37th-octave temperaments: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
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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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Badness: 0.052475
Badness: 0.052475


==Dzelic==
==Ludidzelic==
Dzelic ['d͡zɛlɪk] is named after the Slavic letter dzelo, which represents the number 7, as it takes 7 generator grave minor thirds to reach the third harmonic.
''Ludidzelic'' [lʲudi'd͡zɛlɪk] is named after the {{W|Cyrillic numeral}}s representation of the number 37 (Л = ludi = 30, З = dzelo = 7). Also notably, The 3rd harmonic is also is divided into 7 equal parts.


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
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===13-limit===
===13-limit===
14 periods map to [[13/10]], thus equating a stack of three 11/8 with one 13/10 and making dzelic a [[6656/6655|jacobin]] temperament.
14 periods map to [[13/10]] (a property inherited from 37edo), thus equating a stack of three 11/8 with one 13/10 and making ludidzelic a [[6656/6655|jacobin]] temperament.


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
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{{Optimal ET sequence|legend=1|296, 1369, 1665}}, ...
{{Optimal ET sequence|legend=1|296, 1369, 1665}}, ...


[[Category:37edo]]
{{Navbox fractional-octave}}
[[Category:Rank 2]]
[[Category:Temperament collections]]