Tribilo family

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The tribilo family is a family of rank-2 temperaments in the 2.3.11 subgroup that temper out the nexus comma, the unnoticeable comma with the ratio 1771561/1769472, and a monzo of [-16 -3 0 0 6, however, most of the members of this rank-2 family currently have yet to be explored. For other families that are defined by the tempering of the nexus comma, see the Nexus. This family's name comes from the nexus comma being referred to as the "tribilo comma" in color notation.

Tribilo

This is the parent temperament of the tribilo family.

Subgroup: 2.3.11

Comma list: 1771561/1769472

Sval mapping: [3 0 8], 0 2 1]]

Sval mapping generators: ~121/96, ~1331/768

POTE generator: ~1331/768 = 950.9518 (or ~12/11 = 150.9518)

Optimal GPV sequence9, 15, 24, 87, 111, 135, 159, 1407, 1566, 1725e, 1884e, 2043e, 2202e, 2361e, 2520e, 2679e

Badness: 2.44 × 10-3

Triblet

Subgroup: 2.3.11.13

Comma list: 352/351, 1771561/1769472

Sval mapping: [3 0 8 23], 0 2 1 -5]]

POTE generator: ~1331/768 = 951.4814

Optimal GPV sequence: 9f, 15f, 24, 63, 87, 111, 198, 309f, 507f

Badness: 2.70 × 10-3

Trilobite

Subgroup: 2.3.11.13

Comma list: 85293/85184, 1771561/1769472

Sval mapping: [3 0 8 42], 0 2 1 -13]]

POTE generator: ~1331/768 = 950.7810

Optimal GPV sequence: 24, 111f, 135f, 159, 183, 390, 573, 963f, 1536bef

Badness: 1.65 × 10-3