Canopic 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 canopic family of rank-3 temperaments tempers out the canopic comma (monzo: [0 3 4 -5⟩, ratio: 16875/16807), a no-twos comma.

Canopic a.k.a. mirkwai

Subgroup: 2.3.5.7

Comma list: 16875/16807

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

Mapping generators: ~2, ~3, ~10/7

Optimal tunings:

• WE: ~2 = 1199.9999 ¢, ~3/2 = 701.7827 ¢, ~10/7 = 616.0944 ¢

error map: ⟨-0.000 -0.172 -0.493 +0.900]

• CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.7827 ¢, ~10/7 = 616.0945 ¢

error map: ⟨0.000 -0.172 -0.493 +0.900]

Minimax tuning:

• 7-odd-limit

[[1 0 0 0⟩, [0 4/7 -4/7 5/7⟩, [0 -3/7 3/7 5/7⟩, [0 0 0 1⟩]

eigenmonzo (unchanged-interval) basis: 2.5/3.7

• 9-odd-limit

[[1 0 0 0⟩, [0 8/11 -4/11 5/11⟩, [0 -6/11 3/11 10/11⟩, [0 0 0 1⟩]

eigenmonzo (unchanged-interval) basis: 2.9/5.7

Optimal ET sequence: 31, 41, 72, 152, 224

Badness (Sintel): 1.51

Projection pairs: 5 84375/16807 7 16875/2401 to 2.3.7/5

Indra

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372

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

Mapping generators: ~2, ~3, ~10/7

Mapping to lattice: [⟨0 2 1 2 3], ⟨0 -1 2 1 -3]]

Lattice basis:

15/14 length = 0.6184, 55/36 length = 0.7585

Angle (15/14, 55/36) = 68.1048 deg

Optimal tunings:

• WE: ~2 = 1199.9693 ¢, ~3/2 = 701.7444 ¢, ~10/7 = 616.1152 ¢

error map: ⟨-0.031 -0.241 -0.443 +0.899 +0.183]

• CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.7342 ¢, ~10/7 = 616.1422 ¢

error map: ⟨0.000 -0.221 -0.400 +0.946 +0.256]

Minimax tuning:

• 11-odd-limit

[[1 0 0 0 0⟩, [10 10 -3 0 -5⟩, [0 0 1 0 0⟩, [6 6 -1 0 -3⟩, [20 18 -6 0 -9⟩]

eigenmonzo (unchanged-interval) basis: 2.5.11/9

Optimal ET sequence: 31, 41, 72, 152, 224, 631d, 855d

Badness (Sintel): 0.320

Projection pairs: 5 84375/16807 7 16875/2401 11 1372/125 to 2.3.7/5

Scales: indra31

Shibi

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 729/728, 1375/1372

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

Optimal tunings:

• WE: ~2 = 1199.9762 ¢, ~3/2 = 701.7232 ¢, ~10/7 = 616.1317 ¢
• CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.7261 ¢, ~10/7 = 616.1467 ¢

Optimal ET sequence: 31f, 39df, 41, 72, 111, 152f, 183, 224, 631d, 855d

Badness (Sintel): 0.674

Yajna

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 625/624, 1375/1372

Mapping: [⟨1 0 -5 -4 5 -24], ⟨0 1 3 3 0 11], ⟨0 0 5 4 -3 20]]

Optimal tunings:

• WE: ~2 = 1200.0073 ¢, ~3/2 = 701.7067 ¢, ~10/7 = 616.1052 ¢
• CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.7089 ¢, ~10/7 = 616.0986 ¢

Minimax tuning:

• 13-odd-limit

[[1 0 0 0 0 0⟩, [4/5 6/5 -4/5 0 0 1/5⟩, [8/5 2/5 -3/5 0 0 2/5⟩, [44/25 26/25 -24/25 0 0 11/25⟩, [62/25 48/25 -27/25 0 0 3/25⟩, [8/5 2/5 -8/5 0 0 7/5⟩]

eigenmonzo (unchanged-interval) basis: 2.9/5.13/5

• 15-odd-limit

[[1 0 0 0 0 0⟩, [0 1 0 0 0 0⟩, [5/4 1/2 0 -5/16 0 5/16⟩, [1 1 0 -1/4 0 1/4⟩, [5/4 3/2 0 3/16 0 -3/16⟩, [1 1 0 -5/4 0 5/4⟩]

eigenmonzo (unchanged-interval) basis: 2.3.13/7

Optimal ET sequence: 31, 49f, 72, 103, 121, 152f, 193, 224

Badness (Sintel): 0.655

Vibhu

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 540/539, 1375/1372

Mapping: [⟨1 0 -5 -4 5 -13], ⟨0 1 3 3 0 6], ⟨0 0 5 4 -3 14]]

Optimal tunings:

• WE: ~2 = 1200.1587 ¢, ~3/2 = 701.2394 ¢, ~10/7 = 616.6507 ¢
• CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.2689 ¢, ~10/7 = 616.5306 ¢

Optimal ET sequence: 31, 64cdf, 72, 103, 111, 152, 175f, 183, 469f

Badness (Sintel): 0.772

Vish

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 364/363, 540/539

Mapping: [⟨1 0 0 0 2 2], ⟨0 1 3 3 0 -2], ⟨0 0 5 4 -3 -10]]

Optimal tunings:

• WE: ~2 = 1199.9463 ¢, ~3/2 = 702.3912 ¢, ~10/7 = 615.5733 ¢
• CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.3742 ¢, ~10/7 = 615.6198 ¢

Optimal ET sequence: 31f, 41, 72, 121, 193

Badness (Sintel): 0.870