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| === Overview to extensions === | | === Overview to extensions === |
| Lemba finds the perfect fifth three steps away by tempering out [[1029/1024]]. Astrology, five steps away by tempering out [[3125/3072]]. Decimal, two steps away by tempering out [[25/24]] and [[49/48]]. Pajara slices the ~7/4 into two. Injera slices the ~5/1 into four. Hedgehog slices the ~7/1 into five. | | Lemba finds the perfect fifth three steps away by tempering out [[1029/1024]]. Astrology, five steps away by tempering out [[3125/3072]]. Decimal, two steps away by tempering out [[25/24]] and [[49/48]]. Diminished splits the ~7/5 period into a further two. Pajara slices the ~7/4 into two. Injera slices the ~5/1 into four. Hedgehog slices the ~7/1 into five. |
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| Lemba, astrology, doublewide, and diminished are discussed below; others in the clan are | | Lemba, astrology, and doublewide are discussed below; others in the clan are |
| | * [[Diminished]] → [[Dimipent family #Diminished|Dimipent family]] |
| * [[Pajara]] → [[Diaschismic family #Pajara|Diaschismic family]] | | * [[Pajara]] → [[Diaschismic family #Pajara|Diaschismic family]] |
| * [[Decimal]] → [[Dicot family #Decimal|Dicot family]] | | * [[Decimal]] → [[Dicot family #Decimal|Dicot family]] |
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| Badness: 0.035284 | | Badness: 0.035284 |
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| == Diminished ==
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| <div style="float: right">[[:de:Verminderte Temperaturen|Deutsch]]</div>
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| {{See also| Dimipent family #Diminished }}
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 36/35, 50/49
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| [[Mapping]]: [{{val| 4 0 3 5 }}, {{val| 0 1 1 1 }}]
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| Mapping generators: ~6/5, ~3
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| [[Optimal tuning]] ([[POTE]]): ~6/5 = 1\4, ~3/2 = 699.523
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| {{Val list|legend=1| 4, 8d, 12 }}
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| [[Badness]]: 0.022401
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| Scales: [[diminished12]]
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 36/35, 50/49, 56/55
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| Mapping: [{{val| 4 0 3 5 14 }}, {{val| 0 1 1 1 0 }}]
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| Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 709.109
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| Optimal GPV sequence: {{Val list| 4, 8d, 12, 32cddee, 44cddeee }}
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| Badness: 0.022132
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| Scales: [[diminished12]]
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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, 40/39, 50/49, 66/65
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| Mapping: [{{val| 4 0 3 5 14 15 }}, {{val| 0 1 1 1 0 0 }}]
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| Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 713.773
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| Optimal GPV sequence: {{Val list| 4, 8d, 12f, 20cdef }}
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| Badness: 0.019509
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| Scales: [[diminished12]]
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| === Demolished ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 36/35, 45/44, 50/49
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| Mapping: [{{val| 4 0 3 5 -5 }}, {{val| 0 1 1 1 3 }}]
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| Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 689.881
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| Optimal GPV sequence: {{Val list| 12, 28, 40de }}
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| Badness: 0.026574
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| === Cohedim ===
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| This temperament has been documented in Graham Breed's temperament finder as ''hemidim'', the same name as [[Dimipent family #Hemidim|11-limit 4e&24 and 13-limit 4ef&24]]. For 11-limit 8bce&12 temperament, ''cohedim'' arguably makes more sense.
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| Subgroup: 2.3.5.7.11
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| Comma list: 36/35, 50/49, 125/121
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| Mapping: [{{val| 4 1 4 6 6 }}, {{val| 0 2 2 2 3 }}]
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| Mapping generators: ~6/5, ~11/7
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| Optimal tuning (POTE): ~6/5 = 1\4, ~12/11 = 101.679
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| Optimal GPV sequence: {{Val list| 8bce, 12 }}
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| Badness: 0.054965
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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, 50/49, 66/65, 125/121
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| Mapping: [{{val| 4 1 4 6 6 7 }}, {{val| 0 2 2 2 3 3 }}]
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| Optimal tuning (POTE): ~6/5 = 1\4, ~12/11 = 102.299
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| Optimal GPV sequence: {{Val list| 8bcef, 12f }}
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| Badness: 0.041707
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| == Doublewide == | | == Doublewide == |