Dimcomp family

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 dimcomp family of rank-3 temperaments tempers out the dimcomp comma (monzo: [-1 -4 8 -4⟩, ratio: 390625/388962).

Dimcomp

Subgroup: 2.3.5.7

Comma list: 390625/388962

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

mapping generators: ~25/21, ~3, ~5

Optimal tunings:

• WE: ~25/21 = 300.0036 ¢, ~3/2 = 702.0854 ¢, ~5/4 = 385.6631 ¢

error map: ⟨+0.014 +0.145 -0.622 +0.454]

• CWE: ~25/21 = 300.0000 ¢, ~3/2 = 702.0885 ¢, ~5/4 = 385.6745 ¢

error map: ⟨0.000 +0.133 -0.639 +0.435]

Optimal ET sequence: 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952

Badness (Sintel): 3.45

Undecimal dimcomp

Subgroup: 2.3.5.7.11

Comma list: 1375/1372, 6250/6237

Mapping: [⟨4 0 0 -1 5], ⟨0 1 0 -1 -3], ⟨0 0 1 2 3]]

Optimal tunings:

• WE: ~25/21 = 300.0093 ¢, ~3/2 = 701.9976 ¢, ~5/4 = 385.6591 ¢

error map: ⟨+0.037 +0.080 -0.580 +0.597 -0.176]

• CWE: ~25/21 = 300.0000 ¢, ~3/2 = 702.0009 ¢, ~5/4 = 385.6895 ¢

error map: ⟨0.000 +0.046 -0.624 +0.552 -0.252]

Optimal ET sequence: 12, …, 68, 72, 140, 152, 224, 364, 436, 588

Badness (Sintel): 0.751

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 625/624, 1375/1372, 2080/2079

Mapping: [⟨4 0 0 -1 5 -16], ⟨0 1 0 -1 -3 -1], ⟨0 0 1 2 3 4]]

Optimal tunings:

• WE: ~25/21 = 300.0140 ¢, ~3/2 = 701.9679 ¢, ~5/4 = 385.5977 ¢
• CWE: ~25/21 = 300.0000 ¢, ~3/2 = 701.9549 ¢, ~5/4 = 385.6140 ¢

Optimal ET sequence: 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c

Badness (Sintel): 0.767

Octopod

Octopod is octoid with an independent generator for prime 13.

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 1375/1372, 4000/3993

Mapping: [⟨8 1 3 3 16 0], ⟨0 3 4 5 3 0], ⟨0 0 0 0 0 1]]

mapping generators: ~12/11, ~7/5, ~13

Optimal tunings:

• WE: ~12/11 = 150.0093 ¢, ~7/5 = 583.9356 ¢, ~13/8 = 840.6906 ¢

error map: ⟨-0.055 -0.155 -0.592 +0.832 +0.380 -0.001]

• CWE: ~12/11 = 150.0000 ¢, ~7/5 = 583.9477 ¢, ~13/8 = 840.6394 ¢

error map: ⟨0.000 -0.112 -0.523 +0.913 +0.525 +0.112]

Optimal ET sequence: 72, 144, 152f, 224, 824d

Badness (Sintel): 1.16