Nexus 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 nexus family is a family of rank-4 temperaments tempers 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-4 family currently have yet to be explored. For other families that are defined by the tempering of this comma, see the Nexus.

Nexus

This is the parent temperament of the nexus family. In this temperament, the 5-limit and 7-limit parts are represented by independent generators.

Subgroup: 2.3.5.7.11

Comma list: 1771561/1769472

Mapping: [⟨3 0 0 0 8], ⟨0 2 0 0 1], ⟨0 0 1 0 0], ⟨0 0 0 1 0]]

Mapping generators: ~121/96, ~1331/768, ~5/1, ~7/1

POTE generators: ~1331/768 = 950.9518, ~5/4 = 386.2068, ~7/4 = 968.6966

Optimal ET sequence: 9, 15, 24, 39d, 48, 57, 63, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566

Badness: 0.588 × 10^-6

13-limit

Todo: review Add optimal ET sequence & badness

Subgroup: 2.3.5.7.11.13

Comma list: 1771561/1769472, 676/675

Mapping: [⟨3 0 0 0 8 -3], ⟨0 2 0 0 1 3], ⟨0 0 1 0 0 1], ⟨0 0 0 1 0 0]⟩

Mapping generators: ⟨1200.000, 1902.167, 2786.583, 3368.823, 4151.084, 4439.834]

POTE generators: ⟨400.0000, 951.0837, 2786.5829, 3368.8230]

Optimal ET sequence: 

Badness: