Nexus clan

The nexus clan, a.k.a. tribilo family, is a clan 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 clan currently have yet to be explored. For other families that are defined by the tempering of the nexus comma, see the Nexus. The tribilo family comes from the nexus comma being referred to as the "tribilo comma" in color notation.

Tribilo

This is the parent temperament of the nexus clan.

Subgroup: 2.3.11

Comma list: 1771561/1769472

Sval mapping: [⟨3 0 8], ⟨0 2 1]]

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

Optimal tuning (POTE): ~121/96 = 1\3, ~1331/768 = 950.9518 (or ~12/11 = 150.9518)

Optimal ET sequence: 9, 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]]

Optimal tuning (POTE): ~121/96 = 1\3, ~1331/768 = 951.4814

Optimal ET 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]]

Optimal tuning (POTE): ~121/96 = 1\3, ~1331/768 = 950.7810

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

Badness: 1.65 × 10^-3