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17th-octave temperaments: Difference between revisions

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Comma list: 64/63, 99/98, 243/242
Comma list: 64/63, 99/98, 243/242


Mapping: {{mapping| 17 27 0 48 59 | 0 0 1 0 0 }}
{{Mapping|legend=0| 17 27 0 48 59 | 0 0 1 0 0 }}


Optimal tunings:  
Optimal tunings:  
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Comma list: 64/63, 78/77, 99/98, 144/143
Comma list: 64/63, 78/77, 99/98, 144/143


Mapping: {{mapping| 17 27 0 48 59 63 | 0 0 1 0 0 0 }}
{{Mapping|legend=0| 17 27 0 48 59 63 | 0 0 1 0 0 0 }}


Optimal tunings:  
Optimal tunings:  
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== Chlorine ==
== Chlorine ==
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. 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.  
: ''For extensions, see [[Ragismic microtemperaments #Chlorine]].''
 
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.  


The name of this temperament comes from chlorine, the 17th element, and has no relation to the [[chlorisma]].
The name of this temperament comes from chlorine, the 17th element, and has no relation to the [[chlorisma]].
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[[Badness]] (Sintel): 1.81
[[Badness]] (Sintel): 1.81
=== 7-limit ===
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 4375/4374, {{monzo| -49 4 22 -3 }}
{{Mapping|legend=1| 17 0 26 -87 | 0 2 1 10 }}
[[Optimal tuning]]s:
* [[WE]]: ~25/24 = 70.5880{{c}}, ~{{monzo| 24 -5 -9 2 }} = 950.9962{{c}}
: [[error map]]: {{val| -0.004 +0.037 -0.030 -0.019 }}
* [[CWE]]: ~25/24 = 70.5882{{c}}, ~{{monzo| 24 -5 -9 2 }} = 950.9990{{c}}
: error map: {{val| 0.000 +0.043 -0.021 -0.013 }}
{{Optimal ET sequence|legend=1| 289, 323, 612, 935, 1547, 3706, 5253 }}
[[Badness]] (Sintel): 1.05
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 41503/41472, 1879453125/1879048192
Mapping: {{mapping| 17 0 26 -87 207 | 0 2 1 10 -11 }}
Optimal tunings:
* WE: ~25/24 = 70.5905{{c}}, ~693/400 = 951.0054{{c}}
* CWE: ~25/24 = 70.5882{{c}}, ~693/400 = 950.9754{{c}}
{{Optimal ET sequence|legend=0| 289, 323, 612, 3349de, 3961de, …, 5797ddee }}
Badness (Sintel): 2.11


{{Navbox fractional-octave}}
{{Navbox fractional-octave}}


[[Category:17edo]]
[[Category:17edo]]
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