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.

Windrose

The temperament is called windrose because there are 32 cardinal directions commonly assigned to a compass rose. It is defined as a 608 & 1600 temperament. The maximal evenness pattern created inside the generator 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. Higher-dimensional versions of this are lower in badness than low-dimensional ones.

7-limit

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, this is the most just intonation-friendly 32nd-octave temperament. 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.

Subgroup: 2.3.5.7.11.13

Comma list: 3025/3024, 4096/4095, 256000/255789, 5942475/5940688

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

POTE Generator: 5.2381¢

Dike

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

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¢