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Cloudy clan: Difference between revisions

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Line 34: Line 34:
POTE generator: ~21/20 = 73.264
POTE generator: ~21/20 = 73.264


Vals: {{Val list| 15, 35, 50, 65, 115d }}
Optimal GPV sequence: {{Val list| 15, 35, 50, 65, 115d }}


Badness: 0.045070
Badness: 0.045070


== Decic ==
== Decic ==
{{main| Decic }}
The ''decic'' temperament (10&50) tempers out the [[cloudy comma]], 16807/16384 and the [[225/224|marvel comma]], 225/224 in the 7-limit, as well as the [[15/14ths equal temperament|linus comma]], {{monzo|11 -10 -10 10}}. This temperament is supported by [[10edo|10]], [[50edo|50]], and [[60edo|60]] EDOs, and can be extended naturally to the 11-, 13-, and 17-limit by adding 385/384, 105/104, and 170/169 to the comma list in this order.
The ''decic'' temperament (10&50) tempers out the [[cloudy comma]], 16807/16384 and the [[225/224|marvel comma]], 225/224 in the 7-limit, as well as the [[15/14ths equal temperament|linus comma]], {{monzo|11 -10 -10 10}}. This temperament is supported by [[10edo|10]], [[50edo|50]], and [[60edo|60]] EDOs, and can be extended naturally to the 11-, 13-, and 17-limit by adding 385/384, 105/104, and 170/169 to the comma list in this order.


Line 53: Line 55:
[[POTE generator]]: ~3/2 = 698.696
[[POTE generator]]: ~3/2 = 698.696


[[Tuning ranges]]:
{{Val list|legend=1| 10, 30b, 40, 50, 60, 110d, 170cdd }}
* 7-odd-limit [[diamond monotone]]: ~3/2 = [680.000, 720.000] (34\60 to 6\10)
* 9-odd-limit diamond monotone: ~3/2 = [696.000, 720.000] (29\50 to 6\10)
* 7- and 9-odd-limit [[diamond tradeoff]]: ~3/2 = [693.129, 702.512]
* 7-odd-limit diamond monotone and tradeoff: ~3/2 = [693.129, 702.512]
* 9-odd-limit diamond monotone and tradeoff: ~3/2 = [696.000, 702.512]
 
{{Val list|legend=1| 10, 50, 60, 110d, 170cdd }}


[[Badness]]: 0.089135
[[Badness]]: 0.089135
Line 75: Line 70:
POTE generator: ~3/2 = 696.791
POTE generator: ~3/2 = 696.791


Tuning ranges:
Optimal GPV sequence: {{Val list| 10, 30be, 40, 50 }}
* 11-odd-limit diamond monotone: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
* 11-odd-limit diamond tradeoff: ~3/2 = [689.363, 702.512]
* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [696.000, 700.000]
 
Vals: {{Val list| 10, 50 }}


Badness: 0.063900
Badness: 0.063900
Line 95: Line 85:
POTE generator: ~3/2 = 696.993
POTE generator: ~3/2 = 696.993


Tuning ranges:
Optimal GPV sequence: {{Val list| 10, 30be, 40, 50 }}
* 13- and 15-odd-limit diamond monotone: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
* 13- and 15-odd-limit diamond tradeoff: ~3/2 = [689.363, 702.512]
* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = [696.000, 700.000]
 
Vals: {{Val list| 10, 50 }}


Badness: 0.036880
Badness: 0.036880
Line 115: Line 100:
POTE generator: ~3/2 = 697.085
POTE generator: ~3/2 = 697.085


Tuning ranges:
Optimal GPV sequence: {{Val list| 10, 30beg, 40, 50 }}
* 17-odd-limit diamond monotone: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
* 17-odd-limit diamond tradeoff: ~3/2 = [689.363, 704.955]
* 17-odd-limit diamond monotone and tradeoff: ~3/2 = [696.000, 700.000]
 
Vals: {{Val list| 10, 50 }}


Badness: 0.025064
Badness: 0.025064
Line 165: Line 145:
POTE generator: ~3/2 = 702.733
POTE generator: ~3/2 = 702.733


Vals: {{Val list| 15, 45, 60, 75de, 135de }}
Optimal GPV sequence: {{Val list| 15, 45, 60, 75de, 135de }}


Badness: 0.077420
Badness: 0.077420
Line 180: Line 160:
POTE generator: ~3/2 = 701.715
POTE generator: ~3/2 = 701.715


Vals: {{Val list| 15, 45f, 60, 135de, 195cddee }}
Optimal GPV sequence: {{Val list| 15, 45f, 60, 135de, 195cddee }}


Badness: 0.051740
Badness: 0.051740
Line 195: Line 175:
POTE generator: ~3/2 = 700.318
POTE generator: ~3/2 = 700.318


Vals: {{Val list| 15, 45e, 60e }}
Optimal GPV sequence: {{Val list| 15, 45e, 60e }}


Badness: 0.044405
Badness: 0.044405
Line 210: Line 190:
POTE generator: ~3/2 = 701.647
POTE generator: ~3/2 = 701.647


Vals: {{Val list| 15f, 45e, 60e }}
Optimal GPV sequence: {{Val list| 15f, 45e, 60e }}


Badness: 0.055361
Badness: 0.055361
Line 238: Line 218:
POTE generator: ~5/4 = 393.438
POTE generator: ~5/4 = 393.438


Vals: {{Val list| 15, 40, 55, 125cd, 180ccdde }}
Optimal GPV sequence: {{Val list| 15, 40, 55, 125cd, 180ccdde }}


Badness: 0.065192
Badness: 0.065192
Line 251: Line 231:
POTE generator: ~5/4 = 392.798
POTE generator: ~5/4 = 392.798


Vals: {{Val list| 15, 40, 55 }}
Optimal GPV sequence: {{Val list| 15, 40, 55 }}


Badness: 0.048440
Badness: 0.048440
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