# Nexus family

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

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

Wedgie: ⟨⟨⟨⟨6 0 0 3 -16]]]]

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 multival, 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]

Wedgie: ⟨⟨⟨⟨]]]]

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