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| Line 3: |
Line 3: |
| Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, 2430/2401 gives quasisuper, and 4375/4374 gives modus. | | Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, 2430/2401 gives quasisuper, and 4375/4374 gives modus. |
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| Discussed under their respective 5-limit families are [[Father family #Mother|mother]], [[Meantone family #Dominant|dominant]], [[Augmented family #Augene|augene]], [[Porcupine family #Porcupine|porcupine]], [[Diaschismic family #Pajara|pajara]], [[Kleismic family #Catalan|catalan]], [[Tetracot family #Modus|modus]], [[Passion family #Septimal passion|passion]], and [[Immunity family #Immunized|immunized]]. The rest are considered below. | | Discussed under their respective 5-limit families are: |
| | * ''[[Father]]'' → [[Father family #Mother]] |
| | * ''[[Dominant]]'' → [[Meantone family #Dominant]] |
| | * ''[[Augene]]'' → [[Augmented family #Augene]] |
| | * [[Porcupine]] → [[Porcupine family #Septimal porcupine]] |
| | * [[Pajara]] → [[Diaschismic family #Pajara]] |
| | * ''[[Blacksmith]]'' → [[Limma family #Blacksmith]] |
| | * ''[[Catalan]]'' → [[Kleismic family #Catalan]] |
| | * ''[[Modus]]'' → [[Tetracot family #Modus]] |
| | * ''[[Passion]]'' → [[Passion family #Septimal passion]] |
| | * ''[[Immunized]]'' → [[Immunity family #Immunized]] |
| | |
| | The rest are considered below. |
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| == Archy == | | == Archy == |
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Line 335: |
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| Badness: 0.037482 | | Badness: 0.037482 |
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| == Blacksmith ==
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| [[File:blacksmith10.jpg|alt=blacksmith10.jpg|thumb|Lattice of blacksmith]]
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| === 5-limit (blackwood) ===
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| Subgroup: 2.3.5
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| [[Comma]]: 256/243
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| [[Mapping]]: [{{val| 5 8 0 }}, {{val| 0 0 1 }}]
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| Mapping generators: ~9/8, ~5
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| [[POTE generator]]: ~5/4 = 399.594
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| {{Val list|legend=1| 5, 10, 15 }}
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| [[Badness]]: 0.063760
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|
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| === 7-limit ===
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| Subgroup: 2.3.5.7
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| [[Comma list]]: 28/27, 49/48
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| [[Mapping]]: [{{val| 5 8 0 14 }}, {{val| 0 0 1 0 }}]
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| Mapping generators: ~7/6, ~5
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| {{Multival|legend=1| 0 5 0 8 0 -14 }}
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| [[POTE generator]]: ~5/4 = 392.767
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| {{Val list|legend=1| 5, 10, 15, 40b, 55b }}
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| [[Badness]]: 0.025640
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|
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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|
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| Comma list: 28/27, 49/48, 55/54
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| Mapping: [{{val| 5 8 0 14 29 }}, {{val| 0 0 1 0 -1 }}]
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| POTE generator: ~5/4 = 394.948
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| Vals: {{Val list| 5, 10, 15, 40be, 55be, 70bde, 85bcde}}
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| Badness: 0.024641
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|
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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|
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| Comma list: 28/27, 40/39, 49/48, 55/54
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| Mapping: [{{val| 5 8 0 14 29 7 }}, {{val| 0 0 1 0 -1 1 }}]
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| POTE generator: ~5/4 = 391.037
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| Vals: {{Val list| 5, 10, 15, 25e, 40bef}}
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| Badness: 0.020498
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|
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| === Farrier ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 28/27, 49/48, 77/75
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| Mapping: [{{val| 5 8 0 14 -6 }}, {{val| 0 0 1 0 2 }}]
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| POTE generator: ~5/4 = 398.070
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| Vals: {{Val list| 5e, 10e, 15 }}
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| Badness: 0.029200
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|
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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|
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| Comma list: 28/27, 40/39, 49/48, 66/65
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| Mapping: [{{val| 5 8 0 14 -6 7 }}, {{val| 0 0 1 0 2 1 }}]
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| POTE generator: ~5/4 = 396.812
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| Vals: {{Val list| 5e, 10e, 15 }}
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| Badness: 0.022325
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|
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| === Ferrum ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 28/27, 35/33, 49/48
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| Mapping: [{{val| 5 8 0 14 6 }}, {{val| 0 0 1 0 1 }}]
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| POTE generator: ~5/4 = 374.763
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| Vals: {{Val list| 5e, 10 }}
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| Badness: 0.030883
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| == Beatles == | | == Beatles == |