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| == Chlorine == | | == Chlorine == |
| The name of chlorine temperament comes from chlorine, the 17th element, and has no relation to the [[chlorisma]].
| | : ''For extensions, see [[Ragismic microtemperaments #Chlorine]].'' |
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| Chlorine temperament has a period of 1/17 octave. It tempers out the [[septendecima]], {{monzo| -52 -17 34 }}, by which 17 chromatic semitones (25/24) exceed an octave. This temperament can be described as 289 & 323 temperament, which tempers out {{monzo| -49 4 22 -3 }} as well as the ragisma. Not only the semitwelfth, but also the ~5/4 can be used as a generator. | | Chlorine has a period of 1/17 octave. It tempers out {{monzo| -52 -17 34 }}, the [[septendecima]], by which 17 classical chromatic semitones ((25/24)<sup>17</sup>) exceed an octave. |
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| | The name of this temperament comes from chlorine, the 17th element, and has no relation to the [[chlorisma]]. |
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| [[Subgroup]]: 2.3.5 | | [[Subgroup]]: 2.3.5 |
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| {{Mapping|legend=1| 17 0 26 | 0 2 1 }} | | {{Mapping|legend=1| 17 0 26 | 0 2 1 }} |
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| : mapping generators: ~25/24, ~{{monzo| 26 9 -17 }} | | : mapping generators: ~25/24, ~{{monzo| 26 9 -17 }} |
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| [[Optimal tuning]]s: | | [[Optimal tuning]]s: |
| * [[CTE]]: ~25/24 = 70.588{{c}} (1\17), ~{{monzo| 26 9 -17 }} = 950.982{{c}} | | * [[WE]]: ~25/24 = 70.5887{{c}}, ~{{monzo| 26 9 -17 }} = 950.9807{{c}} |
| * [[CWE]]: ~25/24 = 70.588{{c}} (1\17), ~{{monzo| 26 9 -17 }} = 950.978{{c}} | | : [[error map]]: {{val| +0.008 +0.006 -0.027 }} |
| | * [[CWE]]: ~25/24 = 70.5882{{c}}, ~{{monzo| 26 9 -17 }} = 950.9776{{c}} |
| | : error map: {{val| 0.000 -0.000 -0.042 }} |
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| {{Optimal ET sequence|legend=1| 34, 153, 187, 221, 255, 289, 323, 612, 3349, 3961, 4573, 5185, 5797 }} | | {{Optimal ET sequence|legend=1| 34, 153, 187, 221, 255, 289, 323, 612, 3349, 3961, 4573, 5185, 5797 }} |
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| [[Badness]] (Sintel): 1.81 | | [[Badness]] (Sintel): 1.81 |
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| === 7-limit ===
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 4375/4374, {{monzo| -49 4 22 -3 }}
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| {{Mapping|legend=1| 17 0 26 -87 | 0 2 1 10 }}
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| [[Optimal tuning]]s:
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| * [[CTE]]: ~25/24 = 70.588{{c}} (1\17), ~{{monzo| 24 -5 -9 2 }} = 950.998{{c}}
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| * [[CWE]]: ~25/24 = 70.588{{c}} (1\17), ~{{monzo| 24 -5 -9 2 }} = 950.999{{c}}
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| {{Optimal ET sequence|legend=1| 289, 323, 612, 935, 1547 }}
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| [[Badness]] (Sintel): 1.05
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 4375/4374, 41503/41472, 1879453125/1879048192
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| Mapping: {{mapping| 17 0 26 -87 207 | 0 2 1 10 -11 }}
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| Optimal tunings:
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| * CTE: ~25/24 = 70.588{{c}} (1\17), ~693/400 = 950.978{{c}}
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| * CWE: ~25/24 = 70.588{{c}} (1\17), ~693/400 = 950.975{{c}}
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| {{Optimal ET sequence|legend=0| 289, 323, 612 }}
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| Badness (Sintel): 2.11
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| == Leaves ==
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| Defined as the {{nowrap|323 & 2023}} temperament. 2 generators reach [[17/13]], 7 generators reach [[5/4]], 10 generators produce [[13/11]].
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 1729951171875/1727094849536, {{monzo|10 39 -14 -14}}
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| [[Mapping]]: [{{val|17 10 31 9}}, {{val|0 14 7 32}}]
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| : mapping generators: ~25/24, ~6125/5832
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| [[Optimal tuning]]s:
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| * [[CTE]]: ~25/24 = 70.588{{c}} (1\17), ~6125/5832 = 85.427{{c}}
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| * [[CWE]]: ~25/24 = 70.588{{c}} (1\17), ~6125/5832 = 85.426{{c}}
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| {{Optimal ET sequence|legend=1| 323, 1700d, 2023, 2346}}
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| [[Badness]] (Sintel): 32.032
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 160083/160000, 198359290368/198165034375, 1729951171875/1727094849536
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| Mapping: [{{val|17 10 31 9 106}}, {{val|0 14 7 32 -39}}]
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| Optimal tunings:
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| * CTE: ~25/24 = 70.588{{c}} (1\17), ~6125/5832 = 85.421{{c}}
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| * CWE: ~25/24 = 70.588{{c}} (1\17), ~6125/5832 = 85.420{{c}}
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| {{Optimal ET sequence|legend=0| 323, 1700d, 2023, 2346e}}
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| Badness (Sintel): 20.456
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 160083/160000, 928125/927472, 1990656/1990625, 4831530/4826809
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| Mapping: [{{val|17 10 31 9 106 98}}, {{val|0 14 7 32 -39 -29}}]
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| Optimal tunings:
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| * CTE: ~25/24 = 70.588{{c}} (1\17), ~1024/975 = 85.421{{c}}
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| * CWE: ~25/24 = 70.588{{c}} (1\17), ~1024/975 = 85.420{{c}}
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| {{Optimal ET sequence|legend=0| 323, 1700d, 2023, 2346e}}
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| Badness (Sintel): 10.096
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| === 17-limit ===
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 39325/39304, 57375/57344, 71874/71825, 111537/111475, 140800/140777
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| Mapping: [{{val|17 10 31 9 106 98 107}}, {{val|0 14 7 32 -39 -29 -31}}]
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| Optimal tunings:
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| * CTE: ~25/24 = 70.588{{c}} (1\17), ~765/728 = 85.421{{c}}
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| * CWE: ~25/24 = 70.588{{c}} (1\17), ~765/728 = 85.421{{c}}
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| {{Optimal ET sequence|legend=0| 323, 1700d, 2023, 2346e}}
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| Badness (Sintel): 6.678
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| {{Navbox fractional-octave}} | | {{Navbox fractional-octave}} |
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| [[Category:17edo]] | | [[Category:17edo]] |