The Nexus
The Nexus is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the nexus comma- the unnoticeable comma with the ratio 1771561/1769472, and a monzo of [-16 -3 0 0 6⟩. Among the known branches of this collection are Nexus, Binexus, Nexiquart, Nexal and Tribilo, with "Dinexus" and "Trinexus" as proposed names for other branches.
Rank-4 temperament
The parent temperament of this whole collection is rank-4 temperament.
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⟩. In this temperament, 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
Rank-3 temperaments
From the Rank-4 parent temperament, there are several rank three temperaments that can be derived.
Binexus
This temperament adds the schisma to the list of tempered out commas on account of the schisma being an unnoticeable comma for adding the 5-limit to the mix.
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:
Nexiquart
This temperament can be seen as adding the quartisma to the list of tempered out commas on account of the quartisma being an unnoticeable comma for adding the 7-limit to the mix.
Commas: 1771561/1769472, 117440512/117406179
POTE generators:
Map:
Wedgie:
EDOs:
Badness:
Rank-2 temperaments
So far, the only rank-2 temperaments in the Nexus are the Nexal family and the Tribilo family, with the parent temperaments of each being listed here.
Nexal
Nexal is the full 11-limit Rank-2 temperament that tempers out the nexus comma.
Commas: 1771561/1769472
POTE generators:
Map:
Wedgie:
EDOs:
Badness:
Tribilo
Tribilo is the pure Rank-2 2.3.11 temperament that tempers out the nexus comma- it's name comes from the nexus comma being referred to as the "tribilo comma" in color notation.
Commas: 1771561/1769472
POTE generators:
Map:
Wedgie:
EDOs:
Badness: