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35th-octave temperaments: Difference between revisions

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→Bromine: expand to 11-limit and 19-limit via 2730edo's consistency, also can't keep the "normal" matrix due to limitations of the sintel's finder so 152 and -7 for 19-limit in the mapping
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Bromine is named after the 35th chemical element.
Bromine is named after the 35th chemical element.


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Comma list: {{monzo|47 -7 -7 -7}}, {{monzo|6 -37 13 8}}
[[Comma list]]: {{monzo|47 -7 -7 -7}}, {{monzo|6 -37 13 8}}


Mapping: [{{val|35 0 -418 653}}, {{val|0 1 9 -10}}]
[[Mapping]]: [{{val|35 0 -418 653}}, {{val|0 1 9 -10}}]


Mapping generators: ~38263752/37515625 = 1\35, ~3
Mapping generators: ~38263752/37515625 = 1\35, ~3


Optimal tuning (CTE): ~3/2 = 701.973
[[Optimal tuning]] ([[CTE]]): ~3/2 = 701.973


{{Optimal ET sequence|legend=1|665, 2065, 2730, 3395, 4060, 7455}}
[[Support]]ing [[ET]]s: {{EDOs|665, 2065, 2730, 3395, 4060, 7455}}


=== 2.3.5.7.13 subgroup ===
=== 11-limit ===


Subgroup: 2.3.5.7.13
While 665edo still tunes bromine in the 11-limit, it is not recommended due to error on the 11th harmonic. [[2730edo]] or [[3395edo]] are better tunings. Alternately, considering bromine as a no-11s temperament keeps it within the realm of [[very high accuracy temperaments]], having [[TE error]] of less than 0.005 cents per octave.


Comma list: 1990656/1990625, 1686616064/1686498489, 44302336000/44295075909
Subgroup: 2.3.5.7.11


Sval mapping: [{{val|35 0 -418 653 1239}}, {{val|0 1 9 -10 -20}}]
Comma list: 151263/151250, 115091701760/115063885233, 45137758519296/45135986328125


Sval mapping generators: ~38263752/37515625 = 1\35, ~3
Mapping: [{{val|35 0 -418 653 2451}}, {{val|0 1 9 -10 -42}}]


Optimal tuning (CTE): ~3/2 = 701.973
Mapping generators: ~1203125/1179648 = 1\35, ~3
 
Optimal tuning (CTE): ~3/2 = 701.975
 
=== 13-limit ===
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 123201/123200, 151263/151250, 1990656/1990625, 8683257856/8681088735
 
Mapping: [{{val|35 0 -418 653 2451 1239}}, {{val|0 1 9 -10 -42 -20}}]
 
Mapping generators: ~1485/1456 = 1\35, ~3
 
Optimal tuning (CTE): ~3/2 = 701.975


Supporting ETs: 665, 3395, ...
Supporting ETs: 665, 3395, ...


=== 2.3.5.7.13.17 subgroup ===
=== 17-limit ===


The period is mapped to ~51/50.
The period is mapped to ~51/50.


Subgroup: 2.3.5.7.13.17
Subgroup: 2.3.5.7.11.13.17


Comma list: 426496/426465, 1990656/1990625, 6251648/6251175, 51200000/51195483
Comma list: 12376/12375, 123201/123200, 194481/194480, 1713660/1713481, 24635975/24634368


Sval mapping: [{{val|35 0 -418 653 1239 -800}}, {{val|0 1 9 -10 -20 17}}]
Mapping: [{{val|35 0 -418 653 2451 1239 -800}}, {{val|0 1 9 -10 -42 -20 17}}]


Sval mapping generators: ~51/50 = 1\35, ~3
Mapping generators: ~51/50 = 1\35, ~3


Optimal tuning (CTE): ~3/2 = 701.973
Optimal tuning (CTE): ~3/2 = 701.97...


Supporting ETs: {{EDOs|665, 2730, 3395, 6125, 7455, 10185}}...
Supporting ETs: {{EDOs|665, 2730, 3395, 6125, 7455, 10185}}...
=== 19-limit ===
[[Subgroup]]: 2.3.5.7.11.13.17.19
[[Comma list]]: 12376/12375, 12636/12635, 13377/13376, 14080/14079, 14365/14364, 486400/486387
[[Mapping]]: [{{val|35 0 -418 653 2451 1239 -800 152}}, {{val|0 1 9 -10 -42 -20 17 -7}}]
[[Mapping]] [[generator]]s: ~51/50 = 1\35, ~3
[[Optimal tuning]] ([[CTE]]): ~3/2 = 701.97...
[[Support]]ing [[ET]]s: {{EDOs|665, 2730, 3395, 6125, 6790h, 7455eh}}...


== Tritonopodismic (rank-3) ==
== Tritonopodismic (rank-3) ==
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