Nexus clan: Difference between revisions

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m FloraC moved page Tribilo family to Nexus clan: Minimal subgroup is 2.3.11 so "nexus clan" should be fine
 
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The '''tribilo family''' is a family of rank-2 temperaments in the 2.3.11 subgroup that temper 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-2 family currently have yet to be explored. For other families that are defined by the tempering of the nexus comma, see [[the Nexus]]. This family's name comes from the nexus comma being referred to as the "tribilo comma" in [[color notation]].
{{Technical data page}}
The '''nexus clan''', also known as the '''tribilo clan''', is a [[Temperament families and clans|clan]] of [[rank-2 temperament]]s in the 2.3.11 [[subgroup]] that temper 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-2 clan currently have yet to be explored. For other temperaments that are defined by the tempering of the nexus comma, see [[the Nexus]]. The name ''tribilo clan'' comes from the nexus comma being referred to as the "tribilo comma" in [[color notation]].


== Tribilo ==
== Tribilo ==
This is the parent temperament of the tribilo family.
This is the parent temperament of the nexus clan.


Subgroup: 2.3.11
[[Subgroup]]: 2.3.11


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


[[Sval]] [[mapping]]: [{{val| 3 0 8 }}, {{val| 0 2 1 }}]
{{Mapping|legend=2| 3 0 8 | 0 2 1 }}


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


[[POTE generator]]: ~1331/768 = 950.9518 (or ~12/11 = 150.9518)
[[Optimal tuning]] ([[POTE]]): ~121/96 = 1\3, ~1331/768 = 950.9518 (or ~12/11 = 150.9518)


{{Optimal ET sequence|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 }}
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[[Badness]]: 2.44 × 10<sup>-3</sup>
[[Badness]]: 2.44 × 10<sup>-3</sup>


=== Triblet ===
== Triblet ==
Subgroup: 2.3.11.13
[[Subgroup]]: 2.3.11.13


Comma list: 352/351, 1771561/1769472
[[Comma list]]: 352/351, 1771561/1769472


Sval mapping: [{{val| 3 0 8 23 }}, {{val| 0 2 1 -5 }}]
{{Mapping|legend=2| 3 0 8 23 | 0 2 1 -5 }}


POTE generator: ~1331/768 = 951.4814
[[Optimal tuning]] ([[POTE]]): ~121/96 = 1\3, ~1331/768 = 951.4814


{{Optimal ET sequence|legend=1| 9f, 15f, 24, 63, 87, 111, 198, 309f, 507f }}
{{Optimal ET sequence|legend=1| 9f, 15f, 24, 63, 87, 111, 198, 309f, 507f }}


Badness: 2.70 × 10<sup>-3</sup>
[[Badness]]: 2.70 × 10<sup>-3</sup>


=== Trilobite ===
== Trilobite ==
[[Subgroup]]: 2.3.11.13


Subgroup: 2.3.11.13
[[Comma list]]: 85293/85184, 1771561/1769472


Comma list: 85293/85184, 1771561/1769472
{{Mapping|legend=2| 3 0 8 42 | 0 2 1 -13 }}


Sval mapping: [{{val| 3 0 8 42 }}, {{val| 0 2 1 -13 }}]
[[Optimal tuning]] ([[POTE]]): ~121/96 = 1\3, ~1331/768 = 950.7810
 
POTE generator: ~1331/768 = 950.7810


{{Optimal ET sequence|legend=1| 24, 111f, 135f, 159, 183, 390, 573, 963f, 1536bef }}
{{Optimal ET sequence|legend=1| 24, 111f, 135f, 159, 183, 390, 573, 963f, 1536bef }}


Badness: 1.65 × 10<sup>-3</sup>
[[Badness]]: 1.65 × 10<sup>-3</sup>


[[Category:Temperament families]]
[[Category:Temperament clans]]
[[Category:Pages with mostly numerical content]]
[[Category:Nexus clan| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]

Latest revision as of 00:36, 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 clan, also known as the tribilo clan, is a clan of rank-2 temperaments in the 2.3.11 subgroup that temper 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-2 clan currently have yet to be explored. For other temperaments that are defined by the tempering of the nexus comma, see the Nexus. The name tribilo clan comes from the nexus comma being referred to as the "tribilo comma" in color notation.

Tribilo

This is the parent temperament of the nexus clan.

Subgroup: 2.3.11

Comma list: 1771561/1769472

Sval mapping: [⟨3 0 8], ⟨0 2 1]]

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

Optimal tuning (POTE): ~121/96 = 1\3, ~1331/768 = 950.9518 (or ~12/11 = 150.9518)

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

Badness: 2.44 × 10-3

Triblet

Subgroup: 2.3.11.13

Comma list: 352/351, 1771561/1769472

Sval mapping: [⟨3 0 8 23], ⟨0 2 1 -5]]

Optimal tuning (POTE): ~121/96 = 1\3, ~1331/768 = 951.4814

Optimal ET sequence: 9f, 15f, 24, 63, 87, 111, 198, 309f, 507f

Badness: 2.70 × 10-3

Trilobite

Subgroup: 2.3.11.13

Comma list: 85293/85184, 1771561/1769472

Sval mapping: [⟨3 0 8 42], ⟨0 2 1 -13]]

Optimal tuning (POTE): ~121/96 = 1\3, ~1331/768 = 950.7810

Optimal ET sequence: 24, 111f, 135f, 159, 183, 390, 573, 963f, 1536bef

Badness: 1.65 × 10-3

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