Porcupine rank-3 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 porcupine rank-3 family of temperaments tempers out the porcupine comma or maximal diesis, 250/243. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.

Rank-3 porcupine

Subgroup: 2.3.5.7

Comma list: 250/243

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

mapping generators: ~2, ~10/9, ~7

Optimal tunings:

• WE: ~2 = 1199.5444 ¢, ~10/9 = 163.8881 ¢, ~7/4 = 969.6868 ¢

error map: ⟨-0.456 +5.469 -7.121 -0.050]

• CWE: ~2 = 1200.0000 ¢, ~10/9 = 164.0621 ¢, ~7/4 = 969.4180 ¢

error map: ⟨0.000 +5.859 -6.624 +0.592]

Optimal ET sequence: 7d, 8d, 14c, 15, 22, 37, 51, 73c

Badness (Sintel): 2.36

Sonic

Subgroup: 2.3.5.7.11

Comma list: 55/54, 100/99

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

Optimal tunings:

• WE: ~2 = 1200.3290 ¢, ~11/10 = 164.1227 ¢, ~7/4 = 968.1067 ¢

error map: ⟨+0.329 +6.335 -5.940 -0.061 -6.492]

• CWE: ~2 = 1200.0000 ¢, ~11/10 = 163.9951 ¢, ~7/4 = 968.2673 ¢

error map: ⟨0.000 +6.060 -6.289 -0.559 -7.298]

Optimal ET sequence: 7d, 8d, 14c, 15, 22, 37, 51, 88b

Badness (Sintel): 0.629

Tikal

Subgroup: 2.3.5.7.11

Comma list: 56/55, 250/243

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

Optimal tunings:

• WE: ~2 = 1195.9857 ¢, ~11/10 = 160.9790 ¢, ~7/4 = 967.7973 ¢

error map: ⟨-4.014 +7.079 -3.252 -9.057 +13.346]

• CWE: ~2 = 1200.0000 ¢, ~11/10 = 162.1977 ¢, ~7/4 = 964.6202 ¢

error map: ⟨0.000 +11.452 +2.698 -4.206 +24.291]

Optimal ET sequence: 7d, 8d, 15, 30dee, 37ee, 52bee

Badness (Sintel): 2.37