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.

Fractional-octave temperaments

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← 51st-octave • 52nd-octave • 53rd-octave →

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

Todo: improve synopsis