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| * [[Orwell]] (+225/224) → [[Semicomma family #Orwell|Semicomma family]] | | * [[Orwell]] (+225/224) → [[Semicomma family #Orwell|Semicomma family]] |
| * ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]] | | * ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]] |
| | * ''[[Quartonic]]'' (+4000/3969) → [[Quartonic family]] |
| * ''[[Buzzard]]'' (+5120/5103) → [[Vulture family #Buzzard|Vulture family]] | | * ''[[Buzzard]]'' (+5120/5103) → [[Vulture family #Buzzard|Vulture family]] |
| * ''[[Trisensory]]'' (+78732/78125) → [[Sensipent family #Trisensory|Sensipent family]] | | * ''[[Trisensory]]'' (+78732/78125) → [[Sensipent family #Trisensory|Sensipent family]] |
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| Badness: 0.023683 | | Badness: 0.023683 |
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| == Quartonic ==
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| Quartonic tempers out the quartonic comma, {{monzo| 3 -18 11 }} = 390625000/387420489 in the 5-limit. This temperament can be described as 26 & 27 temperament, which tempers out the orwellisma and the octagar comma, 4000/3969. The name "quartonic" means quarter-tone, which is the generator of this temperament (representing ~[[36/35]] and ~[[40/39]]). Alternative extension [[Turkish maqam music temperaments|yarman]] (80 & 159) slices the quartonic generator in three.
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| [[Subgroup]]: 2.3.5
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| [[Comma list]]: 390625000/387420489
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| {{Mapping|legend=1| 1 2 3 | 0 -11 -18 }}
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| : Mapping generators: ~2, ~250/243
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| [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~250/243 = 45.233
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| {{Optimal ET sequence|legend=1| 26, 27, 53, 239, 292, 345, 398, 451 }}
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| [[Badness]]: 0.117250
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| === 7-limit ===
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 1728/1715, 4000/3969
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| {{Mapping|legend=1| 1 2 3 3 | 0 -11 -18 -5 }}
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| {{Multival|legend=1| 11 18 5 3 -23 -39 }}
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| [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~36/35 = 45.139
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| {{Optimal ET sequence|legend=1| 26, 27, 53, 80, 133d, 186d, 319d }}
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| [[Badness]]: 0.042632
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 176/175, 540/539, 2200/2187
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| Mapping: {{mapping| 1 2 3 3 5 | 0 -11 -18 -5 -41 }}
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| Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.041
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| {{Optimal ET sequence|legend=1| 26e, 27e, 53, 80, 213d, 293bcd }}
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| Badness: 0.034031
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 169/168, 176/175, 325/324, 540/539
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| Mapping: {{mapping| 1 2 3 3 5 4 | 0 -11 -18 -5 -41 -8 }}
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| Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.080
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| {{Optimal ET sequence|legend=1| 26e, 27e, 53, 80, 133d, 213d}}
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| Badness: 0.023875
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| === Quarto ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 100/99, 245/242, 864/847
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| Mapping: {{mapping| 1 2 3 3 4 | 0 -11 -18 -5 -14 }}
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| Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.132
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| {{Optimal ET sequence|legend=1| 26, 27e, 53e, 80e }}
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| Badness: 0.041786
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 78/77, 100/99, 144/143, 245/242
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| Mapping: {{mapping| 1 2 3 3 4 4 | 0 -11 -18 -5 -14 -8 }}
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| Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.205
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| {{Optimal ET sequence|legend=1| 26, 27e, 53e }}
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| Badness: 0.027692
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| === Quartz ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 99/98, 385/384, 4000/3969
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| Mapping: {{mapping| 1 2 3 3 3 | 0 -11 -18 -5 12 }}
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| Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.385
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| {{Optimal ET sequence|legend=1| 26, 53 }}
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| Badness: 0.053285
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 99/98, 169/168, 275/273, 385/384
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| Mapping: {{mapping| 1 2 3 3 3 4 | 0 -11 -18 -5 12 -8 }}
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| Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.387
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| {{Optimal ET sequence|legend=1| 26, 53, 132e, 185cdef, 238cdef}}
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| Badness: 0.028818
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| === Biquartonic ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 1728/1715, 2420/2401, 2560/2541
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| Mapping: {{mapping| 2 4 6 6 7 | 0 -11 -18 -5 -1 }}
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| Optimal tuning (POTE): ~99/70 = 1\2, ~36/35 = 45.129
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| {{Optimal ET sequence|legend=1| 26, 54c, 80, 186de, 266dde }}
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| Badness: 0.060737
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 169/168, 325/324, 364/363, 640/637
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| Mapping: {{mapping| 2 4 6 6 7 8 | 0 -11 -18 -5 -1 -8 }}
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| Optimal tuning (POTE): ~55/39 = 1\2, ~36/35 = 45.153
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| {{Optimal ET sequence|legend=1| 26, 54c, 80, 106, 186de }}
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| Badness: 0.039891
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| === Yarm ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 1331/1323, 1728/1715, 4000/3969
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| Mapping: {{mapping| 1 2 3 3 4 | 0 -33 -54 -15 -43 }}
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| Optimal tuning (POTE): ~2 = 1\1, ~100/99 = 15.046
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| {{Optimal ET sequence|legend=1| 79, 80, 239dd, 319dd }}
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| Badness: 0.099950
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 169/168, 325/324, 640/637, 1331/1323
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| Mapping: {{mapping| 1 2 3 3 4 4 | 0 -33 -54 -15 -43 -24 }}
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| Optimal tuning (POTE): ~2 = 1\1, ~100/99 = 15.060
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| {{Optimal ET sequence|legend=1| 79, 80, 159d, 239dd }}
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| Badness: 0.061645
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| ==== 17-limit ====
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 169/168, 325/324, 561/560, 640/637, 850/847
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| Mapping: {{mapping| 1 2 3 3 4 4 4 | 0 -33 -54 -15 -43 -24 7 }}
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| Optimal tuning (POTE): ~2 = 1\1, ~100/99 = 15.066
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| {{Optimal ET sequence|legend=1| 79, 80, 159d, 239dd }}
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| Badness: 0.046718
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| == Sentinel == | | == Sentinel == |