Didymus rank-3 family: Difference between revisions

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Urania -> Rastmic rank three clan (more fitting there)
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The '''didymus rank-3 family''' are rank-3 temperaments tempering out the didymus comma, [[81/80]]. If nothing else is tempered out we have a [[7-limit]] [[planar temperament]], with an [[11-limit]] comma we get an 11-limit temperament, and so forth.
The '''didymus rank-3 family''' are rank-3 temperaments tempering out the didymus comma, [[81/80]]. If nothing else is tempered out we have a [[7-limit]] [[planar temperament]], with an [[11-limit]] comma we get an 11-limit temperament, and so forth.


Temperaments discussed elsewhere include:
* ''Urania'' (+243/242 or 121/120): [[Rastmic rank three clan#Urania|Rastmic rank three clan]]
== Didymus ==
== Didymus ==
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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{{Optimal ET sequence|legend=1| 7d, 12, 17c, 19, 24, 31e, 36 }}
{{Optimal ET sequence|legend=1| 7d, 12, 17c, 19, 24, 31e, 36 }}


== Urania  ==
[[Subgroup]]: 2.3.5.7.11
[[Comma list]]: 81/80, 121/120
{{Mapping|legend=1| 1 1 0 0 2 | 0 2 8 0 5 | 0 0 0 1 0 }}
[[Mapping to lattice]]: [{{val| 0 2 8 0 5 }}, {{val| 0 0 0 -1 0 }}]
Lattice basis:
: 11/9 length = 0.2536, 8/7 length = 2.807
: Angle (11/9, 8/7) = 90 degrees
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/9 = 348.0938, ~7/4 = 963.6042
{{Optimal ET sequence|legend=1| 7, 14c, 17c, 24, 31, 100de, 131bde, 162bde }}
[[Badness]]: 0.842 × 10<sup>-3</sup>
[[Complexity spectrum]]: 11/9, 4/3, 12/11, 11/10, 10/9, 9/8, 11/8, 6/5, 5/4, 8/7, 7/6, 9/7, 14/11, 7/5
Scales: [[urania24]]


== Terpsichore  ==
== Terpsichore  ==