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Mint temperaments: Difference between revisions

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{{Mapping|legend=1| 1 1 2 2 | 0 3 2 4 }}
{{Mapping|legend=1| 1 1 2 2 | 0 3 2 4 }}
: mapping generators: ~2, ~7/6
: mapping generators: ~2, ~7/6


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~7/6 = 231.845
* [[CTE]]: ~2 = 1200.000{{c}}, ~7/6 = 231.845{{c}}
: [[error map]]: {{val| 0.000 -6.421 +77.376 -41.447 }}
: [[error map]]: {{val| 0.000 -6.421 +77.376 -41.447 }}
* [[POTE]]: ~2 = 1200.000, ~7/6 = 239.977
* [[POTE]]: ~2 = 1200.000{{c}}, ~7/6 = 239.977{{c}}
: error map: {{val| 0.000 +17.976 +93.640 -8.918 }}
: error map: {{val| 0.000 +17.976 +93.640 -8.918 }}


{{Optimal ET sequence|legend=1| 1bd, …, 4bcd, 5 }}
{{Optimal ET sequence|legend=1| 1bd, …, 4bcd, 5 }}


[[Badness]] (Sintel): 1.1864
[[Badness]] (Sintel): 1.19


== Progression ==
== Progression ==
Line 49: Line 48:


{{Mapping|legend=1| 1 1 2 2 | 0 5 3 7 }}
{{Mapping|legend=1| 1 1 2 2 | 0 5 3 7 }}
: mapping generators: ~2, ~15/14
: mapping generators: ~2, ~15/14


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~15/14 = 138.611
* [[CTE]]: ~2 = 1200.000{{c}}, ~15/14 = 138.611{{c}}
: [[error map]]: {{val| 0.000 -8.900 +29.519 +1.451 }}
: [[error map]]: {{val| 0.000 -8.900 +29.519 +1.451 }}
* [[POTE]]: ~2 = 1200.000, ~15/14 = 140.927
* [[POTE]]: ~2 = 1200.000{{c}}, ~15/14 = 140.927{{c}}
: error map: {{val| 0.000 +2.680 +36.467 +17.663 }}
: error map: {{val| 0.000 +2.680 +36.467 +17.663 }}


{{Optimal ET sequence|legend=1| 8d, 9, 17c }}
{{Optimal ET sequence|legend=1| 8d, 9, 17c }}


[[Badness]] (Sintel): 1.2237
[[Badness]] (Sintel): 1.22


=== 11-limit ===
=== 11-limit ===
Line 70: Line 68:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~12/11 = 138.556
* CTE: ~2 = 1200.000{{c}}, ~12/11 = 138.556{{c}}
* POTE: ~2 = 1200.000, ~12/11 = 140.747
* POTE: ~2 = 1200.000{{c}}, ~12/11 = 140.747{{c}}


{{Optimal ET sequence|legend=0| 8d, 9, 17c }}
{{Optimal ET sequence|legend=0| 8d, 9, 17c }}


Badness (Sintel): 0.8612
Badness (Sintel): 0.861


=== 13-limit ===
=== 13-limit ===
Line 85: Line 83:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~13/12 = 138.741
* CTE: ~2 = 1200.000{{c}}, ~13/12 = 138.741{{c}}
* POTE: ~2 = 1200.000, ~13/12 = 140.751
* POTE: ~2 = 1200.000{{c}}, ~13/12 = 140.751{{c}}


{{Optimal ET sequence|legend=0| 8d, 9, 17c }}
{{Optimal ET sequence|legend=0| 8d, 9, 17c }}


Badness (Sintel): 0.7503
Badness (Sintel): 0.750


=== 17-limit ===
=== 17-limit ===
Line 100: Line 98:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~13/12 = 138.649
* CTE: ~2 = 1200.000{{c}}, ~13/12 = 138.649{{c}}
* POTE: ~2 = 1200.000, ~13/12 = 141.404
* POTE: ~2 = 1200.000{{c}}, ~13/12 = 141.404{{c}}


{{Optimal ET sequence|legend=0| 8d, 9, 17cg }}
{{Optimal ET sequence|legend=0| 8d, 9, 17cg }}


Badness (Sintel): 0.8529
Badness (Sintel): 0.853


=== 19-limit ===
=== 19-limit ===
Line 115: Line 113:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~13/12 = 138.750
* CTE: ~2 = 1200.000{{c}}, ~13/12 = 138.750{{c}}
* POTE: ~2 = 1200.000, ~13/12 = 140.479
* POTE: ~2 = 1200.000{{c}}, ~13/12 = 140.479{{c}}


{{Optimal ET sequence|legend=0| 8d, 9, 17cg }}
{{Optimal ET sequence|legend=0| 8d, 9, 17cg }}


Badness (Sintel): 1.0244
Badness (Sintel): 1.02


== Subklei ==
== Subklei ==
Line 130: Line 128:


{{Mapping|legend=1| 1 3 4 4 | 0 -6 -7 -5 }}
{{Mapping|legend=1| 1 3 4 4 | 0 -6 -7 -5 }}
: mapping generators: ~2, ~7/6
: mapping generators: ~2, ~7/6


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~7/6 = 284.986
* [[CTE]]: ~2 = 1200.000{{c}}, ~7/6 = 284.986{{c}}
: [[error map]]: {{val| 0.000 -11.870 +18.785 +6.245 }}
: [[error map]]: {{val| 0.000 -11.870 +18.785 +6.245 }}
* [[POTE]]: ~2 = 1200.000, ~7/6 = 284.219
* [[POTE]]: ~2 = 1200.000{{c}}, ~7/6 = 284.219{{c}}
: error map: {{val| 0.000 -7.268 +24.154 +10.080 }}
: error map: {{val| 0.000 -7.268 +24.154 +10.080 }}


{{Optimal ET sequence|legend=1| 4, 13cd, 17c, 21, 38c }}
{{Optimal ET sequence|legend=1| 4, 13cd, 17c, 21, 38c }}


[[Badness]] (Sintel): 1.5463
[[Badness]] (Sintel): 1.55


=== 11-limit ===
=== 11-limit ===
Line 151: Line 148:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/6 = 284.265
* CTE: ~2 = 1200.000{{c}}, ~7/6 = 284.265{{c}}
* POTE: ~2 = 1200.000, ~7/6 = 283.253
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 283.253{{c}}


{{Optimal ET sequence|legend=0| 4e, …, 13cdee, 17c }}
{{Optimal ET sequence|legend=0| 4e, …, 13cdee, 17c }}


Badness (Sintel): 1.4761
Badness (Sintel): 1.48


==== 13-limit ====
==== 13-limit ====
Line 166: Line 163:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/6 = 283.918
* CTE: ~2 = 1200.000{{c}}, ~7/6 = 283.918{{c}}
* POTE: ~2 = 1200.000, ~7/6 = 282.856
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 282.856{{c}}


{{Optimal ET sequence|legend=0| 4ef, …, 13cdeef, 17c }}
{{Optimal ET sequence|legend=0| 4ef, …, 13cdeef, 17c }}


Badness (Sintel): 1.3357
Badness (Sintel): 1.34


=== Subkla ===
=== Subkla ===
Line 181: Line 178:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/6 = 284.870
* CTE: ~2 = 1200.000{{c}}, ~7/6 = 284.870{{c}}
* POTE: ~2 = 1200.000, ~7/6 = 283.822
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 283.822{{c}}


{{Optimal ET sequence|legend=0| 4, 17c, 21, 38ce }}
{{Optimal ET sequence|legend=0| 4, 17c, 21, 38ce }}


Badness (Sintel): 1.5620
Badness (Sintel): 1.56


==== 13-limit ====
==== 13-limit ====
Line 196: Line 193:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/6 = 284.758
* CTE: ~2 = 1200.000{{c}}, ~7/6 = 284.758{{c}}
* POTE: ~2 = 1200.000, ~7/6 = 283.882
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 283.882{{c}}


{{Optimal ET sequence|legend=0| 4, 17c, 38ce }}
{{Optimal ET sequence|legend=0| 4, 17c, 38ce }}


Badness (Sintel): 1.5166
Badness (Sintel): 1.52


== Naian ==
== Naian ==
Line 211: Line 208:


{{Mapping|legend=1| 1 5 5 7 | 0 -9 -7 -11 }}
{{Mapping|legend=1| 1 5 5 7 | 0 -9 -7 -11 }}
: mapping generators: ~2, ~98/75
: mapping generators: ~2, ~98/75


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~98/75 = 456.494
* [[CTE]]: ~2 = 1200.000{{c}}, ~98/75 = 456.494{{c}}
: [[error map]]: {{val| 0.000, -10.401, +18.228, +9.740 }}
: [[error map]]: {{val| 0.000, -10.401, +18.228, +9.740 }}
* [[CWE]]: ~2 = 1200.000, ~98/75 = 456.012
* [[CWE]]: ~2 = 1200.000{{c}}, ~98/75 = 456.012{{c}}
: error map: {{val| 0.000, -6.059, +21.606, +15.047 }}
: error map: {{val| 0.000, -6.059, +21.606, +15.047 }}


{{Optimal ET sequence|legend=1| 8d, 13b, 21 }}
{{Optimal ET sequence|legend=1| 8d, 13b, 21 }}


[[Badness]] (Sintel): 2.8912
[[Badness]] (Sintel): 2.89


=== 11-limit ===
=== 11-limit ===
Line 232: Line 228:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~77/60 = 456.625
* CTE: ~2 = 1200.000{{c}}, ~77/60 = 456.625{{c}}
* CWE: ~2 = 1200.000, ~77/60 = 455.798
* CWE: ~2 = 1200.000{{c}}, ~77/60 = 455.798{{c}}


{{Optimal ET sequence|legend=0| 8d, 13b, 21 }}
{{Optimal ET sequence|legend=0| 8d, 13b, 21 }}


Badness (Sintel): 1.9522
Badness (Sintel): 1.95


=== 13-limit ===
=== 13-limit ===
Line 247: Line 243:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~13/10 = 456.767
* CTE: ~2 = 1200.000{{c}}, ~13/10 = 456.767{{c}}
* CWE: ~2 = 1200.000, ~13/10 = 455.730
* CWE: ~2 = 1200.000{{c}}, ~13/10 = 455.730{{c}}


{{Optimal ET sequence|legend=0| 8d, 13b, 21 }}
{{Optimal ET sequence|legend=0| 8d, 13b, 21 }}


Badness (Sintel): 1.5538
Badness (Sintel): 1.55


=== 17-limit ===
=== 17-limit ===
Line 262: Line 258:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~13/10 = 456.821
* CTE: ~2 = 1200.000{{c}}, ~13/10 = 456.821{{c}}
* CWE: ~2 = 1200.000, ~13/10 = 455.732
* CWE: ~2 = 1200.000{{c}}, ~13/10 = 455.732{{c}}


{{Optimal ET sequence|legend=0| 8d, 13b, 21 }}
{{Optimal ET sequence|legend=0| 8d, 13b, 21 }}


Badness (Sintel): 1.4332
Badness (Sintel): 1.43


== Slurpee ==
== Slurpee ==
Line 277: Line 273:


{{Mapping|legend=1| 1 2 3 3 | 0 -7 -11 -3 }}
{{Mapping|legend=1| 1 2 3 3 | 0 -7 -11 -3 }}
: mapping generators: ~2, ~21/20
: mapping generators: ~2, ~21/20


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~21/20 = 72.776
* [[CTE]]: ~2 = 1200.000{{c}}, ~21/20 = 72.776{{c}}
: [[error map]]: {{val| 0.000 -11.385 +13.153 +12.847 }}
: [[error map]]: {{val| 0.000 -11.385 +13.153 +12.847 }}
* [[POTE]]: ~2 = 1200.000, ~21/20 = 72.303
* [[POTE]]: ~2 = 1200.000{{c}}, ~21/20 = 72.303{{c}}
: error map: {{val| 0.000 -8.075 +18.355 +14.265 }}
: error map: {{val| 0.000 -8.075 +18.355 +14.265 }}


{{Optimal ET sequence|legend=1| 16, 17c, 33 }}
{{Optimal ET sequence|legend=1| 16, 17c, 33 }}


[[Badness]] (Sintel): 2.9070
[[Badness]] (Sintel): 2.91


=== 11-limit ===
=== 11-limit ===
Line 298: Line 293:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~21/20 = 72.681
* CTE: ~2 = 1200.000{{c}}, ~21/20 = 72.681{{c}}
* POTE: ~2 = 1200.000, ~21/20 = 72.297
* POTE: ~2 = 1200.000{{c}}, ~21/20 = 72.297{{c}}


{{Optimal ET sequence|legend=0| 16, 17c, 33 }}
{{Optimal ET sequence|legend=0| 16, 17c, 33 }}


Badness (Sintel): 1.6700
Badness (Sintel): 1.67


=== 13-limit ===
=== 13-limit ===
Line 313: Line 308:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~21/20 = 72.653
* CTE: ~2 = 1200.000{{c}}, ~21/20 = 72.653{{c}}
* POTE: ~2 = 1200.000, ~21/20 = 72.409
* POTE: ~2 = 1200.000{{c}}, ~21/20 = 72.409{{c}}


{{Optimal ET sequence|legend=0| 16, 17c, 33 }}
{{Optimal ET sequence|legend=0| 16, 17c, 33 }}


Badness (Sintel): 1.3678
Badness (Sintel): 1.37


== Shallowtone ==
== Shallowtone ==
Line 332: Line 327:


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~3/2 = 681.278
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 681.278{{c}}
: [[error map]]: {{val| 0.000 -20.677 +0.906 +6.510 }}
: [[error map]]: {{val| 0.000 -20.677 +0.906 +6.510 }}
* [[CWE]]: ~2 = 1200.000, ~3/2 = 681.245
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 681.245{{c}}
: error map: {{val| 0.000 -20.710 +1.239 +6.110 }}
: error map: {{val| 0.000 -20.710 +1.239 +6.110 }}


{{Optimal ET sequence|legend=1| 7, 30b, 37b }}
{{Optimal ET sequence|legend=1| 7, 30b, 37b }}


[[Badness]] (Sintel): 7.7857
[[Badness]] (Sintel): 7.79


=== 11-limit ===
=== 11-limit ===
Line 349: Line 344:


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000, ~3/2 = 681.254
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 681.254{{c}}
* CWE: ~2 = 1200.000, ~3/2 = 681.327
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 681.327{{c}}


{{Optimal ET sequence|legend=0| 7, 30b, 37b }}
{{Optimal ET sequence|legend=0| 7, 30b, 37b }}


Badness (Sintel): 4.2942
Badness (Sintel): 4.29


=== 13-limit ===
=== 13-limit ===
Line 364: Line 359:


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000, ~3/2 = 681.237
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 681.237{{c}}
* CWE: ~2 = 1200.000, ~3/2 = 681.267
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 681.267{{c}}


{{Optimal ET sequence|legend=0| 7, 30b, 37b }}
{{Optimal ET sequence|legend=0| 7, 30b, 37b }}


Badness (Sintel): 3.1927
Badness (Sintel): 3.19


== Notes ==
== References ==


[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Mint temperaments| ]] <!-- main article -->
[[Category:Mint temperaments| ]] <!-- main article -->
[[Category:Mint| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Mint_temperaments"