Xenharmonic Wiki

Miscellaneous 5-limit temperaments: Difference between revisions

← Older edit
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,016 edits
No edit summary
→Satin: update
 
(116 intermediate revisions by 11 users not shown)
Line 1: Line 1:
Below are listed some high badness temperaments (Badness > 0.2).
{{Technical data page}}
Below are listed some [[5-limit]] [[regular temperament|temperament]]s that do not belong to some other temperament collection, the majority of which are [[restriction]]s to the 5-limit of temperaments that emerge more fully in higher [[prime limit|limits]] or [[subgroup]]s; they are sorted by [[TE logflat badness]], of which most have Sintel's > 4.7 (Smith's > 0.20). Most of these temperaments have low accuracy, high-complexity generators, or large number of generators for simple consonances. This is not an exhaustive list. Only expect to find a temperament here if you have not found it in:
* Individual [[temperament families and clans]]
* Individual [[equivalence continuum|equivalence continua]]
* [[Very low accuracy temperaments]]
* [[Very high accuracy temperaments]]


== Stump ==
== Unidecmic ==
: ''See also: [[Sensamagic clan #Pycnic]] and [[Marvel temperaments #Triton]]''
: ''For extensions, see [[Gamelismic clan #Unidec]].''


Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma]]: 273375/262144
[[Comma list]]: 31381059609/31250000000


[[Mapping]]: [{{Val|1 0 6}}, {{Val|0 3 -7}}]
{{Mapping|legend=1| 2 -1 -3 | 0 6 11 }}
: mapping generators: ~177147/125000, ~25000/19683


[[POTE generator]]: ~64/45 = 631.737
[[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 }}


{{Val list|legend=1| 17, 19 }}
{{Optimal ET sequence|legend=1| 26, 46, 72, 118, 2524, 2642, 2760 }}


[[Badness]]: 0.200600
[[Badness]] (Sintel): 1.93
 
== Quasithird ==
: ''For extensions, see [[Ragismic microtemperaments #Quasithird]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 55 -64 20 }}
 
{{Mapping|legend=1| 4 0 -11 | 0 5 16 }}
: mapping generators: ~51200000/43046721, ~1594323/1280000
 
[[Optimal tuning]]s:
* [[WE]]: ~51200000/43046721 = 299.9990{{c}}, ~1594323/1280000 = 380.3934{{c}}
: [[error map]]: {{val| -0.004 +0.012 -0.008 }}
* [[CWE]]: ~51200000/43046721 = 300.0000{{c}}, ~1594323/1280000 = 380.3944{{c}}
: error map: {{val| 0.000 +0.017 -0.004 }}
 
{{Optimal ET sequence|legend=1| 60, 104c, 164, 224, 388, 612, 1612, 2224, 2836, 6284, 9120, 15404 }}
 
[[Badness]] (Sintel): 2.33
 
== Supersharp ==
: ''For extensions, see [[Trienstonic clan #Octokaidecal]].''
 
Supersharp tempers out [[800/729]], the difference between the [[27/20]] wolf fourth and the [[40/27]] wolf fifth, splitting the octave into two 27/20~40/27 semioctaves. It generally requires a very sharp fifth, even sharper than 3\5, as a generator. This means that five steps from the [[generator sequence #JI scales obtained from guided generator sequences|Zarlino generator sequence]] starting with 6/5 are tempered to one and a half octaves. The only reasonable 7-limit extension adds 28/27 and 50/49 to the comma list, taking advantage of the existing semioctave.
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 800/729
 
{{Mapping|legend=1| 2 0 -5 | 0 1 3 }}
: mapping generators: ~27/20, ~3
 
[[Optimal tuning]]s:
* [[WE]]: ~27/20 = 596.986{{c}}, ~3/2 = 725.434{{c}} (~10/9 = 128.448{{c}})
: [[error map]]: {{val| -6.029 +17.450 -13.027 }}
* [[CWE]]: ~27/20 = 600.000{{c}}, ~3/2 = 726.548{{c}} (~10/9 = 126.548{{c}})
: error map: {{val| 0.000 +24.593 -6.670 }}
 
{{Optimal ET sequence|legend=1| 8, 10, 18, 28b }}
 
[[Badness]] (Sintel): 2.88
 
== Avila ==
: ''For extensions, see [[Septisemi temperaments #Avila]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 729/640
 
{{Mapping|legend=1| 1 0 -7 | 0 1 6 }}
: mapping generators: ~2, ~3
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1210.600{{c}}, ~3/2 = 667.437{{c}}
: [[error map]]: {{val| +10.600 -23.917 +7.711 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 663.474{{c}}
: error map: {{val| 0.000 -38.481 -5.472 }}
 
{{Optimal ET sequence|legend=1| 2c, 7c, 9, 20b, 29b }}
 
[[Badness]] (Sintel): 4.27
 
== Lafa ==
This temperament was named by [[Petr Pařízek]] in 2011, referring to the characteristic that stacking 12 generators makes 6/1 – "l" for 12, "f" for 6<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>. Its ploidacot is therefore beta-dodecacot.
 
[[Subgroup]]: 2.3.5
 
[[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
 
== 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
 
== 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 ==
== Untriton ==
: ''See also: [[Marvel temperaments #Untriton]] and [[Porwell temperaments #Aufo]]''
: ''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 }}


Subgroup: 2.3.5
[[Badness]] (Sintel): 7.20


[[Comma]]: 2270041927734375/2251799813685248
== Nessafof ==
: ''For extensions, see [[Porwell temperaments #Nessafof]].''


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


[[POTE generator]]: ~45/32 = 588.722
[[Comma list]]: {{monzo| 25 15 -21 }}


{{Val list|legend=1| 51, 53, 267, 320, 373, 426, 479, 532, 2607bc }}
{{Mapping|legend=1| 3 2 5 | 0 7 5 }}


[[Badness]]: 0.307073
[[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}}


== Wronecki ==
{{Optimal ET sequence|legend=1| 15, 54b, 69, 84, 99, 183, 282, 465, 1212c, 1677cc }}
Subgroup: 2.3.5


[[Comma]]: 531441/500000
[[Badness]] (Sintel): 7.81


[[Mapping]]: [{{Val|6 0 -5}}, {{Val|0 1 2}}]
== Lemba ==
: ''For extensions, see [[Jubilismic clan #Lemba]].''


[[POTE generator]]: ~3/2 = 695.040
[[Subgroup]]: 2.3.5


{{Val list|legend=1| 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bbc }}
[[Comma list]]: 140625/131072


[[Badness]]: 0.341757
{{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 }}
 
{{Optimal ET sequence|legend=1| 10, 16, 26, 88cc }}
 
[[Badness]] (Sintel): 7.85
 
== Delorean ==
: ''For extensions, see [[Mint temperaments #Subklei]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 17496/15625
 
{{Mapping|legend=1| 1 3 4 | 0 -6 -7 }}
 
[[Optimal tuning]]s:
* [[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, 13c, 17c, 21, 38c }}
 
[[Badness]] (Sintel): 8.35
 
== Majvam ==
: ''For extensions, see [[No-sevens subgroup temperaments #Majvam]], [[Cataharry temperaments #Majvamoid]], and [[Parkleiness temperaments #Majvamic]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 2404631929946112/2384185791015625
 
{{Mapping|legend=1| 1 10 5 | 0 -22 -7 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[Badness]] (Sintel): 8.37
 
== Beatles ==
: ''For extensions, see [[Archytas clan #Beatles]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 524288/492075
 
{{Mapping|legend=1| 1 1 5 | 0 2 -9 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[Badness]] (Sintel): 8.41
 
== Magus ==
: ''For extensions, see [[Sensamagic clan #Magus]] and [[Starling temperaments #Amigo]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 50331648/48828125
 
{{Mapping|legend=1| 1 -2 2 | 0 11 1 }}
 
[[Optimal tuning]]s:
* [[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]] (Sintel): 8.45


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


Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma]]: 553584375/536870912
[[Comma list]]: 553584375/536870912


[[Mapping]]: [{{Val| 1 4 -3 }}, {{Val| 0 -5 11 }}]
{{Mapping|legend=1| 1 4 -3 | 0 -5 11 }}


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


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


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


== Wizard ==
== Wizard ==
{{see also| Marvel temperaments #Wizard }}
: ''For extensions, see [[Marvel temperaments #Wizard]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 2197265625/2147483648
 
{{Mapping|legend=1| 2 1 5 | 0 6 -1 }}
: 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}}
 
{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 548bcc }}
 
[[Badness]] (Sintel): 9.06
 
Scales (Scala files): [[wizard22]]
 
== Merman ==
: ''For extensions, see [[Marvel temperaments #Merman]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{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
 
== Nusecond ==
: ''For extensions, see [[Starling temperaments #Nusecond]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 51018336/48828125
 
{{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 }}


Subgroup: 2.3.5
{{Mapping|legend=1| 1 2 3 | 0 -19 -31 }}


[[Comma]]: 2197265625/2147483648
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.0000{{c}}, ~1594323/1562500 = 26.2323{{c}}
* [[POTE]]: ~2 = 1200.0000{{c}}, ~1594323/1562500 = 26.2342{{c}}


[[Mapping]]: [{{Val| 2 1 5 }}, {{Val| 0 6 -1 }}]
{{Optimal ET sequence|legend=1| 45, 46, 91, 137, 183, 869, 1052, 1235, 1418c }}


Mapping generators: ~42875/32768, ~9375/8192
[[Badness]] (Sintel): 11.8


[[POTE generator]]: ~5/4 = 383.212
== Thuja ==
: ''For extensions, see [[Buzzardsmic clan #Thuja]].''
{{See also| Hypovishnuzma }}


{{Val list|legend=1| 22, 50, 72, 166, 238c, 310c, 548bc }}
[[Subgroup]]: 2.3.5


[[Badness]]: 0.386367
[[Comma list]]: 254803968/244140625


Scales (Scala files): [[wizard22]]
{{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
 
== Leapday ==
: ''For extensions, see [[Hemifamity temperaments #Leapday]] and [[Porwell temperaments #Polypyth]].''
 
[[Subgroup]]: 2.3.5


== Hogzilla ==
[[Comma list]]: 10737418240/10460353203
Subgroup: 2.3.5


[[Comma]]: 4428675/4194304
{{Mapping|legend=1| 1 0 -31 | 0 1 21 }}


[[Mapping]]: [{{Val|1 0 11}}, {{Val|0 2 -11}}]
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 704.100{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 704.179{{c}}


[[POTE generator]]: ~1215/1024 = 252.649
{{Optimal ET sequence|legend=1| 17c, 29, 46, 121, 167, 455bc, 622bbc }}


{{Val list|legend=1| 14, 19 }}
[[Badness]] (Sintel): 12.3


[[Badness]]: 0.424685
== Vines ==
: ''For extensions, see [[Starling temperaments #Vines]].''


== Merman ==
[[Subgroup]]: 2.3.5
{{see also| Marvel temperaments #Merman }}


Sugbroup: 2.3.5
[[Comma list]]: 156728328192/152587890625


[[Comma]]: 1121008359375/1099511627776
{{Mapping|legend=1| 2 7 8 | 0 -8 -7 }}


[[Mapping]]: [{{Val| 1 5 -5 }}, {{Val| 0 -7 15 }}]
[[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}}


[[POTE generator]]: ~45/32 = 585.634
{{Optimal ET sequence|legend=1| 4, …, 42, 46, 96, 142, 330c, 472cc }}


{{Val list|legend=1| 41, 84, 125, 209, 334c, 543bc }}
[[Badness]] (Sintel): 12.7


[[Badness]]: 0.453848
== Emka ==
: ''For extensions, see [[Hemimean clan #Emka]] and [[Horwell temperaments #Emkay]].''


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


[[Comma]]: 17578125/16777216
[[Comma list]]: {{monzo| -50 -8 27 }}


[[Mapping]]: [{{Val|1 3 2}}, {{Val|0 -9 2}}]
{{Mapping|legend=1| 1 14 6 | 0 -27 -8 }}


[[POTE generator]]: ~2048/1875 = 189.049
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~9765625/7077888 = 551.777{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~9765625/7077888 = 551.784{{c}}


{{Val list|legend=1| 13, 19, 89c, 108c, 127c, 146cc }}
{{Optimal ET sequence|legend=1| 37, 50, 87, 137, 224 }}


[[Badness]]: 0.460168
[[Badness]] (Sintel): 12.8


== Misneb ==
== Misneb ==
{{see also| Marvel temperaments #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}}


Subgroup: 2.3.5
{{Optimal ET sequence|legend=1| 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc }}


[[Comma]]: 145964630126953125/144115188075855872
[[Badness]] (Sintel): 14.3


[[Mapping]]: [{{Val|1 3 1}}, {{Val|0 -15 14}}]
== Semisept ==
: ''For extensions, see [[Hemimean clan #Semisept]].''


[[POTE generator]]: ~16/15 = 113.240
[[Subgroup]]: 2.3.5


{{Val list|legend=1| 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc }}
[[Comma list]]: 782757789696/762939453125


[[Badness]]: 0.609540
{{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
 
[[Comma list]]: 35595703125/34359738368
 
{{Mapping|legend=1| 1 4 1 | 0 -11 6 }}
 
[[Optimal tuning]]s:
* [[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, 355bcc }}
 
[[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 [[Cloudy clan #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 }}


Subgroup: 2.3.5
[[Badness]] (Sintel): 16.2


[[Comma]]: 35595703125/34359738368
== Anthoine ==
: ''For extensions, see [[Buzzardsmic clan #Anthoine]].''


[[Mapping]]: [{{Val| 1 4 1 }}, {{Val| 0 -11 6 }}]
[[Subgroup]]: 2.3.5


[[POTE generator]]: ~75/64 = 263.658
[[Comma list]]: 286102294921875/281474976710656


{{Val list|legend=1| 9, 23b, 32, 41, 91, 132, 223c, 355bc }}
{{Mapping|legend=1| 1 8 2 | 0 -20 1 }}


[[Badness]]: 0.670947
[[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 ==
{{see also| Orwellismic temperaments #Sentinel }}
: ''For extensions, see [[Orwellismic temperaments #Sentinel]].''


Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


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


[[Mapping]]: [{{val| 1 3 -3 }}, {{val| 0 -4 15 }}]
{{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
 
== Kumonga ==
: ''For extensions, see [[Starling temperaments #Kumonga]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 1289945088/1220703125
 
{{Mapping|legend=1| 1 4 4 | 0 -13 -9 }}
 
[[Optimal tuning]]s:  
* [[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 }}
 
[[Badness]] (Sintel): 17.1
 
== Mirkat ==
: ''For extensions, see [[Mirkwai clan #Mirkat]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 20 -39 18 }}
 
{{Mapping|legend=1| 3 2 1 | 0 6 13 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2000000/1594323 = 400.000{{c}}, ~10/9 = 183.593{{c}}
* [[CWE]]: ~2000000/1594323 = 400.000{{c}}, ~10/9 = 183.585{{c}}
 
{{Optimal ET sequence|legend=1| 33c, 39, 72, 111, 183, 438, 621, 1425b }}
 
[[Badness]] (Sintel): 17.6
 
== Semidimi ==
: ''For extensions, see [[Ragismic microtemperaments #Semidimi]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -12 -73 55 }}


[[POTE generator]]: ~512/405 = 425.474
{{Mapping|legend=1| 1 36 48 | 0 -55 -73 }}


{{Val list|legend=1| 14, 17, 31, 79, 110, 361bc }}
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~162/125 = 449.127{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~162/125 = 449.127{{c}}


[[Badness]]: 0.723413
{{Optimal ET sequence|legend=1| 8, …, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}


== Undeka ==
[[Badness]] (Sintel): 17.7
{{see also| Keemic temperaments #Undeka }}


Subgroup: 2.3.5
== Slender ==
: ''For extensions, see [[Marvel temperaments #Slender]].''


[[Comma]]: 48828125/45349632
[[Subgroup]]: 2.3.5


[[Mapping]]: [{{Val|11 0 8}}, {{Val|0 1 1}}]
[[Comma list]]: {{monzo| -46 10 13 }}


[[POTE generator]]: ~3/2 = 703.829
{{Mapping|legend=1| 1 2 2 | 0 -13 10 }}


{{Val list|legend=1| 22, 77c, 99c, 121c }}
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~16875/16384 = 38.380{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~16875/16384 = 38.400{{c}}


[[Badness]]: 0.727539
{{Optimal ET sequence|legend=1| 31, 94, 125, 781bcc }}
 
[[Badness]] (Sintel): 17.8


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


Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 6103515625/5804752896
[[Comma list]]: 6103515625/5804752896


[[Mapping]]: [{{val| 1 5 5 }}, {{val| 0 -14 -11 }}]
{{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 }}


[[POTE generator]]: ~3125/2592 = 292.702
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~4374/3125 = 541.735{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~4374/3125 = 541.726{{c}}


{{Val list|legend=1| 4, 37, 41 }}
{{Optimal ET sequence|legend=1| 11c, 20c, 31, 113c, 144c, 175c }}


[[Badness]]: 0.767824
[[Badness]] (Sintel): 19.2


== Chromo ==
== Chromo ==
{{see also| Keemic temperaments #Chromo }}
: ''For extensions, see [[Keemic temperaments #Chromo]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 1220703125/1146617856
 
{{Mapping|legend=1| 1 1 2 | 0 13 7 }}


Subgroup: 2.3.5
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~25/24 = 54.138{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~25/24 = 53.922{{c}}


[[Comma]]: 1220703125/1146617856
{{Optimal ET sequence|legend=1| 22, 45, 67c, 89c }}


[[Mapping]]: [{{Val|1 1 2}}, {{Val|0 13 7}}]
[[Badness]] (Sintel): 19.8


[[POTE generator]]: ~25/24 = 53.922
== Tertiosec ==
: ''For extensions, see [[Marvel temperaments #Tertiosec]].''


{{Val list|legend=1| 22, 45, 67c, 89c }}
[[Subgroup]]: 2.3.5


[[Badness]]: 0.842835
[[Comma list]]: {{monzo| -89 21 24 }}


== Diesic ==
{{Mapping|legend=1| 3 7 5 | 0 -8 7 }}
{{see also| Orwellismic temperaments #Diesic }}
 
[[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}}
 
{{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171 }}
 
[[Badness]] (Sintel): 20.0
 
== Fervor ==
: ''For extensions, see [[Archytas clan #Fervor]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 67108864/61509375
 
{{Mapping|legend=1| 1 4 -2 | 0 -5 9 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[Badness]] (Sintel): 20.0
 
== Bohpier ==
: ''For extensions, see [[Sensamagic clan #Bohpier]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 1220703125/1162261467
 
{{Mapping|legend=1| 1 0 0 | 0 13 19 }}
 
[[Optimal tuning]]s:
* [[CTE]] and [[POTE]]: ~2 = 1200.000{{c}}, ~27/25 = 146.476{{c}}
 
{{Optimal ET sequence|legend=1| 8, …, 41, 131, 172, 213c }}
 
[[Badness]] (Sintel): 20.2
 
== Elvis ==
: ''For extensions, see [[Jubilismic clan #Elvis]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 36905625/33554432
 
{{Mapping|legend=1| 2 1 10 | 0 2 -5 }}
 
[[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}}
 
{{Optimal ET sequence|legend=1| 26, 80bc, 106bbcc, 132bbcc }}
 
[[Badness]] (Sintel): 20.7


Subgroup: 2.3.5
== Enneadecacot ==
[[Subgroup]]: 2.3.5


[[Comma list]]: 10460353203/9765625000
[[Comma list]]: {{monzo| 79 -22 -19 }}


[[Mapping]]: [{{val| 1 2 3 }}, {{val| 0 -13 -21 }}]
{{Mapping|legend=1| 1 1 3 | 0 19 -22 }}


[[POTE generator]]: ~6561/6250 = 38.571
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.0000{{c}}, ~34171875/33554432 = 36.9607{{c}}
* [[POTE]]: ~2 = 1200.0000{{c}}, ~34171875/33554432 = 36.9622{{c}}


{{Val list|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}
{{Optimal ET sequence|legend=1| 32, 65, 292, 357, 422, 487, 1396c }}


[[Badness]]: 1.344681
[[Badness]] (Sintel): 20.9


== Vinegar ==
== Vinegar ==
Subgroup: 2.3.5
: ''For extensions, see [[Starling temperaments #Vinegar]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 16000000/14348907
 
{{Mapping|legend=1| 3 0 -5 | 0 2 5 }}
 
[[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}})
 
{{Optimal ET sequence|legend=1| 15, 39c, 54, 69b }}
 
[[Badness]] (Sintel): 21.2
 
== Oolong ==
: ''For extensions, see [[Starling temperaments #Oolong]].''


[[Comma]]: 16000000/14348907
[[Subgroup]]: 2.3.5


[[Mapping]]: [{{Val|3 0 -5}}, {{Val|0 2 5}}]
[[Comma list]]: 793437161472/762939453125


[[POTE generator]]: ~10/9 = 156.861
{{Mapping|legend=1| 1 6 7 | 0 -17 -18 }}


{{Val list|legend=1| 15, 39c, 54, 69b, 84b }}
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 311.726{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 311.694{{c}}


[[Badness]]: 0.903002
{{Optimal ET sequence|legend=1| 23, 27, 50, 77 }}
 
[[Badness]] (Sintel): 22.1


== Oncle ==
== Oncle ==
{{see also| Gamelismic clan #Oncle }}
: ''For extensions, see [[Gamelismic clan #Oncle]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 145282683375/137438953472
 
{{Mapping|legend=1| 1 1 6 | 0 3 -19 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[Badness]] (Sintel): 29.2
 
== Quasiorwell ==
: ''For extensions, see [[Breedsmic temperaments #Quasiorwell]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -93 3 38 }}


Subgroup: 2.3.5
{{Mapping|legend=1| 1 31 0 | 0 -38 3 }}


[[Comma]]: 145282683375/137438953472
[[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}}


[[Mapping]]: [{{Val|1 1 6}}, {{Val|0 3 -19}}]
{{Optimal ET sequence|legend=1| 31, …, 177, 208, 239, 270, 841, 1111, 1381, 2492c }}


[[POTE generator]]: ~4096/3645 = 232.521
[[Badness]] (Sintel): 30.6


{{Val list|legend=1| 31, 98c, 129c, 160bc, 289bbcc }}
== Diesic ==
: ''For extensions, see [[Orwellismic temperaments #Diesic]].''


[[Badness]]: 1.244699
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 10460353203/9765625000
 
{{Mapping|legend=1| 1 2 3 | 0 -13 -21 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[Badness]] (Sintel): 31.5
 
== Quartemka ==
: ''For extensions, see [[Gamelismic clan #Quartemka]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 2 -32 21 }}
 
{{Mapping|legend=1| 1 4 6 | 0 -21 -32 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[Badness]] (Sintel): 32.4


== Genocchi ==
== Genocchi ==
Subgroup: 2.3.5
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 2359296/1953125
 
{{Mapping|legend=1| 1 0 2 | 0 9 2 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[Badness]] (Sintel): 33.0
 
== Casablanca ==
: ''For extensions, see [[Starling temperaments #Casablanca]].''


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


[[Mapping]]: [{{Val|1 0 2}}, {{Val|0 9 2}}]
[[Comma list]]: {{monzo| 22 14 -19 }}


[[POTE generator]]: ~768/625 = 212.444
{{Mapping|legend=1| 1 -7 -14 | 0 19 14 }}


{{Val list|legend=1| 6b, 11b, 17c }}
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~864/625 = 542.142{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~864/625 = 542.208{{c}}


[[Badness]]: 1.404977
{{Optimal ET sequence|legend=1| 11b, 20b, 31, 73, 104c, 135c }}
 
[[Badness]] (Sintel): 33.4


== Archaeotherium ==
== Archaeotherium ==
{{see also| Gamelismic clan #Archaeotherium }}
: ''For extensions, see [[Gamelismic clan #Archaeotherium]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 597871125/536870912


Subgroup: 2.3.5
{{Mapping|legend=1| 1 1 5 | 0 3 -14 }}


[[Comma]]: 597871125/536870912
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~1215/1024 = 229.947{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~1215/1024 = 230.351{{c}}


[[Mapping]]: [{{Val|1 1 5}}, {{Val|0 3 -14}}]
{{Optimal ET sequence|legend=1| 21, 26, 73bc, 99bc }}


[[POTE generator]]: ~1215/1024 = 230.351
[[Badness]] (Sintel): 33.7


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


[[Badness]]: 1.434855
[[Comma list]]: 8589934592/7688671875
 
{{Mapping|legend=1| 1 1 3 | 0 8 -9 }}
 
: Mapping generators: ~2, ~16/15
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.0000{{c}}, ~16/15 = 88.7331{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 88.8168{{c}}
 
{{Optimal ET sequence|legend=1| 13, 14, 27 }}
 
[[Badness]] (Sintel): 41.1


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


Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


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


[[Mapping]]: [{{Val|1 1 9}}, {{Val|0 2 -23}}]
{{Mapping|legend=1| 1 1 9 | 0 2 -23 }}


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


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


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


== Phillips ==
== Phillips ==
{{see also| Orwellismic temperaments #Phillips }}
: ''For extensions, see [[Orwellismic temperaments #Phillips]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 9685512225/8589934592
 
{{Mapping|legend=1| 2 0 33 | 0 1 -9 }}
 
[[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}}
 
{{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc, 118bbc }}
 
[[Badness]] (Sintel): 52.3
 
== Satin ==
: ''For extensions, see [[Garischismic clan #Satin]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 104 -70 3 }}
 
{{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:
* [[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| 103, 167, 270, 643, 913, 1183, 2636, 3819c, 5002c }}
 
[[Badness]] (Sintel): 72.4
 
== Rarity ==
: ''For extensions, see [[No-sevens subgroup temperaments #Rarity]].''
 
The rarity temperament is notable due to the fact that it offers a [[7L 4s]] scale of reasonable hardness, in the 5-limit and among relatively small edos.
 
[[Subgroup]]: 2.3.5


Subgroup: 2.3.5
[[Comma list]]: {{monzo| -57 17 13 }}


[[Comma]]: 9685512225/8589934592
{{Mapping|legend=1| 1 11 -10 | 0 -13 17 }}
: Mapping generators: ~2, ~16384/10125


[[Mapping]]: [{{Val|2 0 33}}, {{Val|0 1 -9}}]
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~16384/10125 = 869.392{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~16384/10125 = 869.402{{c}}


[[POTE generator]]: ~3/2 = 691.455
{{Optimal ET sequence|legend=1| 11, 29, 69, 98c }}


{{Val list|legend=1| 14, 26, 66b, 92bc, 118bbc }}
[[Badness]] (Sintel): 99.2


[[Badness]]: 2.228904
== Jorgensen ==
: ''For extensions, see [[Hemifamity temperaments #Jorgensen]].''


== Triskaidekic ==
[[Subgroup]]: 2.3.5
{{see also| Orwellismic temperaments #Triskaidekic }}


Subgroup: 2.3.5
[[Comma list]]: {{monzo| 111 -70 }}


[[Comma]]: 1220703125/1073741824
{{Mapping|legend=1| 70 111 0 | 0 0 1 }}
: mapping generators: ~{{monzo| 46 -29 }}, ~5


[[Mapping]]: [{{Val|13 0 30}}, {{Val|0 1 0}}]
[[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 }}


[[POTE generator]]: ~3/2 = 696.142
{{Optimal ET sequence|legend=1| 70, 140, 350, 490 }}


{{Val list|legend=1| 13, 26, 91c }}
[[Badness]] (Sintel): 203


[[Badness]]: 2.241568
== References ==


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