32nd-octave temperaments

These are temperaments with period 1/32 of an octave.

32edo is a wasteland as far as LCJI is concerned, but some of its multiples are good at harmonics, and thus can produce temperaments with period of 1/32 of an octave.

Todo: cleanup , expand Complete the data. Work out the data for intermediate subgroups.

Windrose

The temperament is called windrose because there are 32 cardinal directions commonly assigned to a compass rose. It is defined as the 608 & 1600 temperament. The maximal evenness pattern created inside the period is a 12L 7s, if mapped to a keyboard, which has a 2/3 step ratio and thus offers elegant microtempering that plays with the just noticeable difference.

Subgroup: 2.3.5.7

Comma list: [38 9 -8 -12⟩, [15 -28 32 -16⟩

Mapping: [⟨32 44 68 89], ⟨0 16 15 2]]

POTE Generator: 15.7517¢

Germanium

It is named after germanium, the 32nd element, defined as 224 & 1376. It tempers out 3025/3024, 4096/4095, 4375/4374 and 9801/9800 in the 13-limit, although if only these commas are taken, they make a rank-3 1/2-octave temperament called rym.

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 3025/3024, 4096/4095, 4375/4374, 5942475/5940688

Mapping: [⟨32 51 75 89 110 118], ⟨0 -2 -5 6 5 3]]

Mapping generators: ~1352/1323, ~245/143

POTE Generator: 932.263¢ ~245/143 (5.2381¢ reduced)

Vals: 224, 1376, 1600

Dike

Defined as the 2016dijk & 1600 temperament, since the warts on the val spell out the Dutch word for dike, dijk.

37-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37

Comma list: 4200/4199, 5916/5915, 7425/7424, 8991/8990, 33264/33263, 34452/34447, 59653/59644, 253487/253460, 930291/930248, 246938625/246907808

Mapping: [⟨32 59 72 111 113 129 140 141 165 178 182 169], ⟨0 -18 5 -46 -5 -23 -20 -11 -44 -49 -51 -5]]

POTE Generator: 17.2544¢

Vals: 416dijk, 1600, 2016dijk