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, schisnex, nexiquart, altinex, and tribilo.
Temperaments discussed elsewhere are:
- Tyr, {3025/3024, 102487/102400} → Lehmerismic temperaments #Tyr
Rank-4 temperaments
The parent temperament of this whole collection is rank-4 temperament. However, there are other rank-4 extensions which have yet to be explored.
Nexus
The parent temperament for the Nexus is Nexus temperament itself. 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
Badness: 0.588 × 10-6
Rank-3 temperaments
From the rank-4 parent temperament, there are several rank-3 temperaments that can be derived.
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Schisnex
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.
Subgroup: 2.3.5.7.11
Comma list: 32805/32768, 1771561/1769472
Mapping:
Wedgie:
POTE generators: ⟨400.0000, 950.8701, 3368.5689]
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.
Subgroup: 2.3.5.7.11
Comma list: 19712/19683, 1771561/1769472
Mapping:
Wedgie:
POTE generators:
Vals:
Badness:
Rank-2 temperaments
So far, among the only known rank-2 temperaments in the Nexus are Altinex and Tribilo temperament.
Altinex
Commas: 19712/19683, 32805/32768, 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 – its name comes from the nexus comma being referred to as the "tribilo comma" in color notation.
Subgroup: 2.3.11
Comma list: 1771561/1769472
Mapping:
Wedgie:
POTE generator:
Vals:
Badness: