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 and Binexus, with the names "Dinexus" and "Trinexus" being proposed for additional temperaments. The different branches of the Nexus family are named on the basis of how many unnoticeable commas between different pure p-limits they temper out within the full 11-limit.

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.

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, ~7

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 rank-2 temperament.

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

POTE generators:

Map:

Wedgie:

EDOs:

Badness: