Rastmic clan: Difference between revisions
Update keys; separate neutrominant alone since it's an extension to both suhajira and mohaha |
→Mohaha: move +13-limit migration here |
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Mohaha is the 2.3.5.11 subgroup temperament with a generator of a neutral third, two of which make up a fifth, and which can be taken to represent 11/9. Mohaha can be thought of, intuitively, as "meantone with quartertones"; as is the 3/2 generator subdivided in half, so is the [[~]][[25/24]] chromatic semitone divided into two equal ~[[33/32]] quarter tones (in the 2.3.5.11 subgroup). Within this paradigm, mohaha is the temperament that splits the 3/2 into two equal 11/9's, that splits the 6/5 into two equal 11/10~12/11's, and that maps four 3/2's to 5/1. It has a heptatonic mos with three larger steps and four smaller ones, going [[4L 3s|sLsLsLs]]. Taking septimal meantone mapping of 7 leads to [[#Migration]], flattone mapping of 7 leads to [[#Ptolemy]], and dominant mapping of 7 leads to [[#Neutrominant]]. | Mohaha is the 2.3.5.11 subgroup temperament with a generator of a neutral third, two of which make up a fifth, and which can be taken to represent 11/9. Mohaha can be thought of, intuitively, as "meantone with quartertones"; as is the 3/2 generator subdivided in half, so is the [[~]][[25/24]] chromatic semitone divided into two equal ~[[33/32]] quarter tones (in the 2.3.5.11 subgroup). Within this paradigm, mohaha is the temperament that splits the 3/2 into two equal 11/9's, that splits the 6/5 into two equal 11/10~12/11's, and that maps four 3/2's to 5/1. It has a heptatonic mos with three larger steps and four smaller ones, going [[4L 3s|sLsLsLs]]. Taking septimal meantone mapping of 7 leads to [[#Migration]], flattone mapping of 7 leads to [[#Ptolemy]], and dominant mapping of 7 leads to [[#Neutrominant]]. | ||
=== 2.3.5.11 subgroup === | |||
[[Subgroup]]: 2.3.5.11 | [[Subgroup]]: 2.3.5.11 | ||
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Scales: [[mohaha7]], [[mohaha10]] | Scales: [[mohaha7]], [[mohaha10]] | ||
=== Mohoho === | ==== Mohoho ==== | ||
Subgroup: 2.3.5.11.13 | Subgroup: 2.3.5.11.13 | ||
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Badness: 0.025516 | Badness: 0.025516 | ||
==== 13-limit ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 66/65, 81/80, 121/120, 126/125 | |||
Mapping: {{mapping| 1 1 0 -3 2 4 | 0 2 8 20 5 -1 }} | |||
Optimal tuning: | |||
* CTE: ~2 = 1\1, ~11/9 = 348.5444 | |||
* CTWE: ~2 = 1\1, ~11/9 = 348.5009 | |||
{{Optimal ET sequence|legend=1| 7d, 24d, 31 }} | |||
Badness: 0.028071 | |||
=== Ptolemy === | === Ptolemy === | ||