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| These are rank-3 temperaments tempering out [[3025/3024]]. Temperaments discussed elsewhere are:
| | {{Technical data page}} |
| * ''[[Oxpecker]]'', {121/120, 126/125} → [[Starling family #Oxpecker|Starling family]]
| | This is a collection of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] that [[temper out]] the lehmerisma, [[3025/3024]]. |
| * ''[[Manwe]]'', {176/175, 1331/1323} → [[Valinorsmic clan #Manwe|Valinorsmic clan]]
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| * ''[[Spectacle]]'', {225/224, 243/242} → [[Marvel family #Spectacle|Marvel family]]
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| * ''[[Portent]]'', {385/384, 441/440} → [[Gamelismic family #Portent|Gamelismic family]]
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| * ''[[Indra]]'', {540/539, 1375/1372} → [[Mirkwai family #Indra|Mirkwai family]]
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| * ''[[Tolerant]]'', {896/891, 2200/2187} → [[Pentacircle clan #Tolerant|Pentacircle clan]]
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| * ''[[Freya]]'', {2401/2400, 3025/3024} → [[Breed family #Freya|Breed family]]
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| * ''[[Triglav]]'', {3025/3024, 3136/3125} → [[Hemimean family #Triglav|Hemimean family]]
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| * ''[[Thor]]'', {3025/3024, 4375/4374} → [[Ragismic family #Thor|Ragismic family]]
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| * ''[[Kapo]]'', {3025/3024, 5120/5103} → [[Hemifamity family #Kapo|Hemifamity family]]
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| Considered below are tyr, skadi, ganesha, hanuman, lux, and galaxy, but we can begin by looking at the rank-4 temperament.
| | Temperaments discussed elsewhere are: |
| | * ''[[Oxpecker]]'' (+121/120 or 126/125) → [[Biyatismic clan #Oxpecker|Biyatismic clan]] |
| | * ''[[Manwe]]'' (+176/175) → [[Valinorsmic clan #Manwe|Valinorsmic clan]] |
| | * ''[[Spectacle]]'' (+225/224 or 243/242) → [[Rastmic rank-3 clan #Spectacle|Rastmic rank-3 clan]] |
| | * ''[[Portent]]'' (+385/384 or 441/440) → [[Gamelismic family #Portent|Gamelismic family]] |
| | * ''[[Indra]]'' (+540/539) → [[Swetismic temperaments #Indra|Swetismic temperaments]] |
| | * ''[[Tolerant]]'' (+896/891) → [[Pentacircle clan #Tolerant|Pentacircle clan]] |
| | * ''[[Freya]]'' (+2401/2400) → [[Breed family #Freya|Breed family]] |
| | * ''[[Triglav]]'' (+3136/3125) → [[Hemimean family #Triglav|Hemimean family]] |
| | * ''[[Thor]]'' (+4375/4374) → [[Ragismic family #Thor|Ragismic family]] |
| | * ''[[Kapo]]'' (+5120/5103) → [[Aberschismic family #Kapo|Aberschismic family]] |
| | * ''[[Ganesha]]'' (+5632/5625) → [[Vishdelismic clan #Ganesha|Vishdelismic clan]] |
| | * ''[[Tyr]]'' (+102487/102400) → [[Landscape family #Tyr|Landscape family]] |
| | * ''[[Lux]]'' (+131072/130977) → [[Olympic clan #Lux|Olympic clan]] |
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| == Lehmerismic ==
| | Considered below are skadi, hanuman, and galaxy, in the order of increasing [[badness]]. For the rank-4 temperament, see [[Rank-4 temperament #Lehmerismic (3025/3024)]]. |
| Subgroup: 2.3.5.7.11
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| [[Comma list]]: [[3025/3024]]
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| [[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 1 2 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 2 1 }}]
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| Mapping generators: ~2, ~3, ~5, ~55/36
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| {{Val list|legend=1| 7d, 8d, 10, 15, 23de, 24d, 26, 31, 41, 65d, 72, 118, 152, 224, 270, 342, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }}
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| == Tyr ==
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| {{See also| Landscape family }}
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| Subgroup: 2.3.5.7.11
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| [[Comma list]]: 3025/3024, 102487/102400 | |
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| [[Mapping]]: [{{val| 3 0 0 4 8 }}, {{val| 0 2 0 -4 1 }}, {{val| 0 0 1 2 0 }}]
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| Mapping generators: ~63/50, ~400/231, ~5
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| {{Val list|legend=1| 15, 24d, 33cd, 39d, 54c, 57, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566, 2091e, 2361e, 2433e, 2703e, 3045e, 3315ee, 3657ee }}
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| [[Badness]]: 0.259 × 10<sup>-3</sup> | |
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| === Borneo ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 676/675, 1001/1000, 3025/3024
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| Mapping: [{{val| 3 0 0 4 8 -3 }}, {{val| 0 2 0 -4 1 3 }}, {{val| 0 0 1 2 0 1 }}]
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| Vals: {{Val list| 15, 24d, 33cdff, 39df, 57f, 72, 111, 159, 183, 198, 270 }}
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| Badness: 0.549 × 10<sup>-3</sup>
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| Complexity spectrum: 12/11, 15/13, 11/8, 4/3, 11/10, 18/13, 6/5, 5/4, 13/12, 15/11, 11/9, 13/10, 10/9, 7/5, 16/15, 13/11, 9/8, 16/13, 8/7, 14/11, 15/14, 7/6, 14/13, 9/7
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| == Skadi == | | == Skadi == |
| Subgroup: 2.3.5.7.11 | | [[Subgroup]]: 2.3.5.7.11 |
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| [[Comma list]]: 3025/3024, 703125/702464 | | [[Comma list]]: 3025/3024, 703125/702464 |
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| [[Mapping]]: [{{val| 1 0 5 8 1 }}, {{val| 0 1 1 3 2 }}, {{val| 0 0 -6 -14 -1 }}]
| | {{Mapping|legend=1| 1 0 -1 -6 0 | 0 1 1 3 2 | 0 0 6 14 1 }} |
| | | : mapping generators: ~2, ~3, ~11/9 |
| Mapping generators: ~2, ~3, ~18/11
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| {{Val list|legend=1| 31, 90e, 114de, 121, 152, 311, 342, 836, 1178, 2014, 3192ce, 5206ce }}
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| [[Badness]]: 0.349 × 10<sup>-3</sup>
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| == Ganesha ==
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| === 7-limit (quasiorwellismic) ===
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| Subgroup: 2.3.5.7
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| [[Comma list]]: 29360128/29296875
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| [[Mapping]]: [{{val| 1 0 0 -22 }}, {{val| 0 1 0 1 }}, {{val| 0 0 1 10 }}]
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| Mapping generators: ~2, ~3, ~5
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| [[POTE generator]]s: ~3/2 = 702.0901, ~5/4 = 386.6931 | | [[Optimal tuning]]s: |
| | * [[WE]]: ~2 = 1200.0399{{c}}, ~3/2 = 701.9113{{c}}, ~11/9 = 347.3783{{c}} |
| | : [[error map]]: {{val| +0.040 -0.004 -0.132 +0.085 -0.037 }} |
| | * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9144{{c}}, ~11/9 = 347.3654{{c}} |
| | : error map: {{val| 0.000 -0.041 -0.207 +0.033 -0.124 }} |
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| {{Val list|legend=1| 31, 87, 118, 152, 239, 270, 571, 723, 841, 993, 1263, 1564c, 1834c, 2104c }} | | {{Optimal ET sequence|legend=1| 24d, 31, 90e, 114de, 121, 152, 311, 342, 836, 1178, 2014, 3192ce, 5206ce }} |
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| [[Badness]]: 1.13 × 10<sup>-3</sup> | | [[Badness]] (Sintel): 0.419 |
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| [[Comma list]]: 3025/3024, 5632/5625
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| [[Mapping]]: [{{val| 1 0 0 -22 -9 }}, {{val| 0 1 0 1 2 }}, {{val| 0 0 1 10 4 }}]
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| [[POTE generator]]s: ~3/2 = 702.2251, ~5/4 = 386.6908
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| {{Val list|legend=1| 31, 65d, 87, 118, 152, 239, 270, 962, 1232, 1502 }}
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| [[Badness]]: 0.390 × 10<sup>-3</sup>
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| == Hanuman == | | == Hanuman == |
| Subgroup: 2.3.5.7.11 | | [[Subgroup]]: 2.3.5.7.11 |
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| [[Comma list]]: 3025/3024, 4000/3993 | | [[Comma list]]: 3025/3024, 4000/3993 |
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| [[Mapping]]: [{{val| 1 2 0 -8 1 }}, {{val| 0 -3 0 11 1 }}, {{val| 0 0 1 4 1 }}]
| | {{Mapping|legend=1| 1 2 0 -8 1 | 0 -3 0 11 1 | 0 0 1 4 1 }} |
| | : mapping generators: ~2, ~11/10, ~5 |
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| Mapping generators: ~2, ~11/10, ~5
| | [[Optimal tuning]]s: |
| | * [[WE]]: ~2 = 1199.9539{{c}}, ~11/10 = 165.9317{{c}}, ~5/4 = 385.9220{{c}} |
| | : [[error map]]: {{val| -0.046 +0.158 -0.484 +0.111 +0.398 }} |
| | * [[CWE]]: ~2 = 1200.0000{{c}}, ~11/10 = 165.9501{{c}}, ~5/4 = 385.8882{{c}} |
| | : error map: {{val| 0.000 +0.195 -0.426 +0.178 +0.520 }} |
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| {{Val list|legend=1| 15, 42bc, 49bcde, 50d, 57, 65d, 72, 152, 224, 311, 463, 535, 998 }} | | {{Optimal ET sequence|legend=1| 15, 42bc, 49bcde, 50d, 57, 65d, 72, 152, 224, 311, 463, 535, 998 }} |
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| [[Badness]]: 0.500 × 10<sup>-3</sup> | | [[Badness]] (Sintel): 0.600 |
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| === 13-limit === | | === 13-limit === |
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| Comma list: 625/624, 1575/1573, 2080/2079 | | Comma list: 625/624, 1575/1573, 2080/2079 |
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| Mapping: [{{val| 1 2 0 -8 1 -6 }}, {{val| 0 -3 0 11 1 3 }}, {{val| 0 0 1 4 1 4 }}] | | Mapping: {{mapping| 1 2 0 -8 1 -6 | 0 -3 0 11 1 3 | 0 0 1 4 1 4 }} |
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| Vals: {{Val list| 15, 50d, 57f, 65d, 72, 87, 137, 152f, 224, 311, 535, 918c }}
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| Badness: 0.653 × 10<sup>-3</sup>
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| == Lux ==
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| === 7-limit ===
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| Subgroup: 2.3.5.7
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| [[Comma list]]: 26843545600/26795786661
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| [[Mapping]]: [{{val| 1 0 0 6 }}, {{val| 0 1 4 -1 }}, {{val| 0 0 -5 -2 }}]
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| Mapping generators: ~2, ~3, ~40960/35721
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| {{Multival|legend=1|rank=3| 5 2 13 30 }}
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| [[POTE generator]]s: ~3/2 = 702.1152, ~40960/35721 = 235.5941
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| {{Val list|legend=1| 41, 87, 128, 142, 178, 183, 224, 270, 494, 764, 1034, 1798, 6428bcdd, 8226bbcddd }}
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| [[Badness]]: 1.71 × 10<sup>-3</sup>
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| [[Comma list]]: 3025/3024, 131072/130977
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| [[Mapping]]: [{{val| 1 0 0 6 5 }}, {{val| 0 1 4 -1 -3 }}, {{val| 0 0 -5 -2 4 }}]
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| {{Multival|legend=1|rank=3| 5 2 -4 13 -1 10 30 25 34 71 }}
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| [[POTE generator]]s: ~3/2 = 702.1117, ~55/48 = 235.5784
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| {{Val list|legend=1| 41, 87, 137, 178, 183, 224, 270, 494, 764, 1839, 2109, 2603, 3367d }}
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| [[Badness]]: 0.508 × 10<sup>-3</sup>
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 2080/2079, 3025/3024, 4096/4095
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| Mapping: [{{val| 1 0 0 6 5 6 }}, {{val| 0 1 4 -1 -3 -5 }}, {{val| 0 0 -5 -2 4 7 }}]
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| POTE generators: ~3/2 = 702.0674, ~55/48 = 235.5870
| | Optimal tunings: |
| | * WE: ~2 = 1200.0188{{c}}, ~11/10 = 166.0060{{c}}, ~5/4 = 385.6865{{c}} |
| | * CWE: ~2 = 1200.0000{{c}}, ~11/10 = 166.0007{{c}}, ~5/4 = 385.6918{{c}} |
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| Vals: {{Val list| 41, 46, 87, 137, 178, 183, 224, 270, 494, 764, 1075, 1569, 1839, 2333, 3408d }}
| | {{Optimal ET sequence|legend=0| 15, 50d, 57f, 65d, 72, 87, 137, 152f, 224, 311, 535, 918c }} |
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| Badness: 0.360 × 10<sup>-3</sup> | | Badness (Sintel): 0.610 |
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| == Galaxy == | | == Galaxy == |
| Subgroup: 2.3.5.7.11 | | [[Subgroup]]: 2.3.5.7.11 |
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| [[Comma list]]: 3025/3024, 20614528/20588575 | | [[Comma list]]: 3025/3024, 20614528/20588575 |
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| [[Mapping]]: [{{val| 1 0 5 -4 -5 }}, {{val| 0 1 3 -3 -3 }}, {{val| 0 0 -9 14 16 }}]
| | {{Mapping|legend=1| 1 0 -4 10 11 | 0 1 3 -3 -3 | 0 0 9 -14 -16 }} |
| | : mapping generators: ~2, ~3, ~1936/1715 |
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| Mapping generators: ~2, ~3, ~6125/3456
| | [[Optimal tuning]]s: |
| | * [[WE]]: ~2 = 1199.9912{{c}}, ~3/2 = 701.9805{{c}}, ~1936/1715 = 208.9296{{c}} |
| | : [[error map]]: {{val| -0.009 +0.017 +0.003 +0.156 -0.204 }} |
| | * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9856{{c}}, ~1936/1715 = 208.9333{{c}} |
| | : error map: {{val| 0.000 +0.023 +0.020 +0.174 -0.184 }} |
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| {{Multival|legend=1| 9 -14 -16 -14 -20 5 34 35 6 21 }} | | {{Optimal ET sequence|legend=1| 46, 103, 121, 149, 167, 224, 270, 494, 764, 1631, 1901, 2395, 2665 }} |
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| [[POTE generator]]s: ~3/2 = 701.9856, ~6125/3456 = 991.0688 | | [[Badness]] (Sintel): 1.01 |
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| {{Val list|legend=1| 46, 103, 121, 149, 167, 224, 270, 494, 764, 1631, 1901, 2395, 2665 }}
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| [[Badness]]: 0.841 × 10<sup>-3</sup>
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| === 13-limit === | | === 13-limit === |
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| Comma list: 1716/1715, 3025/3024, 4225/4224 | | Comma list: 1716/1715, 3025/3024, 4225/4224 |
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| Mapping: [{{val| 1 0 5 -4 -5 -4 }}, {{val| 0 1 3 -3 -3 -4 }}, {{val| 0 0 -9 14 16 17 }}] | | Mapping: {{mapping| 1 0 -4 10 11 13 | 0 1 3 -3 -3 -4 | 0 0 9 -14 -16 -17 }} |
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| POTE generators: ~3/2 = 701.9368, ~484/273 = 991.0597
| | Optimal tunings: |
| | * WE: ~2 = 1200.0131{{c}}, ~3/2 = 701.9445{{c}}, ~44/39 = 208.9426{{c}} |
| | * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.9368{{c}}, ~44/39 = 208.9373{{c}} |
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| Vals: {{val list| 46, 75e, 103, 121, 149, 224, 270, 494, 764, 1137, 1258, 1361, 1631, 2125 }}
| | {{Optimal ET sequence|legend=0| 46, 75e, 103, 121, 149, 224, 270, 494, 764, 1137, 1258, 1361, 1631, 2125 }} |
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| Badness: 0.463 × 10<sup>-3</sup> | | Badness (Sintel): 0.433 |
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| === 17-limit === | | === 17-limit === |
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| Comma list: 715/714, 936/935, 1225/1224, 4225/4224 | | Comma list: 715/714, 936/935, 1225/1224, 4225/4224 |
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| Mapping: [{{val| 1 0 5 -4 -5 -4 -1 }}, {{val| 0 1 3 -3 -3 -4 -2 }}, {{val| 0 0 -9 14 16 17 10 }}] | | Mapping: {{mapping| 1 0 -4 10 11 13 9 | 0 1 3 -3 -3 -4 -2 | 0 0 9 -14 -16 -17 -10 }} |
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| POTE generators: ~3/2 = 702.1144, ~85/48 = 991.1035
| | Optimal tunings: |
| | * WE: ~2 = 1199.9094{{c}}, ~3/2 = 702.0614{{c}}, ~44/39 = 208.8807{{c}} |
| | * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0462{{c}}, ~44/39 = 208.9167{{c}} |
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| Vals: {{val list| 46, 75e, 103, 121, 149, 167, 224, 270, 494g }}
| | {{Optimal ET sequence|legend=0| 46, 75e, 103, 121, 149, 167, 224, 270, 494g }} |
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| Badness: 0.933 × 10<sup>-3</sup> | | Badness (Sintel): 0.888 |
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| | [[Category:Lehmerismic temperaments| ]] <!-- main article --> |
| [[Category:Temperament collections]] | | [[Category:Temperament collections]] |
| [[Category:Lehmerismic temperaments| ]] <!-- main article --> | | [[Category:Catalogs of rank-3 temperaments]] |
| [[Category:Rank 3]]
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