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Misty family: Difference between revisions

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Line 14: Line 14:
: mapping generators: ~512/405, ~3
: mapping generators: ~512/405, ~3


[[Optimal tuning]]s:
[[Optimal tuning]]s:  
* [[CTE]]: ~512/405 = 400.0000{{c}}, ~3/2 = 703.2481{{c}}
* [[WE]]: ~512/405 = 399.8595{{c}}, ~3/2 = 702.8645{{c}}
* [[POTE]]: ~512/405 = 400.000{{c}}, ~3/2 = 703.111{{c}}
: [[error map]]: {{val| -0.421 +0.488 +0.261 }}
* [[CWE]]: ~512/405 = 400.0000{{c}}, ~3/2 = 703.1489{{c}}
: error map: {{val| 0.000 +1.194 +1.091 }}
<!-- * [[CTE]]: ~512/405 = 400.0000{{c}}, ~3/2 = 703.2481{{c}}
* [[POTE]]: ~512/405 = 400.000{{c}}, ~3/2 = 703.111{{c}} -->


{{Optimal ET sequence|legend=1| 12, 51, 63, 75, 87, 99, 285, 384, 483c }}
{{Optimal ET sequence|legend=1| 12, 51, 63, 75, 87, 99, 285, 384, 483c, 867bc }}


[[Badness]] (Smith): 0.106540
[[Badness]] (Sintel): 2.50


=== Overview to extensions ===
=== Overview to extensions ===
Line 36: Line 40:
{{Mapping|legend=1| 3 0 26 56 | 0 1 -4 -10 }}
{{Mapping|legend=1| 3 0 26 56 | 0 1 -4 -10 }}


[[Optimal tuning]] ([[CTE]]): ~63/50 = 400.0000{{c}}, ~3/2 = 703.1448{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~63/50 = 399.8579{{c}}, ~3/2 = 702.7714{{c}}
: [[error map]]: {{val| -0.426 +0.390 +0.611 -0.236 }}
* [[CWE]]: ~63/50 = 400.0000{{c}}, ~3/2 = 703.0551{{c}}
: error map: {{val| 0.000 +1.100 +1.466 +0.623 }}
<!-- * [[CTE]]: ~63/50 = 400.0000{{c}}, ~3/2 = 703.1448{{c}} -->


{{Optimal ET sequence|legend=1| 12, …, 87, 99 }}
{{Optimal ET sequence|legend=1| 12, …, 87, 99 }}


[[Badness]] (Smith): 0.036802
[[Badness]] (Sintel): 0.931


=== Undecimal misty ===
=== Undecimal misty ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 441/440, 3136/3125, 4375/4356
Comma list: 441/440, 896/891, 3136/3125


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


Optimal tunings:
Optimal tunings:  
* CTE: ~44/35 = 400.0000{{c}}, ~3/2 = 703.3127{{c}}
* WE: ~44/35 = 399.8727{{c}}, ~3/2 = 702.9867{{c}}
* POTE: ~44/35 = 400.000{{c}}, ~3/2 = 703.210{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~3/2 = 703.2385{{c}}
<!-- * CTE: ~44/35 = 400.0000{{c}}, ~3/2 = 703.3127{{c}}
* POTE: ~44/35 = 400.000{{c}}, ~3/2 = 703.210{{c}} -->


{{Optimal ET sequence|legend=0| 12, …, 87, 99e, 186e }}
{{Optimal ET sequence|legend=0| 12, …, 87, 99e, 186e }}


Badness (Smith): 0.035932
Badness (Sintel): 1.19


==== 13-limit ====
==== 13-limit ====
Line 64: Line 75:
Mapping: {{mapping| 3 0 26 56 77 92 | 0 1 -4 -10 -14 -17 }}
Mapping: {{mapping| 3 0 26 56 77 92 | 0 1 -4 -10 -14 -17 }}


Optimal tunings:
Optimal tunings:  
* CTE: ~44/35 = 400.0000{{c}}, ~3/2 = 703.3859{{c}}
* WE: ~44/35 = 399.8888{{c}}, ~3/2 = 703.1080{{c}}
* POTE: ~44/35 = 400.000{{c}}, ~3/2 = 703.303{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~3/2 = 703.3258{{c}}
<!-- * CTE: ~44/35 = 400.0000{{c}}, ~3/2 = 703.3859{{c}}
* POTE: ~44/35 = 400.000{{c}}, ~3/2 = 703.303{{c}} -->


{{Optimal ET sequence|legend=0| 12f, …, 87, 186ef }}
{{Optimal ET sequence|legend=0| 12f, …, 87, 186ef }}


Badness (Smith): 0.027820
Badness (Sintel): 1.15


===== 17-limit =====
===== 17-limit =====
Line 79: Line 92:
Mapping: {{mapping| 3 0 26 56 77 92 -2 | 0 1 -4 -10 -14 -17 3 }}
Mapping: {{mapping| 3 0 26 56 77 92 -2 | 0 1 -4 -10 -14 -17 3 }}


Optimal tunings:
Optimal tunings:  
* CTE: ~34/27 = 400.0000{{c}}, ~3/2 = 703.3686{{c}}
* WE: ~34/27 = 399.8046{{c}}, ~3/2 = 702.8894{{c}}
* POTE: ~34/27 = 400.000{{c}}, ~3/2 = 703.233{{c}}
* CWE: ~34/27 = 400.0000{{c}}, ~3/2 = 703.2597{{c}}
<!-- * CTE: ~34/27 = 400.0000{{c}}, ~3/2 = 703.3686{{c}}
* POTE: ~34/27 = 400.000{{c}}, ~3/2 = 703.233{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 87, 99ef, 186efg }}
{{Optimal ET sequence|legend=0| 12f, 87, 99ef, 186efg }}


Badness (Smith): 0.023908
Badness (Sintel): 1.22


===== 19-limit =====
===== 19-limit =====
Line 94: Line 109:
Mapping: {{mapping| 3 0 26 56 77 92 -2 8 | 0 1 -4 -10 -14 -17 3 1 }}
Mapping: {{mapping| 3 0 26 56 77 92 -2 8 | 0 1 -4 -10 -14 -17 3 1 }}


Optimal tunings:
Optimal tunings:  
* CTE: ~24/19 = 400.0000{{c}}, ~3/2 = 703.3626{{c}}
* WE: ~24/19 = 399.7530{{c}}, ~3/2 = 702.7601{{c}}
* POTE: ~34/27 = 400.000{{c}}, ~3/2 = 703.253{{c}}
* CWE: ~24/19 = 400.0000{{c}}, ~3/2 = 703.2216{{c}}
<!-- * CTE: ~24/19 = 400.0000{{c}}, ~3/2 = 703.3626{{c}}
* POTE: ~24/19 = 400.000{{c}}, ~3/2 = 703.253{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 87, 99ef, 186efgh }}
{{Optimal ET sequence|legend=0| 12f, 87, 99ef, 186efgh }}


Badness (Smith): 0.019878
Badness (Sintel): 1.21


==== Mystic ====
==== Mystic ====
Line 109: Line 126:
Mapping: {{mapping| 3 0 26 56 77 -46 | 0 1 -4 -10 -14 12 }}
Mapping: {{mapping| 3 0 26 56 77 -46 | 0 1 -4 -10 -14 12 }}


Optimal tunings:
Optimal tunings:  
* CTE: ~44/35 = 400.0000{{c}}, ~3/2 = 703.3285{{c}}
* WE: ~44/35 = 399.9543{{c}}, ~3/2 = 702.2310{{c}}
* POTE: ~44/35 = 400.000{{c}}, ~3/2 = 703.311{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~3/2 = 703.3140{{c}}
<!-- * CTE: ~44/35 = 400.0000{{c}}, ~3/2 = 703.3285{{c}}
* POTE: ~44/35 = 400.000{{c}}, ~3/2 = 703.311{{c}} -->


{{Optimal ET sequence|legend=0| 12, 87, 186e, 273e }}
{{Optimal ET sequence|legend=0| 12, 87, 186e, 273e }}


Badness (Smith): 0.036872
Badness (Sintel): 1.52


=== Semimist ===
=== Semimist ===
Line 125: Line 144:
: mapping generators: ~55/49, ~3
: mapping generators: ~55/49, ~3


Optimal tunings:
Optimal tunings:  
* CTE: ~55/49 = 200.0000{{c}}, ~3/2 = 703.0864{{c}}
* WE: ~55/49 = 199.9260{{c}}, ~3/2 = 702.7162{{c}}
* POTE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.9764{{c}}
* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 703.0062{{c}}
<!-- * CTE: ~55/49 = 200.0000{{c}}, ~3/2 = 703.0864{{c}}
* POTE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.9764{{c}} -->


{{Optimal ET sequence|legend=0| 12, 174e, 186, 198, 408cde, 606bcde }}
{{Optimal ET sequence|legend=0| 12, 174e, 186, 198, 408cde, 606bcde }}


Badness (Smith): 0.068509
Badness (Sintel): 2.26


==== 13-limit ====
==== 13-limit ====
Line 140: Line 161:
Mapping: {{mapping| 6 0 52 112 173 203 | 0 1 -4 -10 -16 -19 }}
Mapping: {{mapping| 6 0 52 112 173 203 | 0 1 -4 -10 -16 -19 }}


Optimal tunings:
Optimal tunings:  
* CTE: ~55/49 = 200.0000{{c}}, ~3/2 = 703.1045{{c}}
* WE: ~55/49 = 199.9293{{c}}, ~3/2 = 702.7602{{c}}
* POTE: ~55/49 = 200.0000{{c}}, ~3/2 = 703.0087{{c}}
* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 703.0343{{c}}
<!-- * CTE: ~55/49 = 200.0000{{c}}, ~3/2 = 703.1045{{c}}
* POTE: ~55/49 = 200.0000{{c}}, ~3/2 = 703.0087{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 174ef, 186, 198 }}
{{Optimal ET sequence|legend=0| 12f, 174ef, 186, 198 }}


Badness (Smith): 0.044073
Badness (Sintel): 1.82


=== Hemimist ===
=== Hemimist ===
Line 156: Line 179:
: mapping generators: ~63/50, ~400/231
: mapping generators: ~63/50, ~400/231


Optimal tuning (POTE): ~63/50 = 400.0000{{c}}, ~400/231 = 951.5721{{c}}
Optimal tunings:
* WE: ~63/50 = 399.8922{{c}}, ~400/231 = 951.2704{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~400/231 = 951.5363{{c}}
<!-- * POTE: ~63/50 = 400.0000{{c}}, ~400/231 = 951.5721{{c}} -->


{{Optimal ET sequence|legend=0| 24d, 87, 111, 198 }}
{{Optimal ET sequence|legend=0| 24d, 87, 111, 198 }}


Badness (Smith): 0.047439
Badness (Sintel): 1.57


==== 13-limit ====
==== 13-limit ====
Line 169: Line 195:
Mapping: {{mapping| 3 0 26 56 8 23 | 0 2 -8 -20 1 -5 }}
Mapping: {{mapping| 3 0 26 56 8 23 | 0 2 -8 -20 1 -5 }}


Optimal tuning (POTE): ~63/50 = 400.0000{{c}}, ~26/15 = 951.5810{{c}}
Optimal tunings:
* WE: ~63/50 = 399.8818{{c}}, ~26/15 = 951.2442{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~26/15 = 951.5358{{c}}
<!-- * POTE: ~63/50 = 400.0000{{c}}, ~26/15 = 951.5810{{c}} -->


{{Optimal ET sequence|legend=0| 24d, 87, 111, 198 }}
{{Optimal ET sequence|legend=0| 24d, 87, 111, 198 }}


Badness (Smith): 0.022923
Badness (Sintel): 0.947


== Fog ==
== Fog ==
Line 183: Line 212:


{{Mapping|legend=1| 3 0 26 37 | 0 1 -4 -6 }}
{{Mapping|legend=1| 3 0 26 37 | 0 1 -4 -6 }}
: mapping generators: ~80/63, ~3


Optimal tunings:
[[Optimal tuning]]s:  
* CTE: ~80/63 = 400.0000{{c}}, ~3/2 = 704.3694{{c}}
* [[WE]]: ~80/63 = 399.7918{{c}}, ~3/2 = 703.7511{{c}}
* POTE: ~80/63 = 400.000{{c}}, ~3/2 = 704.118{{c}}
: [[error map]]: {{val| -0.624 +1.172 -4.232 +4.712 }}
* [[CWE]]: ~80/63 = 400.0000{{c}}, ~3/2 = 704.1865{{c}}
: error map: {{val| 0.000 +2.232 -3.060 +6.055 }}
<!-- * CTE: ~80/63 = 400.0000{{c}}, ~3/2 = 704.3694{{c}}
* POTE: ~80/63 = 400.000{{c}}, ~3/2 = 704.118{{c}} -->


{{Optimal ET sequence|legend=1| 12, 39c, 51, 63, 75 }}
{{Optimal ET sequence|legend=1| 12, 39c, 51, 63, 75 }}


[[Badness]]: 0.086866
[[Badness]] (Sintel): 2.20


=== 11-limit ===
=== 11-limit ===
Line 200: Line 232:
Mapping: {{mapping| 3 0 26 37 58 | 0 1 -4 -6 -10 }}
Mapping: {{mapping| 3 0 26 37 58 | 0 1 -4 -6 -10 }}


Optimal tunings:
Optimal tunings:  
* CTE: ~44/35 = 400.0000{{c}}, ~3/2 = 704.6253{{c}}
* WE: ~44/35 = 399.8078{{c}}, ~3/2 = 704.0728{{c}}
* POTE: ~44/35 = 400.000{{c}}, ~3/2 = 704.411{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~3/2 = 704.4697{{c}}
<!-- * CTE: ~44/35 = 400.0000{{c}}, ~3/2 = 704.6253{{c}}
* POTE: ~44/35 = 400.000{{c}}, ~3/2 = 704.411{{c}} -->


{{Optimal ET sequence|legend=0| 12, 39ce, 51, 63, 138de }}
{{Optimal ET sequence|legend=0| 12, 39ce, 51, 63, 138de }}


Badness (Smith): 0.051348
Badness (Sintel): 1.70


== Subgroup extensions ==
== Subgroup extensions ==
Line 212: Line 246:
The [[S-expression]]-based comma list for this extension is {([[5120/5103|S8/S9]]), [[2025/2023|S15/S17]], [[256/255|S16]], [[1701/1700|S18/S20]], ([[2500/2499|S50]])}, and for the 2.3.5.7.17.19-subgroup extension, {([[5120/5103|S8/S9]]), [[256/255|S16]], [[324/323|S18]], [[400/399|S20]], [[1445/1444|S17/S19]], ([[2500/2499|S50]])}.  
The [[S-expression]]-based comma list for this extension is {([[5120/5103|S8/S9]]), [[2025/2023|S15/S17]], [[256/255|S16]], [[1701/1700|S18/S20]], ([[2500/2499|S50]])}, and for the 2.3.5.7.17.19-subgroup extension, {([[5120/5103|S8/S9]]), [[256/255|S16]], [[324/323|S18]], [[400/399|S20]], [[1445/1444|S17/S19]], ([[2500/2499|S50]])}.  


[[Subgroup]]: 2.3.5.7.17
Subgroup: 2.3.5.7.17


[[Comma list]]: 256/255, 1701/1700, 2025/2023
Comma list: 256/255, 1701/1700, 2025/2023


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


[[Optimal tuning]] ([[CTE]]): ~34/27 = 400.0000{{c}}, ~3/2 = 703.0963{{c}}
Optimal tunings:
* WE: ~34/27 = 399.8023{{c}}, ~3/2 = 702.6087{{c}}
* CWE: ~34/27 = 400.0000{{c}}, ~3/2 = 702.9837{{c}}
<!-- * CTE: ~34/27 = 400.0000{{c}}, ~3/2 = 703.0963{{c}} -->


{{Optimal ET sequence|legend=1| 12, 87, 99, 309cdg, 408cdgg, 507cdggg }}
{{Optimal ET sequence|legend=0| 12, 87, 99, 309cdg, 408cdgg, 507cdggg }}


[[Badness]] (Smith): 0.0186
Badness (Sintel): 0.688


==== 2.3.5.7.17.19 subgroup ====
==== 2.3.5.7.17.19 subgroup ====
Line 232: Line 269:
Subgroup-val mapping: {{mapping| 3 0 26 56 -2 8 | 0 1 -4 -10 3 1 }}
Subgroup-val mapping: {{mapping| 3 0 26 56 -2 8 | 0 1 -4 -10 3 1 }}


Optimal tuning (CTE): ~24/19 = 400.0000{{c}}, ~3/2 = 703.0778{{c}}
Optimal tunings:
* WE: ~24/19 = 399.7556{{c}}, ~3/2 = 702.4862{{c}}
* CWE: ~24/19 = 400.0000{{c}}, ~3/2 = 702.9418{{c}}
<!-- * CTE: ~24/19 = 400.0000{{c}}, ~3/2 = 703.0778{{c}} -->


{{Optimal ET sequence|legend=0| 12, 87, 99, 210gh, 309cdghh }}
{{Optimal ET sequence|legend=0| 12, 87, 99, 210gh, 309cdghh }}


Badness (Smith): 0.0132
Badness (Sintel): 0.637


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