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37th-octave temperaments: Difference between revisions

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{{Infobox fractional-octave|37}}
[[37edo]] has an extremely precise mapping for the 11th harmonic, and it is a strong 2.5.7.13 tuning besides that, therefore various 37th-octave temperaments occur naturally between any two numbers whose greatest common divisor is 37.
[[37edo]] has an extremely precise mapping for the 11th harmonic, and it is a strong 2.5.7.13 tuning besides that, therefore various 37th-octave temperaments occur naturally between any two numbers whose greatest common divisor is 37.
== 37-11-commatic (rank-1) ==
{{Main|37-11-comma}}
Subgroup: 2.11
Comma list: {{monzo|128 -37}}
{{mapping|legend=2| 37 28 }}
: mapping generators: ~35184372088832/34522712143931 = 1\37
[[Support]]ing [[ET]]s: 37N, N = 1 to 485


== Rubidium ==
== Rubidium ==
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[[Optimal tuning]] ([[POTE]]): ~3/2 = 703.3903
[[Optimal tuning]] ([[POTE]]): ~3/2 = 703.3903


{{Val list|legend=1| 37, 74, 111 }}
{{Optimal ET sequence|legend=1| 37, 74, 111 }}


[[Badness]]: 0.312105
[[Badness]]: 0.312105
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Optimal tuning (POTE): ~3/2 = 703.0355
Optimal tuning (POTE): ~3/2 = 703.0355


Optimal GPV sequence: {{Val list| 37, 74, 111 }}
{{Optimal ET sequence|legend=1| 37, 74, 111 }}


Badness: 0.101001
Badness: 0.101001
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Optimal tuning (POTE): ~3/2 = 703.0520
Optimal tuning (POTE): ~3/2 = 703.0520


Optimal GPV sequence: {{Val list| 37, 74, 111 }}
{{Optimal ET sequence|legend=1| 37, 74, 111 }}


Badness: 0.048732
Badness: 0.048732
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[[Optimal tuning]] ([[CTE]]): ~24000/16807 = 612.4003
[[Optimal tuning]] ([[CTE]]): ~24000/16807 = 612.4003


{{Val list|legend=1| 37, 222b, 259b, 296, 629 }}
{{Optimal ET sequence|legend=1| 37, 222b, 259b, 296, 629 }}


[[Badness]]: 0.784746
[[Badness]]: 0.784746
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Optimal tuning (CTE): ~768/359 = 612.4003
Optimal tuning (CTE): ~768/359 = 612.4003


Optimal GPV sequence: {{Val list| 37, 259b, 296, 629 }}
{{Optimal ET sequence|legend=1| 37, 259b, 296, 629 }}


Badness: 0.167327
Badness: 0.167327
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Optimal tuning (CTE): ~462/325 = 612.4206
Optimal tuning (CTE): ~462/325 = 612.4206


Optimal GPV sequence: {{Val list| 37, 259b, 296, 629f }}
{{Optimal ET sequence|legend=1| 37, 259b, 296, 629f }}


Badness: 0.076183
Badness: 0.076183
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Optimal tuning (CTE): ~121/85 = 612.4187
Optimal tuning (CTE): ~121/85 = 612.4187


Optimal GPV sequence: {{Val list| 37, 259b, 296, 629f }}
{{Optimal ET sequence|legend=1| 37, 259b, 296, 629f }}


Badness: 0.052475
Badness: 0.052475
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Optimal tuning (CTE): ~11979/10240 = 271.712
Optimal tuning (CTE): ~11979/10240 = 271.712


Optimal GPV sequence: {{EDOs|296, 1369, 1665}}, ...
{{Optimal ET sequence|legend=1|296, 1369, 1665}}, ...


[[Category:37edo]]
{{Navbox fractional-octave}}
[[Category:Rank 2]]
[[Category:Temperament collections]]
Retrieved from "https://en.xen.wiki/w/37th-octave_temperaments"