Miscellaneous 5-limit temperaments: Difference between revisions

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-septendecic, identical to gothic and not a distinctive name. -newt, -cotoneum, -hemififths, -countritonic (duplicates from the continua)
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Below are listed some high-badness 5-limit temperaments (Smith [[TE logflat badness]] > 0.2, sorted by the same metric). Most of these are temperaments which 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:  
{{Technical data page}}
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]]
* [[Fractional-octave temperaments]]
* [[Very low accuracy temperaments]]
* [[Very low accuracy temperaments]]
* [[Very high accuracy temperaments]]
* [[Very high accuracy temperaments]]


== Lafayette ==
== Unidecmic ==
: ''For extensions, see [[Mint temperaments #Progression]].''
: ''For extensions, see [[Gamelismic clan #Unidec]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 31381059609/31250000000
 
{{Mapping|legend=1| 2 -1 -3 | 0 6 11 }}
: mapping generators: ~177147/125000, ~25000/19683
 
[[Optimal tuning]]s:
* [[WE]]: ~177147/125000 = 600.0124{{c}}, ~25000/19683 = 416.9619{{c}}
: [[error map]]: {{val| +0.025 -0.196 +0.235 }}
* [[CWE]]: ~177147/125000 = 600.0000{{c}}, ~25000/19683 = 416.9561{{c}}
: error map: {{val| 0.000 -0.236 +0.172 }}
 
{{Optimal ET sequence|legend=1| 26, 46, 72, 118, 2524, 2642, 2760 }}
 
[[Badness]] (Sintel): 1.93
 
== Quasithird ==
: ''For extensions, see [[Ragismic microtemperaments #Quasithird]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 55 -64 20 }}
 
{{Mapping|legend=1| 4 0 -11 | 0 5 16 }}
: mapping generators: ~51200000/43046721, ~1594323/1280000
 
[[Optimal tuning]]s:
* [[WE]]: ~51200000/43046721 = 299.9990{{c}}, ~1594323/1280000 = 380.3934{{c}}
: [[error map]]: {{val| -0.004 +0.012 -0.008 }}
* [[CWE]]: ~51200000/43046721 = 300.0000{{c}}, ~1594323/1280000 = 380.3944{{c}}
: error map: {{val| 0.000 +0.017 -0.004 }}
 
{{Optimal ET sequence|legend=1| 60, 104c, 164, 224, 388, 612, 1612, 2224, 2836, 6284, 9120, 15404 }}
 
[[Badness]] (Sintel): 2.33
 
== Supersharp ==
: ''For extensions, see [[Trienstonic clan #Octokaidecal]].''
 
Supersharp tempers out [[800/729]], the difference between the [[27/20]] wolf fourth and the [[40/27]] wolf fifth, splitting the octave into two 27/20~40/27 semioctaves. It generally requires a very sharp fifth, even sharper than 3\5, as a generator. This means that five steps from the [[generator sequence #JI scales obtained from guided generator sequences|Zarlino generator sequence]] starting with 6/5 are tempered to one and a half octaves. The only reasonable 7-limit extension adds 28/27 and 50/49 to the comma list, taking advantage of the existing semioctave.
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 800/729
 
{{Mapping|legend=1| 2 0 -5 | 0 1 3 }}
: mapping generators: ~27/20, ~3
 
[[Optimal tuning]]s:
* [[WE]]: ~27/20 = 596.986{{c}}, ~3/2 = 725.434{{c}} (~10/9 = 128.448{{c}})
: [[error map]]: {{val| -6.029 +17.450 -13.027 }}
* [[CWE]]: ~27/20 = 600.000{{c}}, ~3/2 = 726.548{{c}} (~10/9 = 126.548{{c}})
: error map: {{val| 0.000 +24.593 -6.670 }}
 
{{Optimal ET sequence|legend=1| 8, 10, 18, 28b }}
 
[[Badness]] (Sintel): 2.88
 
== Avila ==
: ''For extensions, see [[Septisemi temperaments #Avila]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 729/640
 
{{Mapping|legend=1| 1 0 -7 | 0 1 6 }}
: mapping generators: ~2, ~3
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1210.600{{c}}, ~3/2 = 667.437{{c}}
: [[error map]]: {{val| +10.600 -23.917 +7.711 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 663.474{{c}}
: error map: {{val| 0.000 -38.481 -5.472 }}
 
{{Optimal ET sequence|legend=1| 2c, 7c, 9, 20b, 29b }}
 
[[Badness]] (Sintel): 4.27
 
== Lafa ==
This temperament was named by [[Petr Pařízek]] in 2011, referring to the characteristic that stacking 12 generators makes 6/1 – "l" for 12, "f" for 6<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>. Its ploidacot is therefore beta-dodecacot.


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 3456/3125
[[Comma list]]: {{monzo| 77 -31 -12 }}


{{Mapping|legend=1| 1 1 2 | 0 5 3 }}
{{Mapping|legend=1| 1 -1 9 | 0 12 -31 }}
: mapping generators: ~2, ~{{monzo| -32 13 5 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000, ~25/24 = 140.995
* [[WE]]: ~2 = 1199.9693{{c}}, ~{{monzo| -32 13 5 }} = 258.4963{{c}}
: [[error map]]: {{val| -0.031 +0.031 +0.026 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~{{monzo| -32 13 5 }} = 258.5031{{c}}
: error map: {{val| 0.000 +0.082 +0.091 }}


{{Optimal ET sequence|legend=1| 8, 9, 17c }}
{{Optimal ET sequence|legend=1| 65, 246, 311, 376, 441, 2711, 3152, 3593, 4034, 4475, 4916, 5357, 10273bc, 15630bbcc }}


[[Badness]]: 0.200483
[[Badness]] (Sintel): 4.33


== Stump ==
== Lafayette ==
: ''For extensionss, see [[Sensamagic clan #Pycnic]] and [[Marvel temperaments #Triton]].''
: ''For extensions, see [[Mint temperaments #Progression]].''


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 273375/262144
[[Comma list]]: 3456/3125


{{Mapping|legend=1| 1 0 6 | 0 3 -7 }}
{{Mapping|legend=1| 1 1 2 | 0 5 3 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000, ~64/45 = 631.737
* [[CTE]]: ~2 = 1200.000{{c}}, ~25/24 = 138.722{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~25/24 = 140.995{{c}}


{{Optimal ET sequence|legend=1| 17, 19 }}
{{Optimal ET sequence|legend=1| 8, 9, 17c }}


[[Badness]]: 0.200600
[[Badness]] (Sintel): 4.70


== Dodifo ==
== Dodifo ==
Line 43: Line 130:
[[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:  
* [[POTE]]: ~2 = 1200.000, ~768/625 = 357.088
* [[CTE]]: ~2 = 1200.000{{c}}, ~768/625 = 357.087{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~768/625 = 357.088{{c}}


{{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]]: 0.213112
[[Badness]] (Sintel): 5.00


== Mabila ==
== Doublewide ==
: ''For extensions, see [[Mabila family]].''
: ''For extensions, see [[Jubilismic clan #Doublewide]].''


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 268435456/263671875
[[Comma list]]: 390625/373248


{{Mapping|legend=1| 1 6 1 | 0 -10 3 }}
{{Mapping|legend=1| 2 1 3 | 0 4 3 }}
: mapping generators: ~625/432, ~6/5


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000, ~512/375 = 529.685
* [[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| 9, 25, 34, 77, 111, 145, 256c }}
{{Optimal ET sequence|legend=1| 4, 14b, 18, 22, 48, 70c, 118c }}


[[Badness]]: 0.232481
[[Badness]] (Sintel): 5.32


== Semidimfourth ==
== Shibboleth ==
: ''For extensions, see [[Ragismic microtemperaments #Semidimfourth]].''
: ''For extensions, see [[Gamelismic clan #Superkleismic]], [[Starling temperaments #Gilead]], and [[Sensamagic clan #Superthird]].''


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: {{monzo| 7 41 -31 }}
[[Comma list]]: 1953125/1889568


{{Mapping|legend=1| 1 21 28 | 0 -31 -41 }}
{{Mapping|legend=1| 1 4 5 | 0 -9 -10 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000, ~162/125 = 448.449
* [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 321.773{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 321.852{{c}}


{{Optimal ET sequence|legend=1| 8, 91, 99, 190, 289, 388, 677, 3674, 4351, 5028, 5705, 6382, 13441c, 19823bcc }}
{{Optimal ET sequence|legend=1| 15, 26, 41, 179c }}


[[Badness]]: 0.233376
[[Badness]] (Sintel): 5.34


== Undim ==
== Semidimfourth ==
{{See also| Undim family }}
: ''For extensions, see [[Ragismic microtemperaments #Semidimfourth]].''


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 2199023255552/2179240250625
[[Comma list]]: {{monzo| 7 41 -31 }}


{{Mapping|legend=1| 4 6 11 | 0 1 -5 }}
{{Mapping|legend=1| 1 21 28 | 0 -31 -41 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~300.000, ~3/2 = 702.605
* [[CTE]]: ~2 = 1200.000{{c}}, ~162/125 = 448.449{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~162/125 = 448.449{{c}}


{{Optimal ET sequence|legend=1| 12, 140, 152, 164, 1076bc, 1228bc }}
{{Optimal ET sequence|legend=1| 8, …, 91, 99, 190, 289, 388, 677, 3674, 4351, 5028, 5705, 6382, 13441c, 19823bcc }}


[[Badness]]: 0.241703
[[Badness]] (Sintel): 5.47


== Mynic ==
== Mynic ==
Line 112: Line 206:


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


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


[[Badness]]: 0.249965
[[Badness]] (Sintel): 5.86


== Progress ==
== Progress ==
Line 128: Line 223:


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


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


[[Badness]]: 0.246073
[[Badness]] (Sintel): 5.77
 
== Abigail ==
: ''For extensions, see [[Ragismic microtemperaments #Abigail]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 25 -48 22 }}
 
{{Mapping|legend=1| 2 7 13 | 0 -11 -24 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~{{monzo| -12 24 -11 }} = 600.000{{c}}, ~200000/177147 = 208.907{{c}}
* [[CWE]]: ~{{monzo| -12 24 -11 }} = 600.000{{c}}, ~200000/177147 = 208.906{{c}}
 
{{Optimal ET sequence|legend=1| 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]]: {{monzo| -13 -46 37 }}
 
{{Mapping|legend=1| 1 15 19 | 0 -37 -46 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~625/486 = 435.081{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~625/486 = 435.081{{c}}
 
{{Optimal ET sequence|legend=1| 80, 171, 593, 764, 935, 1106, 3489, 4595, 5701 }}
 
[[Badness]] (Sintel): 6.19


== Gamera ==
== Gamera ==
Line 139: Line 269:
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 12207031250000000000/12157665459056928801
[[Comma list]]: {{monzo| 10 -40 23 }}


{{Mapping|legend=1| 1 6 10 | 0 -23 -40 }}
{{Mapping|legend=1| 1 6 10 | 0 -23 -40 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~2500/2187 = 230.345
* [[CTE]]: ~2 = 1200.000{{c}}, ~2500/2187 = 230.345{{c}}
* [[CWE]]: ~2 = 1200.000, ~2500/2187 = 230.345
* [[CWE]]: ~2 = 1200.000{{c}}, ~2500/2187 = 230.345{{c}}


{{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 163: Line 291:


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


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


[[Badness]]: 0.283570
[[Badness]] (Sintel): 6.65


== Kangaroo ==
== Kangaroo ==
Line 179: Line 308:


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


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


[[Badness]]: 0.295767
[[Badness]] (Sintel): 6.94


== Tertiaseptal ==
== Tertiaseptal ==
Line 190: Line 320:
[[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:  
* [[POTE]]: ~2 = 1200.000, ~17578125/16777216 = 77.191
* [[CTE]]: ~2 = 1200.000{{c}}, ~17578125/16777216 = 77.186{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~17578125/16777216 = 77.191{{c}}


{{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]]: 0.297544
[[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]]: 0.306809


== Untriton ==
== Untriton ==
Line 222: Line 337:
[[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:  
* [[POTE]]: ~2 = 1200.000, ~45/32 = 588.722
* [[CTE]]: ~2 = 1200.000{{c}}, ~45/32 = 588.727{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~45/32 = 588.722{{c}}


{{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]]: 0.307073
[[Badness]] (Sintel): 7.20
 
== Counterhanson ==
: ''For extensions, see [[Ragismic microtemperaments #Counterkleismic]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{Monzo| -20 -24 25 }} = 298023223876953125/296148833645101056
 
{{Mapping|legend=1| 1 -5 -4 | 0 25 24 }}
 
[[Optimal tuning]]s:
* [[POTE]]: ~2 = 1200.000, ~6/5 = 316.081
 
{{Optimal ET sequence|legend=1| 19, 148, 167, 186, 205, 224, 429, 653, 1082, 1735c }}
 
[[Badness]]: 0.317551


== Nessafof ==
== Nessafof ==
Line 254: Line 354:
[[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 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~78125/62208 = 400.000, ~9765625/8957952 = 157.392
* [[CTE]]: ~78125/62208 = 400.000{{c}}, ~9765625/8957952 = 157.392{{c}}
* [[CWE]]: ~78125/62208 = 400.000, ~9765625/8957952 = 157.409
* [[CWE]]: ~78125/62208 = 400.000{{c}}, ~9765625/8957952 = 157.409{{c}}


{{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: 7.807


== Sevond ==
== Lemba ==
: ''For extensions, see [[Keemic temperaments #Sevond]].''
: ''For extensions, see [[Jubilismic clan #Lemba]].''


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 5000000/4782969
[[Comma list]]: 140625/131072


{{Mapping|legend=1| 7 0 -6 | 0 1 2 }}
{{Mapping|legend=1| 2 2 5 | 0 3 -1 }}
: Mapping generators: ~375/256, ~75/64


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~171.429, ~3/2 = 706.288
* [[CTE]]: ~375/256 = 600.000{{c}}, ~75/64 = 232.986{{c}}
: [[error map]]: {{val| 0.000 -2.998 -19.300 }}
* [[CWE]]: ~375/256 = 600.000{{c}}, ~75/64 = 231.832{{c}}
: error map: {{val| 0.000 -6.458 -18.146 }}


{{Optimal ET sequence|legend=1| 7, 42, 49, 56, 119 }}
{{Optimal ET sequence|legend=1| 10, 16, 26, 88cc }}


[[Badness]]: 0.339335
[[Badness]] (Sintel): 7.85
 
== Absurdity ==
: ''For extensions, see [[Porwell temperaments #Absurdity]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 10460353203/10240000000
 
{{Mapping|legend=1| 7 0 -17 | 0 1 3 }}
 
[[Optimal tuning]]s:
* [[POTE]]: ~171.429, ~10/9 = 185.901
 
{{Optimal ET sequence|legend=1| 7, 70, 77, 84, 329, 413b, 497b }}
 
[[Badness]]: 0.341202
 
== Wronecki ==
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 531441/500000
 
{{Mapping|legend=1| 6 0 -5 | 0 1 2 }}
 
[[Optimal tuning]]s:
* [[POTE]]: ~200.000, ~3/2 = 695.040
 
{{Optimal ET sequence|legend=1| 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bbc }}
 
[[Badness]]: 0.341757


== Delorean ==
== Delorean ==
Line 324: Line 396:


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


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


[[Badness]]: 0.355937
[[Badness]] (Sintel): 8.35


== Majvam ==
== Majvam ==
: ''For extensionss, see [[Subgroup temperaments #Majvam]], [[Cataharry temperaments #Majvamoid]], and [[Parkleiness temperaments #Majvamic]].''
: ''For extensions, see [[No-sevens subgroup temperaments #Majvam]], [[Cataharry temperaments #Majvamoid]], and [[Parkleiness temperaments #Majvamic]].''


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
Line 340: Line 413:


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


{{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]]: 0.356948
[[Badness]] (Sintel): 8.37


== Beatles ==
== Beatles ==
Line 356: Line 430:


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


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


[[Badness]]: 0.358542
[[Badness]] (Sintel): 8.41


== Magus ==
== Magus ==
: ''For extensionss, see [[Sensamagic clan #Magus]] and [[Starling temperaments #Amigo]].''
: ''For extensions, see [[Sensamagic clan #Magus]] and [[Starling temperaments #Amigo]].''


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
Line 372: Line 447:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000, ~5/4 = 391.225
* [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 391.068{{c}}
 
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 391.225{{c}}
{{Optimal ET sequence|legend=1| 3, 40, 43, 46, 181c, 227c, 273c, 319c }}
 
[[Badness]]: 0.360162
 
== Countermeantone ==
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{Monzo| 10 23 -20 }} = 96402615118848/95367431640625
 
{{Mapping|legend=1| 1 10 12 | 0 -20 -23 }}
 
[[Optimal tuning]]s:
* [[POTE]]: ~2 = 1200.000, ~104976/78125 = 504.913


{{Optimal ET sequence|legend=1| 19, 126, 145, 164, 183, 713, 896c, 1079c, 1262c }}
{{Optimal ET sequence|legend=1| 3, …, 40, 43, 46, 181c, 227c, 273c, 319c }}


[[Badness]]: 0.373477
[[Badness]] (Sintel): 8.45


== Tritonic ==
== Tritonic ==
Line 402: Line 464:


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


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


[[Badness]]: 0.378527
[[Badness]] (Sintel): 8.88


== Wizard ==
== Wizard ==
Line 416: Line 479:


{{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{{c}}, ~9375/8192 = 216.950{{c}}
* [[POTE]]: ~42875/32768 = 600.000{{c}}, ~9375/8192 = 216.788{{c}}


{{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]]: 0.386367
[[Badness]] (Sintel): 9.06


Scales (Scala files): [[wizard22]]
Scales (Scala files): [[wizard22]]
== Quindromeda ==
{{See also| Quindromeda family }}
[[Subgroup]]: 2.3.5
[[Comma list]]: 72057594037927936/71489976421753125
{{Mapping|legend=1| 1 2 0 | 0 -5 28 }}
[[Optimal tuning]]s:
* [[POTE]]: ~2 = 1200.000, ~4428675/4194304 = 99.526
{{Optimal ET sequence|legend=1| 12, 193, 205, 217, 422 }}
[[Badness]]: 0.399849
== Hogzilla ==
: ''For extensions, see [[Semaphoresmic clan #Helayo]].''
[[Subgroup]]: 2.3.5
[[Comma list]]: 4428675/4194304
{{Mapping|legend=1| 1 0 11 | 0 2 -11 }}
[[Optimal tuning]]s:
* [[POTE]]: ~2 = 1200.000, ~1215/1024 = 252.649
{{Optimal ET sequence|legend=1| 14, 19 }}
[[Badness]]: 0.424685
== Quintaleap ==
{{See also| Quintaleap family }}
[[Subgroup]]: 2.3.5
[[Comma list]]: 137438953472/134521003125
{{Mapping|legend=1| 1 2 1 | 0 -5 16 }}
[[Optimal tuning]]s:
* [[POTE]]: ~2 = 1200.000, ~135/128 = 99.267
{{Optimal ET sequence|legend=1| 12, 109, 121, 133 }}
[[Badness]]: 0.444506


== Merman ==
== Merman ==
Line 481: Line 496:
[[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:  
* [[POTE]]: ~2 = 1200.000, ~45/32 = 585.634
* [[CTE]]: ~2 = 1200.000{{c}}, ~45/32 = 585.653{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~45/32 = 585.634{{c}}


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


[[Badness]]: 0.453848
[[Badness]] (Sintel): 10.6
 
== Unsmate ==
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 17578125/16777216
 
{{Mapping|legend=1| 1 3 2 | 0 -9 2 }}
 
[[Optimal tuning]]s:
* [[POTE]]: ~2 = 1200.000, ~2048/1875 = 189.049
 
{{Optimal ET sequence|legend=1| 13, 19, 89c, 108c, 127c, 146cc }}
 
[[Badness]]: 0.460168


== Nusecond ==
== Nusecond ==
Line 516: Line 518:


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


{{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]]: 0.466493
[[Badness]] (Sintel): 10.9


== Comic ==
== Comic ==
Line 530: Line 533:


{{Mapping|legend=1| 2 1 -3 | 0 2 7 }}
{{Mapping|legend=1| 2 1 -3 | 0 2 7 }}
: mapping generators: ~2187/1600, ~40/27


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~600.000, ~81/80 = 55.382
* [[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 }}
{{Optimal ET sequence|legend=1| 20c, 22, 86b, 108b, 130b }}


[[Badness]]: 0.491181
[[Badness]] (Sintel): 11.5


== Sfourth ==
== Sfourth ==
Line 543: Line 551:
[[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{{c}}, ~1594323/1562500 = 26.2323{{c}}
* [[POTE]]: ~2 = 1200.0000{{c}}, ~1594323/1562500 = 26.2342{{c}}


{{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]]: 0.504555
[[Badness]] (Sintel): 11.8


== Thuja ==
== Thuja ==
: ''For extensions, see [[Starling temperaments #Thuja]].''
: ''For extensions, see [[Buzzardsmic clan #Thuja]].''
{{See also| Hypovishnuzma }}


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
Line 564: Line 574:


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


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


[[Badness]]: 0.511109
[[Badness]] (Sintel): 12.0


== Leapday ==
== Leapday ==
: ''For extensionss, see [[Hemifamity temperaments #Leapday]] and [[Porwell temperaments #Polypyth]].''
: ''For extensions, see [[Hemifamity temperaments #Leapday]] and [[Porwell temperaments #Polypyth]].''


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
Line 580: Line 591:


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


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


[[Badness]]: 0.523182
[[Badness]] (Sintel): 12.3


== Vines ==
== Vines ==
Line 596: Line 608:


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


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


[[Badness]]: 0.541831
[[Badness]] (Sintel): 12.7


== Emka ==
== Emka ==
: ''For extensionss, see [[Hemimean clan #Emka]] and [[Horwell temperaments #Emkay]].''
: ''For extensions, see [[Hemimean clan #Emka]] and [[Horwell temperaments #Emkay]].''


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
Line 612: Line 625:


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


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


[[Badness]]: 0.544752
[[Badness]] (Sintel): 12.8


== Misneb ==
== Misneb ==
Line 623: Line 637:
[[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:  
* [[POTE]]: ~2 = 1200.000, ~16/15 = 113.240
* [[CTE]]: ~2 = 1200.000{{c}}, ~16/15 = 113.233{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~16/15 = 113.240{{c}}


{{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]]: 0.609540
[[Badness]] (Sintel): 14.3


== Semisept ==
== Semisept ==
Line 644: Line 659:


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


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


[[Badness]]: 0.630576
[[Badness]] (Sintel): 14.8
 
== Kwai ==
: ''For extensions, see [[Mirkwai clan #Kwai].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 5629499534213120/5559060566555523
 
{{Mapping|legend=1| 1 2 16 | 0 -1 -33 }}
 
[[Optimal tuning]]s:
* [[POTE]]: ~2 = 1200.000, ~3/2 = 702.630
 
{{Optimal ET sequence|legend=1| 41, 111, 152 }}
 
[[Badness]]: 0.636715
 
== Mowgli ==
: ''For extensions, see [[Hemimean clan #Mowglic]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 0 22 -15 }} = 31381059609/30517578125
 
{{Mapping|legend=1| 1 0 0 | 0 15 22 }}
 
[[Optimal tuning]]s:
* [[POTE]]: ~2 = 1200.000, ~27/25 = 126.724
 
{{Optimal ET sequence|legend=1| 19, 85c, 104c, 123, 142, 161 }}
 
[[Badness]]: 0.653871


== Septimin ==
== Septimin ==
Line 692: Line 676:


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


{{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]]: 0.670947
[[Badness]] (Sintel): 15.7


== Slurpee ==
== Slurpee ==
Line 708: Line 693:


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


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


[[Badness]]: 0.689274
[[Badness]] (Sintel): 16.2


== Pentadecal ==
== Pentadecal ==
Line 724: Line 710:


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


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


[[Badness]]: 0.692042
[[Badness]] (Sintel): 16.2


== Sentinel ==
== Anthoine ==
: ''For extensions, see [[Orwellismic temperaments #Sentinel]].''
: ''For extensions, see [[Buzzardsmic clan #Anthoine]].''


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 8968066875/8589934592
[[Comma list]]: 286102294921875/281474976710656


{{Mapping|legend=1| 1 3 -3 | 0 -4 15 }}
{{Mapping|legend=1| 1 8 2 | 0 -20 1 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000, ~512/405 = 425.474
* [[WE]]: ~2 = 1200.303{{c}}, ~5/4 = 385.024{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 384.920{{c}}


{{Optimal ET sequence|legend=1| 14, 17, 31, 79, 110, 361bc }}
{{Optimal ET sequence|legend=1| 25, 28, 53 }}


[[Badness]]: 0.723413
[[Badness]] (Sintel): 16.5


== Undeka ==
== Sentinel ==
: ''For extensions, see [[Keemic temperaments #Undeka]].''
: ''For extensions, see [[Orwellismic temperaments #Sentinel]].''


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 48828125/45349632
[[Comma list]]: 8968066875/8589934592


{{Mapping|legend=1| 11 0 8 | 0 1 1 }}
{{Mapping|legend=1| 1 3 -3 | 0 -4 15 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~109.091, ~3/2 = 703.829
* [[CTE]]: ~2 = 1200.000{{c}}, ~512/405 = 425.590{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~512/405 = 425.474{{c}}


{{Optimal ET sequence|legend=1| 22, 77c, 99c, 121c }}
{{Optimal ET sequence|legend=1| 14, 17, 31, 79, 110, 361bbcc }}


[[Badness]]: 0.727539
[[Badness]] (Sintel): 17.0


== Kumonga ==
== Kumonga ==
Line 772: Line 761:


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


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


[[Badness]]: 0.729609
[[Badness]] (Sintel): 17.1


== Mirkat ==
== Mirkat ==
Line 788: Line 778:


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


{{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: 17.631


== Semidimi ==
== Semidimi ==
Line 807: Line 795:


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


{{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]]: 0.754866
[[Badness]] (Sintel): 17.7


== Slender ==
== Slender ==
Line 818: Line 807:
[[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 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~16875/16384 = 38.380
* [[CTE]]: ~2 = 1200.000{{c}}, ~16875/16384 = 38.380{{c}}
* [[CWE]]: ~2 = 1200.000, ~16875/16384 = 38.400
* [[CWE]]: ~2 = 1200.000{{c}}, ~16875/16384 = 38.400{{c}}


{{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: 17.842


== Quasitemp ==
== Quasitemp ==
Line 842: Line 829:


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


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


[[Badness]]: 0.767824
[[Badness]] (Sintel): 18.0


== Cypress ==
== Cypress ==
Line 858: Line 846:


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


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


[[Badness]]: 0.816635
[[Badness]] (Sintel): 19.2


== Chromo ==
== Chromo ==
Line 874: Line 863:


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


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


[[Badness]]: 0.842835
[[Badness]] (Sintel): 19.8


== Tertiosec ==
== Tertiosec ==
Line 890: Line 880:


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


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


[[Badness]]: 0.851003
[[Badness]] (Sintel): 20.0


== Fervor ==
== Fervor ==
Line 906: Line 897:


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


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


[[Badness]]: 0.852612
[[Badness]] (Sintel): 20.0


== Bohpier ==
== Bohpier ==
Line 922: Line 914:


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


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


[[Badness]]: 0.860534
[[Badness]] (Sintel): 20.2


== Elvis ==
== Elvis ==
Line 938: Line 930:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~600.000, ~45/32 = 554.546
* [[CTE]]: ~6075/4096 = 600.000{{c}}, ~64/45 = 644.844{{c}}
* [[POTE]]: ~6075/4096 = 600.000{{c}}, ~64/45 = 645.454{{c}}
 
{{Optimal ET sequence|legend=1| 26, 80bc, 106bbcc, 132bbcc }}
 
[[Badness]] (Sintel): 20.7
 
== Enneadecacot ==
[[Subgroup]]: 2.3.5


{{Optimal ET sequence|legend=1| 26, 80bc, 106bc, 132bc }}
[[Comma list]]: {{monzo| 79 -22 -19 }}


[[Badness]]: 0.884000
{{Mapping|legend=1| 1 1 3 | 0 19 -22 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.0000{{c}}, ~34171875/33554432 = 36.9607{{c}}
* [[POTE]]: ~2 = 1200.0000{{c}}, ~34171875/33554432 = 36.9622{{c}}
 
{{Optimal ET sequence|legend=1| 32, 65, 292, 357, 422, 487, 1396c }}
 
[[Badness]] (Sintel): 20.9


== Vinegar ==
== Vinegar ==
Line 954: Line 962:


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


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


[[Badness]]: 0.903002
[[Badness]] (Sintel): 21.2


== Oolong ==
== Oolong ==
Line 970: Line 979:


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


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


[[Badness]]: 0.942789
[[Badness]] (Sintel): 22.1


== Oncle ==
== Oncle ==
Line 986: Line 996:


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


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


[[Badness]]: 1.244699
[[Badness]] (Sintel): 29.2


== Quasiorwell ==
== Quasiorwell ==
Line 1,002: Line 1,013:


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


{{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: 30.581


== Diesic ==
== Diesic ==
Line 1,021: Line 1,030:


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


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


[[Badness]]: 1.344681
[[Badness]] (Sintel): 31.5


== Quartemka ==
== Quartemka ==
Line 1,032: Line 1,042:
[[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:  
* [[POTE]]: ~2 = 1200.000, ~27/25 = 137.962
* [[CTE]]: ~2 = 1200.000{{c}}, ~27/25 = 137.963{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~27/25 = 137.962{{c}}


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


[[Badness]]: 1.381216
[[Badness]] (Sintel): 32.4


== Genocchi ==
== Genocchi ==
Line 1,051: Line 1,062:


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


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


[[Badness]]: 1.404977
[[Badness]] (Sintel): 33.0


== Casablanca ==
== Casablanca ==
Line 1,062: Line 1,074:
[[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:  
* [[POTE]]: ~2 = 1200.000, ~864/625 = 542.208
* [[CTE]]: ~2 = 1200.000{{c}}, ~864/625 = 542.142{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~864/625 = 542.208{{c}}


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


[[Badness]]: 1.423736
[[Badness]] (Sintel): 33.4


== Archaeotherium ==
== Archaeotherium ==
Line 1,083: Line 1,096:


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


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


[[Badness]]: 1.434855
[[Badness]] (Sintel): 33.7


== Octacoid ==
== Octacoid ==
Line 1,096: Line 1,110:
{{Mapping|legend=1| 1 1 3 | 0 8 -9 }}
{{Mapping|legend=1| 1 1 3 | 0 8 -9 }}


: mapping generators: ~2, ~16/15
: Mapping generators: ~2, ~16/15


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


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


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


== Quasimoha ==
== Quasimoha ==
Line 1,111: Line 1,125:
[[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:  
* [[POTE]]: ~2 = 1200.000, ~1048576/885735 = 348.600
* [[CTE]]: ~2 = 1200.000{{c}}, ~1048576/885735 = 348.462{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~1048576/885735 = 348.600{{c}}


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


[[Badness]]: 1.986675
[[Badness]] (Sintel): 46.6


== Phillips ==
== Phillips ==
Line 1,132: Line 1,147:


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


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


[[Badness]]: 2.228904
[[Badness]] (Sintel): 52.3


== Triskaidekic ==
== Satin ==
: ''For extensions, see [[Orwellismic temperaments #Triskaidekic]].''
: ''For extensions, see [[Garischismic clan #Satin]].''


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 1220703125/1073741824
[[Comma list]]: {{monzo| 104 -70 3 }}


{{Mapping|legend=1| 13 0 30 | 0 1 0 }}
{{Mapping|legend=1| 1 2 12 | 0 -3 -70 }}
: mapping generators: ~2, ~{{monzo| -34 23 -1 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~92.308, ~3/2 = 696.142
* [[WE]]: ~2 = 1199.9008{{c}}, ~{{monzo| -34 23 -1 }} = 165.8930{{c}}
: [[error map]]: {{val| -0.099 +0.168 -0.015 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~{{monzo| -34 23 -1 }} = 165.9079{{c}}
: error map: {{val| 0.000 +0.321 +0.130 }}


{{Optimal ET sequence|legend=1| 13, 26, 91c }}
{{Optimal ET sequence|legend=1| 94, 217, 528, 745, 1273, 2018b }}


[[Badness]]: 2.241568
[[Badness]] (Sintel): 66.9


== Satin ==
== Lockerbie ==
: ''For extensions, see [[Canousmic temperaments #Satin]].''
: ''For extensions, see [[Breedsmic temperaments #Lockerbie]].''


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: {{monzo| 104 -70 3 }}
[[Comma list]]: {{monzo| 91 51 -74 }}


{{Mapping|legend=1| 1 2 12 | 0 -3 -70 }}
{{Mapping|legend=1| 1 -25 -16 | 0 74 51 }}
: mapping generators: ~2, ~{{monzo| 36 20 -29 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000, ~{{monzo| -34 23 -1 }} = 165.907
* [[CTE]]: ~2 = 1200.0000{{c}}, ~{{monzo| 36 20 -29 }} = 431.1069{{c}}
: [[error map]]: {{val| 0.0000 -0.0444 +0.1382 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~{{monzo| 36 20 -29 }} = 431.1073{{c}}
: error map: {{val| 0.0000 -0.0174 +0.1568 }}


{{Optimal ET sequence|legend=1| 94, 217, 528, 745, 1273 }}
{{Optimal ET sequence|legend=1| 103, 167, 270, 643, 913, 1183, 2636, 3819c, 5002c }}


[[Badness]]: 2.853049
[[Badness]] (Sintel): 72.4


== Rarity ==
== Rarity ==
Line 1,180: Line 1,204:


{{Mapping|legend=1| 1 11 -10 | 0 -13 17 }}
{{Mapping|legend=1| 1 11 -10 | 0 -13 17 }}
: Mapping generators: ~2, ~16384/10125
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~16384/10125 = 869.392{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~16384/10125 = 869.402{{c}}
{{Optimal ET sequence|legend=1| 11, 29, 69, 98c }}
[[Badness]] (Sintel): 99.2
== Jorgensen ==
: ''For extensions, see [[Hemifamity temperaments #Jorgensen]].''
[[Subgroup]]: 2.3.5
[[Comma list]]: {{monzo| 111 -70 }}


: mapping generators: ~2, ~16384/10125
{{Mapping|legend=1| 70 111 0 | 0 0 1 }}
: mapping generators: ~{{monzo| 46 -29 }}, ~5


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~16384/10125 = 869.392
* [[WE]]: ~{{monzo| 46 -29 }} = 17.1388{{c}}, ~5/4 = 386.8829{{c}}
* [[CWE]]: ~2 = 1200.000, ~16384/10125 = 869.402
: [[error map]]: {{val| -0.285 +0.451 -0.000 }}
* [[CWE]]: ~{{monzo| 46 -29 }} = 17.1429{{c}}, ~5/4 = 386.7543{{c}}
: error map: {{val| 0.000 +0.902 +0.441 }}


{{Optimal ET sequence|legend=1| 11, 29, 69, 98c }}
{{Optimal ET sequence|legend=1| 70, 140, 350, 490 }}
 
[[Badness]] (Sintel): 203


[[Badness]]: 4.23
== References ==


[[Category:Temperament collections]]
[[Category:Temperament collections]]

Latest revision as of 08:53, 16 May 2026

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:

Unidecmic

For extensions, see Gamelismic clan #Unidec.

Subgroup: 2.3.5

Comma list: 31381059609/31250000000

Mapping: [⟨2 -1 -3], ⟨0 6 11]]

mapping generators: ~177147/125000, ~25000/19683

Optimal tunings:

  • WE: ~177147/125000 = 600.0124 ¢, ~25000/19683 = 416.9619 ¢
error map: ⟨+0.025 -0.196 +0.235]
  • CWE: ~177147/125000 = 600.0000 ¢, ~25000/19683 = 416.9561 ¢
error map: ⟨0.000 -0.236 +0.172]

Optimal ET sequence: 26, 46, 72, 118, 2524, 2642, 2760

Badness (Sintel): 1.93

Quasithird

For extensions, see Ragismic microtemperaments #Quasithird.

Subgroup: 2.3.5

Comma list: [55 -64 20⟩

Mapping: [⟨4 0 -11], ⟨0 5 16]]

mapping generators: ~51200000/43046721, ~1594323/1280000

Optimal tunings:

  • WE: ~51200000/43046721 = 299.9990 ¢, ~1594323/1280000 = 380.3934 ¢
error map: ⟨-0.004 +0.012 -0.008]
  • CWE: ~51200000/43046721 = 300.0000 ¢, ~1594323/1280000 = 380.3944 ¢
error map: ⟨0.000 +0.017 -0.004]

Optimal ET sequence: 60, 104c, 164, 224, 388, 612, 1612, 2224, 2836, 6284, 9120, 15404

Badness (Sintel): 2.33

Supersharp

For extensions, see Trienstonic clan #Octokaidecal.

Supersharp tempers out 800/729, the difference between the 27/20 wolf fourth and the 40/27 wolf fifth, splitting the octave into two 27/20~40/27 semioctaves. It generally requires a very sharp fifth, even sharper than 3\5, as a generator. This means that five steps from the Zarlino generator sequence starting with 6/5 are tempered to one and a half octaves. The only reasonable 7-limit extension adds 28/27 and 50/49 to the comma list, taking advantage of the existing semioctave.

Subgroup: 2.3.5

Comma list: 800/729

Mapping: [⟨2 0 -5], ⟨0 1 3]]

mapping generators: ~27/20, ~3

Optimal tunings:

  • WE: ~27/20 = 596.986 ¢, ~3/2 = 725.434 ¢ (~10/9 = 128.448 ¢)
error map: ⟨-6.029 +17.450 -13.027]
  • CWE: ~27/20 = 600.000 ¢, ~3/2 = 726.548 ¢ (~10/9 = 126.548 ¢)
error map: ⟨0.000 +24.593 -6.670]

Optimal ET sequence: 8, 10, 18, 28b

Badness (Sintel): 2.88

Avila

For extensions, see Septisemi temperaments #Avila.

Subgroup: 2.3.5

Comma list: 729/640

Mapping: [⟨1 0 -7], ⟨0 1 6]]

mapping generators: ~2, ~3

Optimal tunings:

  • WE: ~2 = 1210.600 ¢, ~3/2 = 667.437 ¢
error map: ⟨+10.600 -23.917 +7.711]
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 663.474 ¢
error map: ⟨0.000 -38.481 -5.472]

Optimal ET sequence: 2c, 7c, 9, 20b, 29b

Badness (Sintel): 4.27

Lafa

This temperament was named by Petr Pařízek in 2011, referring to the characteristic that stacking 12 generators makes 6/1 – "l" for 12, "f" for 6[1]. Its ploidacot is therefore beta-dodecacot.

Subgroup: 2.3.5

Comma list: [77 -31 -12⟩

Mapping: [⟨1 -1 9], ⟨0 12 -31]]

mapping generators: ~2, ~[-32 13 5⟩

Optimal tunings:

  • WE: ~2 = 1199.9693 ¢, ~[-32 13 5⟩ = 258.4963 ¢
error map: ⟨-0.031 +0.031 +0.026]
  • CWE: ~2 = 1200.0000 ¢, ~[-32 13 5⟩ = 258.5031 ¢
error map: ⟨0.000 +0.082 +0.091]

Optimal ET sequence: 65, 246, 311, 376, 441, 2711, 3152, 3593, 4034, 4475, 4916, 5357, 10273bc, 15630bbcc

Badness (Sintel): 4.33

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

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: [10 -40 23⟩

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

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

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

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

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.
See also: Hypovishnuzma

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

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

Anthoine

For extensions, see Buzzardsmic clan #Anthoine.

Subgroup: 2.3.5

Comma list: 286102294921875/281474976710656

Mapping: [⟨1 8 2], ⟨0 -20 1]]

Optimal tunings:

  • WE: ~2 = 1200.303 ¢, ~5/4 = 385.024 ¢
  • CWE: ~2 = 1200.000 ¢, ~5/4 = 384.920 ¢

Optimal ET sequence: 25, 28, 53

Badness (Sintel): 16.5

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

Satin

For extensions, see Garischismic clan #Satin.

Subgroup: 2.3.5

Comma list: [104 -70 3⟩

Mapping: [⟨1 2 12], ⟨0 -3 -70]]

mapping generators: ~2, ~[-34 23 -1⟩

Optimal tunings:

  • WE: ~2 = 1199.9008 ¢, ~[-34 23 -1⟩ = 165.8930 ¢
error map: ⟨-0.099 +0.168 -0.015]
  • CWE: ~2 = 1200.0000 ¢, ~[-34 23 -1⟩ = 165.9079 ¢
error map: ⟨0.000 +0.321 +0.130]

Optimal ET sequence: 94, 217, 528, 745, 1273, 2018b

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

Jorgensen

For extensions, see Hemifamity temperaments #Jorgensen.

Subgroup: 2.3.5

Comma list: [111 -70⟩

Mapping: [⟨70 111 0], ⟨0 0 1]]

mapping generators: ~[46 -29⟩, ~5

Optimal tunings:

  • WE: ~[46 -29⟩ = 17.1388 ¢, ~5/4 = 386.8829 ¢
error map: ⟨-0.285 +0.451 -0.000]
  • CWE: ~[46 -29⟩ = 17.1429 ¢, ~5/4 = 386.7543 ¢
error map: ⟨0.000 +0.902 +0.441]

Optimal ET sequence: 70, 140, 350, 490

Badness (Sintel): 203

References

  1. ↑ Yahoo! Tuning Group | Suggested names for the unclasified temperaments
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