52nd-octave temperaments
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
For information on the EDO corresponding to this temperament collection, 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⟩
Subgroup-val 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, ...
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: [⟨52 52 146 119 162 243], ⟨0 1 0 2 1 -1]]
Mapping generators: ~78/77, ~3/2
Optimal tuning (CTE): ~3/2 = 702.261
Optimal ET sequence: 104, 260, 364, 832, 1196, 2028bdefg
Badness (Sintel): 1.501