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{{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.
'''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.


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.
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.


Temperaments not discussed here include:
== Rank-4 temperaments ==
* ''[[tyr]]'', {3025/3024, 102487/102400} → [[Lehmerismic temperaments #Tyr]]
{{main| Nexus family }}


= Rank-4 temperaments =
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.
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 ==
=== Nexus ===
{{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 for the Nexus is Nexus temperament itself. In this temperament, the 5-limit and 7-limit parts are represented by independent generators.
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Mapping generators: ~121/96, ~1331/768, ~5/1, ~7/1
Mapping generators: ~121/96, ~1331/768, ~5/1, ~7/1
{{Multival|legend=1|rank=4| 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
[[POTE generator]]s: ~1331/768 = 950.9518 or ~12/11 = 150.9518, ~5/4 = 386.2068, ~7/4 = 968.6966


{{Val list|legend=1| 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-3 temperaments that can be derived.
From the rank-4 parent temperament, there are several rank-3 temperaments that can be derived.


== Schisnex ==
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.


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


{{Multival|legend=1|rank=3| 0 6 0 -48 0 -3 -90 0 16 -173 }}
[[POTE generator]]s: ~1331/768 = 950.8701, ~7/4 = 968.5689
 
[[POTE generator]]s: ~1331/768 = 950.8701 or ~12/11 = 150.8701, ~7/4 = 968.5689


{{Val list|legend=1| 24, 48, 111cd, 135, 159, 183, 342 }}
{{Optimal ET sequence|legend=1| 24, 48c, 111cd, 135, 159, 183, 342, 1209, 1551e, 1893e, 2235ce }}


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


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[[Mapping]]: [{{val| 3 0 0 -32 8 }}, {{val| 0 2 0 17 1 }}, {{val| 0 0 1 0 0 }}]
[[Mapping]]: [{{val| 3 0 0 -32 8 }}, {{val| 0 2 0 17 1 }}, {{val| 0 0 1 0 0 }}]


{{Multival|legend=1|rank=3| 6 0 0 -51 -3 0 -64 16 0 -168 }}
[[POTE generator]]s: ~1331/768 = 951.1077, ~5/4 = 386.3748
 
[[POTE generator]]s: ~1331/768 = 951.1077 or ~12/11 = 151.1077, ~5/4 = 386.3748


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


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


= Rank-2 temperaments =
== Rank-2 temperaments ==
Rank-2 temperaments in the Nexus include [[Ragismic microtemperaments #Hemiennealimmal|hemiennealimmal]], [[Misty family #Hemimist|hemimist]], [[Schismatic family #Hemiterm|hemiterm]], [[Mirkwai clan #Mirkat|mirkat]], [[Kleismic family #Tritikleismic|tritikleismic]], [[Landscape microtemperaments #Terture|terture]], and [[Landscape microtemperaments #Avicenna|avicenna]].  
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]].  
 
Considered below are ''altinex'' and the 2.3.11 subgroup temperament tribilo.
 
== Altinex ==
{{See also| Schismatic family }}
 
Subgroup: 2.3.5.7.11
 
[[Comma list]]: 385/384, 14700/14641, 19712/19683
 
[[Mapping]]: [{{val| 3 0 45 -32 8 }}, {{val| 0 2 -16 17 1 }}]
 
Mapping generators: ~121/96, ~121/70
 
[[POTE generator]]s: ~121/70 = 950.9629
 
{{Val list|legend=1| 24, 135, 159 }}


[[Badness]]: 0.1012
Considered below is the 2.3.11 subgroup temperament tribilo.  


== Tribilo ==
=== Tribilo ===
{{Main| Tribilo family }}
{{Main| 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]].
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]].
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[[POTE generator]]: ~1331/768 = 950.9518
[[POTE generator]]: ~1331/768 = 950.9518


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


Badness:
Badness:


[[Category:Regular temperament theory]]
[[Category:Commatic realms]]
[[Category:Commatic realm]]
[[Category:The Nexus| ]] <!-- main article -->
[[Category:The Nexus| ]] <!-- main article -->
[[Category:Nexus]]
[[Category:Nexus]]
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