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Cloudy clan: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings (1/)
Switch to Sintel's badness, WE & CWE tunings (2/2)
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: mapping generators: ~21/20, ~3
: mapping generators: ~21/20, ~3


[[Optimal tuning]] ([[POTE]]): ~21/20 = 80.000{{c}}, ~3/2 = 700.223{{c}} (~126/125 = 19.777{{c}})
[[Optimal tuning]]s:
* [[WE]]: ~21/20 = 80.1141{{c}}, ~3/2 = 700.2213{{c}} (~126/125 = 19.8053{{c}})
: [[error map]]: {{val| +1.711 +0.977 -2.127 -4.035 }}
* [[CWE]]: ~21/20 = 80.0000{{c}}, ~3/2 = 701.2357{{c}} (~126/125 = 19.7643{{c}})
: error map: {{val| 0.000 -0.719 -5.078 -8.826 }}


{{Optimal ET sequence|legend=1| 15, 45, 60 }}
{{Optimal ET sequence|legend=1| 15, 45, 60 }}


[[Badness]] (Smith): 0.114833
[[Badness]] (Sintel): 2.91


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 15 0 11 42 52 | 0 1 1 0 0 }}
Mapping: {{mapping| 15 0 11 42 52 | 0 1 1 0 0 }}


Optimal tuning (POTE): ~21/20 = 80.000{{c}}, ~3/2 = 702.733{{c}} (~56/55 = 17.267{{c}})
Optimal tunings:
* WE: ~21/20 = 80.0213{{c}}, ~3/2 = 702.9194{{c}} (~56/55 = 17.2721{{c}})
* CWE: ~21/20 = 80.0000{{c}}, ~3/2 = 702.8751{{c}} (~56/55 = 17.1249{{c}})


{{Optimal ET sequence|legend=0| 15, 45, 60, 75de, 135de }}
{{Optimal ET sequence|legend=0| 15, 45, 60, 75de, 135de }}


Badness (Smith): 0.077420
Badness (Sintel): 2.56


==== 13-limit ====
==== 13-limit ====
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Mapping: {{mapping| 15 0 11 42 52 8 | 0 1 1 0 0 2 }}
Mapping: {{mapping| 15 0 11 42 52 8 | 0 1 1 0 0 2 }}


Optimal tuning (POTE): ~21/20 = 80.000{{c}}, ~3/2 = 701.715{{c}} (~91/90 = 18.285{{c}})
Optimal tunings:
* WE: ~21/20 = 80.0207{{c}}, ~3/2 = 701.8966{{c}} (~91/90 = 18.2900{{c}})
* CWE: ~21/20 = 80.0000{{c}}, ~3/2 = 701.8545{{c}} (~91/90 = 18.1455{{c}})


{{Optimal ET sequence|legend=0| 15, 45f, 60, 135de, 195cddee }}
{{Optimal ET sequence|legend=0| 15, 45f, 60, 135de, 195cddee }}


Badness (Smith): 0.051740
Badness (Sintel): 2.14


=== Quindecal ===
=== Quindecal ===
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Mapping: {{mapping| 15 0 11 42 28 | 0 1 1 0 1 }}
Mapping: {{mapping| 15 0 11 42 28 | 0 1 1 0 1 }}


Optimal tuning (POTE): ~21/20 = 80.000{{c}}, ~3/2 = 700.318{{c}} (~126/125 = 19.682{{c}})
Optimal tunings:
* WE: ~21/20 = 80.1322{{c}}, ~3/2 = 701.4751{{c}} (~126/125 = 19.7148{{c}})
* CWE: ~21/20 = 80.0000{{c}}, ~3/2 = 701.5453{{c}} (~126/125 = 18.4547{{c}})


{{Optimal ET sequence|legend=0| 15, 45e, 60e }}
{{Optimal ET sequence|legend=0| 15, 45e, 60e }}


Badness (Smith): 0.044405
Badness (Sintel): 1.47


==== 13-limit ====
==== 13-limit ====
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Mapping: {{mapping| 15 0 11 42 28 103 | 0 1 1 0 1 -2 }}
Mapping: {{mapping| 15 0 11 42 28 103 | 0 1 1 0 1 -2 }}


Optimal tuning (POTE): ~21/20 = 80.000{{c}}, ~3/2 = 701.647{{c}} (~65/64 = 18.353{{c}})
Optimal tunings:
* WE: ~21/20 = 80.1015{{c}}, ~3/2 = 702.5374{{c}} (~126/125 = 18.3763{{c}})
* CWE: ~21/20 = 80.0000{{c}}, ~3/2 = 701.8504{{c}} (~126/125 = 18.1496{{c}})


{{Optimal ET sequence|legend=0| 15f, 45e, 60e }}
{{Optimal ET sequence|legend=0| 15f, 60e, 135deef }}


Badness (Smith): 0.055361
Badness (Sintel): 2.29


== Quinkee ==
== Quinkee ==
Quinkee has a period of 1/5 octave and tempers out the [[keega]] (1029/1000), from which it derives its name. It may be described as the {{nowrap| 15 & 40 }} temperament. It was named by [[Xenllium]] in 2021.  
Quinkee has a period of 1/5 octave and tempers out the [[keega]] (1029/1000), from which it derives its name. It may be described as the {{nowrap| 15 & 55 }} temperament. It was named by [[Xenllium]] in 2021.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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[[Comma list]]: 1029/1000, 6144/6125
[[Comma list]]: 1029/1000, 6144/6125


{{Mapping|legend=1| 5 9 12 14 | 0 -3 -1 0 }}
{{Mapping|legend=1| 5 0 9 14 | 0 3 1 0 }}
: mapping generators: ~8/7, ~10/7


[[Optimal tuning]] ([[POTE]]): ~8/7 = 240.000{{c}}, ~5/4 = 393.439{{c}} (~25/24 = 86.561{{c}})
[[Optimal tuning]]s:
* [[WE]]: ~8/7 = 240.0512{{c}}, ~10/7 = 633.5744{{c}} (~25/24 = 86.5794{{c}})
: [[error map]]: {{val| +0.256 -1.232 +7.722 -8.108 }}
* [[CWE]]: ~8/7 = 240.0000{{c}}, ~10/7 = 633.4834{{c}} (~25/24 = 86.5160{{c}})
: error map: {{val| 0.000 -1.505 +7.170 -8.826 }}


{{Optimal ET sequence|legend=1| 15, 40, 55, 125cd, 180ccdd }}
{{Optimal ET sequence|legend=1| 15, 40, 55 }}


[[Badness]] (Smith): 0.184222
[[Badness]] (Sintel): 4.66


=== 11-limit ===
=== 11-limit ===
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Comma list: 121/120, 176/175, 1029/1000
Comma list: 121/120, 176/175, 1029/1000


Mapping: {{mapping| 5 9 12 14 18 | 0 -3 -1 0 -2 }}
Mapping: {{mapping| 5 0 9 14 12 | 0 3 1 0 2 }}


Optimal tuning (POTE): ~8/7 = 240.000{{c}}, ~5/4 = 393.438{{c}} (~22/21 = 86.562{{c}})
Optimal tunings:
* WE: ~8/7 = 240.0916{{c}}, ~10/7 = 633.6802{{c}} (~22/21 = 86.5947{{c}})
* CWE: ~8/7 = 240.0000{{c}}, ~10/7 = 633.5204{{c}} (~22/21 = 86.4796{{c}})


{{Optimal ET sequence|legend=0| 15, 40, 55, 125cd, 180ccdde }}
{{Optimal ET sequence|legend=0| 15, 40, 55 }}


Badness (Smith): 0.065192
Badness (Sintel): 2.16


=== 13-limit ===
=== 13-limit ===
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Comma list: 66/65, 105/104, 121/120, 637/625
Comma list: 66/65, 105/104, 121/120, 637/625


Mapping: {{mapping| 5 9 12 14 18 20 | 0 -3 -1 0 -2 -4 }}
Mapping: {{mapping| 5 9 12 14 18 20 | 0 3 1 0 2 4 }}


Optimal tuning (POTE): ~8/7 = 240.000{{c}}, ~5/4 = 392.798{{c}} (~22/21 = 87.202{{c}})
Optimal tunings:
* WE: ~8/7 = 240.0392{{c}}, ~10/7 = 632.9013{{c}} (~22/21 = 87.2162{{c}})
* CWE: ~8/7 = 240.0000{{c}}, ~10/7 = 632.8351{{c}} (~22/21 = 87.1649{{c}})


{{Optimal ET sequence|legend=0| 15, 40, 55 }}
{{Optimal ET sequence|legend=0| 15, 40, 55 }}


Badness (Smith): 0.048440
Badness (Sintel): 2.00


[[Category:Temperament clans]]
[[Category:Temperament clans]]
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