The Nexus: Difference between revisions
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'''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 {{monzo|-16 -3 0 0 6}}. Among the known branches of this collection are 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 {{monzo|-16 -3 0 0 6}}. Among the known branches of this collection are Nexus, Schisnex, Nexiquart, Nexal and Tribilo, with "Dinexus" and "Trinexus" as proposed names for other branches. | ||
= Rank-4 temperaments = | = Rank-4 temperaments = | ||
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From the Rank-4 parent temperament, there are several rank three temperaments that can be derived. | From the Rank-4 parent temperament, there are several rank three temperaments that can be derived. | ||
== | == 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. | 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. | ||
Revision as of 16:17, 23 April 2021
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, Nexal and Tribilo, with "Dinexus" and "Trinexus" as proposed names for other branches.
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 found.
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.
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.
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.
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: 19712/19683, 1771561/1769472
POTE generators:
Map:
Wedgie:
EDOs:
Badness:
Rank-2 temperaments
So far, the only known rank-2 temperaments in the Nexus belong to either the Nexal family or the Tribilo family. The parent temperaments of both families are 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: