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Line 54: |
| * [[Godzilla]] → [[Slendro clan #Godzilla|Slendro clan]] | | * [[Godzilla]] → [[Slendro clan #Godzilla|Slendro clan]] |
| * [[Mothra]] → [[Gamelismic clan #Mothra|Gamelismic clan]] | | * [[Mothra]] → [[Gamelismic clan #Mothra|Gamelismic clan]] |
| | * [[Mohaha]] → [[Neutral clan #Neutral|Neutral clan]] |
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| The rest are considered below. | | The rest are considered below. |
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| === Mohaha ===
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| {{See also| No-sevens subgroup temperaments #Mohaha }}
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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]].
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| [[Subgroup]]: 2.3.5.11
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| [[Comma list]]: 81/80, 121/120
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| {{Mapping|legend=2| 1 1 0 2 | 0 2 8 5 }}
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| : sval mapping generators: ~2, ~11/9
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| {{Mapping|legend=3| 1 1 0 0 2 | 0 2 8 0 5 }}
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| : gencom: [2 11/9; 81/80 121/120]
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| [[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~11/9 = 348.8296
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| {{Optimal ET sequence|legend=1| 7, 17c, 24, 31, 69e, 100e, 131bee }}
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| Scales: [[mohaha7]], [[mohaha10]]
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| ==== Mohoho ====
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| Subgroup: 2.3.5.11.13
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| Comma list: 66/65, 81/80, 121/120
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| Sval mapping: {{mapping| 1 1 0 2 4| 0 2 8 5 -1 }}
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| : sval mapping generators: ~2, ~11/9
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| Gencom mapping: {{mapping| 1 1 0 0 2 4 | 0 2 8 0 5 -1 }}
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| : gencom: [2 11/9; 66/65 81/80 121/120]
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| Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 348.8794
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| {{Optimal ET sequence|legend=1| 7, 17c, 24, 31, 55 }}
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| Scales: [[mohaha7]], [[mohaha10]]
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| === Dequarter === | | === Dequarter === |
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Line 935: |
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| Badness: 0.026288 | | Badness: 0.026288 |
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| === Migration ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 81/80, 121/120, 126/125
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| Mapping: {{mapping| 1 1 0 -3 2 | 0 2 8 20 5 }}
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| : mapping generators: ~2, ~11/9
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| Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 348.5324
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| {{Optimal ET sequence|legend=1| 7d, 24d, 31, 100de, 131bdee, 162bdee }}
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| Badness: 0.025516
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| ==== 13-limit ==== | | ==== 13-limit ==== |
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Line 1,119: |
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| Scales: [[flattone12]] | | Scales: [[flattone12]] |
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| === Ptolemy ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 81/80, 121/120, 525/512
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| Mapping: {{mapping| 1 1 0 8 2 | 0 2 8 -18 5 }}
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| : mapping generators: ~2, ~11/9
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| Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 346.922
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| {{Optimal ET sequence|legend=1| 7, 31dd, 38d, 45e, 83bcddee }}
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| Badness: 0.058785
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| ==== 13-limit ==== | | ==== 13-limit ==== |
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Line 1,350: |
| Badness: 0.021098 | | Badness: 0.021098 |
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| === Neutrominant ===
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| <span style="display: block; text-align: right;">[[:de:maqamisch|Deutsch]]</span>
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| {{Main| Neutrominant }}
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| The neutrominant temperament (formerly ''maqamic'' temperament) has a hemififth generator (~11/9) and tempers out 36/35 and 121/120. It makes the most sense if viewed as an adaptive temperament, whereby 7/4 and 9/5 simply share an equivalence class in the resulting scales, but don't need to share a particular tempered "middle-of-the-road" intonation.
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| Subgroup: 2.3.5.7.11
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| Comma list: 36/35, 64/63, 121/120
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| Mapping: {{mapping| 1 1 0 4 2 | 0 2 8 -4 5 }}
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| : mapping generators: ~2, ~11/9
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| Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.934
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| {{Optimal ET sequence|legend=1| 7, 17c, 24d, 41cd }}
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| Badness: 0.040240
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 36/35, 64/63, 66/65, 121/120
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| Mapping: {{mapping| 1 1 0 4 2 4 | 0 2 8 -4 5 -1 }}
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| Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.816
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| {{Optimal ET sequence|legend=1| 7, 17c, 24d, 41cd }}
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| Badness: 0.027214
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| == Sharptone == | | == Sharptone == |