52nd-octave temperaments
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See 52edo.
52-31/29-commatic
This temperament establishes the mapping of 31/29 to 5\52.
Subgroup: 2.29.31
Comma list: 2.29.31 [-5 -52 52⟩
Sval mapping: [⟨52 0 5], ⟨0 1 1]]
- sval mapping generators: ~2.29.31 [2 -21 21⟩ = 1\52, ~29
Optimal tuning (CTE): ~29/16 = 1029.613
Supporting ETs: 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 [-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.
Subgroup: 2.5.11.13.19.29.31
Comma list: 6656/6655, 600704/600625, 1308736/1308625, 35934301/35932160, 17179869184/17174157715
Sval mapping: [⟨52 1 197 124 238 475 480], ⟨0 7 -1 4 -1 -13 13]]
- sval mapping generators: ~1460875/1441792, ~1045/832
Optimal tuning (CTE): ~134560000/107132311 = 394.757
Optimal ET sequence: 988, 1456, 2444, ...