52nd-octave temperaments: Difference between revisions

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See [[52edo]].

== 52-31/29-commatic ==

This temperament establishes the mapping of [[31/29]] to 5\52.

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[[Support]]ing [[ET]]s: {{EDOs|52, 260, 416, 624, 676, 988, 1092, 1352, 1768}},...

== French deck ==

A period-52 temperament described as the 988 & 2444 temperament for the 2.5.11.13.19.29.31 subgroup, and tempers out the comma 2.29.31 {{monzo|-5 -52 52}}, which means 5 periods are equal to 31/29. Called so because there's 52 playing cards in the traditional deck. 1789edo does not support it as 1789 is a prime number, and therefore is not divisible by 52.

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{{Optimal ET sequence|legend=1|988, 1456, 2444}}, ...

== Tellurium ==

Tellurium preserves [[26edo]]'s accurate mappings of [[8/7]] and [[13/12]]; it brings in mappings of [[11/9]] and [[51/49]] from 52edo.

Subgroup: 2.3.7.11.13.17

[[Comma list]]: 8624/8619, 22528/22491, 34969/34944, 41503/41472

[[Mapping]]: [{{val| 52 52 146 119 162 243 }}, {{val| 0 1 0 2 1 -1 }}]

Mapping generators: ~78/77, ~3/2

Optimal tuning ([[CTE]]): ~3/2 = 702.261

{{Optimal ET sequence|legend=1| 104, 260, 364, 832, 1196, 2028bdefg }}

[[Badness]] (Dirichlet): 1.501

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 See [[52edo]].
 == 52-31/29-commatic ==
 This temperament establishes the mapping of [[31/29]] to 5\52.
@@ Line 16: / Line 17: @@
 [[Support]]ing [[ET]]s: {{EDOs|52, 260, 416, 624, 676, 988, 1092, 1352, 1768}},...
 == French deck ==
 A period-52 temperament described as the 988 & 2444 temperament for the 2.5.11.13.19.29.31 subgroup, and tempers out the comma 2.29.31 {{monzo|-5 -52 52}}, which means 5 periods are equal to 31/29. Called so because there's 52 playing cards in the traditional deck. 1789edo does not support it as 1789 is a prime number, and therefore is not divisible by 52.
@@ Line 30: / Line 32: @@
 {{Optimal ET sequence|legend=1|988, 1456, 2444}}, ...
+== Tellurium ==
+Tellurium preserves [[26edo]]'s accurate mappings of [[8/7]] and [[13/12]]; it brings in mappings of [[11/9]] and [[51/49]] from 52edo.
+Subgroup: 2.3.7.11.13.17
+[[Comma list]]: 8624/8619, 22528/22491, 34969/34944, 41503/41472
+[[Mapping]]: [{{val| 52 52 146 119 162 243 }}, {{val| 0 1 0 2 1 -1 }}]
+Mapping generators: ~78/77, ~3/2
+Optimal tuning ([[CTE]]): ~3/2 = 702.261
+{{Optimal ET sequence|legend=1| 104, 260, 364, 832, 1196, 2028bdefg }}
+[[Badness]] (Dirichlet): 1.501
 {{Navbox fractional-octave}}