# 52nd-octave temperaments

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 sequence988, 1456, 2444, ...