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Miscellaneous 5-limit temperaments: Difference between revisions

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3 significant figures are absolutely enough for badness. More precision offers no extra insight. Also note the specific badness metric being used
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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]]
* [[Fractional-octave temperaments]]
* [[Subgroup temperaments]] and pages linked therefrom
* [[Very low accuracy temperaments]]
* [[Very low accuracy temperaments]]
* [[Very high accuracy temperaments]].
* [[Very high accuracy temperaments]]
 
== Ennealimmal ==
: ''For extensions, see [[Septiennealimmal clan #Ennealimmal]].''
 
The 5-limit version of ennealimmal tempers out the [[ennealimma]], the amount by which a stack of nine [[27/25]]'s falls short of the octave. Since the [[7-limit]] temperament (definable by tempering out both [[2401/2400]] and [[4375/4374]], the two smallest superparticular ratios in the 7-limit) is far more natural to think of than the 5-limit, the 5-limit temperament is only provided below for bookkeeping purposes.
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 1 -27 18 }}
 
{{Mapping|legend=1| 9 1 1 | 0 2 3 }}
: mapping generators: ~27/25, ~5/3
 
[[Optimal tuning]]s:
* [[WE]]: ~27/25 = 133.3333{{c}}, ~5/3 = 884.3190{{c}}
: [[error map]]: {{val| -0.000 +0.016 -0.023 }}
* [[CWE]]: ~27/25 = 133.3333{{c}}, ~5/3 = 884.3191{{c}}
: error map: {{val| 0.000 +0.017 -0.023 }}
 
{{Optimal ET sequence|legend=1| 27, 45, 72, 99, 171, 441, 612, 1665, 2277, 2889, 3501, 6390, 16281, 22671, 29061c }}
 
[[Badness]] (Sintel): 0.403
 
== Unidecmic ==
: ''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
 
== Aluminium ==
: ''For extensions, see [[Ragismic microtemperaments #Aluminium]].''
 
Aluminium tempers out {{monzo| 92 -39 -13 }} in the 5-limit, and sets [[135/128]] to 1/13 of an [[octave]].
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 92 -39 -13 }}
 
{{Mapping|legend=1| 13 0 92 | 0 1 -3 }}
: mapping generators: ~135/128, ~3
 
[[Optimal tuning]]s:
* [[WE]]: ~135/128 = 92.3068{{c}}, ~3/2 = 701.9791{{c}}
: [[error map]]: {{val| -0.012 +0.012 +0.009 }}
* [[CWE]]: ~135/128 = 92.3077{{c}}, ~3/2 = 701.9897{{c}}
: error map: {{val| 0.000 +0.032 +0.033 }}
 
{{Optimal ET sequence|legend=1| 65, 299, 364, 429, 494, 559, 1053, 1612, 5889, 7501, 9113, 10725, 23062bc, 33787bcc, 44512bbcc }}
 
[[Badness]] (Sintel): 2.89
 
== 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 name="petr's long post">[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
 
[[Comma list]]: {{monzo| 77 -31 -12 }}
 
{{Mapping|legend=1| 1 -1 9 | 0 12 -31 }}
: mapping generators: ~2, ~{{monzo| -32 13 5 }}
 
[[Optimal tuning]]s:
* [[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| 65, 246, 311, 376, 441, 2711, 3152, 3593, 4034, 4475, 4916, 5357, 10273bc, 15630bbcc }}
 
[[Badness]] (Sintel): 4.33


== Lafayette ==
== Lafayette ==
Line 18: Line 162:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000, ~25/24 = 140.995
* [[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| 8, 9, 17c }}
{{Optimal ET sequence|legend=1| 8, 9, 17c }}


[[Badness]] (Smith): 0.200
[[Badness]] (Sintel): 4.70
 
== Neon ==
: ''For extensions, see [[Ragismic microtemperaments #Deca]], [[Landscape microtemperaments #Zinc]], and [[20th-octave temperaments #Calcium]].''
{{See also| Neon comma }}


== Stump ==
Neon tempers out {{monzo| 21 60 -50 }} in the 5-limit, equating [[3125/2916]] with one step of [[10edo]]. It was named by [[Eliora]] in 2023 after the 10th element.
: ''For extensions, see [[Sensamagic clan #Pycnic]] and [[Marvel temperaments #Triton]].''


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


[[Comma list]]: 273375/262144
[[Comma list]]: {{monzo| 21 60 -50 }}


{{Mapping|legend=1| 1 0 6 | 0 3 -7 }}
{{Mapping|legend=1| 10 4 9 | 0 5 6 }}
: mapping generators: ~3125/2916, {{monzo| 10 29 -24 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000, ~64/45 = 631.737
* [[WE]]: ~3125/2916 = 119.9999{{c}}, {{monzo| 10 29 -24 }} = 284.3890{{c}}
: [[error map]]: {{val| -0.001 -0.011 +0.019 }}
* [[CWE]]: ~3125/2916 = 120.0000{{c}}, {{monzo| 10 29 -24 }} = 284.3891{{c}}
: error map: {{val| 0.000 -0.010 +0.021 }}


{{Optimal ET sequence|legend=1| 17, 19 }}
{{Optimal ET sequence|legend=1| 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650 }}


[[Badness]] (Smith): 0.201
[[Badness]] (Sintel): 4.85


== Dodifo ==
== Dodifo ==
Line 45: Line 197:
[[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]] (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 ==
: ''For extensions, see [[Gamelismic clan #Superkleismic]], [[Starling temperaments #Gilead]], and [[Sensamagic clan #Superthird]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 1953125/1889568
 
{{Mapping|legend=1| 1 4 5 | 0 -9 -10 }}
 
[[Optimal tuning]]s:
* [[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| 15, 26, 41, 179c }}
 
[[Badness]] (Sintel): 5.34


== Semidimfourth ==
== Semidimfourth ==
Line 66: Line 256:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000, ~162/125 = 448.449
* [[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| 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 82: Line 273:


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


== Progress ==
== Progress ==
Line 98: Line 290:


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


== Abigail ==
== Abigail ==
Line 114: Line 307:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~{{monzo| -12 24 -11 }} = 600.000, ~200000/177147 = 208.907
* [[CTE]]: ~{{monzo| -12 24 -11 }} = 600.000{{c}}, ~200000/177147 = 208.907{{c}}
* [[CWE]]: ~{{monzo| -12 24 -11 }} = 600.000, ~200000/177147 = 208.906
* [[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 }}
{{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 133: Line 324:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~625/486 = 435.081
* [[CTE]]: ~2 = 1200.000{{c}}, ~625/486 = 435.081{{c}}
* [[CWE]]: ~2 = 1200.000, ~625/486 = 435.081
* [[CWE]]: ~2 = 1200.000{{c}}, ~625/486 = 435.081{{c}}


{{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 147: Line 336:
[[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 171: Line 358:


[[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]] (Smith): 0.284
[[Badness]] (Sintel): 6.65
 
== Octoid ==
: ''For extensions, see [[Ragismic microtemperaments #Octoid]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -5 -32 24 }}
 
{{Mapping|legend=1| 8 1 3 | 0 3 4 }}
: Mapping generators: ~2125764/1953125, ~4374/3125
 
[[Optimal tuning]]s:
* [[WE]]: ~2125764/1953125 = 150.001{{c}}, ~4374/3125 = 584.027{{c}}
* [[CWE]]: ~2125764/1953125 = 150.000{{c}}, ~4374/3125 = 584.025{{c}}
 
{{Optimal ET sequence|legend=1| 8, 56bcc, 64c, 72, 152, 224, 376, 976 }}
 
[[Badness]] (Sintel): 6.69


== Kangaroo ==
== Kangaroo ==
Line 187: Line 393:


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


== Tertiaseptal ==
== Tertiaseptal ==
Line 198: Line 405:
[[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]] (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 230: Line 422:
[[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]] (Smith): 0.307
[[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]] (Smith): 0.318


== Nessafof ==
== Nessafof ==
Line 262: Line 439:
[[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: 7.81


== Lemba ==
== Lemba ==
Line 284: Line 459:


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


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


{{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 323: Line 481:


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


== Majvam ==
== Majvam ==
Line 339: Line 498:


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


== Beatles ==
== Beatles ==
Line 355: Line 515:


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


== Magus ==
== Magus ==
Line 371: Line 532:


[[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]] (Smith): 0.360


== Countermeantone ==
{{Optimal ET sequence|legend=1| 3, …, 40, 43, 46, 181c, 227c, 273c, 319c }}
[[Subgroup]]: 2.3.5


[[Comma list]]: {{Monzo| 10 23 -20 }} = 96402615118848/95367431640625
[[Badness]] (Sintel): 8.45
 
{{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 }}
 
[[Badness]] (Smith): 0.373


== Tritonic ==
== Tritonic ==
Line 401: Line 549:


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


== Wizard ==
== Wizard ==
Line 415: Line 564:


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


Scales (Scala files): [[wizard22]]
Scales (Scala files): [[wizard22]]


== Hogzilla ==
== Tridecatonic ==
: ''For extensions, see [[Semaphoresmic clan #Helayo]].''
: ''For extensions, see [[Octagar temperaments #Tridecatonic]], [[Ragismic microtemperaments #Trideci]], and [[Varunismic temperaments #Bosonic]].''
 
Tridecatonic tempers out the [[devil's tridecalimma]], the comma which associates the [[10/9]] minor tone with [[13edo|2\13]].


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


[[Comma list]]: 4428675/4194304
[[Comma list]]: {{monzo| -11 26 -13 }}


{{Mapping|legend=1| 1 0 11 | 0 2 -11 }}
{{Mapping|legend=1| 13 0 -11 | 0 1 2 }}
: mapping generators: ~531441/500000, ~3


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000, ~1215/1024 = 252.649
* [[WE]]: ~531441/500000 = 92.3166{{c}}, ~3/2 = 701.2353{{c}}
: [[error map]]: {{val| +0.116 -0.688 +0.737 }}
* [[CWE]]: ~531441/500000 = 92.3077{{c}}, ~3/2 = 701.2353{{c}}
: error map: {{val| 0.000 -0.797 +0.617 }}


{{Optimal ET sequence|legend=1| 14, 19 }}
{{Optimal ET sequence|legend=1| 26, 39, 65, 286, 351, 416, 481, 546 }}


[[Badness]] (Smith): 0.425
[[Badness]] (Sintel): 10.3


== Merman ==
== Merman ==
Line 448: Line 603:
[[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]] (Smith): 0.454
[[Badness]] (Sintel): 10.6
 
== Hendecatonic ==
: ''For extensions, see [[Porwell temperaments #Hendecatonic]] and [[Marvel temperaments #Hendeca]].''
 
The 5-limit version of hendecatonic simply equates a stack of eleven [[16/15]]'s with the [[octave]].  


== Unsmate ==
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 17578125/16777216
[[Comma list]]: 8796093022208/8649755859375


{{Mapping|legend=1| 1 3 2 | 0 -9 2 }}
{{Mapping|legend=1| 11 0 43 | 0 1 -1 }}
: Mapping generators: ~16/15, ~3


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000, ~2048/1875 = 189.049
* [[WE]]: ~16/15 = 109.0904{{c}}, ~3/2 = 702.6861{{c}}
: [[error map]]: {{val| -0.445 +0.286 +0.613 }}
* [[CWE]]: ~16/15 = 109.0909{{c}}, ~3/2 = 702.9082{{c}}
: error map: {{val| 0.000 +0.953 +1.687 }}


{{Optimal ET sequence|legend=1| 13, 19, 89c, 108c, 127c, 146cc }}
{{Optimal ET sequence|legend=1| 22, 55, 77, 99, 869bcc, 968bcc, 1067bccc, 1166bccc }}


[[Badness]] (Smith): 0.460
[[Badness]] (Sintel): 10.7


== Nusecond ==
== Nusecond ==
Line 483: Line 647:


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


== Sfourth ==
== Sfourth ==
Line 494: Line 680:
[[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]] (Smith): 0.505
[[Badness]] (Sintel): 11.8


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


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
Line 515: Line 703:


[[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]] (Smith): 0.511
[[Badness]] (Sintel): 12.0
 
== Sesesix ==
: ''For extensions, see [[Horwell temperaments #Fifthplus]].''
 
Sesesix is the 22 & 171 temperament, named by [[Petr Pařízek]] in 2011 for 36 generators giving a major sixth<ref name="petr's long post"/>.
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -74 13 23 }}
 
{{Mapping|legend=1| 1 -12 10 | 1 23 -13 }}
: mapping generators: ~2, ~6328125/4094304
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0899{{c}}, ~6328125/4194304 = 708.8258{{c}}
: [[error map]]: {{val| +0.090 -0.040 -0.151 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~6328125/4194304 = 708.7736{{c}}
: error map: {{val| 0.000 -0.161 -0.371 }}
 
{{Optimal ET sequence|legend=1| 22, 105, 127, 149, 171, 4468bcc, 4639bcc, …, 5323bccc }}
 
[[Badness]] (Sintel): 12.2


== Leapday ==
== Leapday ==
Line 531: Line 742:


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


== Vines ==
== Vines ==
Line 547: Line 759:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~390625/279936 = 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]] (Smith): 0.542
[[Badness]] (Sintel): 12.7


== Emka ==
== Emka ==
Line 563: Line 776:


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


== Misneb ==
== Misneb ==
Line 574: Line 788:
[[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]] (Smith): 0.610
[[Badness]] (Sintel): 14.3


== Semisept ==
== Semisept ==
Line 595: Line 810:


[[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]] (Smith): 0.631
[[Badness]] (Sintel): 14.8
 
== 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]] (Smith): 0.654


== Septimin ==
== Septimin ==
Line 627: Line 827:


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


== Slurpee ==
== Slurpee ==
Line 643: Line 844:


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


== Pentadecal ==
== Pentadecal ==
: ''For extensions, see [[Cloudy clan #Pentadecal]].''
: ''For extensions, see [[Keemic temperaments #Pentadecal]].''


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
Line 659: Line 861:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~648/625 = 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]] (Smith): 0.692
[[Badness]] (Sintel): 16.2
 
== Anthoine ==
: ''For extensions, see [[Buzzardsmic clan #Anthoine]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 286102294921875/281474976710656
 
{{Mapping|legend=1| 1 8 2 | 0 -20 1 }}
 
[[Optimal tuning]]s:
* [[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| 25, 28, 53 }}
 
[[Badness]] (Sintel): 16.5


== Sentinel ==
== Sentinel ==
Line 675: Line 895:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000, ~512/405 = 425.474
* [[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| 14, 17, 31, 79, 110, 361bbcc }}
 
[[Badness]] (Sintel): 17.0
 
== Undeka ==
: ''For extensions, see [[Keemic temperaments #Undeka]].''
 
Undeka has a period of 1/11 octave, like [[#Hendecatonic|hendecatonic]], but this temperament equates a stack of eleven 6/5's and three [[octave]]s, so that three periods represent [[6/5]].
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 48828125/45349632
 
{{Mapping|legend=1| 11 0 8 | 0 1 1 }}
: Mapping generators: ~648/625, ~3
 
[[Optimal tuning]]s:
* [[WE]]: ~648/625 = 109.1809{{c}}, ~3/2 = 704.4091{{c}}
: [[error map]]: {{val| +0.990 +3.444 -7.468 }}
* [[CWE]]: ~648/625 = 109.0909{{c}}, ~3/2 = 704.6983{{c}}
: error map: {{val| 0.000 +2.743 -8.888 }}


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


[[Badness]] (Smith): 0.723
[[Badness]] (Sintel): 17.1


== Kumonga ==
== Kumonga ==
Line 691: Line 934:


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


== Mirkat ==
== Mirkat ==
Line 707: Line 951:


[[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: 17.6


== Semidimi ==
== Semidimi ==
Line 726: Line 968:


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


== Slender ==
== Slender ==
Line 737: Line 980:
[[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: 17.8


== Quasitemp ==
== Quasitemp ==
Line 761: Line 1,002:


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


== Cypress ==
== Cypress ==
Line 777: Line 1,019:


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


== Chromo ==
== Chromo ==
Line 793: Line 1,036:


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


== Tertiosec ==
== Tertiosec ==
Line 809: Line 1,053:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~1073741824/854296875 = 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]] (Smith): 0.851
[[Badness]] (Sintel): 20.0


== Fervor ==
== Fervor ==
Line 825: Line 1,070:


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


== Bohpier ==
== Bohpier ==
Line 841: Line 1,087:


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


== Elvis ==
== Elvis ==
Line 857: Line 1,103:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~6075/4096 = 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, 106bc, 132bc }}
{{Optimal ET sequence|legend=1| 26, 80bc, 106bbcc, 132bbcc }}


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


== Enneadecacot ==
== Enneadecacot ==
Line 871: Line 1,118:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.0000, ~34171875/33554432 = 36.9622
* [[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| 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 887: Line 1,135:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~243/200 = 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]] (Smith): 0.903
[[Badness]] (Sintel): 21.2


== Oolong ==
== Oolong ==
Line 903: Line 1,152:


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


== Oncle ==
== Oncle ==
Line 919: Line 1,169:


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


== Quasiorwell ==
== Quasiorwell ==
Line 935: Line 1,186:


[[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: 30.6


== Diesic ==
== Diesic ==
Line 954: Line 1,203:


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


== Quartemka ==
== Quartemka ==
Line 965: Line 1,215:
[[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]] (Smith): 1.38
[[Badness]] (Sintel): 32.4


== Genocchi ==
== Genocchi ==
Line 984: Line 1,235:


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


== Casablanca ==
== Casablanca ==
Line 995: Line 1,247:
[[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]] (Smith): 1.42
[[Badness]] (Sintel): 33.4


== Archaeotherium ==
== Archaeotherium ==
Line 1,016: Line 1,269:


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


== Octacoid ==
== Octacoid ==
Line 1,032: Line 1,286:


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


== Quasimoha ==
== Quasimoha ==
Line 1,044: Line 1,298:
[[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]] (Smith): 1.99
[[Badness]] (Sintel): 46.6


== Phillips ==
== Phillips ==
Line 1,065: Line 1,320:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~98415/65536 = 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]] (Smith): 2.23
[[Badness]] (Sintel): 52.3


== Triskaidekic ==
== Triskaidekic ==
Line 1,079: Line 1,335:


{{Mapping|legend=1| 13 0 30 | 0 1 0 }}
{{Mapping|legend=1| 13 0 30 | 0 1 0 }}
: Mapping generators: ~128/125, ~3


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~128/125 = 92.308 (1＼13), ~3/2 = 696.142
* [[WE]]: ~128/125 = 92.589{{c}}, ~3/2 = 698.263{{c}}
: [[error map]]: {{val| +3.656 -0.036 -8.647 }}
* [[CWE]]: ~128/125 = 92.308{{c}}, ~3/2 = 698.068{{c}}
: error map: {{val| 0.000 -3.887 -17.083 }}


{{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 ==
: ''For extensions, see [[Canousmic temperaments #Satin]].''
: ''For extensions, see [[Garischismic clan #Satin]].''


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
Line 1,095: Line 1,355:


{{Mapping|legend=1| 1 2 12 | 0 -3 -70 }}
{{Mapping|legend=1| 1 2 12 | 0 -3 -70 }}
: mapping generators: ~2, ~{{monzo| -34 23 -1 }}
[[Optimal tuning]]s:
* [[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| 94, 217, 528, 745, 1273, 2018b }}
[[Badness]] (Sintel): 66.9
== Lockerbie ==
: ''For extensions, see [[Breedsmic temperaments #Lockerbie]].''
[[Subgroup]]: 2.3.5
[[Comma list]]: {{monzo| 91 51 -74 }}
{{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]] (Smith): 2.85
[[Badness]] (Sintel): 72.4


== Rarity ==
== Rarity ==
Line 1,113: Line 1,397:


{{Mapping|legend=1| 1 11 -10 | 0 -13 17 }}
{{Mapping|legend=1| 1 11 -10 | 0 -13 17 }}
: Mapping generators: ~2, ~16384/10125
: Mapping generators: ~2, ~16384/10125


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~16384/10125 = 869.392
* [[CTE]]: ~2 = 1200.000{{c}}, ~16384/10125 = 869.392{{c}}
* [[CWE]]: ~2 = 1200.000, ~16384/10125 = 869.402
* [[CWE]]: ~2 = 1200.000{{c}}, ~16384/10125 = 869.402{{c}}


{{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
 
== Jorgensen ==
: ''For extensions, see [[Hemifamity temperaments #Jorgensen]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 111 -70 }}
 
{{Mapping|legend=1| 70 111 0 | 0 0 1 }}
: mapping generators: ~{{monzo| 46 -29 }}, ~5
 
[[Optimal tuning]]s:
* [[WE]]: ~{{monzo| 46 -29 }} = 17.1388{{c}}, ~5/4 = 386.8829{{c}}
: [[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| 70, 140, 350, 490 }}
 
[[Badness]] (Sintel): 203
 
== Elven ==
: ''For extensions, see [[Sensibeta temperaments #Elven]].''
 
Elven has a period of 1/11 octave, like [[#Hendecatonic|hendecatonic]], but this temperament equates a stack of eleven [[3125/2916]]'s with the octave.  
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -23 -66 55 }}
 
{{Mapping|legend=1| 11 2 7 | 0 5 6 }}
: mapping generators: ~3125/2916, ~{{monzo| 10 29 -24 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~3125/2916 = 109.0998{{c}}, ~{{monzo| 10 29 -24 }} = 336.8921{{c}}
: [[error map]]: {{val| +0.097 +0.705 -1.263 }}
* [[CWE]]: ~3125/2916 = 109.0909{{c}}, ~{{monzo| 10 29 -24 }} = 336.8814{{c}}
: error map: {{val| 0.000 +0.634 -1.389 }}
 
{{Optimal ET sequence|legend=1| 121, 253, 374, 627c }}
 
[[Badness]] (Sintel): 429
 
== References ==


[[Category:Temperament collections]]
[[Category:Temperament collections]]
Retrieved from "https://en.xen.wiki/w/Miscellaneous_5-limit_temperaments"