Hewuermera temperaments: Difference between revisions
m Removing from Category:Temperament using Cat-a-lot |
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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[[POTE generator]]: ~343/288 = 304.639 | [[POTE generator]]: ~343/288 = 304.639 | ||
{{ | {{Optimal ET sequence|legend=1| 63, 130, 323, 453, 776 }} | ||
[[Badness]]: 0.083491 | [[Badness]]: 0.083491 | ||
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POTE generator: ~105/88 = 304.641 | POTE generator: ~105/88 = 304.641 | ||
{{Optimal ET sequence|legend=1| 63, 130, 193, 323e }} | |||
Badness: 0.052236 | Badness: 0.052236 | ||
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POTE generator: ~105/88 = 304.639 | POTE generator: ~105/88 = 304.639 | ||
{{Optimal ET sequence|legend=1| 63, 130, 193, 323e, 453e, 776eef }} | |||
Badness: 0.030433 | Badness: 0.030433 | ||
Revision as of 18:23, 7 May 2023
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 ET sequence: 63, 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
Optimal ET sequence: 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
Optimal ET sequence: 63, 130, 193, 323e, 453e, 776eef
Badness: 0.030433