Miscellaneous 5-limit temperaments: Difference between revisions

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{{Technical data page}}
{{Technical data page}}
Below are listed some [[5-limit]] temperaments that do not belong to some other temperament collection, the majority of which are [[restriction]]s to the 5-limit of temperaments that emerge more fully in higher [[prime limit|limits]] or [[subgroup]]s; they are sorted by Smith [[TE logflat badness]], of which most have > 0.2. Most of these temperaments have low accuracy, high-complexity generators, or large number of generators for simple consonances. This is not an exhaustive list. Only expect to find a temperament here if you have not found it in:  
Below are listed some [[5-limit]] [[regular temperament|temperament]]s that do not belong to some other temperament collection, the majority of which are [[restriction]]s to the 5-limit of temperaments that emerge more fully in higher [[prime limit|limits]] or [[subgroup]]s; they are sorted by [[TE logflat badness]], of which most have Sintel's > 4.7 (Smith's > 0.20). Most of these temperaments have low accuracy, high-complexity generators, or large number of generators for simple consonances. This is not an exhaustive list. Only expect to find a temperament here if you have not found it in:  
* Individual [[temperament families and clans]]
* Individual [[temperament families and clans]]
* Individual [[equivalence continuum|equivalence continua]]
* Individual [[equivalence continuum|equivalence continua]]
Line 18: Line 18:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~25/24 = 138.722
* [[POTE]]: ~2 = 1200.000, ~25/24 = 140.995
* [[POTE]]: ~2 = 1200.000, ~25/24 = 140.995


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


[[Badness]] (Smith): 0.200
[[Badness]] (Sintel): 4.70


== Stump ==
== Stump ==
Line 34: Line 35:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~64/45 = 631.504
* [[POTE]]: ~2 = 1200.000, ~64/45 = 631.737
* [[POTE]]: ~2 = 1200.000, ~64/45 = 631.737


{{Optimal ET sequence|legend=1| 17, 19 }}
{{Optimal ET sequence|legend=1| 17, 19, 207bbccc }}


[[Badness]] (Smith): 0.201
[[Badness]] (Sintel): 4.71


== Dodifo ==
== Dodifo ==
Line 45: Line 47:
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: {{Monzo| -67 -9 35 }}
[[Comma list]]: {{monzo| -67 -9 35 }}


{{Mapping|legend=1| 1 12 5 | 0 -35 -9 }}
{{Mapping|legend=1| 1 12 5 | 0 -35 -9 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~768/625 = 357.087
* [[POTE]]: ~2 = 1200.000, ~768/625 = 357.088
* [[POTE]]: ~2 = 1200.000, ~768/625 = 357.088


{{Optimal ET sequence|legend=1| 37, 84, 205, 289, 494, 783, 2060, 2843, 3626 }}
{{Optimal ET sequence|legend=1| 37, 84, 205, 289, 494, 783, 2060, 2843, 3626 }}


[[Badness]] (Smith): 0.213
[[Badness]] (Sintel): 5.00
 
== Doublewide ==
: ''For extensions, see [[Jubilismic clan #Doublewide]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 390625/373248
 
{{Mapping|legend=1| 2 1 3 | 0 4 3 }}
 
: mapping generators: ~625/432, ~6/5
 
[[Optimal tuning]]s:
* [[WE]]: ~625/432 = 600.6814{{c}}, ~6/5 = 325.8892{{c}} (~144/125 = 274.7921{{c}})
: [[error map]]: {{val| +1.363 +2.283 -6.602 }}
* [[CWE]]: ~625/432 = 600.0000{{c}}, ~6/5 = 325.8147{{c}} (~144/125 = 274.185{{c}})
: error map: {{val| 0.000 +1.304 -8.869 }}
 
{{Optimal ET sequence|legend=1| 4, 14b, 18, 22, 48, 70c, 118c }}
 
[[Badness]] (Sintel): 5.32


== Shibboleth ==
== Shibboleth ==
Line 69: Line 93:
* [[POTE]]: ~2 = 1200.000, ~6/5 = 321.852
* [[POTE]]: ~2 = 1200.000, ~6/5 = 321.852


{{Optimal ET sequence|legend=1| 15, 26, 41, 179c, 220c, 261cc, 302cc }}
{{Optimal ET sequence|legend=1| 15, 26, 41, 179c }}


[[Badness]] (Smith): 0.228
[[Badness]] (Sintel): 5.34


== Semidimfourth ==
== Semidimfourth ==
Line 83: Line 107:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~162/125 = 448.449
* [[POTE]]: ~2 = 1200.000, ~162/125 = 448.449
* [[POTE]]: ~2 = 1200.000, ~162/125 = 448.449


{{Optimal ET sequence|legend=1| 8, 91, 99, 190, 289, 388, 677, 3674, 4351, 5028, 5705, 6382, 13441c, 19823bcc }}
{{Optimal ET sequence|legend=1| 8, …, 91, 99, 190, 289, 388, 677, 3674, 4351, 5028, 5705, 6382, 13441c, 19823bcc }}


[[Badness]] (Smith): 0.233
[[Badness]] (Sintel): 5.47


== Mynic ==
== Mynic ==
Line 99: Line 124:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~6/5 = 310.030
* [[POTE]]: ~2 = 1200.000, ~6/5 = 310.140
* [[POTE]]: ~2 = 1200.000, ~6/5 = 310.140


{{Optimal ET sequence|legend=1| 27, 31, 58, 89, 325cc }}
{{Optimal ET sequence|legend=1| 27, 31, 58, 89 }}


[[Badness]] (Smith): 0.250
[[Badness]] (Sintel): 5.86


== Progress ==
== Progress ==
Line 115: Line 141:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000, ~64/45 = 561.264
* [[CTE]]: ~2 = 1200.000, ~45/32 = 638.922
* [[POTE]]: ~2 = 1200.000, ~45/32 = 638.736


{{Optimal ET sequence|legend=1| 2, 13, 15, 32c, 47bc, 62bc }}
{{Optimal ET sequence|legend=1| 2, 13, 15, 32c, 47bc, 62bc }}


[[Badness]] (Smith): 0.246
[[Badness]] (Sintel): 5.77


== Abigail ==
== Abigail ==
Line 136: Line 163:
{{Optimal ET sequence|legend=1| 46, 132, 178, 224, 270, 494, 1752, 2246, 2740, 4986, 7726b }}
{{Optimal ET sequence|legend=1| 46, 132, 178, 224, 270, 494, 1752, 2246, 2740, 4986, 7726b }}


[[Badness]]:
[[Badness]] (Sintel): 5.97
* Smith: 0.255
* Dirichlet: 5.97


== Supermajor ==
== Supermajor ==
Line 155: Line 180:
{{Optimal ET sequence|legend=1| 80, 171, 593, 764, 935, 1106, 3489, 4595, 5701 }}
{{Optimal ET sequence|legend=1| 80, 171, 593, 764, 935, 1106, 3489, 4595, 5701 }}


[[Badness]]:
[[Badness]] (Sintel): 6.19
* Smith: 0.264
* Dirichlet: 6.19


== Gamera ==
== Gamera ==
Line 174: Line 197:
{{Optimal ET sequence|legend=1| 26, 73, 99, 224, 323, 547, 870 }}
{{Optimal ET sequence|legend=1| 26, 73, 99, 224, 323, 547, 870 }}


[[Badness]]:
[[Badness]] (Sintel): 6.39
* Smith: 0.273
* Dirichlet: 6.39


== Tritriple ==
== Tritriple ==
Line 188: Line 209:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~864/625 = 559.328
* [[POTE]]: ~2 = 1200.000, ~864/625 = 559.332
* [[POTE]]: ~2 = 1200.000, ~864/625 = 559.332


{{Optimal ET sequence|legend=1| 15, 88, 103, 118, 959, 1077 }}
{{Optimal ET sequence|legend=1| 15, 88, 103, 118, 959, 1077 }}


[[Badness]] (Smith): 0.284
[[Badness]] (Sintel): 6.65


== Kangaroo ==
== Kangaroo ==
Line 204: Line 226:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000, ~27/20 = 561.195
* [[CTE]]: ~2 = 1200.000, ~40/27 = 637.879
* [[POTE]]: ~2 = 1200.000, ~40/27 = 638.805


{{Optimal ET sequence|legend=1| 15, 47b, 62b }}
{{Optimal ET sequence|legend=1| 15, 47b, 62b }}


[[Badness]] (Smith): 0.296
[[Badness]] (Sintel): 6.94


== Tertiaseptal ==
== Tertiaseptal ==
Line 215: Line 238:
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 579357147216796875/576460752303423488
[[Comma list]]: {{monzo| -59 5 22 }}


{{Mapping|legend=1| 1 3 2 | 0 -22 5 }}
{{Mapping|legend=1| 1 3 2 | 0 -22 5 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~17578125/16777216 = 77.186
* [[POTE]]: ~2 = 1200.000, ~17578125/16777216 = 77.191
* [[POTE]]: ~2 = 1200.000, ~17578125/16777216 = 77.191


{{Optimal ET sequence|legend=1| 31, 109, 140, 171, 1679c, 1850c, 2021c, 2192c, 2363c, 2534c, 2705c, 2876c, 3047c }}
{{Optimal ET sequence|legend=1| 31, 109, 140, 171, 1679c, 1850c, 2021c, 2192c, 2363c, 2534c, 2705c, 2876c, 3047c }}


[[Badness]] (Smith): 0.298
[[Badness]] (Sintel): 6.98
 
== Gracecordial ==
: ''For extensions, see [[Marvel temperaments #Gracecordial]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 17433922005/17179869184
 
{{Mapping|legend=1| 1 0 34 | 0 1 -20 }}
 
[[Optimal tuning]]s:
* [[POTE]]: ~2 = 1200.000, ~3/2 = 700.734
 
{{Optimal ET sequence|legend=1| 12, 113, 125, 137 }}
 
[[Badness]] (Smith): 0.307


== Untriton ==
== Untriton ==
Line 247: Line 255:
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 2270041927734375/2251799813685248
[[Comma list]]: {{monzo| -51 19 9 }}


{{Mapping|legend=1| 1 6 -7 | 0 -9 19 }}
{{Mapping|legend=1| 1 6 -7 | 0 -9 19 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~45/32 = 588.727
* [[POTE]]: ~2 = 1200.000, ~45/32 = 588.722
* [[POTE]]: ~2 = 1200.000, ~45/32 = 588.722


{{Optimal ET sequence|legend=1| 51, 53, 267, 320, 373, 426, 479, 532, 2607bc }}
{{Optimal ET sequence|legend=1| 51, 53, 267, 320, 373, 426, 479, 532, 2607bc }}


[[Badness]] (Smith): 0.307
[[Badness]] (Sintel): 7.20


== Counterhanson ==
== Counterhanson ==
Line 263: Line 272:
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: {{Monzo| -20 -24 25 }} = 298023223876953125/296148833645101056
[[Comma list]]: {{monzo| -20 -24 25 }}


{{Mapping|legend=1| 1 -5 -4 | 0 25 24 }}
{{Mapping|legend=1| 1 -5 -4 | 0 25 24 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~6/5 = 316.084
* [[POTE]]: ~2 = 1200.000, ~6/5 = 316.081
* [[POTE]]: ~2 = 1200.000, ~6/5 = 316.081


{{Optimal ET sequence|legend=1| 19, 148, 167, 186, 205, 224, 429, 653, 1082, 1735c }}
{{Optimal ET sequence|legend=1| 19, …, 148, 167, 186, 205, 224, 429, 653, 1082, 1735c }}


[[Badness]] (Smith): 0.318
[[Badness]] (Sintel): 7.45


== Nessafof ==
== Nessafof ==
Line 279: Line 289:
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 481469424205824/476837158203125
[[Comma list]]: {{monzo| 25 15 -21 }}


{{Mapping|legend=1| 3 2 5 | 0 7 5 }}
{{Mapping|legend=1| 3 2 5 | 0 7 5 }}
Line 289: Line 299:
{{Optimal ET sequence|legend=1| 15, 54b, 69, 84, 99, 183, 282, 465, 1212c, 1677cc }}
{{Optimal ET sequence|legend=1| 15, 54b, 69, 84, 99, 183, 282, 465, 1212c, 1677cc }}


[[Badness]]:
[[Badness]] (Sintel): 7.81
* Smith: 0.333
* Dirichlet: 7.81


== Lemba ==
== Lemba ==
Line 312: Line 320:
{{Optimal ET sequence|legend=1| 10, 16, 26, 88cc }}
{{Optimal ET sequence|legend=1| 10, 16, 26, 88cc }}


[[Badness]]:
[[Badness]] (Sintel): 7.85
* Smith: 0.335
* Dirichlet: 7.85
 
== Wronecki ==
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 531441/500000
 
{{Mapping|legend=1| 6 0 -5 | 0 1 2 }}
 
[[Optimal tuning]]s:
* [[POTE]]: ~10/9 = 200.000, ~3/2 = 695.040
 
{{Optimal ET sequence|legend=1| 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bbc }}
 
[[Badness]] (Smith): 0.342


== Delorean ==
== Delorean ==
Line 340: Line 332:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~6/5 = 284.817
* [[POTE]]: ~2 = 1200.000, ~6/5 = 284.293
* [[POTE]]: ~2 = 1200.000, ~6/5 = 284.293


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


[[Badness]] (Smith): 0.356
[[Badness]] (Sintel): 8.35


== Majvam ==
== Majvam ==
Line 356: Line 349:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~125/96 = 459.006
* [[POTE]]: ~2 = 1200.000, ~125/96 = 458.995
* [[POTE]]: ~2 = 1200.000, ~125/96 = 458.995


{{Optimal ET sequence|legend=1| 34, 115, 149, 183, 217, 400, 617 }}
{{Optimal ET sequence|legend=1| 34, 115, 149, 183, 217, 400, 617 }}


[[Badness]] (Smith): 0.357
[[Badness]] (Sintel): 8.37


== Beatles ==
== Beatles ==
Line 372: Line 366:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~512/405 = 356.492
* [[POTE]]: ~2 = 1200.000, ~512/405 = 355.930
* [[POTE]]: ~2 = 1200.000, ~512/405 = 355.930


{{Optimal ET sequence|legend=1| 10, 17c, 27, 64b, 91bc, 118bc }}
{{Optimal ET sequence|legend=1| 10, 17c, 27, 64b, 91bc, 118bc }}


[[Badness]] (Smith): 0.359
[[Badness]] (Sintel): 8.41


== Magus ==
== Magus ==
Line 388: Line 383:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~5/4 = 391.068
* [[POTE]]: ~2 = 1200.000, ~5/4 = 391.225
* [[POTE]]: ~2 = 1200.000, ~5/4 = 391.225


{{Optimal ET sequence|legend=1| 3, 40, 43, 46, 181c, 227c, 273c, 319c }}
{{Optimal ET sequence|legend=1| 3, …, 40, 43, 46, 181c, 227c, 273c, 319c }}


[[Badness]] (Smith): 0.360
[[Badness]] (Sintel): 8.45


== Countermeantone ==
== Countermeantone ==
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: {{Monzo| 10 23 -20 }} = 96402615118848/95367431640625
[[Comma list]]: {{monzo| 10 23 -20 }}


{{Mapping|legend=1| 1 10 12 | 0 -20 -23 }}
{{Mapping|legend=1| 1 -10 -11 | 0 20 23 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000, ~104976/78125 = 504.913
* [[CTE]]: ~2 = 1200.000, ~78125/52488 = 695.082
* [[POTE]]: ~2 = 1200.000, ~78125/52488 = 695.087


{{Optimal ET sequence|legend=1| 19, 126, 145, 164, 183, 713, 896c, 1079c, 1262c }}
{{Optimal ET sequence|legend=1| 19, …, 126, 145, 164, 183, 713, 896c, 1079c, 1262c, 1445c }}


[[Badness]] (Smith): 0.373
[[Badness]] (Sintel): 8.76


== Tritonic ==
== Tritonic ==
Line 418: Line 415:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~45/32 = 580.278
* [[POTE]]: ~2 = 1200.000, ~45/32 = 580.219
* [[POTE]]: ~2 = 1200.000, ~45/32 = 580.219


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


[[Badness]] (Smith): 0.379
[[Badness]] (Sintel): 8.88


== Wizard ==
== Wizard ==
Line 433: Line 431:
{{Mapping|legend=1| 2 1 5 | 0 6 -1 }}
{{Mapping|legend=1| 2 1 5 | 0 6 -1 }}


Mapping generators: ~42875/32768, ~9375/8192
: mapping generators: ~42875/32768, ~9375/8192


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~42875/32768 = 600.000, ~5/4 = 383.212
* [[CTE]]: ~42875/32768 = 600.000, ~9375/8192 = 216.950
* [[POTE]]: ~42875/32768 = 600.000, ~9375/8192 = 216.788


{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 548bc }}
{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 548bcc }}


[[Badness]] (Smith): 0.386
[[Badness]] (Sintel): 9.06


Scales (Scala files): [[wizard22]]
Scales (Scala files): [[wizard22]]
Line 454: Line 453:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000, ~1215/1024 = 252.649
* [[CTE]]: ~2 = 1200.000, ~2048/1215 = 946.982
* [[POTE]]: ~2 = 1200.000, ~2048/1215 = 947.351


{{Optimal ET sequence|legend=1| 14, 19 }}
{{Optimal ET sequence|legend=1| 14, 19 }}


[[Badness]] (Smith): 0.425
[[Badness]] (Sintel): 9.96


== Merman ==
== Merman ==
Line 465: Line 465:
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 1121008359375/1099511627776
[[Comma list]]: {{monzo| -40 15 7 }}


{{Mapping|legend=1| 1 5 -5 | 0 -7 15 }}
{{Mapping|legend=1| 1 5 -5 | 0 -7 15 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~45/32 = 585.653
* [[POTE]]: ~2 = 1200.000, ~45/32 = 585.634
* [[POTE]]: ~2 = 1200.000, ~45/32 = 585.634


{{Optimal ET sequence|legend=1| 41, 84, 125, 209, 334c, 543bc }}
{{Optimal ET sequence|legend=1| 41, 84, 125, 209, 334c, 543bc }}


[[Badness]] (Smith): 0.454
[[Badness]] (Sintel): 10.6


== Unsmate ==
== Unsmate ==
Line 484: Line 485:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~2048/1875 = 188.773
* [[POTE]]: ~2 = 1200.000, ~2048/1875 = 189.049
* [[POTE]]: ~2 = 1200.000, ~2048/1875 = 189.049


{{Optimal ET sequence|legend=1| 13, 19, 89c, 108c, 127c, 146cc }}
{{Optimal ET sequence|legend=1| 13, 19, 89c, 108c, 127c, 146cc }}


[[Badness]] (Smith): 0.460
[[Badness]] (Sintel): 10.8


== Nusecond ==
== Nusecond ==
Line 500: Line 502:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3125/2916 = 154.577
* [[POTE]]: ~2 = 1200.000, ~3125/2916 = 154.523
* [[POTE]]: ~2 = 1200.000, ~3125/2916 = 154.523


{{Optimal ET sequence|legend=1| 8, 23, 31, 70, 101, 132c, 233c, 365bcc }}
{{Optimal ET sequence|legend=1| 8, 23, 31, 70, 101, 132c }}
 
[[Badness]] (Sintel): 10.9
 
== Comic ==
: ''For extensions, see [[Jubilismic clan #Comic]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 5120000/4782969
 
{{Mapping|legend=1| 2 1 -3 | 0 2 7 }}
 
: mapping generators: ~2187/1600, ~40/27
 
[[Optimal tuning]]s:
* [[WE]]: ~2187/1600 = 598.9674{{c}}, ~40/27 = 654.2542{{c}} (~81/80 = 55.2868{{c}})
: [[error map]]: {{val| -2.065 +5.521 -3.436 }}
* [[CWE]]: ~2187/1600 = 600.0000{{c}}, ~40/27 = 655.0201{{c}} (~81/80 = 55.0201{{c}})
: error map: {{val| 0.000 +8.085 -1.173 }}
 
{{Optimal ET sequence|legend=1| 20c, 22, 86b, 108b, 130b }}


[[Badness]] (Smith): 0.466
[[Badness]] (Sintel): 11.5


== Sfourth ==
== Sfourth ==
Line 511: Line 535:
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 617673396283947/610351562500000
[[Comma list]]: {{monzo| -5 31 -19 }}


{{Mapping|legend=1| 1 2 3 | 0 -19 -31 }}
{{Mapping|legend=1| 1 2 3 | 0 -19 -31 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000, ~1594323/1562500 = 26.2342
* [[CTE]]: ~2 = 1200.0000, ~1594323/1562500 = 26.2323
* [[POTE]]: ~2 = 1200.0000, ~1594323/1562500 = 26.2342


{{Optimal ET sequence|legend=1| 45, 46, 91, 137, 183 }}
{{Optimal ET sequence|legend=1| 45, 46, 91, 137, 183, 869, 1052, 1235, 1418c }}


[[Badness]] (Smith): 0.505
[[Badness]] (Sintel): 11.8


== Thuja ==
== Thuja ==
Line 532: Line 557:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3125/2304 = 558.404
* [[POTE]]: ~2 = 1200.000, ~3125/2304 = 558.592
* [[POTE]]: ~2 = 1200.000, ~3125/2304 = 558.592


{{Optimal ET sequence|legend=1| 15, 43, 58 }}
{{Optimal ET sequence|legend=1| 15, 43, 58 }}


[[Badness]] (Smith): 0.511
[[Badness]] (Sintel): 12.0


== Leapday ==
== Leapday ==
Line 548: Line 574:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3/2 = 704.100
* [[POTE]]: ~2 = 1200.000, ~3/2 = 704.179
* [[POTE]]: ~2 = 1200.000, ~3/2 = 704.179


{{Optimal ET sequence|legend=1| 29, 46, 121, 167, 455bc, 622bbc }}
{{Optimal ET sequence|legend=1| 17c, 29, 46, 121, 167, 455bc, 622bbc }}


[[Badness]] (Smith): 0.523
[[Badness]] (Sintel): 12.3


== Vines ==
== Vines ==
Line 564: Line 591:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~390625/279936 = 600.000, ~6/5 = 312.636
* [[POTE]]: ~390625/279936 = 600.000, ~6/5 = 312.713
* [[POTE]]: ~390625/279936 = 600.000, ~6/5 = 312.713


{{Optimal ET sequence|legend=1| 4, 42, 46, 96, 142 }}
{{Optimal ET sequence|legend=1| 4, …, 42, 46, 96, 142, 330c, 472cc }}


[[Badness]] (Smith): 0.542
[[Badness]] (Sintel): 12.7


== Emka ==
== Emka ==
Line 580: Line 608:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~9765625/7077888 = 551.777
* [[POTE]]: ~2 = 1200.000, ~9765625/7077888 = 551.784
* [[POTE]]: ~2 = 1200.000, ~9765625/7077888 = 551.784


{{Optimal ET sequence|legend=1| 37, 50, 87, 137, 224 }}
{{Optimal ET sequence|legend=1| 37, 50, 87, 137, 224 }}


[[Badness]] (Smith): 0.545
[[Badness]] (Sintel): 12.8


== Misneb ==
== Misneb ==
Line 591: Line 620:
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 145964630126953125/144115188075855872
[[Comma list]]: {{monzo| -57 14 15 }}


{{Mapping|legend=1| 1 3 1 | 0 -15 14 }}
{{Mapping|legend=1| 1 3 1 | 0 -15 14 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~16/15 = 113.233
* [[POTE]]: ~2 = 1200.000, ~16/15 = 113.240
* [[POTE]]: ~2 = 1200.000, ~16/15 = 113.240


{{Optimal ET sequence|legend=1| 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc }}
{{Optimal ET sequence|legend=1| 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc }}


[[Badness]] (Smith): 0.610
[[Badness]] (Sintel): 14.3


== Semisept ==
== Semisept ==
Line 612: Line 642:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~192/125 = 735.203
* [[POTE]]: ~2 = 1200.000, ~192/125 = 735.146
* [[POTE]]: ~2 = 1200.000, ~192/125 = 735.146


{{Optimal ET sequence|legend=1| 18, 31, 80, 111 }}
{{Optimal ET sequence|legend=1| 18, 31, 80, 111, 586cc, 697ccc }}


[[Badness]] (Smith): 0.631
[[Badness]] (Sintel): 14.8


== Mowgli ==
== Mowgli ==
Line 623: Line 654:
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: {{monzo| 0 22 -15 }} = 31381059609/30517578125
[[Comma list]]: 31381059609/30517578125


{{Mapping|legend=1| 1 0 0 | 0 15 22 }}
{{Mapping|legend=1| 1 0 0 | 0 15 22 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000, ~27/25 = 126.724
* [[CTE]] and [[POTE]]: ~2 = 1200.000, ~27/25 = 126.724


{{Optimal ET sequence|legend=1| 19, 85c, 104c, 123, 142, 161 }}
{{Optimal ET sequence|legend=1| 19, 85c, 104c, 123, 142, 161, 303 }}


[[Badness]] (Smith): 0.654
[[Badness]] (Sintel): 15.3


== Septimin ==
== Septimin ==
Line 644: Line 675:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~75/64 = 263.571
* [[POTE]]: ~2 = 1200.000, ~75/64 = 263.658
* [[POTE]]: ~2 = 1200.000, ~75/64 = 263.658


{{Optimal ET sequence|legend=1| 9, 23b, 32, 41, 91, 132, 223c, 355bc }}
{{Optimal ET sequence|legend=1| 9, 23b, 32, 41, 91, 132, 223c, 355bcc }}


[[Badness]] (Smith): 0.671
[[Badness]] (Sintel): 15.7


== Slurpee ==
== Slurpee ==
Line 660: Line 692:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~27/25 = 72.659
* [[POTE]]: ~2 = 1200.000, ~27/25 = 72.742
* [[POTE]]: ~2 = 1200.000, ~27/25 = 72.742


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


[[Badness]] (Smith): 0.689
[[Badness]] (Sintel): 16.2


== Pentadecal ==
== Pentadecal ==
Line 676: Line 709:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~648/625 = 80.000, ~3/2 = 703.340
* [[POTE]]: ~648/625 = 80.000, ~3/2 = 702.652
* [[POTE]]: ~648/625 = 80.000, ~3/2 = 702.652


{{Optimal ET sequence|legend=1| 15, 45, 60, 75, 135, 210c, 345cc }}
{{Optimal ET sequence|legend=1| 15, 45, 60, 75, 135, 210c }}


[[Badness]] (Smith): 0.692
[[Badness]] (Sintel): 16.2


== Sentinel ==
== Sentinel ==
Line 692: Line 726:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~512/405 = 425.590
* [[POTE]]: ~2 = 1200.000, ~512/405 = 425.474
* [[POTE]]: ~2 = 1200.000, ~512/405 = 425.474


{{Optimal ET sequence|legend=1| 14, 17, 31, 79, 110, 361bc }}
{{Optimal ET sequence|legend=1| 14, 17, 31, 79, 110, 361bbcc }}


[[Badness]] (Smith): 0.723
[[Badness]] (Sintel): 17.0


== Kumonga ==
== Kumonga ==
Line 708: Line 743:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~144/125 = 223.076
* [[POTE]]: ~2 = 1200.000, ~144/125 = 222.912
* [[POTE]]: ~2 = 1200.000, ~144/125 = 222.912


{{Optimal ET sequence|legend=1| 16, 27, 43, 70, 183cc }}
{{Optimal ET sequence|legend=1| 16, 27, 43, 70, 183cc }}


[[Badness]] (Smith): 0.730
[[Badness]] (Sintel): 17.1


== Mirkat ==
== Mirkat ==
Line 724: Line 760:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2000000/1594323 = 400.000, ~10/9 = 183.583
* [[CTE]]: ~2000000/1594323 = 400.000, ~10/9 = 183.593
* [[CWE]]: ~2000000/1594323 = 400.000, ~10/9 = 183.585
* [[CWE]]: ~2000000/1594323 = 400.000, ~10/9 = 183.585


{{Optimal ET sequence|legend=1| 33c, 39, 72, 111, 183, 438, 621, 1425b }}
{{Optimal ET sequence|legend=1| 33c, 39, 72, 111, 183, 438, 621, 1425b }}


[[Badness]]:
[[Badness]] (Sintel): 17.6
* Smith: 0.752
* Dirichlet: 17.6


== Semidimi ==
== Semidimi ==
Line 743: Line 777:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~162/125 = 449.127
* [[POTE]]: ~2 = 1200.000, ~162/125 = 449.127
* [[POTE]]: ~2 = 1200.000, ~162/125 = 449.127


{{Optimal ET sequence|legend=1| 8, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}
{{Optimal ET sequence|legend=1| 8, …, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}


[[Badness]] (Smith): 0.755
[[Badness]] (Sintel): 17.7


== Slender ==
== Slender ==
Line 754: Line 789:
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 72081298828125/70368744177664
[[Comma list]]: {{monzo| -46 10 13 }}


{{Mapping|legend=1| 1 2 2 | 0 -13 10 }}
{{Mapping|legend=1| 1 2 2 | 0 -13 10 }}
Line 764: Line 799:
{{Optimal ET sequence|legend=1| 31, 94, 125, 781bcc }}
{{Optimal ET sequence|legend=1| 31, 94, 125, 781bcc }}


[[Badness]]:
[[Badness]] (Sintel): 17.8
* Smith: 0.761
* Dirichlet: 17.8


== Quasitemp ==
== Quasitemp ==
Line 778: Line 811:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3125/2592 = 292.591
* [[POTE]]: ~2 = 1200.000, ~3125/2592 = 292.702
* [[POTE]]: ~2 = 1200.000, ~3125/2592 = 292.702


{{Optimal ET sequence|legend=1| 4, 37, 41 }}
{{Optimal ET sequence|legend=1| 4, …, 37, 41 }}


[[Badness]] (Smith): 0.768
[[Badness]] (Sintel): 18.0


== Cypress ==
== Cypress ==
Line 794: Line 828:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~4374/3125 = 541.735
* [[POTE]]: ~2 = 1200.000, ~4374/3125 = 541.726
* [[POTE]]: ~2 = 1200.000, ~4374/3125 = 541.726


{{Optimal ET sequence|legend=1| 11c, 20c, 31, 113c, 144c, 175c, 381bcc }}
{{Optimal ET sequence|legend=1| 11c, 20c, 31, 113c, 144c, 175c }}


[[Badness]] (Smith): 0.817
[[Badness]] (Sintel): 19.2


== Chromo ==
== Chromo ==
Line 810: Line 845:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~25/24 = 54.138
* [[POTE]]: ~2 = 1200.000, ~25/24 = 53.922
* [[POTE]]: ~2 = 1200.000, ~25/24 = 53.922


{{Optimal ET sequence|legend=1| 22, 45, 67c, 89c }}
{{Optimal ET sequence|legend=1| 22, 45, 67c, 89c }}


[[Badness]] (Smith): 0.843
[[Badness]] (Sintel): 19.8


== Tertiosec ==
== Tertiosec ==
Line 826: Line 862:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~1073741824/854296875 = 400.000, ~16/15 = 112.281
* [[CTE]]: ~{{monzo| 30 -7 -8 }} = 400.000, ~16/15 = 112.275
* [[POTE]]: ~{{monzo| 30 -7 -8 }} = 400.000, ~16/15 = 112.281


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


[[Badness]] (Smith): 0.851
[[Badness]] (Sintel): 20.0


== Fervor ==
== Fervor ==
Line 842: Line 879:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~64/45 = 577.593
* [[POTE]]: ~2 = 1200.000, ~64/45 = 577.705
* [[POTE]]: ~2 = 1200.000, ~64/45 = 577.705


{{Optimal ET sequence|legend=1| 2, 25, 27 }}
{{Optimal ET sequence|legend=1| 2, …, 25, 27 }}


[[Badness]] (Smith): 0.853
[[Badness]] (Sintel): 20.0


== Bohpier ==
== Bohpier ==
Line 858: Line 896:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000, ~27/25 = 146.476
* [[CTE]] and [[POTE]]: ~2 = 1200.000, ~27/25 = 146.476


{{Optimal ET sequence|legend=1| 8, 41, 131, 172, 213c }}
{{Optimal ET sequence|legend=1| 8, …, 41, 131, 172, 213c }}


[[Badness]] (Smith): 0.861
[[Badness]] (Sintel): 20.2


== Elvis ==
== Elvis ==
Line 874: Line 912:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~6075/4096 = 600.000, ~45/32 = 554.546
* [[CTE]]: ~6075/4096 = 600.000, ~64/45 = 644.844
* [[POTE]]: ~6075/4096 = 600.000, ~64/45 = 645.454


{{Optimal ET sequence|legend=1| 26, 80bc, 106bc, 132bc }}
{{Optimal ET sequence|legend=1| 26, 80bc, 106bbcc, 132bbcc }}


[[Badness]] (Smith): 0.884
[[Badness]] (Sintel): 20.7


== Enneadecacot ==
== Enneadecacot ==
Line 888: Line 927:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.0000, ~34171875/33554432 = 36.9607
* [[POTE]]: ~2 = 1200.0000, ~34171875/33554432 = 36.9622
* [[POTE]]: ~2 = 1200.0000, ~34171875/33554432 = 36.9622


{{Optimal ET sequence|legend=1| 65, 292, 357, 422, 487, 1396c }}
{{Optimal ET sequence|legend=1| 32, 65, 292, 357, 422, 487, 1396c }}


[[Badness]] (Smith): 0.892
[[Badness]] (Sintel): 20.9


== Vinegar ==
== Vinegar ==
Line 904: Line 944:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~243/200 = 400.000, ~10/9 = 156.861
* [[CTE]]: ~243/200 = 400.000, ~4000/2187 = 955.656 (~10/9 = 155.656)
* [[POTE]]: ~243/200 = 400.000, ~4000/2187 = 956.861 (~10/9 = 156.861)


{{Optimal ET sequence|legend=1| 15, 39c, 54, 69b, 84b }}
{{Optimal ET sequence|legend=1| 15, 39c, 54, 69b }}


[[Badness]] (Smith): 0.903
[[Badness]] (Sintel): 21.2


== Oolong ==
== Oolong ==
Line 920: Line 961:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~6/5 = 311.726
* [[POTE]]: ~2 = 1200.000, ~6/5 = 311.694
* [[POTE]]: ~2 = 1200.000, ~6/5 = 311.694


{{Optimal ET sequence|legend=1| 23, 27, 50, 77 }}
{{Optimal ET sequence|legend=1| 23, 27, 50, 77 }}


[[Badness]] (Smith): 0.943
[[Badness]] (Sintel): 22.1


== Oncle ==
== Oncle ==
Line 936: Line 978:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~4096/3645 = 232.385
* [[POTE]]: ~2 = 1200.000, ~4096/3645 = 232.521
* [[POTE]]: ~2 = 1200.000, ~4096/3645 = 232.521


{{Optimal ET sequence|legend=1| 31, 98c, 129c, 160bc, 289bbcc }}
{{Optimal ET sequence|legend=1| 31, 98c, 129c, 160bc, 289bbcc }}


[[Badness]] (Smith): 1.24
[[Badness]] (Sintel): 29.2


== Quasiorwell ==
== Quasiorwell ==
Line 952: Line 995:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3662109375/2147483648 = 928.896
* [[CTE]]: ~2 = 1200.000, ~{{monzo| -31 1 13 }} = 928.896
* [[CWE]]: ~2 = 1200.000, ~3662109375/2147483648 = 928.893
* [[CWE]]: ~2 = 1200.000, ~{{monzo| -31 1 13 }} = 928.893


{{Optimal ET sequence|legend=1| 31, …, 177, 208, 239, 270, 841, 1111, 1381, 2492c }}
{{Optimal ET sequence|legend=1| 31, …, 177, 208, 239, 270, 841, 1111, 1381, 2492c }}


[[Badness]]:
[[Badness]] (Sintel): 30.6
* Smith: 1.30
* Dirichlet: 30.6


== Diesic ==
== Diesic ==
Line 971: Line 1,012:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~6561/6250 = 38.550
* [[POTE]]: ~2 = 1200.000, ~6561/6250 = 38.571
* [[POTE]]: ~2 = 1200.000, ~6561/6250 = 38.571


{{Optimal ET sequence|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}
{{Optimal ET sequence|legend=1| 31, 156c }}


[[Badness]] (Smith): 1.34
[[Badness]] (Sintel): 31.5


== Quartemka ==
== Quartemka ==
Line 982: Line 1,024:
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 1907348632812500/1853020188851841
[[Comma list]]: {{monzo| 2 -32 21 }}


{{Mapping|legend=1| 1 4 6 | 0 -21 -32 }}
{{Mapping|legend=1| 1 4 6 | 0 -21 -32 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~27/25 = 137.963
* [[POTE]]: ~2 = 1200.000, ~27/25 = 137.962
* [[POTE]]: ~2 = 1200.000, ~27/25 = 137.962


{{Optimal ET sequence|legend=1| 26, 61, 87, 287, 374, 461 }}
{{Optimal ET sequence|legend=1| 26, 61, 87, 287, 374, 461 }}


[[Badness]] (Smith): 1.38
[[Badness]] (Sintel): 32.4


== Genocchi ==
== Genocchi ==
Line 1,001: Line 1,044:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~768/625 = 210.920
* [[POTE]]: ~2 = 1200.000, ~768/625 = 212.444
* [[POTE]]: ~2 = 1200.000, ~768/625 = 212.444


{{Optimal ET sequence|legend=1| 6b, 11b, 17c }}
{{Optimal ET sequence|legend=1| 6b, 11b, 17c }}


[[Badness]] (Smith): 1.40
[[Badness]] (Sintel): 33.0


== Casablanca ==
== Casablanca ==
Line 1,012: Line 1,056:
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 20061226008576/19073486328125
[[Comma list]]: {{monzo| 22 14 -19 }}


{{Mapping|legend=1| 1 -7 -14 | 0 19 14 }}
{{Mapping|legend=1| 1 -7 -14 | 0 19 14 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~864/625 = 542.142
* [[POTE]]: ~2 = 1200.000, ~864/625 = 542.208
* [[POTE]]: ~2 = 1200.000, ~864/625 = 542.208


{{Optimal ET sequence|legend=1| 11b, 20b, 31, 73, 104c, 135c }}
{{Optimal ET sequence|legend=1| 11b, 20b, 31, 73, 104c, 135c }}


[[Badness]] (Smith): 1.42
[[Badness]] (Sintel): 33.4


== Archaeotherium ==
== Archaeotherium ==
Line 1,033: Line 1,078:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~1215/1024 = 229.947
* [[POTE]]: ~2 = 1200.000, ~1215/1024 = 230.351
* [[POTE]]: ~2 = 1200.000, ~1215/1024 = 230.351


{{Optimal ET sequence|legend=1| 21, 26, 73bc, 99bc }}
{{Optimal ET sequence|legend=1| 21, 26, 73bc, 99bc }}


[[Badness]] (Smith): 1.43
[[Badness]] (Sintel): 33.7


== Octacoid ==
== Octacoid ==
Line 1,049: Line 1,095:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~16/15 = 88.7331
* [[CTE]]: ~2 = 1200.0000, ~16/15 = 88.7331
* [[CWE]]: ~2 = 1200.000, ~16/15 = 88.8168
* [[CWE]]: ~2 = 1200.0000, ~16/15 = 88.8168


{{Optimal ET sequence|legend=1| 13, 14, 27 }}
{{Optimal ET sequence|legend=1| 13, 14, 27 }}


[[Badness]] (Smith): 1.75
[[Badness]] (Sintel): 41.1


== Quasimoha ==
== Quasimoha ==
Line 1,061: Line 1,107:
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 2353579470675/2199023255552
[[Comma list]]: {{monzo| -41 23 2 }}


{{Mapping|legend=1| 1 1 9 | 0 2 -23 }}
{{Mapping|legend=1| 1 1 9 | 0 2 -23 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~1048576/885735 = 348.462
* [[POTE]]: ~2 = 1200.000, ~1048576/885735 = 348.600
* [[POTE]]: ~2 = 1200.000, ~1048576/885735 = 348.600


{{Optimal ET sequence|legend=1| 31, 117c, 148bc, 179bc }}
{{Optimal ET sequence|legend=1| 31, 117c, 148bc, 179bc }}


[[Badness]] (Smith): 1.99
[[Badness]] (Sintel): 46.6


== Phillips ==
== Phillips ==
Line 1,082: Line 1,129:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~98415/65536 = 600.000, ~3/2 = 690.708
* [[POTE]]: ~98415/65536 = 600.000, ~3/2 = 691.455
* [[POTE]]: ~98415/65536 = 600.000, ~3/2 = 691.455


{{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc, 118bbc }}
{{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc, 118bbc }}


[[Badness]] (Smith): 2.23
[[Badness]] (Sintel): 52.3


== Triskaidekic ==
== Triskaidekic ==
Line 1,098: Line 1,146:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~128/125 = 92.308 (1＼13), ~3/2 = 696.142
* [[CTE]]: ~128/125 = 92.308, ~3/2 = 701.955
* [[POTE]]: ~128/125 = 92.308, ~3/2 = 696.142


{{Optimal ET sequence|legend=1| 13, 26, 91c }}
{{Optimal ET sequence|legend=1| 13, 26, 91cc }}


[[Badness]] (Smith): 2.24
[[Badness]] (Sintel): 52.6


== Satin ==
== Satin ==
Line 1,114: Line 1,163:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~{{monzo| -34 23 -1 }} = 165.910
* [[POTE]]: ~2 = 1200.000, ~{{monzo| -34 23 -1 }} = 165.907
* [[POTE]]: ~2 = 1200.000, ~{{monzo| -34 23 -1 }} = 165.907


{{Optimal ET sequence|legend=1| 94, 217, 528, 745, 1273 }}
{{Optimal ET sequence|legend=1| 94, 217, 528, 745, 1273 }}


[[Badness]] (Smith): 2.85
[[Badness]] (Sintel): 66.9


== Lockerbie ==
== Lockerbie ==
Line 1,139: Line 1,189:
{{Optimal ET sequence|legend=1| 103, 167, 270, 643, 913, 1183, 2636, 3819c, 5002c }}
{{Optimal ET sequence|legend=1| 103, 167, 270, 643, 913, 1183, 2636, 3819c, 5002c }}


[[Badness]] (Smith): 3.09
[[Badness]] (Sintel): 72.4


== Rarity ==
== Rarity ==
Line 1,160: Line 1,210:
{{Optimal ET sequence|legend=1| 11, 29, 69, 98c }}
{{Optimal ET sequence|legend=1| 11, 29, 69, 98c }}


[[Badness]] (Smith): 4.23
[[Badness]] (Sintel): 99.2


[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Pages with mostly numerical content]]

Latest revision as of 13:04, 23 August 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

Below are listed some 5-limit temperaments that do not belong to some other temperament collection, the majority of which are restrictions to the 5-limit of temperaments that emerge more fully in higher limits or subgroups; they are sorted by TE logflat badness, of which most have Sintel's > 4.7 (Smith's > 0.20). Most of these temperaments have low accuracy, high-complexity generators, or large number of generators for simple consonances. This is not an exhaustive list. Only expect to find a temperament here if you have not found it in:

Lafayette

For extensions, see Mint temperaments #Progression.

Subgroup: 2.3.5

Comma list: 3456/3125

Mapping: [⟨1 1 2], ⟨0 5 3]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~25/24 = 138.722
  • POTE: ~2 = 1200.000, ~25/24 = 140.995

Optimal ET sequence: 8, 9, 17c

Badness (Sintel): 4.70

Stump

For extensions, see Sensamagic clan #Pycnic and Marvel temperaments #Triton.

Subgroup: 2.3.5

Comma list: 273375/262144

Mapping: [⟨1 0 6], ⟨0 3 -7]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~64/45 = 631.504
  • POTE: ~2 = 1200.000, ~64/45 = 631.737

Optimal ET sequence: 17, 19, 207bbccc

Badness (Sintel): 4.71

Dodifo

For extensions, see Porwell temperaments #Dodifo.

Subgroup: 2.3.5

Comma list: [-67 -9 35⟩

Mapping: [⟨1 12 5], ⟨0 -35 -9]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~768/625 = 357.087
  • POTE: ~2 = 1200.000, ~768/625 = 357.088

Optimal ET sequence: 37, 84, 205, 289, 494, 783, 2060, 2843, 3626

Badness (Sintel): 5.00

Doublewide

For extensions, see Jubilismic clan #Doublewide.

Subgroup: 2.3.5

Comma list: 390625/373248

Mapping: [⟨2 1 3], ⟨0 4 3]]

mapping generators: ~625/432, ~6/5

Optimal tunings:

  • WE: ~625/432 = 600.6814 ¢, ~6/5 = 325.8892 ¢ (~144/125 = 274.7921 ¢)
error map: ⟨+1.363 +2.283 -6.602]
  • CWE: ~625/432 = 600.0000 ¢, ~6/5 = 325.8147 ¢ (~144/125 = 274.185 ¢)
error map: ⟨0.000 +1.304 -8.869]

Optimal ET sequence: 4, 14b, 18, 22, 48, 70c, 118c

Badness (Sintel): 5.32

Shibboleth

For extensions, see Gamelismic clan #Superkleismic, Starling temperaments #Gilead, and Sensamagic clan #Superthird.

Subgroup: 2.3.5

Comma list: 1953125/1889568

Mapping: [⟨1 4 5], ⟨0 -9 -10]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~6/5 = 321.773
  • POTE: ~2 = 1200.000, ~6/5 = 321.852

Optimal ET sequence: 15, 26, 41, 179c

Badness (Sintel): 5.34

Semidimfourth

For extensions, see Ragismic microtemperaments #Semidimfourth.

Subgroup: 2.3.5

Comma list: [7 41 -31⟩

Mapping: [⟨1 21 28], ⟨0 -31 -41]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~162/125 = 448.449
  • POTE: ~2 = 1200.000, ~162/125 = 448.449

Optimal ET sequence: 8, …, 91, 99, 190, 289, 388, 677, 3674, 4351, 5028, 5705, 6382, 13441c, 19823bcc

Badness (Sintel): 5.47

Mynic

For extensions, see Starling temperaments #Myna.

Subgroup: 2.3.5

Comma list: 10077696/9765625

Mapping: [⟨1 9 9], ⟨0 -10 -9]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~6/5 = 310.030
  • POTE: ~2 = 1200.000, ~6/5 = 310.140

Optimal ET sequence: 27, 31, 58, 89

Badness (Sintel): 5.86

Progress

For extensions, see Archytas clan #Progress.

Subgroup: 2.3.5

Comma list: 32768/30375

Mapping: [⟨1 0 5], ⟨0 3 -5]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~45/32 = 638.922
  • POTE: ~2 = 1200.000, ~45/32 = 638.736

Optimal ET sequence: 2, 13, 15, 32c, 47bc, 62bc

Badness (Sintel): 5.77

Abigail

For extensions, see Ragismic microtemperaments #Abigail.

Subgroup: 2.3.5

Comma list: [25 -48 22⟩

Mapping: [⟨2 7 13], ⟨0 -11 -24]]

Optimal tunings:

  • CTE: ~[-12 24 -11⟩ = 600.000, ~200000/177147 = 208.907
  • CWE: ~[-12 24 -11⟩ = 600.000, ~200000/177147 = 208.906

Optimal ET sequence: 46, 132, 178, 224, 270, 494, 1752, 2246, 2740, 4986, 7726b

Badness (Sintel): 5.97

Supermajor

For extensions, see Ragismic microtemperaments #Supermajor.

Subgroup: 2.3.5

Comma list: [-13 -46 37⟩

Mapping: [⟨1 15 19], ⟨0 -37 -46]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~625/486 = 435.081
  • CWE: ~2 = 1200.000, ~625/486 = 435.081

Optimal ET sequence: 80, 171, 593, 764, 935, 1106, 3489, 4595, 5701

Badness (Sintel): 6.19

Gamera

For extensions, see Ragismic microtemperaments #Gamera.

Subgroup: 2.3.5

Comma list: 12207031250000000000/12157665459056928801

Mapping: [⟨1 6 10], ⟨0 -23 -40]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~2500/2187 = 230.345
  • CWE: ~2 = 1200.000, ~2500/2187 = 230.345

Optimal ET sequence: 26, 73, 99, 224, 323, 547, 870

Badness (Sintel): 6.39

Tritriple

For extensions, see Gamelismic clan #Tritriple.

Subgroup: 2.3.5

Comma list: [31 20 -27⟩

Mapping: [⟨1 -11 -7], ⟨0 27 20]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~864/625 = 559.328
  • POTE: ~2 = 1200.000, ~864/625 = 559.332

Optimal ET sequence: 15, 88, 103, 118, 959, 1077

Badness (Sintel): 6.65

Kangaroo

For extensions, see Trienstonic clan #Parakangaroo.

Subgroup: 2.3.5

Comma list: 64000/59049

Mapping: [⟨1 0 -3], ⟨0 3 10]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~40/27 = 637.879
  • POTE: ~2 = 1200.000, ~40/27 = 638.805

Optimal ET sequence: 15, 47b, 62b

Badness (Sintel): 6.94

Tertiaseptal

For extensions, see Breedsmic temperaments #Tertiaseptal.

Subgroup: 2.3.5

Comma list: [-59 5 22⟩

Mapping: [⟨1 3 2], ⟨0 -22 5]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~17578125/16777216 = 77.186
  • POTE: ~2 = 1200.000, ~17578125/16777216 = 77.191

Optimal ET sequence: 31, 109, 140, 171, 1679c, 1850c, 2021c, 2192c, 2363c, 2534c, 2705c, 2876c, 3047c

Badness (Sintel): 6.98

Untriton

For extensions, see Marvel temperaments #Untriton, Porwell temperaments #Aufo and Triwellismic temperaments #Interaufo.

Subgroup: 2.3.5

Comma list: [-51 19 9⟩

Mapping: [⟨1 6 -7], ⟨0 -9 19]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~45/32 = 588.727
  • POTE: ~2 = 1200.000, ~45/32 = 588.722

Optimal ET sequence: 51, 53, 267, 320, 373, 426, 479, 532, 2607bc

Badness (Sintel): 7.20

Counterhanson

For extensions, see Ragismic microtemperaments #Counterkleismic.

Subgroup: 2.3.5

Comma list: [-20 -24 25⟩

Mapping: [⟨1 -5 -4], ⟨0 25 24]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~6/5 = 316.084
  • POTE: ~2 = 1200.000, ~6/5 = 316.081

Optimal ET sequence: 19, …, 148, 167, 186, 205, 224, 429, 653, 1082, 1735c

Badness (Sintel): 7.45

Nessafof

For extensions, see Porwell temperaments #Nessafof.

Subgroup: 2.3.5

Comma list: [25 15 -21⟩

Mapping: [⟨3 2 5], ⟨0 7 5]]

Optimal tunings:

  • CTE: ~78125/62208 = 400.000, ~9765625/8957952 = 157.392
  • CWE: ~78125/62208 = 400.000, ~9765625/8957952 = 157.409

Optimal ET sequence: 15, 54b, 69, 84, 99, 183, 282, 465, 1212c, 1677cc

Badness (Sintel): 7.81

Lemba

For extensions, see Jubilismic clan #Lemba.

Subgroup: 2.3.5

Comma list: 140625/131072

Mapping: [⟨2 2 5], ⟨0 3 -1]]

Mapping generators: ~375/256, ~75/64

Optimal tunings:

  • CTE: ~375/256 = 600.000, ~75/64 = 232.986
error map: ⟨0.000 -2.998 -19.300]
  • CWE: ~375/256 = 600.000, ~75/64 = 231.832
error map: ⟨0.000 -6.458 -18.146]

Optimal ET sequence: 10, 16, 26, 88cc

Badness (Sintel): 7.85

Delorean

For extensions, see Mint temperaments #Subklei.

Subgroup: 2.3.5

Comma list: 17496/15625

Mapping: [⟨1 3 4], ⟨0 -6 -7]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~6/5 = 284.817
  • POTE: ~2 = 1200.000, ~6/5 = 284.293

Optimal ET sequence: 4, 13c, 17c, 21, 38c

Badness (Sintel): 8.35

Majvam

For extensions, see No-sevens subgroup temperaments #Majvam, Cataharry temperaments #Majvamoid, and Parkleiness temperaments #Majvamic.

Subgroup: 2.3.5

Comma list: 2404631929946112/2384185791015625

Mapping: [⟨1 10 5], ⟨0 -22 -7]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~125/96 = 459.006
  • POTE: ~2 = 1200.000, ~125/96 = 458.995

Optimal ET sequence: 34, 115, 149, 183, 217, 400, 617

Badness (Sintel): 8.37

Beatles

For extensions, see Archytas clan #Beatles.

Subgroup: 2.3.5

Comma list: 524288/492075

Mapping: [⟨1 1 5], ⟨0 2 -9]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~512/405 = 356.492
  • POTE: ~2 = 1200.000, ~512/405 = 355.930

Optimal ET sequence: 10, 17c, 27, 64b, 91bc, 118bc

Badness (Sintel): 8.41

Magus

For extensions, see Sensamagic clan #Magus and Starling temperaments #Amigo.

Subgroup: 2.3.5

Comma list: 50331648/48828125

Mapping: [⟨1 -2 2], ⟨0 11 1]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~5/4 = 391.068
  • POTE: ~2 = 1200.000, ~5/4 = 391.225

Optimal ET sequence: 3, …, 40, 43, 46, 181c, 227c, 273c, 319c

Badness (Sintel): 8.45

Countermeantone

Subgroup: 2.3.5

Comma list: [10 23 -20⟩

Mapping: [⟨1 -10 -11], ⟨0 20 23]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~78125/52488 = 695.082
  • POTE: ~2 = 1200.000, ~78125/52488 = 695.087

Optimal ET sequence: 19, …, 126, 145, 164, 183, 713, 896c, 1079c, 1262c, 1445c

Badness (Sintel): 8.76

Tritonic

For extensions, see Marvel temperaments #Tritonic.

Subgroup: 2.3.5

Comma list: 553584375/536870912

Mapping: [⟨1 4 -3], ⟨0 -5 11]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~45/32 = 580.278
  • POTE: ~2 = 1200.000, ~45/32 = 580.219

Optimal ET sequence: 29, 31, 60, 91

Badness (Sintel): 8.88

Wizard

For extensions, see Marvel temperaments #Wizard.

Subgroup: 2.3.5

Comma list: 2197265625/2147483648

Mapping: [⟨2 1 5], ⟨0 6 -1]]

mapping generators: ~42875/32768, ~9375/8192

Optimal tunings:

  • CTE: ~42875/32768 = 600.000, ~9375/8192 = 216.950
  • POTE: ~42875/32768 = 600.000, ~9375/8192 = 216.788

Optimal ET sequence: 22, 50, 72, 166, 238c, 310c, 548bcc

Badness (Sintel): 9.06

Scales (Scala files): wizard22

Hogzilla

For extensions, see Semaphoresmic clan #Helayo.

Subgroup: 2.3.5

Comma list: 4428675/4194304

Mapping: [⟨1 0 11], ⟨0 2 -11]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~2048/1215 = 946.982
  • POTE: ~2 = 1200.000, ~2048/1215 = 947.351

Optimal ET sequence: 14, 19

Badness (Sintel): 9.96

Merman

For extensions, see Marvel temperaments #Merman.

Subgroup: 2.3.5

Comma list: [-40 15 7⟩

Mapping: [⟨1 5 -5], ⟨0 -7 15]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~45/32 = 585.653
  • POTE: ~2 = 1200.000, ~45/32 = 585.634

Optimal ET sequence: 41, 84, 125, 209, 334c, 543bc

Badness (Sintel): 10.6

Unsmate

Subgroup: 2.3.5

Comma list: 17578125/16777216

Mapping: [⟨1 3 2], ⟨0 -9 2]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~2048/1875 = 188.773
  • POTE: ~2 = 1200.000, ~2048/1875 = 189.049

Optimal ET sequence: 13, 19, 89c, 108c, 127c, 146cc

Badness (Sintel): 10.8

Nusecond

For extensions, see Starling temperaments #Nusecond.

Subgroup: 2.3.5

Comma list: 51018336/48828125

Mapping: [⟨1 3 4], ⟨0 -11 -13]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~3125/2916 = 154.577
  • POTE: ~2 = 1200.000, ~3125/2916 = 154.523

Optimal ET sequence: 8, 23, 31, 70, 101, 132c

Badness (Sintel): 10.9

Comic

For extensions, see Jubilismic clan #Comic.

Subgroup: 2.3.5

Comma list: 5120000/4782969

Mapping: [⟨2 1 -3], ⟨0 2 7]]

mapping generators: ~2187/1600, ~40/27

Optimal tunings:

  • WE: ~2187/1600 = 598.9674 ¢, ~40/27 = 654.2542 ¢ (~81/80 = 55.2868 ¢)
error map: ⟨-2.065 +5.521 -3.436]
  • CWE: ~2187/1600 = 600.0000 ¢, ~40/27 = 655.0201 ¢ (~81/80 = 55.0201 ¢)
error map: ⟨0.000 +8.085 -1.173]

Optimal ET sequence: 20c, 22, 86b, 108b, 130b

Badness (Sintel): 11.5

Sfourth

For extensions, see Ragismic microtemperaments #Sfourth.

Subgroup: 2.3.5

Comma list: [-5 31 -19⟩

Mapping: [⟨1 2 3], ⟨0 -19 -31]]

Optimal tunings:

  • CTE: ~2 = 1200.0000, ~1594323/1562500 = 26.2323
  • POTE: ~2 = 1200.0000, ~1594323/1562500 = 26.2342

Optimal ET sequence: 45, 46, 91, 137, 183, 869, 1052, 1235, 1418c

Badness (Sintel): 11.8

Thuja

For extensions, see Buzzardsmic clan #Thuja.

Subgroup: 2.3.5

Comma list: 254803968/244140625

Mapping: [⟨1 -4 0], ⟨0 12 5]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~3125/2304 = 558.404
  • POTE: ~2 = 1200.000, ~3125/2304 = 558.592

Optimal ET sequence: 15, 43, 58

Badness (Sintel): 12.0

Leapday

For extensions, see Hemifamity temperaments #Leapday and Porwell temperaments #Polypyth.

Subgroup: 2.3.5

Comma list: 10737418240/10460353203

Mapping: [⟨1 0 -31], ⟨0 1 21]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~3/2 = 704.100
  • POTE: ~2 = 1200.000, ~3/2 = 704.179

Optimal ET sequence: 17c, 29, 46, 121, 167, 455bc, 622bbc

Badness (Sintel): 12.3

Vines

For extensions, see Starling temperaments #Vines.

Subgroup: 2.3.5

Comma list: 156728328192/152587890625

Mapping: [⟨2 7 8], ⟨0 -8 -7]]

Optimal tunings:

  • CTE: ~390625/279936 = 600.000, ~6/5 = 312.636
  • POTE: ~390625/279936 = 600.000, ~6/5 = 312.713

Optimal ET sequence: 4, …, 42, 46, 96, 142, 330c, 472cc

Badness (Sintel): 12.7

Emka

For extensions, see Hemimean clan #Emka and Horwell temperaments #Emkay.

Subgroup: 2.3.5

Comma list: [-50 -8 27⟩

Mapping: [⟨1 14 6], ⟨0 -27 -8]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~9765625/7077888 = 551.777
  • POTE: ~2 = 1200.000, ~9765625/7077888 = 551.784

Optimal ET sequence: 37, 50, 87, 137, 224

Badness (Sintel): 12.8

Misneb

For extensions, see Marvel temperaments #Misneb.

Subgroup: 2.3.5

Comma list: [-57 14 15⟩

Mapping: [⟨1 3 1], ⟨0 -15 14]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~16/15 = 113.233
  • POTE: ~2 = 1200.000, ~16/15 = 113.240

Optimal ET sequence: 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc

Badness (Sintel): 14.3

Semisept

For extensions, see Hemimean clan #Semisept.

Subgroup: 2.3.5

Comma list: 782757789696/762939453125

Mapping: [⟨1 12 6], ⟨0 -17 -6]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~192/125 = 735.203
  • POTE: ~2 = 1200.000, ~192/125 = 735.146

Optimal ET sequence: 18, 31, 80, 111, 586cc, 697ccc

Badness (Sintel): 14.8

Mowgli

For extensions, see Hemimean clan #Mowglic.

Subgroup: 2.3.5

Comma list: 31381059609/30517578125

Mapping: [⟨1 0 0], ⟨0 15 22]]

Optimal tunings:

  • CTE and POTE: ~2 = 1200.000, ~27/25 = 126.724

Optimal ET sequence: 19, 85c, 104c, 123, 142, 161, 303

Badness (Sintel): 15.3

Septimin

For extensions, see Marvel temperaments #Septimin.

Subgroup: 2.3.5

Comma list: 35595703125/34359738368

Mapping: [⟨1 4 1], ⟨0 -11 6]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~75/64 = 263.571
  • POTE: ~2 = 1200.000, ~75/64 = 263.658

Optimal ET sequence: 9, 23b, 32, 41, 91, 132, 223c, 355bcc

Badness (Sintel): 15.7

Slurpee

For extensions, see Mint temperaments #Slurpee.

Subgroup: 2.3.5

Comma list: 177147/156250

Mapping: [⟨1 2 3], ⟨0 -7 -11]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~27/25 = 72.659
  • POTE: ~2 = 1200.000, ~27/25 = 72.742

Optimal ET sequence: 16, 17c, 33

Badness (Sintel): 16.2

Pentadecal

For extensions, see Cloudy clan #Pentadecal.

Subgroup: 2.3.5

Comma list: 30517578125/29386561536

Mapping: [⟨15 0 11], ⟨0 1 1]]

Optimal tunings:

  • CTE: ~648/625 = 80.000, ~3/2 = 703.340
  • POTE: ~648/625 = 80.000, ~3/2 = 702.652

Optimal ET sequence: 15, 45, 60, 75, 135, 210c

Badness (Sintel): 16.2

Sentinel

For extensions, see Orwellismic temperaments #Sentinel.

Subgroup: 2.3.5

Comma list: 8968066875/8589934592

Mapping: [⟨1 3 -3], ⟨0 -4 15]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~512/405 = 425.590
  • POTE: ~2 = 1200.000, ~512/405 = 425.474

Optimal ET sequence: 14, 17, 31, 79, 110, 361bbcc

Badness (Sintel): 17.0

Kumonga

For extensions, see Starling temperaments #Kumonga.

Subgroup: 2.3.5

Comma list: 1289945088/1220703125

Mapping: [⟨1 4 4], ⟨0 -13 -9]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~144/125 = 223.076
  • POTE: ~2 = 1200.000, ~144/125 = 222.912

Optimal ET sequence: 16, 27, 43, 70, 183cc

Badness (Sintel): 17.1

Mirkat

For extensions, see Mirkwai clan #Mirkat.

Subgroup: 2.3.5

Comma list: [20 -39 18⟩

Mapping: [⟨3 2 1], ⟨0 6 13]]

Optimal tunings:

  • CTE: ~2000000/1594323 = 400.000, ~10/9 = 183.593
  • CWE: ~2000000/1594323 = 400.000, ~10/9 = 183.585

Optimal ET sequence: 33c, 39, 72, 111, 183, 438, 621, 1425b

Badness (Sintel): 17.6

Semidimi

For extensions, see Ragismic microtemperaments #Semidimi.

Subgroup: 2.3.5

Comma list: [-12 -73 55⟩

Mapping: [⟨1 36 48], ⟨0 -55 -73]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~162/125 = 449.127
  • POTE: ~2 = 1200.000, ~162/125 = 449.127

Optimal ET sequence: 8, …, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419

Badness (Sintel): 17.7

Slender

For extensions, see Marvel temperaments #Slender.

Subgroup: 2.3.5

Comma list: [-46 10 13⟩

Mapping: [⟨1 2 2], ⟨0 -13 10]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~16875/16384 = 38.380
  • CWE: ~2 = 1200.000, ~16875/16384 = 38.400

Optimal ET sequence: 31, 94, 125, 781bcc

Badness (Sintel): 17.8

Quasitemp

For extensions, see Keemic temperaments #Quasitemp.

Subgroup: 2.3.5

Comma list: 6103515625/5804752896

Mapping: [⟨1 5 5], ⟨0 -14 -11]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~3125/2592 = 292.591
  • POTE: ~2 = 1200.000, ~3125/2592 = 292.702

Optimal ET sequence: 4, …, 37, 41

Badness (Sintel): 18.0

Cypress

For extensions, see Starling temperaments #Cypress.

Subgroup: 2.3.5

Comma list: 258280326/244140625

Mapping: [⟨1 7 10], ⟨0 -12 -17]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~4374/3125 = 541.735
  • POTE: ~2 = 1200.000, ~4374/3125 = 541.726

Optimal ET sequence: 11c, 20c, 31, 113c, 144c, 175c

Badness (Sintel): 19.2

Chromo

For extensions, see Keemic temperaments #Chromo.

Subgroup: 2.3.5

Comma list: 1220703125/1146617856

Mapping: [⟨1 1 2], ⟨0 13 7]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~25/24 = 54.138
  • POTE: ~2 = 1200.000, ~25/24 = 53.922

Optimal ET sequence: 22, 45, 67c, 89c

Badness (Sintel): 19.8

Tertiosec

For extensions, see Marvel temperaments #Tertiosec.

Subgroup: 2.3.5

Comma list: [-89 21 24⟩

Mapping: [⟨3 7 5], ⟨0 -8 7]]

Optimal tunings:

  • CTE: ~[30 -7 -8⟩ = 400.000, ~16/15 = 112.275
  • POTE: ~[30 -7 -8⟩ = 400.000, ~16/15 = 112.281

Optimal ET sequence: 21, 54, 75, 96, 171

Badness (Sintel): 20.0

Fervor

For extensions, see Archytas clan #Fervor.

Subgroup: 2.3.5

Comma list: 67108864/61509375

Mapping: [⟨1 4 -2], ⟨0 -5 9]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~64/45 = 577.593
  • POTE: ~2 = 1200.000, ~64/45 = 577.705

Optimal ET sequence: 2, …, 25, 27

Badness (Sintel): 20.0

Bohpier

For extensions, see Sensamagic clan #Bohpier.

Subgroup: 2.3.5

Comma list: 1220703125/1162261467

Mapping: [⟨1 0 0], ⟨0 13 19]]

Optimal tunings:

  • CTE and POTE: ~2 = 1200.000, ~27/25 = 146.476

Optimal ET sequence: 8, …, 41, 131, 172, 213c

Badness (Sintel): 20.2

Elvis

For extensions, see Jubilismic clan #Elvis.

Subgroup: 2.3.5

Comma list: 36905625/33554432

Mapping: [⟨2 1 10], ⟨0 2 -5]]

Optimal tunings:

  • CTE: ~6075/4096 = 600.000, ~64/45 = 644.844
  • POTE: ~6075/4096 = 600.000, ~64/45 = 645.454

Optimal ET sequence: 26, 80bc, 106bbcc, 132bbcc

Badness (Sintel): 20.7

Enneadecacot

Subgroup: 2.3.5

Comma list: [79 -22 -19⟩

Mapping: [⟨1 1 3], ⟨0 19 -22]]

Optimal tunings:

  • CTE: ~2 = 1200.0000, ~34171875/33554432 = 36.9607
  • POTE: ~2 = 1200.0000, ~34171875/33554432 = 36.9622

Optimal ET sequence: 32, 65, 292, 357, 422, 487, 1396c

Badness (Sintel): 20.9

Vinegar

For extensions, see Starling temperaments #Vinegar.

Subgroup: 2.3.5

Comma list: 16000000/14348907

Mapping: [⟨3 0 -5], ⟨0 2 5]]

Optimal tunings:

  • CTE: ~243/200 = 400.000, ~4000/2187 = 955.656 (~10/9 = 155.656)
  • POTE: ~243/200 = 400.000, ~4000/2187 = 956.861 (~10/9 = 156.861)

Optimal ET sequence: 15, 39c, 54, 69b

Badness (Sintel): 21.2

Oolong

For extensions, see Starling temperaments #Oolong.

Subgroup: 2.3.5

Comma list: 793437161472/762939453125

Mapping: [⟨1 6 7], ⟨0 -17 -18]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~6/5 = 311.726
  • POTE: ~2 = 1200.000, ~6/5 = 311.694

Optimal ET sequence: 23, 27, 50, 77

Badness (Sintel): 22.1

Oncle

For extensions, see Gamelismic clan #Oncle.

Subgroup: 2.3.5

Comma list: 145282683375/137438953472

Mapping: [⟨1 1 6], ⟨0 3 -19]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~4096/3645 = 232.385
  • POTE: ~2 = 1200.000, ~4096/3645 = 232.521

Optimal ET sequence: 31, 98c, 129c, 160bc, 289bbcc

Badness (Sintel): 29.2

Quasiorwell

For extensions, see Breedsmic temperaments #Quasiorwell.

Subgroup: 2.3.5

Comma list: [-93 3 38⟩

Mapping: [⟨1 31 0], ⟨0 -38 3]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~[-31 1 13⟩ = 928.896
  • CWE: ~2 = 1200.000, ~[-31 1 13⟩ = 928.893

Optimal ET sequence: 31, …, 177, 208, 239, 270, 841, 1111, 1381, 2492c

Badness (Sintel): 30.6

Diesic

For extensions, see Orwellismic temperaments #Diesic.

Subgroup: 2.3.5

Comma list: 10460353203/9765625000

Mapping: [⟨1 2 3], ⟨0 -13 -21]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~6561/6250 = 38.550
  • POTE: ~2 = 1200.000, ~6561/6250 = 38.571

Optimal ET sequence: 31, 156c

Badness (Sintel): 31.5

Quartemka

For extensions, see Gamelismic clan #Quartemka.

Subgroup: 2.3.5

Comma list: [2 -32 21⟩

Mapping: [⟨1 4 6], ⟨0 -21 -32]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~27/25 = 137.963
  • POTE: ~2 = 1200.000, ~27/25 = 137.962

Optimal ET sequence: 26, 61, 87, 287, 374, 461

Badness (Sintel): 32.4

Genocchi

Subgroup: 2.3.5

Comma list: 2359296/1953125

Mapping: [⟨1 0 2], ⟨0 9 2]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~768/625 = 210.920
  • POTE: ~2 = 1200.000, ~768/625 = 212.444

Optimal ET sequence: 6b, 11b, 17c

Badness (Sintel): 33.0

Casablanca

For extensions, see Starling temperaments #Casablanca.

Subgroup: 2.3.5

Comma list: [22 14 -19⟩

Mapping: [⟨1 -7 -14], ⟨0 19 14]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~864/625 = 542.142
  • POTE: ~2 = 1200.000, ~864/625 = 542.208

Optimal ET sequence: 11b, 20b, 31, 73, 104c, 135c

Badness (Sintel): 33.4

Archaeotherium

For extensions, see Gamelismic clan #Archaeotherium.

Subgroup: 2.3.5

Comma list: 597871125/536870912

Mapping: [⟨1 1 5], ⟨0 3 -14]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~1215/1024 = 229.947
  • POTE: ~2 = 1200.000, ~1215/1024 = 230.351

Optimal ET sequence: 21, 26, 73bc, 99bc

Badness (Sintel): 33.7

Octacoid

Subgroup: 2.3.5

Comma list: 8589934592/7688671875

Mapping: [⟨1 1 3], ⟨0 8 -9]]

Mapping generators: ~2, ~16/15

Optimal tunings:

  • CTE: ~2 = 1200.0000, ~16/15 = 88.7331
  • CWE: ~2 = 1200.0000, ~16/15 = 88.8168

Optimal ET sequence: 13, 14, 27

Badness (Sintel): 41.1

Quasimoha

For extensions, see Breedsmic temperaments #Quasimoha.

Subgroup: 2.3.5

Comma list: [-41 23 2⟩

Mapping: [⟨1 1 9], ⟨0 2 -23]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~1048576/885735 = 348.462
  • POTE: ~2 = 1200.000, ~1048576/885735 = 348.600

Optimal ET sequence: 31, 117c, 148bc, 179bc

Badness (Sintel): 46.6

Phillips

For extensions, see Orwellismic temperaments #Phillips.

Subgroup: 2.3.5

Comma list: 9685512225/8589934592

Mapping: [⟨2 0 33], ⟨0 1 -9]]

Optimal tunings:

  • CTE: ~98415/65536 = 600.000, ~3/2 = 690.708
  • POTE: ~98415/65536 = 600.000, ~3/2 = 691.455

Optimal ET sequence: 14, 26, 66b, 92bc, 118bbc

Badness (Sintel): 52.3

Triskaidekic

For extensions, see Orwellismic temperaments #Triskaidekic.

Subgroup: 2.3.5

Comma list: 1220703125/1073741824

Mapping: [⟨13 0 30], ⟨0 1 0]]

Optimal tunings:

  • CTE: ~128/125 = 92.308, ~3/2 = 701.955
  • POTE: ~128/125 = 92.308, ~3/2 = 696.142

Optimal ET sequence: 13, 26, 91cc

Badness (Sintel): 52.6

Satin

For extensions, see Canousmic temperaments #Satin.

Subgroup: 2.3.5

Comma list: [104 -70 3⟩

Mapping: [⟨1 2 12], ⟨0 -3 -70]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~[-34 23 -1⟩ = 165.910
  • POTE: ~2 = 1200.000, ~[-34 23 -1⟩ = 165.907

Optimal ET sequence: 94, 217, 528, 745, 1273

Badness (Sintel): 66.9

Lockerbie

For extensions, see Breedsmic temperaments #Lockerbie.

Subgroup: 2.3.5

Comma list: [91 51 -74⟩

Mapping: [⟨1 -25 -16], ⟨0 74 51]]

mapping generators: ~2, ~[36 20 -29⟩

Optimal tunings:

  • CTE: ~2 = 1200.0000, ~[36 20 -29⟩ = 431.1069
error map: ⟨0.0000 -0.0444 +0.1382]
  • CWE: ~2 = 1200.0000, ~[36 20 -29⟩ = 431.1073
error map: ⟨0.0000 -0.0174 +0.1568]

Optimal ET sequence: 103, 167, 270, 643, 913, 1183, 2636, 3819c, 5002c

Badness (Sintel): 72.4

Rarity

For extensions, see No-sevens subgroup temperaments #Rarity.

The rarity temperament is notable due to the fact that it offers a 7L 4s scale of reasonable hardness, in the 5-limit and among relatively small edos.

Subgroup: 2.3.5

Comma list: [-57 17 13⟩

Mapping: [⟨1 11 -10], ⟨0 -13 17]]

Mapping generators: ~2, ~16384/10125

Optimal tunings:

  • CTE: ~2 = 1200.000, ~16384/10125 = 869.392
  • CWE: ~2 = 1200.000, ~16384/10125 = 869.402

Optimal ET sequence: 11, 29, 69, 98c

Badness (Sintel): 99.2

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