, 152f, 261, 292
Badness (Sintel): 1.34
Moctpine
Named by Xenllium in 2026, moctpine tempers out 4000/3993.
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 = 1199.9745 ¢, ~11/10 = 165.9846 ¢, ~7/5 = 583.8721 ¢
- error map: ⟨-0.025 +0.040 -0.707 +0.652 +0.247]
- CWE: ~2 = 1200.0000 ¢, ~11/10 = 165.9939 ¢, ~7/5 = 583.8766 ¢
- error map: ⟨0.000 +0.063 -0.678 +0.686 +0.312]
Optimal ET sequence: 29, 37, 43, 72, 152, 224, 629, 781, 853c
Badness (Sintel): 1.28
Compass
- For the 7-limit version of this temperament, see Miscellaneous 7-limit temperaments #Compass.
Named by Xenllium in 2021, compass tempers out 4375/4356.
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 4375/4356
Mapping: [⟨1 2 0 -2 -4], ⟨0 -5 0 2 6], ⟨0 0 1 2 3]]
- Mapping generators: ~2, ~35/33, ~5
- WE: ~2 = 1200.1322 ¢, ~35/33 = 99.6163 ¢, ~5/4 = 384.7310 ¢
- error map: ⟨+0.132 +0.228 -1.318 +0.133 +0.838]
- CWE: ~2 = 1200.0000 ¢, ~35/33 = 99.5842 ¢, ~5/4 = 384.8078 ¢
- error map: ⟨0.000 +0.124 -1.506 -0.042 +0.611]
Optimal ET sequence: 12, …, 37, 49, 60e, 72, 181, 193, 265, 446c, 518c
Badness (Sintel): 1.68
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 625/624, 1375/1372
Mapping: [⟨1 2 0 -2 -4 -6], ⟨0 -5 0 2 6 5], ⟨0 0 1 2 3 4]]
Optimal tunings:
- WE: ~2 = 1199.9110 ¢, ~35/33 = 99.5193 ¢, ~5/4 = 385.3897 ¢
- CWE: ~2 = 1200.0000 ¢, ~35/33 = 99.5397 ¢, ~5/4 = 385.3536 ¢
Optimal ET sequence: 12f, …, 37, 49f, 72, 121, 193
Badness (Sintel): 1.36