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Amity family: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings (2/)
Switch to Sintel's badness, WE & CWE tunings (3/3)
Line 747: Line 747:
[[Comma list]]: 2401/2400, 1600000/1594323
[[Comma list]]: 2401/2400, 1600000/1594323


{{Mapping|legend=1| 1 3 6 5 | 0 -20 -52 -31 }}
{{Mapping|legend=1| 1 -17 -46 -26 | 0 20 52 31 }}
: mapping generators: ~2, ~40/21


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.0000{{c}}, ~21/20 = 84.8831{{c}}
* [[WE]]: ~2 = 1199.9463{{c}}, ~40/21 = 1115.0701{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~21/20 = 84.880{{c}}
: [[error map]]: {{val| -0.054 +0.361 -0.195 -0.254 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1187{{c}}
: error map: {{val| 0.000 +0.419 -0.142 -0.146 }}


{{Optimal ET sequence|legend=1| 14c, …, 85c, 99, 212, 311, 721, 1032, 1753b }}
{{Optimal ET sequence|legend=1| 14c, …, 85c, 99, 212, 311, 410, 1131, 1541b }}


[[Badness]] (Smith): 0.045473
[[Badness]] (Sintel): 1.15


=== Amical ===
=== Amical ===
Line 762: Line 765:
Comma list: 2401/2400, 131072/130977, 1600000/1594323
Comma list: 2401/2400, 131072/130977, 1600000/1594323


Mapping: {{mapping| 1 3 6 5 -8 | 0 -20 -52 -31 162 }}
Mapping: {{mapping| 1 -17 -46 -26 154 | 0 20 52 31 -162 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.8843{{c}}
* WE: ~2 = 1200.0008{{c}}, ~40/21 = 1115.1165{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.8843{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1157{{c}}


{{Optimal ET sequence|legend=0| 99, 212e, 311, 721, 1032, 1343, 2375bc }}
{{Optimal ET sequence|legend=0| 99, 212e, 311, 721, 1032, 1343 }}


Badness (Smith): 0.100668
Badness (Sintel): 3.33


==== 13-limit ====
==== 13-limit ====
Line 777: Line 780:
Comma list: 2080/2079, 2401/2400, 4096/4095, 741125/739206
Comma list: 2080/2079, 2401/2400, 4096/4095, 741125/739206


Mapping: {{mapping| 1 3 6 5 -8 -5 | 0 -20 -52 -31 162 123 }}
Mapping: {{mapping| 1 -17 -46 -26 154 118 | 0 20 52 31 -162 -123 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.8837{{c}}
* WE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1094{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.8838{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1162{{c}}


{{Optimal ET sequence|legend=0| 99, 212ef, 311, 721, 1032 }}
{{Optimal ET sequence|legend=0| 99, 212ef, 311, 721, 1032 }}


Badness (Smith): 0.049893
Badness (Sintel): 2.06


=== Amorous ===
=== Amorous ===
Line 792: Line 795:
Comma list: 2401/2400, 6250/6237, 19712/19683
Comma list: 2401/2400, 6250/6237, 19712/19683


Mapping: {{mapping| 1 3 6 5 14 | 0 -20 -52 -31 -149 }}
Mapping: {{mapping| 1 -17 -46 -26 -135 | 0 20 52 31 149 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.8883{{c}}
* WE: ~2 = 1200.0380{{c}}, ~40/21 = 1115.1458{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.8896{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1109{{c}}


{{Optimal ET sequence|legend=0| 99e, 212, 311, 2389bccd, 2700bccde, 3011bccde, 3322bccdde }}
{{Optimal ET sequence|legend=0| 99e, 212, 311, 1145c, 1456cd }}


Badness (Smith): 0.048924
Badness (Sintel): 1.62


==== 13-limit ====
==== 13-limit ====
Line 807: Line 810:
Comma list: 625/624, 2080/2079, 2401/2400, 10648/10647
Comma list: 625/624, 2080/2079, 2401/2400, 10648/10647


Mapping: {{mapping| 1 3 6 5 14 17 | 0 -20 -52 -31 -149 -188 }}
apping: {{mapping| 1 -17 -46 -26 -135 -171 | 0 20 52 31 149 188 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.8895{{c}}
* WE: ~2 = 1200.0543{{c}}, ~40/21 = 1115.1594{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.8910{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1095{{c}}


{{Optimal ET sequence|legend=0| 99ef, 212, 311, 1145c, 1456cd, 1767cd }}
{{Optimal ET sequence|legend=0| 99ef, 212, 311, 834, 1145c }}


Badness (Smith): 0.034681
Badness (Sintel): 1.43


=== Pseudoamical ===
=== Pseudoamical ===
Line 822: Line 825:
Comma list: 385/384, 1375/1372, 1600000/1594323
Comma list: 385/384, 1375/1372, 1600000/1594323


Mapping: {{mapping| 1 3 6 5 -1 | 0 -20 -52 -31 63 }}
Mapping: {{mapping| 1 -17 -46 -26 62 | 0 20 52 31 -63 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.9005{{c}}
* WE: ~2 = 1200.3436{{c}}, ~40/21 = 1115.4102{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.9091{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.0925{{c}}


{{Optimal ET sequence|legend=0| 14ce, …, 85cee, 99, 212 }}
{{Optimal ET sequence|legend=0| 99, 113, 212, 961ccdeee }}


Badness (Smith): 0.085837
Badness (Sintel): 2.84


==== 13-limit ====
==== 13-limit ====
Line 837: Line 840:
Comma list: 325/324, 385/384, 1375/1372, 19773/19712
Comma list: 325/324, 385/384, 1375/1372, 19773/19712


Mapping: {{mapping| 1 3 6 5 -1 2 | 0 -20 -52 -31 63 24 }}
Mapping: {{mapping| 1 -17 -46 -26 62 26 | 0 20 52 31 -63 -24 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.9049{{c}}
* WE: ~2 = 1200.4212{{c}}, ~40/21 = 1115.4787{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.9127{{c}}
* CWE: ~2 = 1200.0000{{c}}, 40/21 = 1115.0885{{c}}


{{Optimal ET sequence|legend=0| 14ce, …, 85ceef, 99, 113, 212 }}
{{Optimal ET sequence|legend=0| 99, 113, 212, 537cdeff, 749ccdeefff }}


Badness (Smith): 0.047025
Badness (Sintel): 1.94


=== Pseudoamorous ===
=== Pseudoamorous ===
Line 852: Line 855:
Comma list: 243/242, 441/440, 980000/970299
Comma list: 243/242, 441/440, 980000/970299


Mapping: {{mapping| 1 3 6 5 7 | 0 -20 -52 -31 -50 }}
Mapping: {{mapping| 1 -17 -46 -26 -43 | 0 20 52 31 50 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.9022{{c}}
* WE: ~2 = 1199.8269{{c}}, ~21/11 = 1114.9475{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.8917{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/11 = 1115.1038{{c}}


{{Optimal ET sequence|legend=0| 14c, …, 85ce, 99e, 113, 212e }}
{{Optimal ET sequence|legend=0| 99e, 212e }} *


Badness (Smith): 0.056583
* optimal patent val: [[113edo|113]]
 
Badness (Sintel): 1.87


==== 13-limit ====
==== 13-limit ====
Line 867: Line 872:
Comma list: 243/242, 364/363, 441/440, 1875/1859
Comma list: 243/242, 364/363, 441/440, 1875/1859


Mapping: {{mapping| 1 3 6 5 7 10 | 0 -20 -52 -31 -50 -89 }}
Mapping: {{mapping| 1 -17 -46 -26 -43 -79 | 0 20 52 31 50 89 }}


Optimal tunings:
Optimal tunings:
Line 873: Line 878:
* POTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.9164{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.9164{{c}}


{{Optimal ET sequence|legend=0| 14cf, …, 85ceff, 99ef, 113, 212ef, 325ce, 537cdeef }}
{{Optimal ET sequence|legend=0| 99ef, 113, 212ef }}


Badness (Smith): 0.042826
Badness (Sintel): 1.77


=== Floral ===
=== Floral ===
Line 882: Line 887:
Comma list: 2401/2400, 9801/9800, 14641/14580
Comma list: 2401/2400, 9801/9800, 14641/14580


Mapping: {{mapping| 2 6 12 10 13 | 0 -20 -52 -31 -43 }}
Mapping: {{mapping| 2 -14 -40 -21 -30 | 0 20 52 31 43 }}
: mapping generators: ~99/70, ~66/49


Optimal tunings:
Optimal tunings:
* CTE: ~99/70 = 600.0000{{c}}, ~21/20 = 84.8781{{c}}
* WE: ~99/70 = 600.0000{{c}}, ~66/49 = 515.1257{{c}}
* POTE: ~99/70 = 600.0000{{c}}, ~21/20 = 84.8788{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~66/49 = 515.1215{{c}}


{{Optimal ET sequence|legend=0| 14c, …, 170bccde, 184c, 198, 212, 410 }}
{{Optimal ET sequence|legend=0| 14c, … 198, 212, 410 }}


Badness (Smith): 0.065110
Badness (Sintel): 2.15


==== 13-limit ====
==== 13-limit ====
Line 897: Line 903:
Comma list: 676/675, 1001/1000, 1716/1715, 14641/14580
Comma list: 676/675, 1001/1000, 1716/1715, 14641/14580


Mapping: {{mapping| 2 6 12 10 13 19 | 0 -20 -52 -31 -43 -82 }}
Mapping: {{mapping| 2 -14 -40 -21 -30 -63 | 0 20 52 31 43 82 }}


Optimal tunings:
Optimal tunings:
* CTE: ~99/70 = 600.0000{{c}}, ~21/20 = 84.8759{{c}}
* WE: ~99/70 = 599.9923{{c}}, ~66/49 = 515.1184{{c}}
* POTE: ~99/70 = 600.0000{{c}}, ~21/20 = 84.8750{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~66/49 = 515.1246{{c}}


{{Optimal ET sequence|legend=0| 14c, …, 184cff, 198, 410 }}
{{Optimal ET sequence|legend=0| 14cf, …, 198, 410 }}


Badness (Smith): 0.037013
Badness (Sintel): 1.53


=== Humorous ===
=== Humorous ===
Line 912: Line 918:
Comma list: 2401/2400, 3025/3024, 1600000/1594323
Comma list: 2401/2400, 3025/3024, 1600000/1594323


Mapping: {{mapping| 1 3 6 5 3 | 0 -40 -104 -62 13 }}
Mapping: {{mapping| 1 -37 -98 -57 16 | 0 40 104 62 -13 }}
: mapping generators: ~2, ~3993/2048


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.0000{{c}}, ~4096/3993 = 42.4414{{c}}
* WE: ~2 = 1199.9189{{c}}, ~3993/2048 = 1157.4826{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~4096/3993 = 42.4391{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3993/2048 = 1157.5602{{c}}


{{Optimal ET sequence|legend=0| 85c, 113, 198, 311, 1131, 1442, 1753be }}
{{Optimal ET sequence|legend=0| 85c, 113, 198, 311, 509, 820 }}


Badness (Smith): 0.058249
Badness (Sintel): 1.93


==== 13-limit ====
==== 13-limit ====
Line 927: Line 934:
Comma list: 2080/2079, 2200/2197, 2401/2400, 3025/3024
Comma list: 2080/2079, 2200/2197, 2401/2400, 3025/3024


Mapping: {{mapping| 1 3 6 5 3 6 | 0 -40 -104 -62 13 -65 }}
Mapping: {{mapping| 1 -37 -98 -57 16 -59 | 0 40 104 62 -13 65 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.0000{{c}}, ~40/39 = 42.4425{{c}}
* WE: ~2 = 1199.8903{{c}}, ~39/20 = 1157.4551{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~40/39 = 42.4391{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~39/20 = 1157.5600{{c}}


{{Optimal ET sequence|legend=0| 85c, 113, 198, 311, 1753beff, 2064beff, 2375bceff }}
{{Optimal ET sequence|legend=0| 85c, 113, 198, 311, 509, 820f }}


Badness (Smith): 0.028267
Badness (Sintel): 1.17


== Calamity ==
== Calamity ==
Calamity tempers out 2100875/2097152, the [[rainy comma]], and may be described as the {{nowrap| 46 & 311 }} temperament. It splits the interval of two octaves plus an acute minor third into five.  
Calamity tempers out 2100875/2097152, the [[rainy comma]], and may be described as the {{nowrap| 46 & 311 }} temperament. It splits the interval of grave major sixth plus an octave into five.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 944: Line 951:
[[Comma list]]: 1600000/1594323, 2100875/2097152
[[Comma list]]: 1600000/1594323, 2100875/2097152


{{Mapping|legend=1| 1 13 32 -15 | 0 -25 -65 39 }}
{{Mapping|legend=1| 1 -12 -33 24 | 0 25 65 -39 }}
: mapping generators: ~2, ~35/24


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~48/35 = 547.909{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0332{{c}}, ~35/24 = 652.1081{{c}}
: [[error map]]: {{val| +0.033 +0.348 -0.387 -0.243 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~35/24 = 652.0902{{c}}
: error map: {{val| 0.000 +0.300 -0.452 -0.343 }}


{{Optimal ET sequence|legend=1| 46, 219c, 265, 311 }}
{{Optimal ET sequence|legend=1| 46, 219c, 265, 311 }}


[[Badness]] (Smith): 0.198130
[[Badness]] (Sintel): 5.01


=== 11-limit ===
=== 11-limit ===
Line 957: Line 969:
Comma list: 3025/3024, 12005/11979, 131072/130977
Comma list: 3025/3024, 12005/11979, 131072/130977


Mapping: {{mapping| 1 13 32 -15 -18 | 0 -25 -65 39 47 }}
Mapping: {{mapping| 1 -12 -33 24 29 | 0 25 65 -39 -47 }}


Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~48/35 = 547.908{{c}}
Optimal tunings:
* WE: ~2 = 1199.9938{{c}}, ~35/24 = 652.0887{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~35/24 = 652.0920{{c}}


{{Optimal ET sequence|legend=0| 46, 219c, 265, 311, 979, 1290 }}
{{Optimal ET sequence|legend=0| 46, 219c, 265, 311, 979, 1290 }}


Badness (Smith): 0.060408
Badness (Sintel): 2.00


=== 13-limit ===
=== 13-limit ===
Line 970: Line 984:
Comma list: 2080/2079, 3025/3024, 4096/4095, 12005/11979
Comma list: 2080/2079, 3025/3024, 4096/4095, 12005/11979


Mapping: {{mapping| 1 13 32 -15 -18 -31 | 0 -25 -65 39 47 76 }}
Mapping: {{mapping| 1 -12 -33 24 29 45 | 0 25 65 -39 -47 -76 }}


Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~48/35 = 547.907{{c}}
Optimal tunings:
* WE: ~2 = 1199.9742{{c}}, ~35/24 = 652.0794{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~35/24 = 652.0934{{c}}


{{Optimal ET sequence|legend=0| 46, 265, 311, 668, 979, 1290 }}
{{Optimal ET sequence|legend=0| 46, 265, 311, 668, 979, 1290 }}


Badness (Smith): 0.033617
Badness (Sintel): 1.39


== Familia ==
== Familia ==
Familia tempers out 16875/16807, the [[mirkwai comma]], and may be described as the {{nowrap| 113 & 152 }} temperament. It splits the interval of acute minor tenth (~243/100) in five.
Familia tempers out 16875/16807, the [[mirkwai comma]], and may be described as the {{nowrap| 113 & 152 }} temperament. It is generated by a major sixth, five of which octave reduced make the original generator of amity.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 985: Line 1,001:
[[Comma list]]: 16875/16807, 1600000/1594323
[[Comma list]]: 16875/16807, 1600000/1594323


{{Mapping|legend=1| 1 8 19 20 | 0 -25 -65 -67 }}
{{Mapping|legend=1| 1 -17 -46 -47 | 0 25 65 67 }}
: mapping generators: ~2, ~6561/3920


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~11907/10000 = 307.915{{c}}
* [[WE]]: ~2 = 1199.9165{{c}}, ~6561/3920 = 892.0267{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~11907/10000 = 307.941{{c}}
: [[error map]]: {{val| -0.084 +0.132 -0.736 +0.888 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~6561/3920 = 892.0871{{c}}
: error map: {{val| 0.000 +0.224 -0.649 +1.013 }}


{{Optimal ET sequence|legend=1| 39d, 74cd, 113, 152, 265, 417, 1516ccdd, 1933ccdd }}
{{Optimal ET sequence|legend=1| 39d, 74cd, 113, 152, 265, 417 }}


[[Badness]] (Smith): 0.144551
[[Badness]] (Sintel): 3.66


=== 11-limit ===
=== 11-limit ===
Line 1,000: Line 1,019:
Comma list: 540/539, 1375/1372, 1600000/1594323
Comma list: 540/539, 1375/1372, 1600000/1594323


Mapping: {{mapping| 1 8 19 20 5 | 0 -25 -65 -67 -6 }}
Mapping: {{mapping| 1 -17 -46 -47 -1 | 0 25 65 67 6 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~3200/2673 = 307.915{{c}}
* WE: ~2 = 1199.7927{{c}}, ~2673/1600 = 891.9397{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3200/2673 = 307.906{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~2673/1600 = 892.0909{{c}}


{{Optimal ET sequence|legend=0| 39d, 74cd, 113, 152, 265, 417, 1099cdee }}
{{Optimal ET sequence|legend=0| 39d, 74cd, 113, 152, 417, 569de, 721de }}


Badness (Smith): 0.051740
Badness (Sintel): 1.71


=== 13-limit ===
=== 13-limit ===
Line 1,015: Line 1,034:
Comma list: 540/539, 729/728, 1375/1372, 2205/2197
Comma list: 540/539, 729/728, 1375/1372, 2205/2197


Mapping: {{mapping| 1 8 19 20 5 25 | 0 -25 -65 -67 -6 -83 }}
Mapping: {{mapping| 1 -17 -46 -47 -1 -58 | 0 25 65 67 6 83 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~143/120 = 307.922{{c}}
* WE: ~2 = 1199.7844{{c}}, ~240/143 = 892.9268{{c}}
* POTE: ~2 = 1200.000{{c}}, ~143/120 = 307.913{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~240/143 = 892.0839{{c}}


{{Optimal ET sequence|legend=0| 39df, 74cdf, 113, 152f, 265 }}
{{Optimal ET sequence|legend=0| 39df, 74cdf, 113, 152f, 265 }}


Badness (Smith): 0.038473
Badness (Sintel): 1.59


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