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| Line 200: |
Line 200: |
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| Badness (Smith): 0.017846 | | Badness (Smith): 0.017846 |
|
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| ===== Meantoid =====
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| Dubbed ''meantoid'' here, this extension maps 17/16~19/18 to the augmented unison (C–C♯) and 19/16 to the augmented second (C–D♯). For any tuning flatter than 12edo, the sizes of 17/16 (augmented unison) and 18/17 (minor second) are inverted, so genuine septendecimal and undevicesimal harmony cannot be expected.
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|
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| Subgroup: 2.3.5.7.11.13.17
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|
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| Comma list: 51/50, 66/65, 81/80, 85/84, 99/98
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|
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| Mapping: {{mapping| 1 0 -4 -13 -25 -20 -7 | 0 1 4 10 18 15 7 }}
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|
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| Optimal tunings:
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| * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.036{{c}}
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| * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.448{{c}}
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|
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| {{Optimal ET sequence|legend=0| 12f, 19eg, 31g }}
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|
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| Badness (Smith): 0.019433
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|
| |
| ====== 19-limit ======
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| Subgroup: 2.3.5.7.11.13.17.19
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|
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| Comma list: 51/50, 57/56, 66/65, 81/80, 85/84, 99/98
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|
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| Mapping: {{mapping| 1 0 -4 -13 -25 -20 -7 -10 | 0 1 4 10 18 15 7 9 }}
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|
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| Optimal tunings:
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| * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.216{{c}}
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| * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.394{{c}}
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|
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| {{Optimal ET sequence|legend=0| 12f, 19egh, 31gh }}
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|
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| Badness (Smith): 0.017437
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|
| |
|
| ===== Huygens ===== | | ===== Huygens ===== |
| Line 370: |
Line 338: |
|
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|
| Badness (Smith): 0.025315 | | Badness (Smith): 0.025315 |
|
| |
| ===== Meridetoid =====
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| Subgroup: 2.3.5.7.11.13.17
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|
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| Comma list: 51/50, 78/77, 81/80, 85/84, 99/98
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|
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| Mapping: {{mapping| 1 0 -4 -13 -25 -39 -7 | 0 1 4 10 18 27 7 }}
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|
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| Optimal tunings:
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| * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.610{{c}}
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| * POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.376{{c}}
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|
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| {{Optimal ET sequence|legend=0| 12f, 31fg, 43g }}
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|
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| Badness (Smith): 0.027518
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|
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| ====== 19-limit ======
| |
| Subgroup: 2.3.5.7.11.13.17.19
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|
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| Comma list: 51/50, 57/56, 78/77, 81/80, 85/84, 99/98
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|
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| Mapping: {{mapping| 1 0 -4 -13 -25 -39 -7 -10 | 0 1 4 10 18 27 7 9 }}
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|
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| Optimal tunings:
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| * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.701{{c}}
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| * POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.316{{c}}
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|
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| {{Optimal ET sequence|legend=0| 12f, 19effgh, 31fgh, 43gh }}
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|
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| Badness (Smith): 0.023613
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|
| |
|
| ===== Sauveuric ===== | | ===== Sauveuric ===== |
| Line 678: |
Line 616: |
| Badness (Smith): 0.026836 | | Badness (Smith): 0.026836 |
|
| |
|
| ====== 19-limit ======
| | ===== 19-limit ===== |
| Subgroup: 2.3.5.7.11.13.17.19 | | Subgroup: 2.3.5.7.11.13.17.19 |
|
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|
| Line 692: |
Line 630: |
|
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|
| Badness (Smith): 0.023540 | | Badness (Smith): 0.023540 |
|
| |
| ===== Meanploid =====
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| Subgroup: 2.3.5.7.11.13.17
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|
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| Comma list: 51/50, 65/64, 78/77, 81/80, 85/84
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|
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| Mapping: {{mapping| 1 0 -4 -13 24 10 -7 | 0 1 4 10 -13 -4 7 }}
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|
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| Optimal tunings:
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| * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.661{{c}}
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| * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.415{{c}}
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|
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| {{Optimal ET sequence|legend=0| 12e, 19g, 31fg }}
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|
| |
| Badness (Smith): 0.026094
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|
| |
| ====== 19-limit ======
| |
| Subgroup: 2.3.5.7.11.13.17.19
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|
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| Comma list: 51/50, 57/56, 65/64, 76/75, 78/77, 81/80
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|
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| Mapping: {{mapping| 1 0 -4 -13 24 10 -7 -10 | 0 1 4 10 -13 -4 7 9 }}
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|
| |
| Optimal tunings:
| |
| * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.016{{c}}
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| * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.583{{c}}
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|
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| {{Optimal ET sequence|legend=0| 12e, 19gh, 31fgh }}
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|
| |
| Badness (Smith): 0.023104
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|
| |
|
| === Meanenneadecal === | | === Meanenneadecal === |
| Line 774: |
Line 682: |
| Badness (Smith): 0.022980 | | Badness (Smith): 0.022980 |
|
| |
|
| ====== 19-limit ======
| | ===== 19-limit ===== |
| Subgroup: 2.3.5.7.11.13.17.19 | | Subgroup: 2.3.5.7.11.13.17.19 |
|
| |
|
| Line 788: |
Line 696: |
|
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|
| Badness (Smith): 0.020293 | | Badness (Smith): 0.020293 |
|
| |
| ===== Meanenneadecoid =====
| |
| Subgroup: 2.3.5.7.11.13.17
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|
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| Comma list: 34/33, 45/44, 51/50, 56/55, 78/77
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|
| |
| Mapping: {{mapping| 1 0 -4 -13 -6 -20 -7 | 0 1 4 10 6 15 7 }}
| |
|
| |
| Optimal tunings:
| |
| * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.450{{c}}
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| * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.025{{c}}
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|
| |
| {{Optimal ET sequence|legend=0| 7dfg, 12f, 19g }}
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|
| |
| Badness (Smith): 0.020171
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|
| |
| ====== 19-limit ======
| |
| Subgroup: 2.3.5.7.11.13.17.19
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|
| |
| Comma list: 34/33, 45/44, 51/50, 56/55, 57/55, 78/77
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|
| |
| Mapping: {{mapping| 1 0 -4 -13 -6 -20 -7 -10 | 0 1 4 10 6 15 7 9 }}
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|
| |
| Optimal tunings:
| |
| * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.793{{c}}
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| * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.121{{c}}
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|
| |
| {{Optimal ET sequence|legend=0| 7dfgh, 12f, 19gh }}
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|
| |
| Badness (Smith): 0.018045
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|
| |
|
| ==== Vincenzo ==== | | ==== Vincenzo ==== |
| Line 849: |
Line 727: |
| Badness (Smith): 0.025535 | | Badness (Smith): 0.025535 |
|
| |
|
| ====== 19-limit ======
| | ===== 19-limit ===== |
| Subgroup: 2.3.5.7.11.13.17.19 | | Subgroup: 2.3.5.7.11.13.17.19 |
|
| |
|
| Line 863: |
Line 741: |
|
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|
| Badness (Smith): 0.022302 | | Badness (Smith): 0.022302 |
|
| |
| ===== Vincenzoid =====
| |
| Subgroup: 2.3.5.7.11.13.17
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|
| |
| Comma list: 34/33, 45/44, 51/50, 56/55, 65/64
| |
|
| |
| Mapping: {{mapping| 1 0 -4 -13 -6 10 -7 | 0 1 4 10 6 -4 7 }}
| |
|
| |
| Optimal tunings:
| |
| * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.412{{c}}
| |
| * POTE: ~2 = 1200.000{{c}}, ~3/2 = 695.358{{c}}
| |
|
| |
| {{Optimal ET sequence|legend=0| 7dg, 12, 19g }}
| |
|
| |
| Badness (Smith): 0.022099
| |
|
| |
| ====== 19-limit ======
| |
| Subgroup: 2.3.5.7.11.13.17.19
| |
|
| |
| Comma list: 34/33, 45/44, 51/50, 56/55, 57/55, 65/64
| |
|
| |
| Mapping: {{mapping| 1 0 -4 -13 -6 10 -7 -10 | 0 1 4 10 6 -4 7 9 }}
| |
|
| |
| Optimal tunings:
| |
| * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.950{{c}}
| |
| * POTE: ~2 = 1200.000{{c}}, ~3/2 = 695.725{{c}}
| |
|
| |
| {{Optimal ET sequence|legend=0| 7dgh, 12, 19gh }}
| |
|
| |
| Badness (Smith): 0.019904
| |
|
| |
|
| ==== Meanundec ==== | | ==== Meanundec ==== |