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Misty family: Difference between revisions

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Inherits 5-limit
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Line 58: Line 58:
Comma list: 256/255, 1701/1700, 2025/2023
Comma list: 256/255, 1701/1700, 2025/2023


Subgroup-val mapping: {{mapping| 3 0 26 56 -2 | 0 1 -4 -10 3 }}
{{Mapping|legend=2| 3 0 26 56 -2 | 0 1 -4 -10 3 }}
: mapping generators: ~34/27, ~3
: mapping generators: ~34/27, ~3


Line 74: Line 74:
Comma list: 256/255, 324/323, 400/399, 476/475
Comma list: 256/255, 324/323, 400/399, 476/475


Subgroup-val mapping: {{mapping| 3 0 26 56 -2 8 | 0 1 -4 -10 3 1 }}
{{Mapping|legend=2| 3 0 26 56 -2 8 | 0 1 -4 -10 3 1 }}


Optimal tunings:  
Optimal tunings:  
Line 84: Line 84:
Badness (Sintel): 0.637
Badness (Sintel): 0.637


=== Undecimal misty ===
=== Murky ===
Murky (87 & 99ef) tempers out [[441/440]] and [[896/891]], which joins misty with [[parapyth]]/[[pele]].
 
This extension used to be known as ''undecimal misty'', but was decanonicalized in 2026 in favor of the no-11 no-13 temperament.
 
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 441/440, 896/891, 3136/3125
Comma list: 441/440, 896/891, 3136/3125


Mapping: {{mapping| 3 0 26 56 77 | 0 1 -4 -10 -14 }}
{{Mapping|legend=0| 3 0 26 56 77 | 0 1 -4 -10 -14 }}


Optimal tunings:  
Optimal tunings:  
Line 104: Line 108:
Comma list: 196/195, 352/351, 364/363, 625/624
Comma list: 196/195, 352/351, 364/363, 625/624


Mapping: {{mapping| 3 0 26 56 77 92 | 0 1 -4 -10 -14 -17 }}
{{Mapping|legend=0| 3 0 26 56 77 92 | 0 1 -4 -10 -14 -17 }}


Optimal tunings:  
Optimal tunings:  
Line 119: Line 123:
Comma list: 196/195, 352/351, 364/363, 375/374, 595/594
Comma list: 196/195, 352/351, 364/363, 375/374, 595/594


Mapping: {{mapping| 3 0 26 56 77 92 -2 | 0 1 -4 -10 -14 -17 3 }}
{{Mapping|legend=0| 3 0 26 56 77 92 -2 | 0 1 -4 -10 -14 -17 3 }}


Optimal tunings:  
Optimal tunings:  
Line 134: Line 138:
Comma list: 196/195, 210/209, 352/351, 364/363, 375/374, 595/594
Comma list: 196/195, 210/209, 352/351, 364/363, 375/374, 595/594


Mapping: {{mapping| 3 0 26 56 77 92 -2 8 | 0 1 -4 -10 -14 -17 3 1 }}
{{Mapping|legend=0| 3 0 26 56 77 92 -2 8 | 0 1 -4 -10 -14 -17 3 1 }}


Optimal tunings:  
Optimal tunings:  
Line 144: Line 148:
Badness (Sintel): 1.21
Badness (Sintel): 1.21


==== Mystic ====
=== Hazy ===
Subgroup: 2.3.5.7.11
 
Comma list: 176/175, 1375/1372, 5120/5103
 
{{Mapping|legend=0| 3 0 26 56 96 | 0 1 -4 -10 -18 }}
 
Optimal tunings:
* WE: ~63/50 = 399.8097{{c}}, ~3/2 = 702.4039{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~3/2 = 702.7731{{c}}
 
{{Optimal ET sequence|legend=0| 12, 87e, 99, 111 }}
 
Badness (Sintel): 1.84
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 325/324, 441/440, 896/891, 1001/1000
Comma list: 176/175, 351/350, 847/845, 1375/1372
 
{{Mapping|legend=0| 3 0 26 56 96 111 | 0 1 -4 -10 -18 -21 }}
 
Optimal tunings:
* WE: ~63/50 = 399.8089{{c}}, ~3/2 = 702.3993{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~3/2 = 702.7661{{c}}
 
{{Optimal ET sequence|legend=0| 12f, 87ef, 99, 111 }}
 
Badness (Sintel): 1.54
 
=== Smoky ===
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 2200/2187, 3136/3125


Mapping: {{mapping| 3 0 26 56 77 -46 | 0 1 -4 -10 -14 12 }}
{{Mapping|legend=0| 3 0 26 56 -61 | 0 1 -4 -10 15 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~44/35 = 399.9543{{c}}, ~3/2 = 702.2310{{c}}
* WE: ~63/50 = 400.0072{{c}}, ~3/2 = 702.3068{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~3/2 = 703.3140{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~3/2 = 703.2941{{c}}
 
{{Optimal ET sequence|legend=0| 12e, 87, 186, 273 }}
 
Badness (Sintel): 2.25


{{Optimal ET sequence|legend=0| 12, 87, 186e, 273e }}
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Badness (Sintel): 1.52
Comma list: 325/324, 352/351, 385/384, 3136/3125
 
{{Mapping|legend=0| 3 0 26 56 -61 -46 | 0 1 -4 -10 15 12 }}
 
Optimal tunings:
* WE: ~63/50 = 400.0184{{c}}, ~3/2 = 703.3420{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~3/2 = 703.3101{{c}}
 
{{Optimal ET sequence|legend=0| 12e, 87, 186, 273 }}
 
Badness (Sintel): 1.63
 
=== Ashy ===
Subgroup: 2.3.5.7.11
 
Comma list: 540/539, 3136/3125, 5120/5103
 
{{Mapping|legend=0| 3 0 26 56 -80 | 0 1 -4 -10 19 }}
 
Optimal tunings:
* WE: ~63/50 = 399.7776{{c}}, ~3/2 = 702.4764{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~3/2 = 702.8652{{c}}
 
{{Optimal ET sequence|legend=0| 12e, 99e, 210e }}
 
Badness (Sintel): 1.89
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 352/351, 540/539, 729/728, 3136/3125
 
{{Mapping|legend=0| 3 0 26 56 -80 -65 | 0 1 -4 -10 19 16 }}
 
Optimal tunings:
* WE: ~63/50 = 399.7470{{c}}, ~3/2 = 702.3782{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~3/2 = 702.8135{{c}}
 
{{Optimal ET sequence|legend=0| 12e, 99ef, 111, 210ef, 321cdeff, 531ccddeeffff }}
 
Badness (Sintel): 1.72


=== Semimist ===
=== Semimist ===
Line 164: Line 243:
Comma list: 3136/3125, 5120/5103, 9801/9800
Comma list: 3136/3125, 5120/5103, 9801/9800


Mapping: {{mapping| 6 0 52 112 173 | 0 1 -4 -10 -16 }}
{{Mapping|legend=0| 6 0 52 112 173 | 0 1 -4 -10 -16 }}
: mapping generators: ~55/49, ~3
: mapping generators: ~55/49, ~3


Line 180: Line 259:
Comma list: 352/351, 847/845, 1716/1715, 3136/3125
Comma list: 352/351, 847/845, 1716/1715, 3136/3125


Mapping: {{mapping| 6 0 52 112 173 203 | 0 1 -4 -10 -16 -19 }}
{{Mapping|legend=0| 6 0 52 112 173 203 | 0 1 -4 -10 -16 -19 }}


Optimal tunings:  
Optimal tunings:  
Line 195: Line 274:
Comma list: 3025/3024, 3136/3125, 5120/5103
Comma list: 3025/3024, 3136/3125, 5120/5103


Mapping: {{mapping| 3 0 26 56 8 | 0 2 -8 -20 1 }}
{{Mapping|legend=0| 3 0 26 56 8 | 0 2 -8 -20 1 }}
: mapping generators: ~63/50, ~400/231
: mapping generators: ~63/50, ~400/231


Line 211: Line 290:
Comma list: 352/351, 676/675, 847/845, 3025/3024
Comma list: 352/351, 676/675, 847/845, 3025/3024


Mapping: {{mapping| 3 0 26 56 8 23 | 0 2 -8 -20 1 -5 }}
{{Mapping|legend=0| 3 0 26 56 8 23 | 0 2 -8 -20 1 -5 }}


Optimal tunings:  
Optimal tunings:  
Line 245: Line 324:
Comma list: 100/99, 225/224, 2420/2401
Comma list: 100/99, 225/224, 2420/2401


Mapping: {{mapping| 3 0 26 37 58 | 0 1 -4 -6 -10 }}
{{Mapping|legend=0| 3 0 26 37 58 | 0 1 -4 -6 -10 }}


Optimal tunings:  
Optimal tunings:  
Line 255: Line 334:
Badness (Sintel): 1.70
Badness (Sintel): 1.70


[[Category:Misty family| ]] <!-- main article -->
[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Misty family| ]] <!-- main article -->
[[Category:Catalogs of rank-2 temperaments]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Misty_family"