Hewuermera temperaments: Difference between revisions
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* [[Mirkwai clan #Eris|Eris]] | * [[Mirkwai clan #Eris|Eris]] | ||
* [[26th-octave temperaments #Bosonic|Bosonic]] | * [[26th-octave temperaments #Bosonic|Bosonic]] | ||
= Hemidimfi = | |||
The ''hemidimfi'' (130&193, named by [[User:Xenllium|Xenllium]]) 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]]: [{{val|1 -4 14 -1}}, {{val|0 22 -46 15}}] | |||
[[POTE generator]]: ~343/288 = 304.639 | |||
{{Val list|legend=1| 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: [{{val|1 -4 14 -1 6}}, {{val|0 22 -46 15 -10}}] | |||
POTE generator: ~105/88 = 304.641 | |||
Vals: {{Val list| 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: [{{val|1 -4 14 -1 6 7}}, {{val|0 22 -46 15 -10 -13}}] | |||
POTE generator: ~105/88 = 304.639 | |||
Vals: {{Val list| 63, 130, 193, 323e, 453e, 776eef }} | |||
Badness: 0.030433 | |||
[[Category:Temperament]] | [[Category:Temperament]] | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
Revision as of 22:37, 25 May 2021
Hewuermera rank-two temperaments temper out the hewuermera comma (satribiru-agu, named by Xenllium), 589824/588245 = [16 2 -1 -6⟩, 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, named by Xenllium) 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
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: Template:Val list
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: Template:Val list
Badness: 0.030433