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== Hogzilla ==
{{Technical data page}}
Subgroup: 2.3.5
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 [[equivalence continuum|equivalence continua]]
* [[Very low accuracy temperaments]]
* [[Very high accuracy temperaments]]


[[Comma]]: 4428675/4194304
== Ennealimmal ==
: ''For extensions, see [[Septiennealimmal clan #Ennealimmal]].''


[[Mapping]]: [{{Val|1 0 11}}, {{Val|0 2 -11}}]
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.


[[POTE generator]]: ~1215/1024 = 252.649
[[Subgroup]]: 2.3.5


{{Val list|legend=1| 14, 19 }}
[[Comma list]]: {{monzo| 1 -27 18 }}


[[Badness]]: 0.424685
{{Mapping|legend=1| 9 1 1 | 0 2 3 }}
: mapping generators: ~27/25, ~5/3


== Archaeotherium ==
[[Optimal tuning]]s:
Subgroup: 2.3.5
* [[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 ==
: ''For extensions, see [[Mint temperaments #Progression]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 3456/3125
 
{{Mapping|legend=1| 1 1 2 | 0 5 3 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[Badness]] (Sintel): 4.70
 
== Neon ==
: ''For extensions, see [[Ragismic microtemperaments #Deca]], [[Landscape microtemperaments #Zinc]], and [[20th-octave temperaments #Calcium]].''
{{See also| Neon comma }}
 
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.
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 21 60 -50 }}
 
{{Mapping|legend=1| 10 4 9 | 0 5 6 }}
: mapping generators: ~3125/2916, {{monzo| 10 29 -24 }}
 
[[Optimal tuning]]s:
* [[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| 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650 }}
 
[[Badness]] (Sintel): 4.85
 
== Dodifo ==
: ''For extensions, see [[Porwell temperaments #Dodifo]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -67 -9 35 }}
 
{{Mapping|legend=1| 1 12 5 | 0 -35 -9 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[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 ==
: ''For extensions, see [[Ragismic microtemperaments #Semidimfourth]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 7 41 -31 }}
 
{{Mapping|legend=1| 1 21 28 | 0 -31 -41 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[Badness]] (Sintel): 5.47
 
== Mynic ==
: ''For extensions, see [[Starling temperaments #Myna]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 10077696/9765625
 
{{Mapping|legend=1| 1 9 9 | 0 -10 -9 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[Badness]] (Sintel): 5.86
 
== Progress ==
: ''For extensions, see [[Archytas clan #Progress]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 32768/30375
 
{{Mapping|legend=1| 1 0 5 | 0 3 -5 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[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 ==
: ''For extensions, see [[Ragismic microtemperaments #Gamera]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 10 -40 23 }}
 
{{Mapping|legend=1| 1 6 10 | 0 -23 -40 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~2500/2187 = 230.345{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~2500/2187 = 230.345{{c}}
 
{{Optimal ET sequence|legend=1| 26, 73, 99, 224, 323, 547, 870 }}
 
[[Badness]] (Sintel): 6.39
 
== Tritriple ==
: ''For extensions, see [[Gamelismic clan #Tritriple]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 31 20 -27 }}
 
{{Mapping|legend=1| 1 -11 -7 | 0 27 20 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[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 ==
: ''For extensions, see [[Trienstonic clan #Parakangaroo]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 64000/59049
 
{{Mapping|legend=1| 1 0 -3 | 0 3 10 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[Badness]] (Sintel): 6.94
 
== Tertiaseptal ==
: ''For extensions, see [[Breedsmic temperaments #Tertiaseptal]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -59 5 22 }}
 
{{Mapping|legend=1| 1 3 2 | 0 -22 5 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[Badness]] (Sintel): 6.98
 
== Untriton ==
: ''For extensions, see [[Marvel temperaments #Untriton]], [[Porwell temperaments #Aufo]] and [[Triwellismic temperaments #Interaufo]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -51 19 9 }}
 
{{Mapping|legend=1| 1 6 -7 | 0 -9 19 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[Badness]] (Sintel): 7.20
 
== Nessafof ==
: ''For extensions, see [[Porwell temperaments #Nessafof]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 25 15 -21 }}
 
{{Mapping|legend=1| 3 2 5 | 0 7 5 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~78125/62208 = 400.000{{c}}, ~9765625/8957952 = 157.392{{c}}
* [[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 }}
 
[[Badness]] (Sintel): 7.81
 
== Lemba ==
: ''For extensions, see [[Jubilismic clan #Lemba]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 140625/131072
 
{{Mapping|legend=1| 2 2 5 | 0 3 -1 }}
: Mapping generators: ~375/256, ~75/64
 
[[Optimal tuning]]s:
* [[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 }}


[[Comma]]: 597871125/536870912
{{Optimal ET sequence|legend=1| 10, 16, 26, 88cc }}


[[Mapping]]: [{{Val|1 1 5}}, {{Val|0 3 -14}}]
[[Badness]] (Sintel): 7.85


[[POTE generator]]: ~1215/1024 = 230.351
== Delorean ==
: ''For extensions, see [[Mint temperaments #Subklei]].''


{{Val list|legend=1| 21, 26, 73bc, 99bc }}
[[Subgroup]]: 2.3.5


[[Badness]]: 1.434855
[[Comma list]]: 17496/15625


=== 7-limit ===
{{Mapping|legend=1| 1 3 4 | 0 -6 -7 }}
Subgroup: 2.3.5.7


[[Comma list]]: 405/392, 1029/1024
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 284.817{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 284.293{{c}}


[[Mapping]]: [{{Val|1 1 5 3}}, {{Val|0 3 -14 -1}}]
{{Optimal ET sequence|legend=1| 4, 13c, 17c, 21, 38c }}


[[POTE generator]]: ~8/7 = 230.258
[[Badness]] (Sintel): 8.35


{{Val list|legend=1| 21, 26, 47, 73bc, 99bc }}
== Majvam ==
: ''For extensions, see [[No-sevens subgroup temperaments #Majvam]], [[Cataharry temperaments #Majvamoid]], and [[Parkleiness temperaments #Majvamic]].''


[[Badness]]: 0.146306
[[Subgroup]]: 2.3.5


== Stump ==
[[Comma list]]: 2404631929946112/2384185791015625
{{see also| Sensamagic clan #Pycnic }}
{{see also| Marvel temperaments #Triton }}


Subgroup: 2.3.5
{{Mapping|legend=1| 1 10 5 | 0 -22 -7 }}


[[Comma]]: 273375/262144
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~125/96 = 459.006{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~125/96 = 458.995{{c}}


[[Mapping]]: [{{Val|1 0 6}}, {{Val|0 3 -7}}]
{{Optimal ET sequence|legend=1| 34, 115, 149, 183, 217, 400, 617 }}


[[POTE generator]]: ~64/45 = 631.737
[[Badness]] (Sintel): 8.37


{{Val list|legend=1| 17, 19 }}
== Beatles ==
: ''For extensions, see [[Archytas clan #Beatles]].''


[[Badness]]: 0.200600
[[Subgroup]]: 2.3.5


== Unsmate ==
[[Comma list]]: 524288/492075
Subgroup: 2.3.5


[[Comma]]: 17578125/16777216
{{Mapping|legend=1| 1 1 5 | 0 2 -9 }}


[[Mapping]]: [{{Val|1 3 2}}, {{Val|0 -9 2}}]
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~512/405 = 356.492{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~512/405 = 355.930{{c}}


[[POTE generator]]: ~2048/1875 = 189.049
{{Optimal ET sequence|legend=1| 10, 17c, 27, 64b, 91bc, 118bc }}


{{Val list|legend=1| 13, 19, 89c, 108c, 127c, 146cc }}
[[Badness]] (Sintel): 8.41


[[Badness]]: 0.460168
== Magus ==
: ''For extensions, see [[Sensamagic clan #Magus]] and [[Starling temperaments #Amigo]].''


== Chromo ==
[[Subgroup]]: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 1220703125/1146617856
[[Comma list]]: 50331648/48828125


[[Mapping]]: [{{Val|1 1 2}}, {{Val|0 13 7}}]
{{Mapping|legend=1| 1 -2 2 | 0 11 1 }}


[[POTE generator]]: ~25/24 = 53.922
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 391.068{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 391.225{{c}}


{{Val list|legend=1| 22, 45, 67c, 89c }}
{{Optimal ET sequence|legend=1| 3, …, 40, 43, 46, 181c, 227c, 273c, 319c }}


[[Badness]]: 0.842835
[[Badness]] (Sintel): 8.45


=== 7-limit ===
== Tritonic ==
Subgroup: 2.3.5.7
: ''For extensions, see [[Marvel temperaments #Tritonic]].''


[[Comma list]]: 875/864, 2430/2401
[[Subgroup]]: 2.3.5


[[Mapping]]: [{{Val|1 1 2 2}}, {{Val|0 13 7 18}}]
[[Comma list]]: 553584375/536870912


[[POTE generator]]: ~25/24 = 53.816
{{Mapping|legend=1| 1 4 -3 | 0 -5 11 }}


{{Val list|legend=1| 22, 45, 67c }}
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~45/32 = 580.278{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~45/32 = 580.219{{c}}


[[Badness]]: 0.090769
{{Optimal ET sequence|legend=1| 29, 31, 60, 91 }}
 
[[Badness]] (Sintel): 8.88


== Wizard ==
== Wizard ==
{{see also| Marvel temperaments #Wizard }}
: ''For extensions, see [[Marvel temperaments #Wizard]].''


Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma]]: 2197265625/2147483648
[[Comma list]]: 2197265625/2147483648


[[Mapping]]: [{{Val| 2 1 5 }}, {{Val| 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:
* [[CTE]]: ~42875/32768 = 600.000{{c}}, ~9375/8192 = 216.950{{c}}
* [[POTE]]: ~42875/32768 = 600.000{{c}}, ~9375/8192 = 216.788{{c}}


[[POTE generator]]: ~5/4 = 383.212
{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 548bcc }}


{{Val list|legend=1| 22, 50, 72, 166, 238c, 310c, 548bc }}
[[Badness]] (Sintel): 9.06


[[Badness]]: 0.386367
Scales (Scala files): [[wizard22]]


Scales (Scala files): [[wizard22]]
== Tridecatonic ==
: ''For extensions, see [[Octagar temperaments #Tridecatonic]], [[Ragismic microtemperaments #Trideci]], and [[Varunismic temperaments #Bosonic]].''


== Tritonic ==
Tridecatonic tempers out the [[devil's tridecalimma]], the comma which associates the [[10/9]] minor tone with [[13edo|2\13]].
{{see also| Marvel temperaments #Tritonic }}


Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma]]: 553584375/536870912
[[Comma list]]: {{monzo| -11 26 -13 }}


[[Mapping]]: [{{Val| 1 4 -3 }}, {{Val| 0 -5 11 }}]
{{Mapping|legend=1| 13 0 -11 | 0 1 2 }}
: mapping generators: ~531441/500000, ~3


[[POTE generator]]: ~45/32 = 580.219
[[Optimal tuning]]s:
* [[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 }}


{{Val list|legend=1| 29, 31, 60, 91 }}
{{Optimal ET sequence|legend=1| 26, 39, 65, 286, 351, 416, 481, 546 }}


[[Badness]]: 0.378527
[[Badness]] (Sintel): 10.3


== Merman ==
== Merman ==
{{see also| Marvel temperaments #Merman }}
: ''For extensions, see [[Marvel temperaments #Merman]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -40 15 7 }}
 
{{Mapping|legend=1| 1 5 -5 | 0 -7 15 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[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]].
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 8796093022208/8649755859375
 
{{Mapping|legend=1| 11 0 43 | 0 1 -1 }}
: Mapping generators: ~16/15, ~3
 
[[Optimal tuning]]s:
* [[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 }}


Sugbroup: 2.3.5
{{Optimal ET sequence|legend=1| 22, 55, 77, 99, 869bcc, 968bcc, 1067bccc, 1166bccc }}


[[Comma]]: 1121008359375/1099511627776
[[Badness]] (Sintel): 10.7


[[Mapping]]: [{{Val| 1 5 -5 }}, {{Val| 0 -7 15 }}]
== Nusecond ==
: ''For extensions, see [[Starling temperaments #Nusecond]].''


[[POTE generator]]: ~45/32 = 585.634
[[Subgroup]]: 2.3.5


{{Val list|legend=1| 41, 84, 125, 209, 334c, 543bc }}
[[Comma list]]: 51018336/48828125


[[Badness]]: 0.453848
{{Mapping|legend=1| 1 3 4 | 0 -11 -13 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[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 ==
: ''For extensions, see [[Ragismic microtemperaments #Sfourth]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -5 31 -19 }}
 
{{Mapping|legend=1| 1 2 3 | 0 -19 -31 }}
 
[[Optimal tuning]]s:
* [[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, 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|legend=1| 1 -4 0 | 0 12 5 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[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 ==
: ''For extensions, see [[Hemifamity temperaments #Leapday]] and [[Porwell temperaments #Polypyth]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 10737418240/10460353203
 
{{Mapping|legend=1| 1 0 -31 | 0 1 21 }}
 
[[Optimal tuning]]s:
* [[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| 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|legend=1| 2 7 8 | 0 -8 -7 }}
 
[[Optimal tuning]]s:
* [[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, 330c, 472cc }}
 
[[Badness]] (Sintel): 12.7
 
== Emka ==
: ''For extensions, see [[Hemimean clan #Emka]] and [[Horwell temperaments #Emkay]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -50 -8 27 }}
 
{{Mapping|legend=1| 1 14 6 | 0 -27 -8 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[Badness]] (Sintel): 12.8
 
== Misneb ==
: ''For extensions, see [[Marvel temperaments #Misneb]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -57 14 15 }}
 
{{Mapping|legend=1| 1 3 1 | 0 -15 14 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[Badness]] (Sintel): 14.3
 
== Semisept ==
: ''For extensions, see [[Hemimean clan #Semisept]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 782757789696/762939453125
 
{{Mapping|legend=1| 1 12 6 | 0 -17 -6 }}
 
[[Optimal tuning]]s:
* [[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, 586cc, 697ccc }}
 
[[Badness]] (Sintel): 14.8


== Septimin ==
== Septimin ==
{{see also| Marvel temperaments #Septimin }}
: ''For extensions, see [[Marvel temperaments #Septimin]].''


Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma]]: 35595703125/34359738368
[[Comma list]]: 35595703125/34359738368


[[Mapping]]: [{{Val| 1 4 1 }}, {{Val| 0 -11 6 }}]
{{Mapping|legend=1| 1 4 1 | 0 -11 6 }}


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


{{Val list|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 ==
: ''For extensions, see [[Mint temperaments #Slurpee]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 177147/156250
 
{{Mapping|legend=1| 1 2 3 | 0 -7 -11 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[Badness]] (Sintel): 16.2
 
== Pentadecal ==
: ''For extensions, see [[Keemic temperaments #Pentadecal]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 30517578125/29386561536
 
{{Mapping|legend=1| 15 0 11 | 0 1 1 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[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 ==
: ''For extensions, see [[Orwellismic temperaments #Sentinel]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 8968066875/8589934592
 
{{Mapping|legend=1| 1 3 -3 | 0 -4 15 }}
 
[[Optimal tuning]]s:
* [[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 ==
== Undeka ==
Subgroup: 2.3.5
: ''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| 22, 77c, 99c }}


[[Comma]]: 48828125/45349632
[[Badness]] (Sintel): 17.1


[[Mapping]]: [{{Val|11 0 8}}, {{Val|0 1 1}}]
== Kumonga ==
: ''For extensions, see [[Starling temperaments #Kumonga]].''


[[POTE generator]]: ~3/2 = 703.829
[[Subgroup]]: 2.3.5


{{Val list|legend=1| 22, 77c, 99c, 121c }}
[[Comma list]]: 1289945088/1220703125


[[Badness]]: 0.727539
{{Mapping|legend=1| 1 4 4 | 0 -13 -9 }}


=== 7-limit ===
[[Optimal tuning]]s:
Subgroup: 2.3.5.7
* [[CTE]]: ~2 = 1200.000{{c}}, ~144/125 = 223.076{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~144/125 = 222.912{{c}}


[[Comma list]]: 875/864, 3200/3087
{{Optimal ET sequence|legend=1| 16, 27, 43, 70, 183cc }}


[[Mapping]]: [{{Val|11 0 8 31}}, {{Val|0 1 1 0}}]
[[Badness]] (Sintel): 17.1


{{Multival|legend=1|11 11 0 -8 -31 -31}}
== Mirkat ==
: ''For extensions, see [[Mirkwai clan #Mirkat]].''


[[POTE generator]]: ~3/2 = 708.792
[[Subgroup]]: 2.3.5


{{Val list|legend=1| 11c, 22 }}
[[Comma list]]: {{monzo| 20 -39 18 }}


[[Badness]]: 0.141782
{{Mapping|legend=1| 3 2 1 | 0 6 13 }}


=== 11-limit ===
[[Optimal tuning]]s:
Sugbroup: 2.3.5.7.11
* [[CTE]]: ~2000000/1594323 = 400.000{{c}}, ~10/9 = 183.593{{c}}
* [[CWE]]: ~2000000/1594323 = 400.000{{c}}, ~10/9 = 183.585{{c}}


[[Comma list]]: 100/99, 352/343, 385/384
{{Optimal ET sequence|legend=1| 33c, 39, 72, 111, 183, 438, 621, 1425b }}


[[Mapping]]: [{{Val|11 0 8 31 38}}, {{Val|0 1 1 0 0}}]
[[Badness]] (Sintel): 17.6


[[POTE generator]]: ~3/2 = 706.768
== Semidimi ==
: ''For extensions, see [[Ragismic microtemperaments #Semidimi]].''


{{Val list|legend=1| 11c, 22 }}
[[Subgroup]]: 2.3.5


[[Badness]]: 0.068672
[[Comma list]]: {{monzo| -12 -73 55 }}


=== 13-limit ===
{{Mapping|legend=1| 1 36 48 | 0 -55 -73 }}
Subgroup: 2.3.5.7.11.13


[[Comma list]]: 65/63, 100/99, 169/165, 352/343
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~162/125 = 449.127{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~162/125 = 449.127{{c}}


[[Mapping]]: [{{Val|11 0 8 31 38 23}}, {{Val|0 1 1 0 0 1}}]
{{Optimal ET sequence|legend=1| 8, …, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}


[[POTE generator]]: ~3/2 = 707.764
[[Badness]] (Sintel): 17.7


{{Val list|legend=1| 11cf, 22 }}
== Slender ==
: ''For extensions, see [[Marvel temperaments #Slender]].''


[[Badness]]: 0.056528
[[Subgroup]]: 2.3.5


== Triskaidekic ==
[[Comma list]]: {{monzo| -46 10 13 }}
Subgroup: 2.3.5
 
{{Mapping|legend=1| 1 2 2 | 0 -13 10 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~16875/16384 = 38.380{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~16875/16384 = 38.400{{c}}
 
{{Optimal ET sequence|legend=1| 31, 94, 125, 781bcc }}
 
[[Badness]] (Sintel): 17.8
 
== Quasitemp ==
: ''For extensions, see [[Keemic temperaments #Quasitemp]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 6103515625/5804752896
 
{{Mapping|legend=1| 1 5 5 | 0 -14 -11 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[Badness]] (Sintel): 18.0
 
== Cypress ==
: ''For extensions, see [[Starling temperaments #Cypress]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 258280326/244140625
 
{{Mapping|legend=1| 1 7 10 | 0 -12 -17 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[Badness]] (Sintel): 19.2
 
== Chromo ==
: ''For extensions, see [[Keemic temperaments #Chromo]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 1220703125/1146617856


[[Comma]]: 1220703125/1073741824
{{Mapping|legend=1| 1 1 2 | 0 13 7 }}


[[Mapping]]: [{{Val|13 0 30}}, {{Val|0 1 0}}]
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~25/24 = 54.138{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~25/24 = 53.922{{c}}


[[POTE generator]]: ~3/2 = 696.142
{{Optimal ET sequence|legend=1| 22, 45, 67c, 89c }}


{{Val list|legend=1| 13, 26, 91c }}
[[Badness]] (Sintel): 19.8


[[Badness]]: 2.241568
== Tertiosec ==
: ''For extensions, see [[Marvel temperaments #Tertiosec]].''


=== 7-limit ===
[[Subgroup]]: 2.3.5
Subgroup: 2.3.5.7


[[Comma list]]: 1728/1715, 1875/1792
[[Comma list]]: {{monzo| -89 21 24 }}


[[Mapping]]: [{{Val|13 0 30 16}}, {{Val|0 1 0 1}}]
{{Mapping|legend=1| 3 7 5 | 0 -8 7 }}


{{Multival|legend=1|13 0 13 -30 -16 30}}
[[Optimal tuning]]s:
* [[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}}


[[POTE generator]]: ~3/2 = 694.143
{{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171 }}


{{Val list|legend=1| 13d, 26 }}
[[Badness]] (Sintel): 20.0


[[Badness]]: 0.219050
== Fervor ==
: ''For extensions, see [[Archytas clan #Fervor]].''


=== 11-limit ===
[[Subgroup]]: 2.3.5
Subgroup: 2.3.5.7.11


[[Comma list]]: 99/98, 125/121, 385/384
[[Comma list]]: 67108864/61509375


[[Mapping]]: [{{Val|13 0 30 16 45}}, {{Val|0 1 0 1 0}}]
{{Mapping|legend=1| 1 4 -2 | 0 -5 9 }}


[[POTE generator]]: ~3/2 = 696.296
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~64/45 = 577.593{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~64/45 = 577.705{{c}}


{{Val list|legend=1| 13d, 26, 91cd }}
{{Optimal ET sequence|legend=1| 2, …, 25, 27 }}


[[Badness]]: 0.098847
[[Badness]] (Sintel): 20.0


=== 13-limit ===
== Bohpier ==
Subgroup: 2.3.5.7.11.13
: ''For extensions, see [[Sensamagic clan #Bohpier]].''


[[Comma list]]: 78/77, 99/98, 125/121, 1200/1183
[[Subgroup]]: 2.3.5


[[Mapping]]: [{{Val|13 0 30 16 45 48}}, {{Val|0 1 0 1 0 0}}]
[[Comma list]]: 1220703125/1162261467


[[POTE generator]]: ~3/2 = 695.879
{{Mapping|legend=1| 1 0 0 | 0 13 19 }}


{{Val list|legend=1| 13d, 26, 91cdf }}
[[Optimal tuning]]s:
* [[CTE]] and [[POTE]]: ~2 = 1200.000{{c}}, ~27/25 = 146.476{{c}}


[[Badness]]: 0.059216
{{Optimal ET sequence|legend=1| 8, …, 41, 131, 172, 213c }}


== Phillips ==
[[Badness]] (Sintel): 20.2
Subgroup: 2.3.5


[[Comma]]: 9685512225/8589934592
== Elvis ==
: ''For extensions, see [[Jubilismic clan #Elvis]].''


[[Mapping]]: [{{Val|2 0 33}}, {{Val|0 1 -9}}]
[[Subgroup]]: 2.3.5


[[POTE generator]]: ~3/2 = 691.455
[[Comma list]]: 36905625/33554432


{{Val list|legend=1| 14, 26, 66b, 92bc, 118bbc }}
{{Mapping|legend=1| 2 1 10 | 0 2 -5 }}


[[Badness]]: 2.228904
[[Optimal tuning]]s:  
* [[CTE]]: ~6075/4096 = 600.000{{c}}, ~64/45 = 644.844{{c}}
* [[POTE]]: ~6075/4096 = 600.000{{c}}, ~64/45 = 645.454{{c}}


=== 7-limit ===
{{Optimal ET sequence|legend=1| 26, 80bc, 106bbcc, 132bbcc }}
Subgroup: 2.3.5.7


[[Comma list]]: 1728/1715, 6561/6272
[[Badness]] (Sintel): 20.7


[[Mapping]]: [{{Val|2 0 33 -7}}, {{Val|0 1 -9 4}}]
== Enneadecacot ==
[[Subgroup]]: 2.3.5


{{Multival|legend=1|2 -18 8 -33 7 69}}
[[Comma list]]: {{monzo| 79 -22 -19 }}


[[POTE generator]]: ~3/2 = 691.174
{{Mapping|legend=1| 1 1 3 | 0 19 -22 }}


{{Val list|legend=1| 14, 26, 66b, 92bc }}
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.0000{{c}}, ~34171875/33554432 = 36.9607{{c}}
* [[POTE]]: ~2 = 1200.0000{{c}}, ~34171875/33554432 = 36.9622{{c}}


[[Badness]]: 0.228602
{{Optimal ET sequence|legend=1| 32, 65, 292, 357, 422, 487, 1396c }}


=== 11-limit ===
[[Badness]] (Sintel): 20.9
Subgroup: 2.3.5.7.11


[[Comma list]]: 99/98, 385/384, 729/704
== Vinegar ==
: ''For extensions, see [[Starling temperaments #Vinegar]].''


[[Mapping]]: [{{Val|2 0 33 -7 -12}}, {{Val|0 1 -9 4 6}}]
[[Subgroup]]: 2.3.5


[[POTE generator]]: ~3/2 = 691.040
[[Comma list]]: 16000000/14348907


{{Val list|legend=1| 14, 26, 40, 66b }}
{{Mapping|legend=1| 3 0 -5 | 0 2 5 }}


[[Badness]]: 0.095777
[[Optimal tuning]]s:  
* [[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}})


== Oncle ==
{{Optimal ET sequence|legend=1| 15, 39c, 54, 69b }}
Subgroup: 2.3.5


[[Comma]]: 145282683375/137438953472
[[Badness]] (Sintel): 21.2


[[Mapping]]: [{{Val|1 1 6}}, {{Val|0 3 -19}}]
== Oolong ==
: ''For extensions, see [[Starling temperaments #Oolong]].''


[[POTE generator]]: ~4096/3645 = 232.521
[[Subgroup]]: 2.3.5


{{Val list|legend=1| 31, 98c, 129c, 160bc, 289bbcc }}
[[Comma list]]: 793437161472/762939453125


[[Badness]]: 1.244699
{{Mapping|legend=1| 1 6 7 | 0 -17 -18 }}


=== 7-limit ===
[[Optimal tuning]]s:
Subgroup: 2.3.5.7
* [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 311.726{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 311.694{{c}}


[[Comma list]]: 1029/1024, 2430/2401
{{Optimal ET sequence|legend=1| 23, 27, 50, 77 }}


[[Mapping]]: [{{Val|1 1 6 3}}, {{Val|0 3 -19 -1}}]
[[Badness]] (Sintel): 22.1


[[POTE generator]]: ~8/7 = 232.498
== Oncle ==
: ''For extensions, see [[Gamelismic clan #Oncle]].''


{{Val list|legend=1| 31, 98c, 129c, 160bc }}
[[Subgroup]]: 2.3.5


[[Badness]]: 0.088384
[[Comma list]]: 145282683375/137438953472


== Quasimoha ==
{{Mapping|legend=1| 1 1 6 | 0 3 -19 }}
Subgroup: 2.3.5


[[Comma]]: 2353579470675/2199023255552
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~4096/3645 = 232.385{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~4096/3645 = 232.521{{c}}


[[Mapping]]: [{{Val|1 1 9}}, {{Val|0 2 -23}}]
{{Optimal ET sequence|legend=1| 31, 98c, 129c, 160bc, 289bbcc }}


[[POTE generator]]: ~1048576/885735 = 348.600
[[Badness]] (Sintel): 29.2


{{Val list|legend=1| 31, 117c, 148bc, 179bc }}
== Quasiorwell ==
: ''For extensions, see [[Breedsmic temperaments #Quasiorwell]].''


[[Badness]]: 1.986675
[[Subgroup]]: 2.3.5


=== 7-limit ===
[[Comma list]]: {{monzo| -93 3 38 }}
Subgroup: 2.3.5.7


[[Comma list]]: 2401/2400, 3645/3584
{{Mapping|legend=1| 1 31 0 | 0 -38 3 }}


[[Mapping]]: [{{Val|1 1 9 6}}, {{Val|0 2 -23 -11}}]
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~{{monzo| -31 1 13 }} = 928.896{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~{{monzo| -31 1 13 }} = 928.893{{c}}


[[POTE generator]]: ~49/40 = 348.603
{{Optimal ET sequence|legend=1| 31, …, 177, 208, 239, 270, 841, 1111, 1381, 2492c }}


{{Val list|legend=1| 31, 117c, 148bc, 179bc }}
[[Badness]] (Sintel): 30.6


[[Badness]]: 0.110820
== Diesic ==
: ''For extensions, see [[Orwellismic temperaments #Diesic]].''


=== 11-limit ===
[[Subgroup]]: 2.3.5
Subgroup: 2.3.5.7.11


[[Comma list]]: 243/242, 441/440, 1815/1792
[[Comma list]]: 10460353203/9765625000


[[Mapping]]: [{{Val|1 1 9 6 2}}, {{Val|0 2 -23 -11 5}}]
{{Mapping|legend=1| 1 2 3 | 0 -13 -21 }}


[[POTE generator]]: ~11/9 = 348.639
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~6561/6250 = 38.550{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~6561/6250 = 38.571{{c}}


{{Val list|legend=1| 31, 86ce, 117ce, 148bce }}
{{Optimal ET sequence|legend=1| 31, 156c }}


[[Badness]]: 0.046181
[[Badness]] (Sintel): 31.5


== Genocchi ==
== Quartemka ==
Subgroup: 2.3.5
: ''For extensions, see [[Gamelismic clan #Quartemka]].''


[[Comma]]: 2359296/1953125
[[Subgroup]]: 2.3.5


[[Mapping]]: [{{Val|1 0 2}}, {{Val|0 9 2}}]
[[Comma list]]: {{monzo| 2 -32 21 }}


[[POTE generator]]: ~768/625 = 212.444
{{Mapping|legend=1| 1 4 6 | 0 -21 -32 }}


{{Val list|legend=1| 6b, 11b, 17c }}
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~27/25 = 137.963{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~27/25 = 137.962{{c}}


[[Badness]]: 1.404977
{{Optimal ET sequence|legend=1| 26, 61, 87, 287, 374, 461 }}


== Misneb ==
[[Badness]] (Sintel): 32.4
Subgroup: 2.3.5


[[Comma]]: 145964630126953125/144115188075855872
== Genocchi ==
[[Subgroup]]: 2.3.5


[[Mapping]]: [{{Val|1 3 1}}, {{Val|0 -15 14}}]
[[Comma list]]: 2359296/1953125


[[POTE generator]]: ~16/15 = 113.240
{{Mapping|legend=1| 1 0 2 | 0 9 2 }}


{{Val list|legend=1| 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc }}
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~768/625 = 210.920{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~768/625 = 212.444{{c}}


[[Badness]]: 0.609540
{{Optimal ET sequence|legend=1| 6b, 11b, 17c }}


=== 7-limit ===
[[Badness]] (Sintel): 33.0
Subgroup: 2.3.5.7


[[Comma list]]: 225/224, 4194304/4117715
== Casablanca ==
: ''For extensions, see [[Starling temperaments #Casablanca]].''


[[Mapping]]: [{{Val|1 3 1 3}}, {{Val|0 -15 14 -2}}]
[[Subgroup]]: 2.3.5


{{Multival|legend=1|15 -14 2 -57 -39 44}}
[[Comma list]]: {{monzo| 22 14 -19 }}


[[POTE generator]]: ~16/15 = 113.235
{{Mapping|legend=1| 1 -7 -14 | 0 19 14 }}


{{Val list|legend=1| 21, 32, 53 }}
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~864/625 = 542.142{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~864/625 = 542.208{{c}}


[[Badness]]: 0.140970
{{Optimal ET sequence|legend=1| 11b, 20b, 31, 73, 104c, 135c }}


=== 11-limit ===
[[Badness]] (Sintel): 33.4
Subgroup: 2.3.5.7.11


Comma list: 99/98, 176/175, 1310720/1294139
== Archaeotherium ==
: ''For extensions, see [[Gamelismic clan #Archaeotherium]].''


Mapping: [{{Val|1 3 1 3 1}}, {{Val|0 -15 14 -2 26}}]
[[Subgroup]]: 2.3.5


POTE generator: ~16/15 = 113.323
[[Comma list]]: 597871125/536870912


Vals: {{Val list| 21, 32e, 53, 127, 180de }}
{{Mapping|legend=1| 1 1 5 | 0 3 -14 }}


Badness: 0.085390
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~1215/1024 = 229.947{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~1215/1024 = 230.351{{c}}


==== 13-limit ====
{{Optimal ET sequence|legend=1| 21, 26, 73bc, 99bc }}
Subgroup: 2.3.5.7.11.13


Comma list: 99/98, 176/175, 640/637, 847/845
[[Badness]] (Sintel): 33.7


Mapping: [{{Val|1 3 1 3 1 2}}, {{Val|0 -15 14 -2 26 18}}]
== Octacoid ==
[[Subgroup]]: 2.3.5


POTE generator: ~16/15 = 113.323
[[Comma list]]: 8589934592/7688671875


Vals: {{Val list| 21, 32e, 53, 127, 180de }}
{{Mapping|legend=1| 1 1 3 | 0 8 -9 }}


Badness: 0.045569
: Mapping generators: ~2, ~16/15


=== Musneb ===
[[Optimal tuning]]s:
Subgroup: 2.3.5.7.11
* [[CTE]]: ~2 = 1200.0000{{c}}, ~16/15 = 88.7331{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 88.8168{{c}}


Comma list: 225/224, 385/384, 66550/64827
{{Optimal ET sequence|legend=1| 13, 14, 27 }}


Mapping: [{{Val|1 3 1 3 6}}, {{Val|0 -15 14 -2 -27}}]
[[Badness]] (Sintel): 41.1


POTE generator: ~16/15 = 113.142
== Quasimoha ==
: ''For extensions, see [[Breedsmic temperaments #Quasimoha]].''


Vals: {{Val list| 32, 53, 191de, 244cddee, 297cddee }}
[[Subgroup]]: 2.3.5


Badness: 0.087333
[[Comma list]]: {{monzo| -41 23 2 }}


== Untriton ==
{{Mapping|legend=1| 1 1 9 | 0 2 -23 }}
Subgroup: 2.3.5


[[Comma]]: 2270041927734375/2251799813685248
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~1048576/885735 = 348.462{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~1048576/885735 = 348.600{{c}}


[[Mapping]]: [{{Val|1 6 -7}}, {{Val|0 -9 19}}]
{{Optimal ET sequence|legend=1| 31, 117c, 148bc, 179bc }}


[[POTE generator]]: ~45/32 = 588.722
[[Badness]] (Sintel): 46.6


{{Val list|legend=1| 51, 53, 267, 320, 373, 426, 479, 532, 2607bc }}
== Phillips ==
: ''For extensions, see [[Orwellismic temperaments #Phillips]].''


[[Badness]]: 0.307073
[[Subgroup]]: 2.3.5


=== 7-limit ===
[[Comma list]]: 9685512225/8589934592
Subgroup: 2.3.5.7


[[Comma list]]: 225/224, 125000000/121060821
{{Mapping|legend=1| 2 0 33 | 0 1 -9 }}


[[Mapping]]: [{{Val|1 6 -7 -7}}, {{Val|0 -9 19 20}}]
[[Optimal tuning]]s:  
* [[CTE]]: ~98415/65536 = 600.000{{c}}, ~3/2 = 690.708{{c}}
* [[POTE]]: ~98415/65536 = 600.000{{c}}, ~3/2 = 691.455{{c}}


{{Multival|legend=1|9 -19 -20 -51 -57 7}}
{{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc, 118bbc }}


[[POTE generator]]: ~7/5 = 588.641
[[Badness]] (Sintel): 52.3


{{Val list|legend=1| 51, 53, 316cd, 369cdd, 422cdd }}
== Triskaidekic ==
: ''For extensions, see [[Orwellismic temperaments #Triskaidekic]].''


[[Badness]]: 0.143976
[[Subgroup]]: 2.3.5


==== 11-limit ====
[[Comma list]]: 1220703125/1073741824
Subgroup: 2.3.5.7.11


Comma list: 121/120, 225/224, 22000/21609
{{Mapping|legend=1| 13 0 30 | 0 1 0 }}
: Mapping generators: ~128/125, ~3


Mapping: [{{Val|1 6 -7 -7 1}}, {{Val|0 -9 19 20 5}}]
[[Optimal tuning]]s:  
* [[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 }}


POTE generator: ~7/5 = 588.626
{{Optimal ET sequence|legend=1| 13, 26, 91cc }}


Vals: {{Val list| 51, 53 }}
[[Badness]] (Sintel): 52.6


Badness: 0.074295
== Satin ==
: ''For extensions, see [[Garischismic clan #Satin]].''


==== 13-limit ====
[[Subgroup]]: 2.3.5
Subgroup: 2.3.5.7.11.13


Comma list: 121/120, 225/224, 275/273, 1040/1029
[[Comma list]]: {{monzo| 104 -70 3 }}


Mapping: [{{Val|1 6 -7 -7 1 -12}}, {{Val|0 -9 19 20 5 32}}]
{{Mapping|legend=1| 1 2 12 | 0 -3 -70 }}
: mapping generators: ~2, ~{{monzo| -34 23 -1 }}


POTE generator: ~7/5 = 588.654
[[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 }}


Vals: {{Val list| 51f, 53 }}
{{Optimal ET sequence|legend=1| 94, 217, 528, 745, 1273, 2018b }}


Badness: 0.047441
[[Badness]] (Sintel): 66.9


=== Aufo ===
== Lockerbie ==
Subgroup: 2.3.5.7
: ''For extensions, see [[Breedsmic temperaments #Lockerbie]].''


[[Comma list]]: 6144/6125, 177147/175616
[[Subgroup]]: 2.3.5


[[Mapping]]: [{{Val|1 6 -7 19}}, {{Val|0 -9 19 -33}}]
[[Comma list]]: {{monzo| 91 51 -74 }}


{{Multival|legend=1|9 -19 33 -51 27 130}}
{{Mapping|legend=1| 1 -25 -16 | 0 74 51 }}
: mapping generators: ~2, ~{{monzo| 36 20 -29 }}


[[POTE generator]]: ~45/32 = 588.782
[[Optimal tuning]]s:
* [[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 }}


{{Val list|legend=1| 53, 161, 214 }}
{{Optimal ET sequence|legend=1| 103, 167, 270, 643, 913, 1183, 2636, 3819c, 5002c }}


[[Badness]]: 0.121428
[[Badness]] (Sintel): 72.4


==== 11-limit ====
== Rarity ==
Subgroup: 2.3.5.7.11
: ''For extensions, see [[No-sevens subgroup temperaments #Rarity]].''


Comma list: 121/120, 176/175, 177147/175616
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.


Mapping: [{{Val|1 6 -7 19 1}}, {{Val|0 -9 19 -33 5}}]
[[Subgroup]]: 2.3.5


POTE generator: ~45/32 = 588.811
[[Comma list]]: {{monzo| -57 17 13 }}


Vals: {{Val list| 53, 108e, 161e }}
{{Mapping|legend=1| 1 11 -10 | 0 -13 17 }}
: Mapping generators: ~2, ~16384/10125


Badness: 0.088631
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~16384/10125 = 869.392{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~16384/10125 = 869.402{{c}}


==== 13-limit ====
{{Optimal ET sequence|legend=1| 11, 29, 69, 98c }}
Subgroup: 2.3.5.7.11.13


Comma list: 121/120, 176/175, 351/350, 58806/57967
[[Badness]] (Sintel): 99.2


Mapping: [{{Val|1 6 -7 19 1 -12}}, {{Val|0 -9 19 -33 5 32}}]
== Jorgensen ==
: ''For extensions, see [[Hemifamity temperaments #Jorgensen]].''


POTE generator: ~45/32 = 588.788
[[Subgroup]]: 2.3.5


Vals: {{Val list| 53, 108e, 161e, 214ee }}
[[Comma list]]: {{monzo| 111 -70 }}


Badness: 0.058507
{{Mapping|legend=1| 70 111 0 | 0 0 1 }}
: mapping generators: ~{{monzo| 46 -29 }}, ~5


== Vinegar ==
[[Optimal tuning]]s:
Subgroup: 2.3.5
* [[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 }}


[[Comma]]: 16000000/14348907
{{Optimal ET sequence|legend=1| 70, 140, 350, 490 }}


[[Mapping]]: [{{Val|3 0 -5}}, {{Val|0 2 5}}]
[[Badness]] (Sintel): 203


[[POTE generator]]: ~10/9 = 156.861
== Elven ==
: ''For extensions, see [[Sensibeta temperaments #Elven]].''


{{Val list|legend=1| 15, 39c, 54, 69b, 84b }}
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.


[[Badness]]: 0.903002
[[Subgroup]]: 2.3.5


== Wronecki ==
[[Comma list]]: {{monzo| -23 -66 55 }}
Subgroup: 2.3.5


[[Comma]]: 531441/500000
{{Mapping|legend=1| 11 2 7 | 0 5 6 }}
: mapping generators: ~3125/2916, ~{{monzo| 10 29 -24 }}


[[Mapping]]: [{{Val|6 0 -5}}, {{Val|0 1 2}}]
[[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 }}


[[POTE generator]]: ~3/2 = 695.040
{{Optimal ET sequence|legend=1| 121, 253, 374, 627c }}


{{Val list|legend=1| 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bbc }}
[[Badness]] (Sintel): 429


[[Badness]]: 0.341757
== References ==


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