Nexus family

The nexus family is built up from temperaments that temper out the nexus comma- the unnoticeable comma with the ratio 1771561/1769472, and a monzo of [-16 -3 0 0 6⟩. Among the members of this family are Nexus, Binexus, Dinexus, Trinexus and Tribilo.

Nexus

The 11-limit parent comma for the Nexus family is the the nexus comma with a ratio of 1771561/1769472 and a monzo of [-16 -3 0 0 6⟩. This is a rank-4 temperament in which the 5-limit and 7-limit parts are represented by independent generators.

Period: ~121/96 = 1\3

Optimal (POTE) generators: 950.9518, 386.2068, 968.6966

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

Wedgie: <<<<6 0 0 3 -16]]]]

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

Badness: 0.588×10^-6

Binexus

This temperament adds the schisma to the list of tempered out commas on account of the schisma being the unnoticeable comma adding the 5-limit to the mix. This is a rank-3 temperament.

Commas: 1771561/1769472, 32805/32768

POTE generators: ⟨400.0000, 950.8701, 3368.5689]

Map:

Wedgie:

EDOs: 24p, 135p, 159, 183, 207, 342, 525, 684, 867

Badness:

Dinexus

This temperament can be seen as adding the quartisma to the list of tempered out commas on account of the quartisma being the unnoticeable comma adding the 7-limit to the mix. This is a rank-3 temperament.

Commas: 1771561/1769472, 117440512/117406179

POTE generators:

Map:

Wedgie:

EDOs:

Badness:

Trinexus

This temperament can be seen as either adding the quartisma to Binexus, or adding the schisma to Dinexus. Either way, you end up with a full 11-limit rank-2 temperament.

Commas: 1771561/1769472, 32805/32768, 117440512/117406179

POTE generators:

Map:

Wedgie:

EDOs:

Badness:

Tribilo

Tribilo is the pure Rank-2 2.3.11 temperament that tempers out the Nexus comma.

Commas: 1771561/1769472

POTE generators:

Map:

Wedgie:

EDOs:

Badness: