Mint temperaments: Difference between revisions

m Units & misc. cleanup. - redundant category
Switch to WE & CWE tunings
Line 28: Line 28:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~7/6 = 231.845{{c}}
* [[WE]]: ~2 = 1186.8093{{c}}, ~7/6 = 237.3390{{c}}
: [[error map]]: {{val| -13.191 -3.129 +61.983 -45.851 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/6 = 231.845{{c}}
: error map: {{val| 0.000 +6.291 +85.850 -24.498 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~7/6 = 236.0819{{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{{c}}, ~7/6 = 239.977{{c}}
* [[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 }}
Line 51: Line 55:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~15/14 = 138.611{{c}}
* [[WE]]: ~2 = 1193.9544{{c}}, ~15/14 = 140.2169{{c}}
: [[error map]]: {{val| -6.046 -6.916 +22.246 +0.601 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~15/14 = 139.8991{{c}}
: error map: {{val| 0.000 -2.460 +33.384 +10.468 }}
<!-- * [[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{{c}}, ~15/14 = 140.927{{c}}
* [[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 }}
Line 68: Line 76:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~12/11 = 138.556{{c}}
* WE: ~2 = 1194.7089{{c}}, ~12/11 = 140.1262{{c}}
* POTE: ~2 = 1200.000{{c}}, ~12/11 = 140.747{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 139.8776{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~12/11 = 138.556{{c}}
* 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 }}
Line 83: Line 93:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~13/12 = 138.741{{c}}
* WE: ~2 = 1195.3694{{c}}, ~13/12 = 140.2080{{c}}
* POTE: ~2 = 1200.000{{c}}, ~13/12 = 140.751{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.9749{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~13/12 = 138.741{{c}}
* 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 }}
Line 98: Line 110:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~13/12 = 138.649{{c}}
* WE: ~2 = 1193.8350{{c}}, ~13/12 = 140.6779{{c}}
* POTE: ~2 = 1200.000{{c}}, ~13/12 = 141.404{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 140.5885{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~13/12 = 138.649{{c}}
* 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 }}
Line 113: Line 127:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~13/12 = 138.750{{c}}
* WE: ~2 = 1196.1446{{c}}, ~13/12 = 140.0276{{c}}
* POTE: ~2 = 1200.000{{c}}, ~13/12 = 140.479{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 140.0301{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~13/12 = 138.750{{c}}
* 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 }}
Line 127: Line 143:
[[Comma list]]: 36/35, 1029/1000
[[Comma list]]: 36/35, 1029/1000


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


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~7/6 = 284.986{{c}}
* [[WE]]: ~2 = 1197.5285{{c}}, ~5/3 = 915.8950{{c}}
: [[error map]]: {{val| -2.471 -11.171 +18.366 +3.121 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/3 = 915.4228{{c}}
: error map: {{val| 0.000 -9.418 +21.646 +8.288 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/3 = 915.014{{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{{c}}, ~7/6 = 284.219{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/3 = 915.781{{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 }}
Line 145: Line 165:
Comma list: 36/35, 77/75, 352/343
Comma list: 36/35, 77/75, 352/343


Mapping: {{mapping| 1 3 4 4 7 | 0 -6 -7 -5 -15 }}
Mapping: {{mapping| 1 -3 -3 -1 -8 | 0 6 7 5 15 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~7/6 = 284.265{{c}}
* WE: ~2 = 1196.3345{{c}}, ~5/3 = 913.9469{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 283.253{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 916.2970{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/3 = 915.735{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/3 = 916.747{{c}} -->


{{Optimal ET sequence|legend=0| 4e, …, 13cdee, 17c }}
{{Optimal ET sequence|legend=0| 4e, …, 13cdee, 17c }}
Line 160: Line 182:
Comma list: 26/25, 36/35, 66/65, 352/343  
Comma list: 26/25, 36/35, 66/65, 352/343  


Mapping: {{mapping| 1 3 4 4 7 7 | 0 -6 -7 -5 -15 -14 }}
Mapping: {{mapping| 1 3 4 4 7 7 | 0 6 7 5 15 14 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~7/6 = 283.918{{c}}
* WE: ~2 = 1196.0784{{c}}, ~5/3 = 914.1466{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 282.856{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 916.6712{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/3 = 916.082{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/3 = 917.144{{c}} -->


{{Optimal ET sequence|legend=0| 4ef, …, 13cdeef, 17c }}
{{Optimal ET sequence|legend=0| 4ef, …, 13cdeef, 17c }}
Line 175: Line 199:
Comma list: 36/35, 56/55, 1029/1000
Comma list: 36/35, 56/55, 1029/1000


Mapping: {{mapping| 1 3 4 4 3 | 0 -6 -7 -5 2 }}
Mapping: {{mapping| 1 -3 -3 -1 5 | 0 6 7 5 -2 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~7/6 = 284.870{{c}}
* WE: ~2 = 1196.3809{{c}}, ~5/3 = 913.4153{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 283.822{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 915.8804{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/3 = 915.130{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/3 = 916.178{{c}} -->


{{Optimal ET sequence|legend=0| 4, 17c, 21, 38ce }}
{{Optimal ET sequence|legend=0| 4, 13cd, 17c, 38ce }}


Badness (Sintel): 1.56
Badness (Sintel): 1.56
Line 190: Line 216:
Comma list: 36/35, 56/55, 66/65, 640/637
Comma list: 36/35, 56/55, 66/65, 640/637


Mapping: {{mapping| 1 3 4 4 3 3 | 0 -6 -7 -5 2 3 }}
Mapping: {{mapping| 1 -3 -3 -1 5 6 | 0 6 7 5 -2 -3 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~7/6 = 284.758{{c}}
* WE: ~2 = 1196.5477{{c}}, ~5/3 = 913.4822{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 283.882{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 915.9416{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~7/6 = 284.758{{c}}
* 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 }}
Line 207: Line 235:
[[Comma list]]: 36/35, 9604/9375  
[[Comma list]]: 36/35, 9604/9375  


{{Mapping|legend=1| 1 5 5 7 | 0 -9 -7 -11 }}
{{Mapping|legend=1| 1 -4 -2 -4 | 0 9 7 11 }}
: mapping generators: ~2, ~98/75
: mapping generators: ~2, ~75/49


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~98/75 = 456.494{{c}}
* [[WE]]: ~2 = 1195.8807{{c}}, ~75/49 = 741.8522{{c}}
: [[error map]]: {{val| 0.000, -10.401, +18.228, +9.740 }}
: [[error map]]: {{val| -4.119 -8.808 +14.890 +8.026 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~98/75 = 456.012{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~75/49 = 743.9885{{c}}
: error map: {{val| 0.000, -6.059, +21.606, +15.047 }}
: error map: {{val| 0.000 -6.059 +21.606 +15.047 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~75/49 = 743.506{{c}}
: [[error map]]: {{val| 0.000, -10.401, +18.228, +9.740 }} -->


{{Optimal ET sequence|legend=1| 8d, 13b, 21 }}
{{Optimal ET sequence|legend=1| 8d, 21, 29cd }}


[[Badness]] (Sintel): 2.89
[[Badness]] (Sintel): 2.89
Line 225: Line 255:
Comma list: 36/35, 56/55, 2541/2500  
Comma list: 36/35, 56/55, 2541/2500  


Mapping: {{mapping| 1 5 5 7 5 | 0 -9 -7 -11 -4 }}
Mapping: {{mapping| 1 -4 -2 -4 1 | 0 9 7 11 4 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~77/60 = 456.625{{c}}
* WE: ~2 = 1194.3937{{c}}, ~75/49 = 741.2117{{c}}
* CWE: ~2 = 1200.000{{c}}, ~77/60 = 455.798{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~75/49 = 744.2018{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~75/49 = 743.375{{c}} -->


{{Optimal ET sequence|legend=0| 8d, 13b, 21 }}
{{Optimal ET sequence|legend=0| 8d, 21, 29cde }}


Badness (Sintel): 1.95
Badness (Sintel): 1.95
Line 240: Line 271:
Comma list: 36/35, 56/55, 66/65, 507/500  
Comma list: 36/35, 56/55, 66/65, 507/500  


Mapping: {{mapping| 1 5 5 7 5 6 | 0 -9 -7 -11 -4 -6 }}
Mapping: {{mapping| 1 -4 -2 -4 1 0 | 0 9 7 11 4 6 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~13/10 = 456.767{{c}}
* WE: ~2 = 1193.8564{{c}}, ~20/13 = 740.9635{{c}}
* CWE: ~2 = 1200.000{{c}}, ~13/10 = 455.730{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.2703{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~20/13 = 743.233{{c}} -->


{{Optimal ET sequence|legend=0| 8d, 13b, 21 }}
{{Optimal ET sequence|legend=0| 8d, 21, 29cdef }}


Badness (Sintel): 1.55
Badness (Sintel): 1.55
Line 255: Line 287:
Comma list: 36/35, 51/50, 56/55, 66/65, 170/169  
Comma list: 36/35, 51/50, 56/55, 66/65, 170/169  


Mapping: {{mapping| 1 5 5 7 5 6 6 | 0 -9 -7 -11 -4 -6 -5 }}
Mapping: {{mapping| 1 -4 -2 -4 1 0 1 | 0 9 7 11 4 6 5 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~13/10 = 456.821{{c}}
* WE: ~2 = 1194.2330{{c}}, ~20/13 = 741.1242{{c}}
* CWE: ~2 = 1200.000{{c}}, ~13/10 = 455.732{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.2679{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~20/13 = 743.179{{c}} -->


{{Optimal ET sequence|legend=0| 8d, 13b, 21 }}
{{Optimal ET sequence|legend=0| 8d, 21, 29cdef }}


Badness (Sintel): 1.43
Badness (Sintel): 1.43
Line 276: Line 309:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~21/20 = 72.776{{c}}
* [[WE]]: ~2 = 1197.9281{{c}}, ~21/20 = 72.1780{{c}}
: [[error map]]: {{val| -2.072 -11.345 +13.512 +8.424 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 72.4941{{c}}
: error map: {{val| 0.000 -9.414 +16.251 +13.692 }}
<!-- * [[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{{c}}, ~21/20 = 72.303{{c}}
* [[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 }}
Line 293: Line 330:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~21/20 = 72.681{{c}}
* WE: ~2 = 1198.4220{{c}}, ~21/20 = 72.2015{{c}}
* POTE: ~2 = 1200.000{{c}}, ~21/20 = 72.297{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 72.4470{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~21/20 = 72.681{{c}}
* 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 }}
Line 308: Line 347:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~21/20 = 72.653{{c}}
* WE: ~2 = 1199.0238{{c}}, ~21/20 = 72.3506{{c}}
* POTE: ~2 = 1200.000{{c}}, ~21/20 = 72.409{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 72.4956{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~21/20 = 72.653{{c}}
* 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 }}
Line 323: Line 364:


{{Mapping|legend=1| 1 0 18 -16 | 0 1 -10 12 }}
{{Mapping|legend=1| 1 0 18 -16 | 0 1 -10 12 }}
: mapping generators: ~2, ~3
: mapping generators: ~2, ~3


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 681.278{{c}}
* [[WE]]: ~2 = 1202.4397{{c}}, ~3/2 = 682.6219{{c}}
: [[error map]]: {{val| 0.000 -20.677 +0.906 +6.510 }}
: [[error map]]: {{val| +2.440 -16.893 +6.986 +12.877 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 681.245{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 681.2447{{c}}
: error map: {{val| 0.000 -20.710 +1.239 +6.110 }}
: error map: {{val| 0.000 -20.710 +1.239 +6.110 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 681.278{{c}}
: [[error map]]: {{val| 0.000 -20.677 +0.906 +6.510 }} -->


{{Optimal ET sequence|legend=1| 7, 30b, 37b }}
{{Optimal ET sequence|legend=1| 7, 30b, 37b }}
Line 344: Line 386:


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 681.254{{c}}
* WE: ~2 = 1202.0285{{c}}, ~3/2 = 682.4922{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 681.327{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 681.3267{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 681.254{{c}} -->


{{Optimal ET sequence|legend=0| 7, 30b, 37b }}
{{Optimal ET sequence|legend=0| 7, 30b, 37b }}
Line 359: Line 402:


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 681.237{{c}}
* WE: ~2 = 1201.4928{{c}}, ~3/2 = 682.1188{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 681.267{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 681.2669{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 681.237{{c}} -->


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