Xenharmonic Wiki

Marvel temperaments: Difference between revisions

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m - redundant category
Switch to Sintel's badness, WE & CWE tunings
Line 55: Line 55:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~1225/864 = 600.000{{c}}, ~245/216 = 216.919{{c}}
* [[WE]]: ~1225/864 = 600.3438{{c}}, ~245/216 = 216.8680{{c}}
: [[error map]]: {{val| +0.688 -0.403 -1.463 +0.541 }}
* [[CWE]]: ~1225/864 = 600.0000{{c}}, ~245/216 = 216.7977{{c}}
: error map: {{val| 0.000 -1.169 -3.111 -0.849 }}
<!-- * [[CTE]]: ~1225/864 = 600.000{{c}}, ~245/216 = 216.919{{c}}
: [[error map]]: {{val| 0.000 -0.443 -3.232 +0.361 }}
: [[error map]]: {{val| 0.000 -0.443 -3.232 +0.361 }}
* [[POTE]]: ~1225/864 = 600.000{{c}}, ~245/216 = 216.744{{c}}
* [[POTE]]: ~1225/864 = 600.000{{c}}, ~245/216 = 216.744{{c}}
: error map: {{val| 0.000 -1.492 -3.057 -1.388 }}
: error map: {{val| 0.000 -1.492 -3.057 -1.388 }} -->


{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 382c }}
{{Optimal ET sequence|legend=1| 22, 50, 72, 238c, 310c, 382c, 454bccd }}


[[Badness]] (Smith): 0.040846
[[Badness]] (Sintel): 1.03


=== 11-limit ===
=== 11-limit ===
Line 72: Line 76:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 600.000{{c}}, ~25/22 = 216.900{{c}}
* WE: ~99/70 = 600.3051{{c}}, ~25/22 = 216.8782{{c}}
* POTE: ~99/70 = 600.000{{c}}, ~25/22 = 216.768{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~25/22 = 216.7961{{c}}
<!-- * CTE: ~99/70 = 600.000{{c}}, ~25/22 = 216.900{{c}}
* POTE: ~99/70 = 600.000{{c}}, ~25/22 = 216.768{{c}} -->


{{Optimal ET sequence|legend=0| 22, 50, 72, 166, 238c, 310c }}
{{Optimal ET sequence|legend=0| 22, 50, 72, 166, 238c, 310c }}


Badness (Smith): 0.018539
Badness (Sintel): 0.613


==== Lizard ====
==== Lizard ====
Line 87: Line 93:


Optimal tunings:  
Optimal tunings:  
* CTE: ~55/39 = 600.000{{c}}, ~25/22 = 216.703{{c}}
* WE: ~55/39 = 600.4824{{c}}, ~25/22 = 216.7852{{c}}
* POTE: ~55/39 = 600.000{{c}}, ~25/22 = 216.711{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~25/22 = 216.6247{{c}}
<!-- * CTE: ~55/39 = 600.000{{c}}, ~25/22 = 216.703{{c}}
* POTE: ~55/39 = 600.000{{c}}, ~25/22 = 216.711{{c}} -->


{{Optimal ET sequence|legend=0| 22, 50, 72, 122, 194df }}
{{Optimal ET sequence|legend=0| 22, 50, 72 }}


Badness (Smith): 0.021781
Badness (Sintel): 0.900


===== 17-limit =====
===== 17-limit =====
Line 102: Line 110:


Optimal tunings:  
Optimal tunings:  
* CTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.748{{c}}
* WE: ~17/12 = 600.5032{{c}}, ~17/15 = 216.8002{{c}}
* POTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.619{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.6361{{c}}
<!-- * CTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.748{{c}}
* POTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.619{{c}} -->


{{Optimal ET sequence|legend=0| 22, 50, 72, 122g, 194dfg }}
{{Optimal ET sequence|legend=0| 22, 50, 72 }}


Badness (Smith): 0.014536
Badness (Sintel): 0.741


===== 19-limit =====
===== 19-limit =====
Line 117: Line 127:


Optimal tunings:  
Optimal tunings:  
* CTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.677{{c}}
* WE: ~17/12 = 600.4698{{c}}, ~17/15 = 216.6925{{c}}
* POTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.523{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.5434{{c}}
<!-- * CTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.677{{c}}
* POTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.523{{c}} -->


{{Optimal ET sequence|legend=0| 22h, 50, 72, 122g, 194dfg }}
{{Optimal ET sequence|legend=0| 22h, 50, 72, 122g, 194dfg }}


Badness (Smith): 0.015702
Badness (Sintel): 0.955


==== Gizzard ====
==== Gizzard ====
Line 132: Line 144:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 600.000{{c}}, ~25/22 = 216.928{{c}}
* WE: ~99/70 = 600.2896{{c}}, ~25/22 = 216.9343{{c}}
* POTE: ~99/70 = 600.000{{c}}, ~25/22 = 216.830{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~25/22 = 216.8501{{c}}
<!-- * CTE: ~99/70 = 600.000{{c}}, ~25/22 = 216.928{{c}}
* POTE: ~99/70 = 600.000{{c}}, ~25/22 = 216.830{{c}} -->


{{Optimal ET sequence|legend=0| 22f, 72, 166, 238cf }}
{{Optimal ET sequence|legend=0| 22f, 72, 166, 238cf }}


Badness (Smith): 0.020252
Badness (Sintel): 0.837


===== 17-limit =====
===== 17-limit =====
Line 147: Line 161:


Optimal tunings:  
Optimal tunings:  
* CTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.943{{c}}
* WE: ~17/12 = 600.3227{{c}}, ~17/15 = 216.9414{{c}}
* POTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.825{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.8469{{c}}
<!-- * CTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.943{{c}}
* POTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.825{{c}} -->


{{Optimal ET sequence|legend=0| 22f, 72, 166g, 238cfg }}
{{Optimal ET sequence|legend=0| 22f, 72, 166g, 238cfg }}


Badness (Smith): 0.013624
Badness (Sintel): 0.694


===== 19-limit =====
===== 19-limit =====
Line 162: Line 178:


Optimal tunings:  
Optimal tunings:  
* CTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.918{{c}}
* WE: ~17/12 = 600.2637{{c}}, ~17/15 = 216.9570{{c}}
* POTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.862{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.8687{{c}}
<!-- * CTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.918{{c}}
* POTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.862{{c}} -->


{{Optimal ET sequence|legend=0| 72, 94, 166g }}
{{Optimal ET sequence|legend=0| 72, 94, 166g }}


Badness (Smith): 0.014810
Badness (Sintel): 0.901


=== Mage ===
=== Mage ===
Line 177: Line 195:


Optimal tunings:  
Optimal tunings:  
* CTE: ~77/54 = 600.000{{c}}, ~55/48 = 217.247{{c}}
* WE: ~77/54 = 600.6486{{c}}, ~55/48 = 217.1099{{c}}
* POTE: ~77/54 = 600.000{{c}}, ~55/48 = 216.876{{c}}
* CWE: ~77/54 = 600.0000{{c}}, ~55/48 = 216.9841{{c}}
<!-- * CTE: ~77/54 = 600.000{{c}}, ~55/48 = 217.247{{c}}
* POTE: ~77/54 = 600.000{{c}}, ~55/48 = 216.876{{c}} -->


{{Optimal ET sequence|legend=0| 22, 50e, 72ee }}
{{Optimal ET sequence|legend=0| 22, 50e, 72ee }}


Badness (Smith): 0.057799
Badness (Sintel): 1.91


== Tritonic ==
== Tritonic ==
Line 191: Line 211:
[[Comma list]]: 225/224, 50421/50000
[[Comma list]]: 225/224, 50421/50000


{{Mapping|legend=1| 1 4 -3 -3 | 0 -5 11 12 }}
{{Mapping|legend=1| 1 -1 8 9 | 0 5 -11 -12 }}
: mapping generators: ~2, ~10/7


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~7/5 = 580.286{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1201.3539{{c}}, ~10/7 = 620.4131{{c}}
: [[error map]]: {{val| +1.354 -1.243 -0.027 -1.598 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 619.6778{{c}}
: error map: {{val| 0.000 -3.566 -2.769 -4.959 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~10/7 = 619.714{{c}} -->


{{Optimal ET sequence|legend=1| 29, 31, 60, 91, 122, 213bcd }}
{{Optimal ET sequence|legend=1| 29, 31, 60, 91, 122, 213bcd }}


[[Badness]] (Smith): 0.047578
[[Badness]] (Sintel): 1.20


=== 11-limit ===
=== 11-limit ===
Line 204: Line 230:
Comma list: 121/120, 225/224, 441/440
Comma list: 121/120, 225/224, 441/440


Mapping: {{mapping| 1 4 -3 -3 2 | 0 -5 11 12 3 }}
Mapping: {{mapping| 1 -1 8 9 5 | 0 5 -11 -12 -3 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 580.267{{c}}
Optimal tunings:
* WE: ~2 = 1201.7116{{c}}, ~10/7 = 620.6166{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.6890{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~10/7 = 619.733{{c}} -->


{{Optimal ET sequence|legend=0| 29, 31, 60e }}
{{Optimal ET sequence|legend=0| 29, 31, 60e, 91e, 213bcdeee }}


Badness (Smith): 0.023659
Badness (Sintel): 0.782


==== 13-limit ====
==== 13-limit ====
Line 217: Line 246:
Comma list: 105/104, 121/120, 196/195, 275/273
Comma list: 105/104, 121/120, 196/195, 275/273


Mapping: {{mapping| 1 4 -3 -3 2 -5 | 0 -5 11 12 3 18 }}
Mapping: {{mapping| 1 -1 8 9 5 13 | 0 5 -11 -12 -3 -18 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 580.108{{c}}
Optimal tunings:
* WE: ~2 = 1201.5355{{c}}, ~10/7 = 620.6855{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.8469{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~10/7 = 619.892{{c}} -->


{{Optimal ET sequence|legend=0| 29, 31, 60e }}
{{Optimal ET sequence|legend=0| 29, 31, 60e }}


Badness (Smith): 0.022993
Badness (Sintel): 0.950


==== 17-limit ====
==== 17-limit ====
Line 230: Line 262:
Comma list: 105/104, 121/120, 154/153, 196/195, 273/272
Comma list: 105/104, 121/120, 154/153, 196/195, 273/272


Mapping: {{mapping| 1 4 -3 -3 2 -5 -8 | 0 -5 11 12 3 18 25 }}
Mapping: {{mapping| 1 -1 8 9 5 13 17 | 0 5 -11 -12 -3 -18 -25 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 580.055{{c}}
Optimal tunings:
* WE: ~2 = 1201.5260{{c}}, ~10/7 = 620.7330{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.8986{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~10/7 = 619.945{{c}} -->


{{Optimal ET sequence|legend=0| 29g, 31, 60e }}
{{Optimal ET sequence|legend=0| 29g, 31, 60e }}


Badness (Smith): 0.019093
Badness (Sintel): 0.973


==== 19-limit ====
==== 19-limit ====
Line 243: Line 278:
Comma list: 77/76, 105/104, 121/120, 153/152, 196/195, 273/272
Comma list: 77/76, 105/104, 121/120, 153/152, 196/195, 273/272


Mapping: {{mapping| 1 4 -3 -3 2 -5 -8 -3 | 0 -5 11 12 3 18 25 15 }}
Mapping: {{mapping| 1 -1 8 9 5 13 17 12 | 0 5 -11 -12 -3 -18 -25 -15 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 580.026{{c}}
Optimal tunings:
* WE: ~2 = 1201.3100{{c}}, ~10/7 = 620.6509{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.9328{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~10/7 = 619.974{{c}} -->


{{Optimal ET sequence|legend=0| 29g, 31, 60e }}
{{Optimal ET sequence|legend=0| 29g, 31, 60e }}


Badness (Smith): 0.017010
Badness (Sintel): 1.03


==== 23-limit ====
==== 23-limit ====
Line 256: Line 294:
Comma list: 77/76, 105/104, 115/114, 121/120, 153/152, 161/160, 196/195
Comma list: 77/76, 105/104, 115/114, 121/120, 153/152, 161/160, 196/195


Mapping: {{mapping| 1 4 -3 -3 2 -5 -8 -3 5 | 0 -5 11 12 3 18 25 15 -1 }}
Mapping: {{mapping| 1 -1 8 9 5 13 17 12 4 | 0 5 -11 -12 -3 -18 -25 -15 1 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 580.009{{c}}
Optimal tunings:
* WE: ~2 = 1201.4074{{c}}, ~10/7 = 620.7185{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.9548{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~10/7 = 619.991{{c}} -->


{{Optimal ET sequence|legend=0| 29g, 31, 60e }}
{{Optimal ET sequence|legend=0| 29g, 31, 60e }}


Badness (Smith): 0.014471
Badness (Sintel): 1.04


=== Tritoni ===
=== Tritoni ===
Line 269: Line 310:
Comma list: 225/224, 385/384, 27783/27500
Comma list: 225/224, 385/384, 27783/27500


Mapping: {{mapping| 1 4 -3 -3 17 | 0 -5 11 12 -28 }}
Mapping: {{mapping| 1 -1 8 9 -11 | 0 5 -11 -12 28 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 580.389{{c}}
Optimal tunings:
* WE: ~2 = 1201.0888{{c}}, ~10/7 = 620.1733{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.6146{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~10/7 = 619.611{{c}} -->


{{Optimal ET sequence|legend=0| 31, 91, 122, 153d }}
{{Optimal ET sequence|legend=0| 31, 91, 122, 153d }}


Badness (Smith): 0.045456
Badness (Sintel): 1.50


== Septimin ==
== Septimin ==
Line 284: Line 328:
[[Comma list]]: 225/224, 84035/82944
[[Comma list]]: 225/224, 84035/82944


{{Mapping|legend=1| 1 4 1 5 | 0 -11 6 -10 }}
{{Mapping|legend=1| 1 -7 7 -5 | 0 11 -6 10 }}
: mapping generators: ~2, ~12/7


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~7/6 = 263.632{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1201.2452{{c}}, ~12/7 = 937.3394{{c}}
: [[error map]]: {{val| +1.245 +0.062 -1.633 -1.658 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~12/7 = 936.4036{{c}}
: error map: {{val| 0.000 -1.516 -4.735 -4.790 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~12/7 = 936.368{{c}} -->


{{Optimal ET sequence|legend=1| 41, 91, 132d }}
{{Optimal ET sequence|legend=1| 41, 91, 132d }}


[[Badness]] (Smith): 0.054502
[[Badness]] (Sintel): 1.38


=== 11-limit ===
=== 11-limit ===
Line 297: Line 347:
Comma list: 225/224, 245/242, 385/384
Comma list: 225/224, 245/242, 385/384


Mapping: {{mapping| 1 4 1 5 5 | 0 -11 6 -10 -7 }}
Mapping: {{mapping| 1 -7 7 -5 -2 | 0 11 -6 10 7 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/6 = 263.634{{c}}
Optimal tunings:
* WE: ~2 = 1200.8059{{c}}, ~12/7 = 936.9952{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3906{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~12/7 = 936.366{{c}} -->


{{Optimal ET sequence|legend=0| 41, 91, 223cdef }}
{{Optimal ET sequence|legend=0| 41, 91, 223cdef }}


Badness (Smith): 0.031309
Badness (Sintel): 1.04


=== 13-limit ===
=== 13-limit ===
Line 310: Line 363:
Comma list: 105/104, 144/143, 196/195, 245/242
Comma list: 105/104, 144/143, 196/195, 245/242


Mapping: {{mapping| 1 4 1 5 5 7 | 0 -11 6 -10 -7 -15 }}
Mapping: {{mapping| 1 -7 7 -5 -2 -8 | 0 11 -6 10 7 15 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/6 = 263.700{{c}}
Optimal tunings:
* WE: ~2 = 1200.5990{{c}}, ~12/7 = 936.7670{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3196{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~12/7 = 936.300{{c}} -->


{{Optimal ET sequence|legend=0| 41, 91 }}
{{Optimal ET sequence|legend=0| 41, 91 }}


Badness (Smith): 0.023117
Badness (Sintel): 0.955


== Merman ==
== Merman ==
Line 325: Line 381:
[[Comma list]]: 225/224, 2500000/2470629
[[Comma list]]: 225/224, 2500000/2470629


{{Mapping|legend=1| 1 5 -5 -5 | 0 -7 15 16 }}
{{Mapping|legend=1| 1 -2 10 11 | 0 7 -15 -16 }}
: mapping generators: ~2, ~10/7


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~7/5 = 585.585{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.3898{{c}}, ~10/7 = 614.6413{{c}}
: [[error map]]: {{val| +0.390 -0.435 -1.630 +1.634 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 614.4073{{c}}
: error map: {{val| 0.000 -1.104 -2.423 +0.657 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~10/7 = 614.415{{c}} -->


{{Optimal ET sequence|legend=1| 41, 84, 125 }}
{{Optimal ET sequence|legend=1| 41, 84, 125 }}


[[Badness]] (Smith): 0.055078
[[Badness]] (Sintel): 1.39


=== 11-limit ===
=== 11-limit ===
Line 338: Line 400:
Comma list: 225/224, 441/440, 1344/1331
Comma list: 225/224, 441/440, 1344/1331


Mapping: {{mapping| 1 5 -5 -5 2 | 0 -7 15 16 3 }}
Mapping: {{mapping| 1 -2 10 11 5 | 0 7 -15 -16 -3 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 585.606{{c}}
Optimal tunings:
* WE: ~2 = 1199.9578{{c}}, ~10/7 = 614.3720{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.3943{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~10/7 = 614.394{{c}} -->


{{Optimal ET sequence|legend=0| 41, 84, 125e }}
{{Optimal ET sequence|legend=0| 41, 84, 125e }}


Badness (Smith): 0.036383
Badness (Sintel): 1.20


=== 13-limit ===
=== 13-limit ===
Line 351: Line 416:
Comma list: 144/143, 225/224, 364/363, 441/440
Comma list: 144/143, 225/224, 364/363, 441/440


Mapping: {{mapping| 1 5 -5 -5 2 12 | 0 -7 15 16 3 -17 }}
Mapping: {{mapping| 1 -2 10 11 5 -5 | 0 7 -15 -16 -3 17 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 585.657{{c}}
Optimal tunings:
* WE: ~2 = 1199.7422{{c}}, ~10/7 = 614.2110{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.3442{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~10/7 = 614.343{{c}} -->


{{Optimal ET sequence|legend=0| 41, 84, 125e, 209ef, 293ef }}
{{Optimal ET sequence|legend=0| 41, 84, 125e, 209ef, 293ef }}


Badness (Smith): 0.027544
Badness (Sintel): 1.14


== Slender ==
== Slender ==
Line 367: Line 435:


{{Mapping|legend=1| 1 2 2 3 | 0 -13 10 -6 }}
{{Mapping|legend=1| 1 2 2 3 | 0 -13 10 -6 }}
: mapping generators: ~2, ~49/48


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~49/48 = 38.413{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.3816{{c}}, ~49/48 = 38.4256{{c}}
: [[error map]]: {{val| +0.382 -0.725 -1.295 +1.765 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/48 = 38.4079{{c}}
: error map: {{val| 0.000 -1.257 -2.235 +0.727 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~49/48 = 38.413{{c}} -->


{{Optimal ET sequence|legend=1| 31, 94, 125 }}
{{Optimal ET sequence|legend=1| 31, 94, 125, 406c }}


[[Badness]] (Smith): 0.056934
[[Badness]] (Sintel): 1.44


=== 11-limit ===
=== 11-limit ===
Line 381: Line 455:
Mapping: {{mapping| 1 2 2 3 4 | 0 -13 10 -6 -17 }}
Mapping: {{mapping| 1 2 2 3 4 | 0 -13 10 -6 -17 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~49/48 = 38.387{{c}}
Optimal tunings:
* WE: ~2 = 1199.4983{{c}}, ~49/48 = 38.4030{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 38.3775{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~49/48 = 38.387{{c}} -->


{{Optimal ET sequence|legend=0| 31, 63, 94, 125 }}
{{Optimal ET sequence|legend=0| 31, 63, 94, 125 }}


Badness (Smith): 0.025342
Badness (Sintel): 0.838


=== 13-limit ===
=== 13-limit ===
Line 394: Line 471:
Mapping: {{mapping| 1 2 2 3 4 3 | 0 -13 10 -6 -17 22 }}
Mapping: {{mapping| 1 2 2 3 4 3 | 0 -13 10 -6 -17 22 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~49/48 = 38.314{{c}}
Optimal tunings:
* WE: ~2 = 1200.1728{{c}}, ~49/48 = 38.3192{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 38.3129{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~49/48 = 38.314{{c}} -->


{{Optimal ET sequence|legend=0| 31, 63, 94 }}
{{Optimal ET sequence|legend=0| 31, 63, 94 }}


Badness (Smith): 0.025913
Badness (Sintel): 1.07


== Triton ==
== Triton ==
Line 408: Line 488:


{{Mapping|legend=1| 1 0 6 7 | 0 3 -7 -8 }}
{{Mapping|legend=1| 1 0 6 7 | 0 3 -7 -8 }}
: mapping generators: ~2, ~10/7


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~7/5 = 568.865{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1203.3828{{c}}, ~10/7 = 632.9137{{c}}
: [[error map]]: {{val| +3.383 -3.214 +3.587 -8.457 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 630.9827{{c}}
: error map: {{val| 0.000 -9.007 -3.192 -16.687 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~10/7 = 631.135{{c}} -->


{{Optimal ET sequence|legend=1| 2, 17d, 19, 78bd, 97bd }}
{{Optimal ET sequence|legend=1| 2, 17d, 19, 78bd, 97bd }}


[[Badness]] (Smith): 0.059245
[[Badness]] (Sintel): 1.50


=== 11-limit ===
=== 11-limit ===
Line 422: Line 508:
Mapping: {{mapping| 1 0 6 7 4 | 0 3 -7 -8 -1 }}
Mapping: {{mapping| 1 0 6 7 4 | 0 3 -7 -8 -1 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 569.144{{c}}
Optimal tunings:
* WE: ~2 = 1201.3875{{c}}, ~10/7 = 631.5852{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 630.8007{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~7/5 = 569.144{{c}} -->


{{Optimal ET sequence|legend=0| 2, 17d, 19, 59bde, 78bde, 97bde }}
{{Optimal ET sequence|legend=0| 2, 17d, 19 }}


Badness (Smith): 0.045675
Badness (Sintel): 1.51


== Marvolo ==
== Marvolo ==
Line 434: Line 523:


{{Mapping|legend=1| 1 2 1 1 | 0 -6 19 26 }}
{{Mapping|legend=1| 1 2 1 1 | 0 -6 19 26 }}
: mapping generators: ~2, ~21/20


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~21/20 = 83.348{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.7714{{c}}, ~21/20 = 83.4014{{c}}
: [[error map]]: {{val| +0.772 -0.820 -0.916 +0.381 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 83.3640{{c}}
: error map: {{val| 0.000 -2.139 -2.398 -1.362 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~21/20 = 83.348{{c}} -->


{{Optimal ET sequence|legend=1| 29, 43, 72, 619bcd, 691bcd }}
{{Optimal ET sequence|legend=1| 29, 43, 72, 619bbccd, 691bbccd }}


[[Badness]] (Smith): 0.083338
[[Badness]] (Sintel): 2.11


=== 11-limit ===
=== 11-limit ===
Line 448: Line 543:
Mapping: {{mapping| 1 2 1 1 2 | 0 -6 19 26 21 }}
Mapping: {{mapping| 1 2 1 1 2 | 0 -6 19 26 21 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/20 = 83.340{{c}}
Optimal tunings:
* WE: ~2 = 1200.7075{{c}}, ~21/20 = 83.3888{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3564{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~21/20 = 83.340{{c}} -->


{{Optimal ET sequence|legend=0| 29, 43, 72 }}
{{Optimal ET sequence|legend=0| 29, 43, 72 }}


Badness (Smith): 0.028965
Badness (Sintel): 0.958


=== 13-limit ===
=== 13-limit ===
Line 461: Line 559:
Mapping: {{mapping| 1 2 1 1 2 3 | 0 -6 19 26 21 10 }}
Mapping: {{mapping| 1 2 1 1 2 3 | 0 -6 19 26 21 10 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/20 = 83.330{{c}}
Optimal tunings:
* WE: ~2 = 1200.9467{{c}}, ~21/20 = 83.3956{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3516{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~21/20 = 83.330{{c}} -->


{{Optimal ET sequence|legend=0| 29, 43, 72, 115f }}
{{Optimal ET sequence|legend=0| 29, 43, 72 }}


Badness (Smith): 0.021470
Badness (Sintel): 0.887


=== 17-limit ===
=== 17-limit ===
Line 474: Line 575:
Mapping: {{mapping| 1 2 1 1 2 3 2 | 0 -6 19 26 21 10 30 }}
Mapping: {{mapping| 1 2 1 1 2 3 2 | 0 -6 19 26 21 10 30 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/20 = 83.330{{c}}
Optimal tunings:
* WE: ~2 = 1200.9606{{c}}, ~21/20 = 83.4030{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3594{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~21/20 = 83.330{{c}} -->


{{Optimal ET sequence|legend=0| 29g, 43, 72 }}
{{Optimal ET sequence|legend=0| 29g, 43, 72 }}


Badness (Smith): 0.014924
Badness (Sintel): 0.760


=== 19-limit ===
=== 19-limit ===
Line 487: Line 591:
Mapping: {{mapping| 1 2 1 1 2 3 2 3 | 0 -6 19 26 21 10 30 18 }}
Mapping: {{mapping| 1 2 1 1 2 3 2 3 | 0 -6 19 26 21 10 30 18 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/20 = 83.330{{c}}
Optimal tunings:
* WE: ~2 = 1200.7625{{c}}, ~21/20 = 83.3895{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3551{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~21/20 = 83.330{{c}} -->


{{Optimal ET sequence|legend=0| 29g, 43, 72 }}
{{Optimal ET sequence|legend=0| 29g, 43, 72 }}


Badness (Smith): 0.014722
Badness (Sintel): 0.895


== Enneaportent ==
== Enneaportent ==
Line 499: Line 606:


{{Mapping|legend=1| 9 0 28 11 | 0 2 -1 2 }}
{{Mapping|legend=1| 9 0 28 11 | 0 2 -1 2 }}
: Mapping generators: ~2592/2401, ~12005/6912
: mapping generators: ~2592/2401, ~12005/6912


[[Optimal tuning]] ([[POTE]]): ~2592/2401 = 133.3333{{c}}, ~12005/6912 = 950.1680{{c}} (~1728/1715 = 16.8347{{c}})
[[Optimal tuning]]s:
* [[WE]]: ~2592/2401 = 133.4174{{c}}, ~12005/6912 = 950.7667{{c}} (~1728/1715 = 16.8452{{c}})
: [[error map]]: {{val| +0.756 -0.422 -1.395 +0.298 }}
* [[CWE]]: ~2592/2401 = 133.3333{{c}}, ~12005/6912 = 950.2969{{c}} (~1728/1715 = 16.9636{{c}})
: error map: {{val| 0.000 -1.361 -3.277 -1.565 }}
<!-- * [[POTE]]: ~2592/2401 = 133.3333{{c}}, ~12005/6912 = 950.1680{{c}} (~1728/1715 = 16.8347{{c}}) -->


{{Optimal ET sequence|legend=1| 9, 63, 72, 495bcd }}
{{Optimal ET sequence|legend=1| 9, 54, 63, 72, 495bccd, 567bcccd }}


[[Badness]] (Smith): 0.093679
[[Badness]] (Sintel): 2.37


=== 11-limit ===
=== 11-limit ===
Line 514: Line 626:
Mapping: {{mapping| 9 0 28 11 24 | 0 2 -1 2 1 }}
Mapping: {{mapping| 9 0 28 11 24 | 0 2 -1 2 1 }}


Optimal tuning (POTE): ~121/112 = 133.3333{{c}}, ~210/121 = 950.1873{{c}} (~99/98 = 16.8540{{c}})
Optimal tunings:
* WE: ~121/112 = 133.4071{{c}}, ~210/121 = 950.7131{{c}} (~99/98 = 16.8633{{c}})
* CWE: ~121/112 = 133.3333{{c}}, ~210/121 = 950.2994{{c}} (~99/98 = 16.9661{{c}})
<!-- POTE: ~121/112 = 133.3333{{c}}, ~210/121 = 950.1873{{c}} (~99/98 = 16.8540{{c}}) -->


{{Optimal ET sequence|legend=0| 9, 63, 72, 423cd, 495bcd }}
{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}


Badness (Smith): 0.030426
Badness (Sintel): 1.01


=== 13-limit ===
=== 13-limit ===
Line 527: Line 642:
Mapping: {{mapping| 9 0 28 11 24 19 | 0 2 -1 2 1 2 }}
Mapping: {{mapping| 9 0 28 11 24 19 | 0 2 -1 2 1 2 }}


Optimal tuning (POTE): ~14/13 = 133.3333{{c}}, ~26/15 = 950.2867{{c}} (~105/104 = 16.9534{{c}})
Optimal tunings:
* WE: ~14/13 = 133.4245{{c}}, ~26/15 = 950.9362{{c}} (~105/104 = 16.9650{{c}})
* CWE: ~14/13 = 133.3333{{c}}, ~26/15 = 950.4364{{c}} (~99/98 = 17.1031{{c}})
<!-- POTE: ~14/13 = 133.3333{{c}}, ~26/15 = 950.2867{{c}} (~105/104 = 16.9534{{c}}) -->


{{Optimal ET sequence|legend=0| 9, 63, 72, 279cf }}
{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}


Badness (Smith): 0.022322
Badness (Sintel): 0.922


== Gracecordial ==
== Gracecordial ==
Line 541: Line 659:


{{Mapping|legend=1| 1 0 34 63 | 0 1 -20 -38 }}
{{Mapping|legend=1| 1 0 34 63 | 0 1 -20 -38 }}
: mapping generators: ~2, ~3


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 700.824{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.4904{{c}}, ~3/2 = 701.1103{{c}}
: [[error map]]: {{val| +0.490 -0.354 -1.655 +1.241 }}
* [[CWE]]: ~2 = 1200.3333{{c}}, ~3/2 = 700.8112{{c}}
: error map: {{val| 0.000 -1.144 -2.537 +0.349 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 700.824{{c}} -->


{{Optimal ET sequence|legend=1| 12, 113, 125, 238c, 363c }}
{{Optimal ET sequence|legend=1| 12, …, 113, 125, 238c, 363c }}


[[Badness]] (Smith): 0.096279
[[Badness]] (Sintel): 2.44


=== 11-limit ===
=== 11-limit ===
Line 555: Line 679:
Mapping: {{mapping| 1 0 34 63 -90 | 0 1 -20 -38 59 }}
Mapping: {{mapping| 1 0 34 63 -90 | 0 1 -20 -38 59 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.834{{c}}
Optimal tunings:
* WE: ~2 = 1200.5571{{c}}, ~3/2 = 701.1589{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8328{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.834{{c}} -->


{{Optimal ET sequence|legend=0| 12e, 101cde, 113, 125, 238c }}
{{Optimal ET sequence|legend=0| 12e, 113, 125, 238c }}


Badness (Smith): 0.089588
Badness (Sintel): 2.96


==== 13-limit ====
==== 13-limit ====
Line 568: Line 695:
Mapping: {{mapping| 1 0 34 63 -90 -66 | 0 1 -20 -38 59 44 }}
Mapping: {{mapping| 1 0 34 63 -90 -66 | 0 1 -20 -38 59 44 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.841{{c}}
Optimal tunings:
* WE: ~2 = 1200.6282{{c}}, ~3/2 = 701.2080{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8421{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.841{{c}} -->


{{Optimal ET sequence|legend=0| 12e, 101cde, 113, 125f, 238cf }}
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}


Badness (Smith): 0.052235
Badness (Sintel): 2.16


==== 17-limit ====
==== 17-limit ====
Line 581: Line 711:
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 | 0 1 -20 -38 59 44 7 }}
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 | 0 1 -20 -38 59 44 7 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.841{{c}}
Optimal tunings:
* WE: ~2 = 1200.5058{{c}}, ~3/2 = 701.1360{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8414{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.841{{c}} -->


{{Optimal ET sequence|legend=0| 12e, 101cde, 113, 125f, 238cf }}
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}


Badness (Smith): 0.038565
Badness (Sintel): 1.96


==== 19-limit ====
==== 19-limit ====
Line 594: Line 727:
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 | 0 1 -20 -38 59 44 7 -3 }}
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 | 0 1 -20 -38 59 44 7 -3 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.842{{c}}
Optimal tunings:
* WE: ~2 = 1200.4418{{c}}, ~3/2 = 701.0999{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8425{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.842{{c}} -->


{{Optimal ET sequence|legend=0| 12e, 101cde, 113, 125f, 238cf }}
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}


Badness (Smith): 0.028165
Badness (Sintel): 1.71


==== 23-limit ====
==== 23-limit ====
Line 607: Line 743:
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 | 0 1 -20 -38 59 44 7 -3 30 }}
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 | 0 1 -20 -38 59 44 7 -3 30 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.843{{c}}
Optimal tunings:
* WE: ~2 = 1200.4641{{c}}, ~3/2 = 701.1145{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8444{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.843{{c}} -->


{{Optimal ET sequence|legend=0| 12e, 101cde, 113, 238cfi }}
{{Optimal ET sequence|legend=0| 12e, 113, 238cfi }}


Badness (Smith): 0.021879
Badness (Sintel): 1.57


==== 29-limit ====
==== 29-limit ====
Line 620: Line 759:
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 | 0 1 -20 -38 59 44 7 -3 30 34 }}
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 | 0 1 -20 -38 59 44 7 -3 30 34 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.842{{c}}
Optimal tunings:
* WE: ~2 = 1200.4400{{c}}, ~3/2 = 701.0986{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8428{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.842{{c}} -->


{{Optimal ET sequence|legend=0| 12e, 101cde, 113, 125f, 238cfi }}
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cfi }}


Badness (Smith): 0.018011
Badness (Sintel): 1.50


==== 31-limit ====
==== 31-limit ====
Line 633: Line 775:
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 -79 | 0 1 -20 -38 59 44 7 -3 30 34 53 }}
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 -79 | 0 1 -20 -38 59 44 7 -3 30 34 53 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.838{{c}}
Optimal tunings:
* WE: ~2 = 1200.4178{{c}}, ~3/2 = 701.0822{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8396{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.838{{c}} -->


{{Optimal ET sequence|legend=0| 12e, 101cdek, 113, 125f, 238cfi }}
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cfi }}


Badness (Smith): 0.016007
Badness (Sintel): 1.53


=== Gracecord ===
=== Gracecord ===
Line 646: Line 791:
Mapping: {{mapping| 1 0 34 63 89 | 0 1 -20 -38 -54 }}
Mapping: {{mapping| 1 0 34 63 89 | 0 1 -20 -38 -54 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.885{{c}}
Optimal tunings:
* WE: ~2 = 1200.6064{{c}}, ~3/2 = 701.2398{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8718{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.885{{c}} -->


{{Optimal ET sequence|legend=0| 12, 101cd, 113 }}
{{Optimal ET sequence|legend=0| 12, …, 101cd, 113 }}


Badness (Smith): 0.066964
Badness (Sintel): 2.21


==== 13-limit ====
==== 13-limit ====
Line 659: Line 807:
Mapping: {{mapping| 1 0 34 63 89 113 | 0 1 -20 -38 -54 -69 }}
Mapping: {{mapping| 1 0 34 63 89 113 | 0 1 -20 -38 -54 -69 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.890{{c}}
Optimal tunings:
* WE: ~2 = 1200.6225{{c}}, ~3/2 = 701.2539{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8781{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.890{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}
{{Optimal ET sequence|legend=0| 12f, …, 101cdf, 113 }}


Badness (Smith): 0.044196
Badness (Sintel): 1.83


==== 17-limit ====
==== 17-limit ====
Line 672: Line 823:
Mapping: {{mapping| 1 0 34 63 89 113 -7 | 0 1 -20 -38 -54 -69 7 }}
Mapping: {{mapping| 1 0 34 63 89 113 -7 | 0 1 -20 -38 -54 -69 7 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.870{{c}}
Optimal tunings:
* WE: ~2 = 1200.3308{{c}}, ~3/2 = 701.0632{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8654{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.870{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}
{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}


Badness (Smith): 0.036637
Badness (Sintel): 1.87


==== 19-limit ====
==== 19-limit ====
Line 685: Line 839:
Mapping: {{mapping| 1 0 34 63 89 113 -7 9 | 0 1 -20 -38 -54 -69 7 -3 }}
Mapping: {{mapping| 1 0 34 63 89 113 -7 9 | 0 1 -20 -38 -54 -69 7 -3 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.866{{c}}
Optimal tunings:
* WE: ~2 = 1200.2658{{c}}, ~3/2 = 701.0213{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8629{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.866{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}
{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}


Badness (Smith): 0.027559
Badness (Sintel): 1.68


== Alphorn ==
== Alphorn ==
Line 696: Line 853:
[[Comma list]]: 225/224, 5764801/5668704
[[Comma list]]: 225/224, 5764801/5668704


{{Mapping|legend=1| 1 9 0 13 | 0 -16 5 -22 }}
{{Mapping|legend=1| 1 -7 5 -9 | 0 16 -5 22 }}
: mapping generators: ~2, ~35/24


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~48/35 = 556.221{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1201.3004{{c}}, ~35/24 = 644.4767{{c}}
: [[error map]]: {{val| +1.300 +0.569 -2.195 -2.043 }}
* [[CWE]]: ~2 = 1200.3333{{c}}, ~35/24 = 643.8137{{c}}
: error map: {{val| 0.000 -0.936 -5.382 -4.924 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~35/24 = 643.779{{c}} -->


{{Optimal ET sequence|legend=1| 28d, 41, 151cd, 192cd, 233cd }}
{{Optimal ET sequence|legend=1| 13d, 28d, 41, 151cd, 192cdd, 233ccdd }}


[[Badness]] (Smith): 0.129258
[[Badness]] (Sintel): 3.27


=== 11-limit ===
=== 11-limit ===
Line 709: Line 872:
Comma list: 225/224, 385/384, 12250/11979
Comma list: 225/224, 385/384, 12250/11979


Mapping: {{mapping| 1 9 0 13 3 | 0 -16 5 -22 1 }}
Mapping: {{mapping| 1 -7 5 -9 4 | 0 16 -5 22 -1 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/8 = 556.144{{c}}
Optimal tunings:
* WE: ~2 = 1200.5123{{c}}, ~16/11 = 644.1307{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/11 = 643.8662{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~11/8 = 556.144{{c}} -->


{{Optimal ET sequence|legend=0| 28d, 41, 315cde }}
{{Optimal ET sequence|legend=0| 13d, 28d, 41 }}


Badness (Smith): 0.073459
Badness (Sintel): 2.43


== Misneb ==
== Misneb ==
Line 724: Line 890:
[[Comma list]]: 225/224, 4194304/4117715  
[[Comma list]]: 225/224, 4194304/4117715  


{{Mapping|legend=1| 1 3 1 3 | 0 -15 14 -2 }}
{{Mapping|legend=1| 1 -12 15 1 | 0 15 -14 2 }}
: mapping generators: ~2, ~15/8


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~16/15 = 113.235{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.7642{{c}}, ~15/8 = 1086.5513{{c}}
: [[error map]]: {{val| -0.236 -0.856 -1.569 +4.041 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~15/8 = 1086.7633{{c}}
: error map: {{val| 0.000 -0.506 -0.999 +4.701 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~15/8 = 1086.765{{c}} -->


{{Optimal ET sequence|legend=1| 21, 32, 53 }}
{{Optimal ET sequence|legend=1| 21, 32, 53 }}


[[Badness]] (Smith): 0.140970
[[Badness]] (Sintel): 3.57


=== 11-limit ===
=== 11-limit ===
Line 737: Line 909:
Comma list: 99/98, 176/175, 1310720/1294139
Comma list: 99/98, 176/175, 1310720/1294139


Mapping: {{mapping| 1 3 1 3 1 | 0 -15 14 -2 26 }}
Mapping: {{mapping| 1 -12 15 1 27 | 0 15 -14 2 -26 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~16/15 = 113.323{{c}}
Optimal tunings:
* WE: ~2 = 1200.1654{{c}}, ~15/8 = 1086.8269{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.6766{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~15/8 = 1086.677{{c}} -->


{{Optimal ET sequence|legend=0| 21, 32e, 53, 127, 180de }}
{{Optimal ET sequence|legend=0| 21, 32e, 53, 127 }}


Badness (Smith): 0.085390
Badness (Sintel): 2.82


==== 13-limit ====
==== 13-limit ====
Line 750: Line 925:
Comma list: 99/98, 176/175, 640/637, 847/845
Comma list: 99/98, 176/175, 640/637, 847/845


Mapping: {{mapping| 1 3 1 3 1 2 | 0 -15 14 -2 26 18 }}
Mapping: {{mapping| 1 -12 15 1 27 20 | 0 15 -14 2 -26 -18 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~16/15 = 113.323{{c}}
Optimal tunings:
* WE: ~2 = 1200.1687{{c}}, ~15/8 = 1086.8295{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.6757{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~16/15 = 113.323{{c}} -->


{{Optimal ET sequence|legend=0| 21, 32e, 53, 127, 180de }}
{{Optimal ET sequence|legend=0| 21, 32e, 53, 127 }}


Badness (Smith): 0.045569
Badness (Sintel): 1.88


=== Musneb ===
=== Musneb ===
Line 765: Line 943:
Mapping: {{mapping| 1 3 1 3 6 | 0 -15 14 -2 -27 }}
Mapping: {{mapping| 1 3 1 3 6 | 0 -15 14 -2 -27 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~16/15 = 113.142{{c}}
Optimal tunings:
* WE: ~2 = 1200.0839{{c}}, ~15/8 = 1086.9343{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.8593{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~15/8 = 1086.858{{c}} -->


{{Optimal ET sequence|legend=0| 32, 53, 191de, 244cddee, 297cddee }}
{{Optimal ET sequence|legend=0| 21e, 32, 53 }}


Badness (Smith): 0.087333
Badness (Sintel): 2.89


== Untriton ==
== Untriton ==
Line 778: Line 959:
[[Comma list]]: 225/224, 125000000/121060821
[[Comma list]]: 225/224, 125000000/121060821


{{Mapping|legend=1| 1 6 -7 -7 | 0 -9 19 20 }}
{{Mapping|legend=1| 1 -3 12 13 | 0 9 -19 -20 }}
: mapping generators: ~2, ~10/7


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~7/5 = 588.641{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.8275{{c}}, ~10/7 = 611.2710{{c}}
: [[error map]]: {{val| -0.172 +0.002 -2.533 +3.511 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 611.3614{{c}}
: error map: {{val| 0.000 +0.298 -2.181 +3.946 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~10/7 = 611.359{{c}} -->


{{Optimal ET sequence|legend=1| 51, 53, 316cd, 369cdd, 422cdd }}
{{Optimal ET sequence|legend=1| 51, 53 }}


[[Badness]] (Smith): 0.143976
[[Badness]] (Sintel): 3.64


=== 11-limit ===
=== 11-limit ===
Line 791: Line 978:
Comma list: 121/120, 225/224, 22000/21609
Comma list: 121/120, 225/224, 22000/21609


Mapping: {{mapping| 1 6 -7 -7 1 | 0 -9 19 20 5 }}
Mapping: {{mapping| 1 -3 12 13 6 | 0 9 -19 -20 -5 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 588.626{{c}}
Optimal tunings:
* WE: ~2 = 1200.3591{{c}}, ~10/7 = 611.5569{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 611.3690{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~10/7 = 611.374{{c}} -->


{{Optimal ET sequence|legend=0| 51, 53 }}
{{Optimal ET sequence|legend=0| 51, 53 }}


Badness (Smith): 0.074295
Badness (Sintel): 2.46


=== 13-limit ===
=== 13-limit ===
Line 804: Line 994:
Comma list: 121/120, 225/224, 275/273, 1040/1029
Comma list: 121/120, 225/224, 275/273, 1040/1029


Mapping: {{mapping| 1 6 -7 -7 1 -12 | 0 -9 19 20 5 32 }}
Mapping: {{mapping| 1 -3 12 13 6 20 | 0 9 -19 -20 -5 -32 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 588.654{{c}}
Optimal tunings:
* WE: ~2 = 1200.4078{{c}}, ~10/7 = 611.5536{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 611.3392{{c}}
<!-- POTE: ~2 = 1200.000{{c}}, ~10/7 = 588.654{{c}} -->


{{Optimal ET sequence|legend=0| 51f, 53 }}
{{Optimal ET sequence|legend=0| 51f, 53 }}


Badness (Smith): 0.047441
Badness (Sintel): 1.96


== Naiadical ==
== Naiadical ==
Line 817: Line 1,010:
[[Comma list]]: 225/224, 823543/800000
[[Comma list]]: 225/224, 823543/800000


{{Mapping|legend=1| 1 5 -3 -1 | 0 -9 14 10 }}
{{Mapping|legend=1| 1 -4 11 9 | 0 9 -14 -10 }}
: mapping generators: ~2, ~32/21


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1202.120{{c}}, ~21/16 = 456.652{{c}}
* [[WE]]: ~2 = 1202.1198{{c}}, ~32/21 = 745.4675{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~21/16 = 455.868{{c}}
: [[error map]]: {{val| +2.120 -1.227 +0.459 -4.423 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~32/21 = 744.1318{{c}}
: error map: {{val| 0.000 -4.769 -4.159 -10.144 }}


{{Optimal ET sequence|legend=1| 21, 29, 50, 79d }}
{{Optimal ET sequence|legend=1| 21, 29, 50, 79d, 129cdd, 179bcddd }}


[[Badness]] (Sintel): 3.667
[[Badness]] (Sintel): 3.67


=== 11-limit ===
=== 11-limit ===
Line 832: Line 1,028:
Comma list: 225/224, 245/242, 1617/1600
Comma list: 225/224, 245/242, 1617/1600


Mapping: {{Mapping| 1 5 -3 -1 -3 | 0 -9 14 10 17 }}
Mapping: {{Mapping| 1 -4 11 9 14 | 0 9 -14 -10 -17 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1201.901, ~21/16{{c}} = 456.514{{c}}
* WE: ~2 = 1201.9008{{c}}, ~21/16 = 745.3867{{c}}
* CWE: ~2 = 1200.000, ~21/16{{c}} = 455.822{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~32/21 = 744.1777{{c}}


{{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}
{{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}


Badness (Sintel): 1.998
Badness (Sintel): 2.00


=== 13-limit ===
=== 13-limit ===
Line 847: Line 1,043:
Comma list: 105/104, 196/195, 245/242, 1001/1000
Comma list: 105/104, 196/195, 245/242, 1001/1000


Mapping: {{Mapping| 1 5 -3 -1 -3 -2 | 0 -9 14 10 17 15 }}
Mapping: {{Mapping| 1 -4 11 9 14 13 | 0 9 -14 -10 -17 -15 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1201.786{{c}}, ~13/10 = 456.452{{c}}
* WE: ~2 = 1201.7863{{c}}, ~20/13 = 745.3344{{c}}
* CWE: ~2 = 1200.000{{c}}, ~13/10 = 455.807{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.1931{{c}}


{{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}
{{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}


Badness (Sintel): 1.430
Badness (Sintel): 1.43


=== 17-limit ===
=== 17-limit ===
Line 862: Line 1,058:
Comma list: 105/104, 170/169, 196/195, 221/220, 245/242
Comma list: 105/104, 170/169, 196/195, 221/220, 245/242


Mapping: {{Mapping| 1 5 -3 -1 -3 -2 -2 | 0 -9 14 10 17 15 16 }}
Mapping: {{Mapping| 1 -4 11 9 14 13 14 | 0 9 -14 -10 -17 -15 -16 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1201.921{{c}}, ~13/10 = 456.523{{c}}
* WE: ~2 = 1201.9208{{c}}, ~20/13 = 745.3976{{c}}
* CWE: ~2 = 1200.000{{c}}, ~13/10 = 455.833{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.1669{{c}}


{{Optimal ET sequence|legend=0| 21, 29g, 50, 79dg }}
{{Optimal ET sequence|legend=0| 21, 29g, 50, 79dg }}


Badness (Sintel): 1.260
Badness (Sintel): 1.26


== Quintannic ==
== Quintannic ==
Line 878: Line 1,074:


{{Mapping|legend=1| 1 1 5 7 | 0 5 -23 -36 }}
{{Mapping|legend=1| 1 1 5 7 | 0 5 -23 -36 }}
: mapping generators: ~2, ~10000/9261


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~10000/9261 = 139.838{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.9803{{c}}, ~10000/9261 = 139.9522{{c}}
: [[error map]]: {{val| +0.980 -1.214 -0.313 -0.243 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10000/9261 = 139.8184{{c}}
: error map: {{val| 0.000 -2.863 -2.136 -2.287 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~10000/9261 = 139.838{{c}} -->


{{Optimal ET sequence|legend=1| 43, 60, 103, 266bcd, 369bcd }}
{{Optimal ET sequence|legend=1| 43, 60, 103, 266bcd, 369bcd }}


[[Badness]] (Smith): 0.150565
[[Badness]] (Sintel): 3.81


=== 11-limit ===
=== 11-limit ===
Line 892: Line 1,094:
Mapping: {{mapping| 1 1 5 7 8 | 0 5 -23 -36 -39 }}
Mapping: {{mapping| 1 1 5 7 8 | 0 5 -23 -36 -39 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~320/297 = 139.827{{c}}
Optimal tunings:
* WE: ~2 = 1201.0031{{c}}, ~320/297 = 139.9435{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~320/297 = 139.8053{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~320/297 = 139.827{{c}} -->


{{Optimal ET sequence|legend=0| 43, 60e, 103 }}
{{Optimal ET sequence|legend=0| 43, 60e, 103, 369bcdeee, 472bbcddeee }}


Badness (Smith): 0.052590
Badness (Sintel): 1.74


=== 13-limit ===
=== 13-limit ===
Line 905: Line 1,110:
Mapping: {{mapping| 1 1 5 7 8 3 | 0 5 -23 -36 -39 6 }}
Mapping: {{mapping| 1 1 5 7 8 3 | 0 5 -23 -36 -39 6 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~13/12 = 139.812{{c}}
Optimal tunings:
* WE: ~2 = 1200.8354{{c}}, ~13/12 = 139.9095{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.7997{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~13/12 = 139.812{{c}} -->


{{Optimal ET sequence|legend=0| 43, 60e, 103 }}
{{Optimal ET sequence|legend=0| 43, 60e, 103 }}


Badness (Smith): 0.032730
Badness (Sintel): 1.35


=== 17-limit ===
=== 17-limit ===
Line 918: Line 1,126:
Mapping: {{mapping| 1 1 5 7 8 3 7 | 0 5 -23 -36 -39 6 -25 }}
Mapping: {{mapping| 1 1 5 7 8 3 7 | 0 5 -23 -36 -39 6 -25 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~13/12 = 139.815{{c}}
Optimal tunings:
* WE: ~2 = 1200.7402{{c}}, ~13/12 = 139.9015{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.8038{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~13/12 = 139.815{{c}} -->


{{Optimal ET sequence|legend=0| 43, 60e, 103 }}
{{Optimal ET sequence|legend=0| 43, 60e, 103 }}


Badness (Smith): 0.023038
Badness (Sintel): 1.17


== Gwazy ==
== Gwazy ==
Line 932: Line 1,143:


{{Mapping|legend=1| 2 1 6 4 | 0 8 -5 6 }}
{{Mapping|legend=1| 2 1 6 4 | 0 8 -5 6 }}
: mapping generators: ~2401/1728, ~35/32


[[Optimal tuning]] ([[POTE]]): ~2401/1728 = 600.000{{c}}, ~35/32 = 162.658{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2401/1728 = 599.7132{{c}}, ~35/32 = 162.5806{{c}}
: [[error map]]: {{val| -0.574 -1.597 -0.937 +5.510 }}
* [[CWE]]: ~2401/1728 = 600.0000{{c}}, ~35/32 = 162.6388{{c}}
: error map: {{val| 0.000 -0.844 +0.492 +7.007 }}
<!-- * [[POTE]]: ~2401/1728 = 600.000{{c}}, ~35/32 = 162.658{{c}} -->


{{Optimal ET sequence|legend=1| 22, 74, 96, 118d }}
{{Optimal ET sequence|legend=1| 22, 74, 96, 118d }}


[[Badness]] (Smith): 0.178826
[[Badness]] (Sintel): 4.53


=== 11-limit ===
=== 11-limit ===
Line 946: Line 1,163:
Mapping: {{mapping| 2 1 6 4 8 | 0 8 -5 6 -4 }}
Mapping: {{mapping| 2 1 6 4 8 | 0 8 -5 6 -4 }}


Optimal tuning (POTE): ~363/256 = 600.000{{c}}, ~11/10 = 162.592{{c}}
Optimal tunings:
* WE: ~363/256 = 599.8517{{c}}, ~11/10 = 162.5518{{c}}
* CWE: ~363/256 = 600.0000{{c}}, ~11/10 = 162.5863{{c}}
<!-- * POTE: ~363/256 = 600.000{{c}}, ~11/10 = 162.592{{c}} -->


{{Optimal ET sequence|legend=0| 22, 74, 96, 118d }}
{{Optimal ET sequence|legend=0| 22, 74, 96 }}


Badness (Smith): 0.068410
Badness (Sintel): 2.26


== Tertiosec ==
== Tertiosec ==
Line 959: Line 1,179:
[[Comma list]]: 225/224, 14495514624/13841287201
[[Comma list]]: 225/224, 14495514624/13841287201


{{Mapping|legend=1| 3 7 5 9 | 0 -8 7 -2 }}
{{Mapping|legend=1| 3 -1 12 7 | 0 8 -7 2 }}
: mapping generators: ~3072/2401, ~2048/1715


[[Optimal tuning]] ([[POTE]]): ~3072/2401 = 400.000{{c}}, ~15/14 = 112.283{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~3072/2401 = 399.8257{{c}}, ~2048/1715 = 287.5920{{c}}
: [[error map]]: {{val| -0.523 -1.044 -1.549 +5.138 }}
* [[CWE]]: ~3072/2401 = 400.0000{{c}}, ~2048/1715 = 287.7088{{c}}
: error map: {{val| 0.000 -0.284 -0.276 +6.592 }}
<!-- * [[POTE]]: ~3072/2401 = 400.000{{c}}, ~2048/1715 = 287.717{{c}} -->


{{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171d }}
{{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171d }}


[[Badness]] (Smith): 0.431636
[[Badness]] (Sintel): 10.9


=== 11-limit ===
=== 11-limit ===
Line 972: Line 1,198:
Comma list: 225/224, 3840/3773, 12005/11979
Comma list: 225/224, 3840/3773, 12005/11979


Mapping: {{mapping| 3 7 5 9 9 | 0 -8 7 -2 5 }}
Mapping: {{mapping| 3 -1 12 7 14 | 0 8 -7 2 -5 }}


Optimal tuning (POTE): ~44/35 = 400.000{{c}}, ~15/14 = 112.171{{c}}
Optimal tunings:
* WE: ~44/35 = 399.6550{{c}}, ~33/28 = 287.5803{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~33/28 = 287.8224{{c}}
<!-- * POTE: ~44/35 = 400.000{{c}}, ~33/28 = 287.829{{c}} -->


{{Optimal ET sequence|legend=0| 21, 54, 75e }}
{{Optimal ET sequence|legend=0| 21, 54, 75e }}


Badness (Smith): 0.173485
Badness (Sintel): 5.74


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