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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, Binexus, Nexiquart, Nexal and Tribilo, with "Dinexus" and "Trinexus" as proposed names for other branches.  
{{Technical data page}}
'''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, altinex, and tribilo.


= Rank-4 temperaments =
Because the nexus comma is the difference between (121/96)<sup>3</sup> and 2/1, all nexus temperaments divide 2/1 into three equal parts of (approximately) 400 cents.
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 ==
== Rank-4 temperaments ==
{{main| Nexus family }}
{{main| Nexus family }}


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.
The parent temperament of this whole collection is a rank-4 temperament. However, there are other rank-4 extensions which have yet to be explored.


Period: ~121/96 = 1\3
=== Nexus ===


Optimal (POTE) generators: 950.9518, 386.2068, 968.6966
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.


Comma list: 1771561/1769472
Subgroup: 2.3.5.7.11


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]]: [{{val| 3 0 0 0 8}}, {{val| 0 2 0 0 1}}, {{val| 0 0 1 0 0}}, {{val| 0 0 0 1 0}}]


Mapping generators: ~121/96, ~1331/768, ~5/1, ~7/1
Mapping generators: ~121/96, ~1331/768, ~5/1, ~7/1


Wedgie: <<<<6 0 0 3 -16]]]]
[[POTE generator]]s: ~1331/768 = 950.9518 or ~12/11 = 150.9518, ~5/4 = 386.2068, ~7/4 = 968.6966


EDOs: 9, 15, 24, 39d, 48, 57, 63, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566
{{Optimal ET sequence|legend=1| 9, 15, 24, 33cd, 39d, 48, 57, 63, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566, 2091e, 2361e, 2433e, 2703e, 3045e, 3315ee, 3657ee }}


Badness: 0.588×10<sup>-6</sup>
[[Badness]]: 0.588 × 10<sup>-6</sup>


= Rank-3 temperaments =
== Rank-3 temperaments ==
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-3 temperaments that can be derived.


== Schisminex ==
Temperaments not discussed here include:
* ''[[Tyr]]'', {3025/3024, 102487/102400} → [[Lehmerismic temperaments #Tyr]]
 
=== 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.


Commas: 1771561/1769472, 32805/32768
Subgroup: 2.3.5.7.11


POTE generators: ⟨400.0000, 950.8701, 3368.5689]
[[Comma list]]: 32805/32768, 1771561/1769472


Map:  
[[Mapping]]: [{{val| 3 0 45 0 8 }}, {{val| 0 2 -16 0 1 }}, {{val| 0 0 0 1 0 }}]


Wedgie:  
[[POTE generator]]s: ~1331/768 = 950.8701, ~7/4 = 968.5689


EDOs: 24p, 135p, 159, 183, 207, 342, 525, 684, 867
{{Optimal ET sequence|legend=1| 24, 48c, 111cd, 135, 159, 183, 342, 1209, 1551e, 1893e, 2235ce }}


Badness:
[[Badness]]: 5.155 × 10<sup>-3</sup>


== Nexiquart ==
=== 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.
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
Subgroup: 2.3.5.7.11
 
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 ==
[[Comma list]]: 19712/19683, 1771561/1769472
{{main| Nexal family }}


Nexal is the full 11-limit Rank-2 temperament that tempers out the nexus comma.
[[Mapping]]: [{{val| 3 0 0 -32 8 }}, {{val| 0 2 0 17 1 }}, {{val| 0 0 1 0 0 }}]


Commas: 1771561/1769472
[[POTE generator]]s: ~1331/768 = 951.1077, ~5/4 = 386.3748


POTE generators:
{{Optimal ET sequence|legend=1| 24, 48d, 87d, 111, 159, 246, 270, 1215, 1485, 1755, 2025, 2295b }}


Map:  
[[Badness]]: 6.275 × 10<sup>-3</sup>


Wedgie:
== Rank-2 temperaments ==
Rank-2 temperaments in the Nexus include [[Ragismic microtemperaments #Hemiennealimmal|hemiennealimmal]], [[Misty family #Hemimist|hemimist]], [[Schismatic family #Hemiterm|hemiterm]], [[Schismatic family #Altinex|altinex]], [[Mirkwai clan #Mirkat|mirkat]], [[Kleismic family #Tritikleismic|tritikleismic]], [[Landscape microtemperaments #Terture|terture]], and [[Landscape microtemperaments #Avicenna|avicenna]].


EDOs:
Considered below is the 2.3.11 subgroup temperament tribilo.


Badness:
=== Tribilo ===
{{Main| Nexus clan }}


== 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]].
{{main| Tribilo family }}


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]].
Subgroup: 2.3.11


Commas: 1771561/1769472
[[Comma list]]: 1771561/1769472


POTE generators:  
[[Sval]] [[mapping]]: [{{val| 3 0 8 }}, {{val| 0 2 1 }}]


Map:  
Sval mapping generators: ~121/96, ~1331/768


Wedgie:  
[[POTE generator]]: ~1331/768 = 950.9518


EDOs:
{{Optimal ET sequence|legend=1| 9, 15, 24, 87, 111, 135, 159, 1407, 1566, 1725e, 1884e, 2043e, 2202e, 2361e, 2520e, 2679e }}


Badness:
Badness:


[[Category:Commatic realms]]
[[Category:The Nexus| ]] <!-- main article -->
[[Category:Nexus]]
[[Category:Nexus]]
{{todo|improve readability|expand}}

Latest revision as of 04:41, 12 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 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.

Because the nexus comma is the difference between (121/96)3 and 2/1, all nexus temperaments divide 2/1 into three equal parts of (approximately) 400 cents.

Rank-4 temperaments

Main article: Nexus family

The parent temperament of this whole collection is a 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

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 or ~12/11 = 150.9518, ~5/4 = 386.2068, ~7/4 = 968.6966

Optimal ET sequence: 9, 15, 24, 33cd, 39d, 48, 57, 63, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566, 2091e, 2361e, 2433e, 2703e, 3045e, 3315ee, 3657ee

Badness: 0.588 × 10-6

Rank-3 temperaments

From the rank-4 parent temperament, there are several rank-3 temperaments that can be derived.

Temperaments not discussed here include:

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: [⟨3 0 45 0 8], ⟨0 2 -16 0 1], ⟨0 0 0 1 0]]

POTE generators: ~1331/768 = 950.8701, ~7/4 = 968.5689

Optimal ET sequence: 24, 48c, 111cd, 135, 159, 183, 342, 1209, 1551e, 1893e, 2235ce

Badness: 5.155 × 10-3

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: [⟨3 0 0 -32 8], ⟨0 2 0 17 1], ⟨0 0 1 0 0]]

POTE generators: ~1331/768 = 951.1077, ~5/4 = 386.3748

Optimal ET sequence: 24, 48d, 87d, 111, 159, 246, 270, 1215, 1485, 1755, 2025, 2295b

Badness: 6.275 × 10-3

Rank-2 temperaments

Rank-2 temperaments in the Nexus include hemiennealimmal, hemimist, hemiterm, altinex, mirkat, tritikleismic, terture, and avicenna.

Considered below is the 2.3.11 subgroup temperament tribilo.

Tribilo

Main article: Nexus clan

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

Sval mapping: [⟨3 0 8], ⟨0 2 1]]

Sval mapping generators: ~121/96, ~1331/768

POTE generator: ~1331/768 = 950.9518

Optimal ET sequence: 9, 15, 24, 87, 111, 135, 159, 1407, 1566, 1725e, 1884e, 2043e, 2202e, 2361e, 2520e, 2679e

Badness:

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