Nexus family: Difference between revisions

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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 {{monzo|-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.
{{Technical data page}}
The '''nexus family''' is a family of [[rank-4]] temperaments tempers out the [[nexus comma]], the unnoticeable comma with the ratio 1771561/1769472, and a monzo of {{monzo|-16 -3 0 0 6}}, however, most of the members of this rank-4 family currently have yet to be explored. For other families that are defined by the tempering of this comma, see [[the Nexus]].


== Nexus ==
== Nexus ==
This is the parent temperament of the nexus family. In this temperament, the 5-limit and 7-limit parts are represented by independent generators.


The 11-limit parent comma for the Nexus family is the the nexus comma with a ratio of 1771561/1769472 and a monzo of {{monzo|-16 -3 0 0 6}}. This is a rank-4 temperament.
Subgroup: 2.3.5.7.11


Period: ~121/96 = 1\3
[[Comma list]]: [[1771561/1769472]]


Optimal (POTE) generators: 950.9518, 386.2068, 968.6966
[[Mapping]]: [{{val| 3 0 0 0 8}}, {{val| 0 2 0 0 1}}, {{val| 0 0 1 0 0}}, {{val| 0 0 0 1 0}}]


Comma list: 1771561/1769472
Mapping generators: ~121/96, ~1331/768, ~5/1, ~7/1


Mapping: [{{val| 3 0 0 0 8}}, {{val| 0 2 0 0 1}}, {{val| 0 0 1 0 0}}, {{val| 0 0 0 1 0}}]
[[POTE generator]]s: ~1331/768 = 950.9518, ~5/4 = 386.2068, ~7/4 = 968.6966


Mapping generators: ~121/96, ~1331/768, ~5, ~7
{{Optimal ET sequence|legend=1| 9, 15, 24, 39d, 48, 57, 63, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566 }}


Wedgie: <<<<6 0 0 3 -16]]]]
[[Badness]]: 0.588 × 10<sup>-6</sup>


EDOs: 9, 15, 24, 39d, 48, 57, 63, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566
=== 13-limit ===


Badness: 0.588×10<sup>-6</sup>
{{todo|review|inline=yes|comment=Add optimal ET sequence & badness}}


== Binexus ==
Subgroup: 2.3.5.7.11.13


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.
[[Comma list]]: [[1771561/1769472]], [[676/675]]


Commas: 1771561/1769472, 32805/32768
[[Mapping]]: [⟨3 0 0 0 8 -3], ⟨0 2 0 0 1 3], ⟨0 0 1 0 0 1], ⟨0 0 0 1 0 0]⟩


POTE generators: ⟨400.0000, 950.8701, 3368.5689]
Mapping generators: ⟨1200.000, 1902.167, 2786.583, 3368.823, 4151.084, 4439.834]


Map:  
[[POTE generator]]s: ⟨400.0000, 951.0837, 2786.5829, 3368.8230]


Wedgie:
{{Optimal ET sequence|legend=1| }}


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


Badness:
[[Category:Temperament families]]
 
[[Category:Pages with mostly numerical content]]
[[Category:Nexus]]
[[Category:Nexus family| ]] <!-- main article -->
 
[[Category:Rank 4]]
{{todo|improve readability|discuss title|expand}}

Latest revision as of 00:25, 24 June 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The nexus family is a family of rank-4 temperaments tempers out the nexus comma, the unnoticeable comma with the ratio 1771561/1769472, and a monzo of [-16 -3 0 0 6⟩, however, most of the members of this rank-4 family currently have yet to be explored. For other families that are defined by the tempering of this comma, see the Nexus.

Nexus

This is the parent temperament of the nexus family. In this temperament, the 5-limit and 7-limit parts are represented by independent generators.

Subgroup: 2.3.5.7.11

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

POTE generators: ~1331/768 = 950.9518, ~5/4 = 386.2068, ~7/4 = 968.6966

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

Badness: 0.588 × 10-6

13-limit

Todo: review

Add optimal ET sequence & badness

Subgroup: 2.3.5.7.11.13

Comma list: 1771561/1769472, 676/675

Mapping: [⟨3 0 0 0 8 -3], ⟨0 2 0 0 1 3], ⟨0 0 1 0 0 1], ⟨0 0 0 1 0 0]⟩

Mapping generators: ⟨1200.000, 1902.167, 2786.583, 3368.823, 4151.084, 4439.834]

POTE generators: ⟨400.0000, 951.0837, 2786.5829, 3368.8230]

Optimal ET sequence: 

Badness:

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