Nexus family: Difference between revisions

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:

@@ Line 1: / Line 1: @@
-'''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 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 ==
-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 in which the 5-limit and 7-limit parts are represented by independent generators.
+This is the parent temperament of the nexus family. In this temperament, the 5-limit and 7-limit parts are represented by independent generators.
-Period: ~121/96 = 1\3
+Subgroup: 2.3.5.7.11
-Optimal (POTE) generators: 950.9518, 386.2068, 968.6966
+[[Comma list]]: [[1771561/1769472]]
-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: [{{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
-Wedgie: <<<<6 0 0 3 -16]]]]
+[[POTE generator]]s: ~1331/768 = 950.9518, ~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
-Badness: 0.588×10<sup>-6</sup>
-== Binexus ==
-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 is a rank-3 temperament.
-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.  This is a rank-3 temperament.
-Commas: 1771561/1769472, 117440512/117406179
-POTE generators:
-Map:
-Wedgie:
-EDOs:
-Badness:
-== Nexal ==
-{{main| Nexal family }}
-Nexal is the full 11-limit Rank-2 temperament that tempers out the nexus comma.
-Commas: 1771561/1769472
-POTE generators:
-Map:
-Wedgie:
-EDOs:
+{{Optimal ET sequence|legend=1| 9, 15, 24, 39d, 48, 57, 63, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566 }}
-Badness:
+[[Badness]]: 0.588 × 10<sup>-6</sup>
-== Tribilo ==
+=== 13-limit ===
-{{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]].
+{{todo|review|inline=yes|comment=Add optimal ET sequence & badness}}
-Commas: 1771561/1769472
+Subgroup: 2.3.5.7.11.13
-POTE generators:
+[[Comma list]]: [[1771561/1769472]], [[676/675]]
-Map:
+[[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]⟩
-Wedgie:
+Mapping generators: ⟨1200.000, 1902.167, 2786.583, 3368.823, 4151.084, 4439.834]
-EDOs:
+[[POTE generator]]s: ⟨400.0000, 951.0837, 2786.5829, 3368.8230]
-Badness:
+{{Optimal ET sequence|legend=1| }}
-[[Category:Nexus]]
+[[Badness]]:
-{{todo|improve readability|discuss title|expand}}
+[[Category:Temperament families]]
+[[Category:Pages with mostly numerical content]]
+[[Category:Nexus family| ]] <!-- main article -->
+[[Category:Rank 4]]

Nexus family: Difference between revisions

Latest revision as of 00:25, 24 June 2025

Nexus

13-limit

Navigation menu

Search