Hewuermera temperaments

From Xenharmonic Wiki
Jump to navigation Jump to search

Hewuermera rank-two temperaments temper out the hewuermera comma, 589824/588245 = [16 2 -1 -6 (satribiru-agu), the amount by which a stack of six 8/7s exceed 20/9 (minor whole tone 10/9 plus an octave).

Temperaments dicussed elsewhere include:

Hemidimfi

The hemidimfi (130&193) has a generator of 304.6 cents (about a half of 64/45 tritone) and tempers out the hewuermera (589824/588245) and the sesquiquartisma (2460375/2458624).

Subgroup: 2.3.5.7

Comma list: 589824/588245, 2460375/2458624

Mapping: [1 -4 14 -1], 0 22 -46 15]]

POTE generator: ~343/288 = 304.639

Optimal GPV sequence63, 130, 323, 453, 776

Badness: 0.083491

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 12005/11979, 16384/16335

Mapping: [1 -4 14 -1 6], 0 22 -46 15 -10]]

POTE generator: ~105/88 = 304.641

Vals: 63, 130, 193, 323e

Badness: 0.052236

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 364/363, 540/539, 676/675, 4096/4095

Mapping: [1 -4 14 -1 6 7], 0 22 -46 15 -10 -13]]

POTE generator: ~105/88 = 304.639

Vals: 63, 130, 193, 323e, 453e, 776eef

Badness: 0.030433