Miscellaneous 5-limit temperaments

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

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

Lafayette

For extensions, see Mint temperaments #Progression.

Subgroup: 2.3.5

Comma list: 3456/3125

Mapping[1 1 2], 0 5 3]]

Optimal tunings:

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

Optimal ET sequence8, 9, 17c

Badness (Sintel): 4.70

Stump

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

Subgroup: 2.3.5

Comma list: 273375/262144

Mapping[1 0 6], 0 3 -7]]

Optimal tunings:

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

Optimal ET sequence17, 19, 207bbccc

Badness (Sintel): 4.71

Dodifo

For extensions, see Porwell temperaments #Dodifo.

Subgroup: 2.3.5

Comma list: [-67 -9 35

Mapping[1 12 5], 0 -35 -9]]

Optimal tunings:

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

Optimal ET sequence37, 84, 205, 289, 494, 783, 2060, 2843, 3626

Badness (Sintel): 5.00

Shibboleth

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

Subgroup: 2.3.5

Comma list: 1953125/1889568

Mapping[1 4 5], 0 -9 -10]]

Optimal tunings:

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

Optimal ET sequence15, 26, 41, 179c

Badness (Sintel): 5.34

Semidimfourth

For extensions, see Ragismic microtemperaments #Semidimfourth.

Subgroup: 2.3.5

Comma list: [7 41 -31

Mapping[1 21 28], 0 -31 -41]]

Optimal tunings:

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

Optimal ET sequence8, …, 91, 99, 190, 289, 388, 677, 3674, 4351, 5028, 5705, 6382, 13441c, 19823bcc

Badness (Sintel): 5.47

Mynic

For extensions, see Starling temperaments #Myna.

Subgroup: 2.3.5

Comma list: 10077696/9765625

Mapping[1 9 9], 0 -10 -9]]

Optimal tunings:

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

Optimal ET sequence27, 31, 58, 89

Badness (Sintel): 5.86

Progress

For extensions, see Archytas clan #Progress.

Subgroup: 2.3.5

Comma list: 32768/30375

Mapping[1 0 5], 0 3 -5]]

Optimal tunings:

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

Optimal ET sequence2, 13, 15, 32c, 47bc, 62bc

Badness (Sintel): 5.77

Abigail

For extensions, see Ragismic microtemperaments #Abigail.

Subgroup: 2.3.5

Comma list: [25 -48 22

Mapping[2 7 13], 0 -11 -24]]

Optimal tunings:

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

Optimal ET sequence46, 132, 178, 224, 270, 494, 1752, 2246, 2740, 4986, 7726b

Badness (Sintel): 5.97

Supermajor

For extensions, see Ragismic microtemperaments #Supermajor.

Subgroup: 2.3.5

Comma list: [-13 -46 37

Mapping[1 15 19], 0 -37 -46]]

Optimal tunings:

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

Optimal ET sequence80, 171, 593, 764, 935, 1106, 3489, 4595, 5701

Badness (Sintel): 6.19

Gamera

For extensions, see Ragismic microtemperaments #Gamera.

Subgroup: 2.3.5

Comma list: 12207031250000000000/12157665459056928801

Mapping[1 6 10], 0 -23 -40]]

Optimal tunings:

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

Optimal ET sequence26, 73, 99, 224, 323, 547, 870

Badness (Sintel): 6.39

Tritriple

For extensions, see Gamelismic clan #Tritriple.

Subgroup: 2.3.5

Comma list: [31 20 -27

Mapping[1 -11 -7], 0 27 20]]

Optimal tunings:

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

Optimal ET sequence15, 88, 103, 118, 959, 1077

Badness (Sintel): 6.65

Kangaroo

For extensions, see Trienstonic clan #Parakangaroo.

Subgroup: 2.3.5

Comma list: 64000/59049

Mapping[1 0 -3], 0 3 10]]

Optimal tunings:

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

Optimal ET sequence15, 47b, 62b

Badness (Sintel): 6.94

Tertiaseptal

For extensions, see Breedsmic temperaments #Tertiaseptal.

Subgroup: 2.3.5

Comma list: [-59 5 22

Mapping[1 3 2], 0 -22 5]]

Optimal tunings:

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

Optimal ET sequence31, 109, 140, 171, 1679c, 1850c, 2021c, 2192c, 2363c, 2534c, 2705c, 2876c, 3047c

Badness (Sintel): 6.98

Gracecordial

For extensions, see Marvel temperaments #Gracecordial.

Subgroup: 2.3.5

Comma list: 17433922005/17179869184

Mapping[1 0 34], 0 1 -20]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~3/2 = 700.691
  • POTE: ~2 = 1200.000, ~3/2 = 700.734

Optimal ET sequence12, 113, 125, 137, 1221bbcc

Badness (Sintel): 7.20

Untriton

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

Subgroup: 2.3.5

Comma list: [-51 19 9

Mapping[1 6 -7], 0 -9 19]]

Optimal tunings:

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

Optimal ET sequence51, 53, 267, 320, 373, 426, 479, 532, 2607bc

Badness (Sintel): 7.20

Counterhanson

For extensions, see Ragismic microtemperaments #Counterkleismic.

Subgroup: 2.3.5

Comma list: [-20 -24 25

Mapping[1 -5 -4], 0 25 24]]

Optimal tunings:

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

Optimal ET sequence19, …, 148, 167, 186, 205, 224, 429, 653, 1082, 1735c

Badness (Sintel): 7.45

Nessafof

For extensions, see Porwell temperaments #Nessafof.

Subgroup: 2.3.5

Comma list: [25 15 -21

Mapping[3 2 5], 0 7 5]]

Optimal tunings:

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

Optimal ET sequence15, 54b, 69, 84, 99, 183, 282, 465, 1212c, 1677cc

Badness (Sintel): 7.81

Lemba

For extensions, see Jubilismic clan #Lemba.

Subgroup: 2.3.5

Comma list: 140625/131072

Mapping[2 2 5], 0 3 -1]]

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

Optimal tunings:

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

Optimal ET sequence10, 16, 26, 88cc

Badness (Sintel): 7.85

Wronecki

Subgroup: 2.3.5

Comma list: 531441/500000

Mapping[6 0 -5], 0 1 2]]

Optimal tunings:

  • CTE: ~10/9 = 200.000, ~3/2 = 696.229
  • POTE: ~10/9 = 200.000, ~3/2 = 695.040

Optimal ET sequence12, 66b, 78b, 90b, 102b

Badness (Sintel): 8.02

Delorean

For extensions, see Mint temperaments #Subklei.

Subgroup: 2.3.5

Comma list: 17496/15625

Mapping[1 3 4], 0 -6 -7]]

Optimal tunings:

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

Optimal ET sequence4, 13c, 17c, 21, 38c

Badness (Sintel): 8.35

Majvam

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

Subgroup: 2.3.5

Comma list: 2404631929946112/2384185791015625

Mapping[1 10 5], 0 -22 -7]]

Optimal tunings:

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

Optimal ET sequence34, 115, 149, 183, 217, 400, 617

Badness (Sintel): 8.37

Beatles

For extensions, see Archytas clan #Beatles.

Subgroup: 2.3.5

Comma list: 524288/492075

Mapping[1 1 5], 0 2 -9]]

Optimal tunings:

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

Optimal ET sequence10, 17c, 27, 64b, 91bc, 118bc

Badness (Sintel): 8.41

Magus

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

Subgroup: 2.3.5

Comma list: 50331648/48828125

Mapping[1 -2 2], 0 11 1]]

Optimal tunings:

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

Optimal ET sequence3, …, 40, 43, 46, 181c, 227c, 273c, 319c

Badness (Sintel): 8.45

Countermeantone

Subgroup: 2.3.5

Comma list: [10 23 -20

Mapping[1 -10 -11], 0 20 23]]

Optimal tunings:

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

Optimal ET sequence19, …, 126, 145, 164, 183, 713, 896c, 1079c, 1262c, 1445c

Badness (Sintel): 8.76

Tritonic

For extensions, see Marvel temperaments #Tritonic.

Subgroup: 2.3.5

Comma list: 553584375/536870912

Mapping[1 4 -3], 0 -5 11]]

Optimal tunings:

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

Optimal ET sequence29, 31, 60, 91

Badness (Sintel): 8.88

Wizard

For extensions, see Marvel temperaments #Wizard.

Subgroup: 2.3.5

Comma list: 2197265625/2147483648

Mapping[2 1 5], 0 6 -1]]

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

Optimal tunings:

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

Optimal ET sequence22, 50, 72, 166, 238c, 310c, 548bcc

Badness (Sintel): 9.06

Scales (Scala files): wizard22

Hogzilla

For extensions, see Semaphoresmic clan #Helayo.

Subgroup: 2.3.5

Comma list: 4428675/4194304

Mapping[1 0 11], 0 2 -11]]

Optimal tunings:

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

Optimal ET sequence14, 19

Badness (Sintel): 9.96

Merman

For extensions, see Marvel temperaments #Merman.

Subgroup: 2.3.5

Comma list: [-40 15 7

Mapping[1 5 -5], 0 -7 15]]

Optimal tunings:

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

Optimal ET sequence41, 84, 125, 209, 334c, 543bc

Badness (Sintel): 10.6

Unsmate

Subgroup: 2.3.5

Comma list: 17578125/16777216

Mapping[1 3 2], 0 -9 2]]

Optimal tunings:

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

Optimal ET sequence13, 19, 89c, 108c, 127c, 146cc

Badness (Sintel): 10.8

Nusecond

For extensions, see Starling temperaments #Nusecond.

Subgroup: 2.3.5

Comma list: 51018336/48828125

Mapping[1 3 4], 0 -11 -13]]

Optimal tunings:

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

Optimal ET sequence8, 23, 31, 70, 101, 132c

Badness (Sintel): 10.9

Sfourth

For extensions, see Ragismic microtemperaments #Sfourth.

Subgroup: 2.3.5

Comma list: [-5 31 -19

Mapping[1 2 3], 0 -19 -31]]

Optimal tunings:

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

Optimal ET sequence45, 46, 91, 137, 183, 869, 1052, 1235, 1418c

Badness (Sintel): 11.8

Thuja

For extensions, see Buzzardsmic clan #Thuja.

Subgroup: 2.3.5

Comma list: 254803968/244140625

Mapping[1 -4 0], 0 12 5]]

Optimal tunings:

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

Optimal ET sequence15, 43, 58

Badness (Sintel): 12.0

Leapday

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

Subgroup: 2.3.5

Comma list: 10737418240/10460353203

Mapping[1 0 -31], 0 1 21]]

Optimal tunings:

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

Optimal ET sequence17c, 29, 46, 121, 167, 455bc, 622bbc

Badness (Sintel): 12.3

Vines

For extensions, see Starling temperaments #Vines.

Subgroup: 2.3.5

Comma list: 156728328192/152587890625

Mapping[2 7 8], 0 -8 -7]]

Optimal tunings:

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

Optimal ET sequence4, …, 42, 46, 96, 142, 330c, 472cc

Badness (Sintel): 12.7

Emka

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

Subgroup: 2.3.5

Comma list: [-50 -8 27

Mapping[1 14 6], 0 -27 -8]]

Optimal tunings:

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

Optimal ET sequence37, 50, 87, 137, 224

Badness (Sintel): 12.8

Misneb

For extensions, see Marvel temperaments #Misneb.

Subgroup: 2.3.5

Comma list: [-57 14 15

Mapping[1 3 1], 0 -15 14]]

Optimal tunings:

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

Optimal ET sequence21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc

Badness (Sintel): 14.3

Semisept

For extensions, see Hemimean clan #Semisept.

Subgroup: 2.3.5

Comma list: 782757789696/762939453125

Mapping[1 12 6], 0 -17 -6]]

Optimal tunings:

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

Optimal ET sequence18, 31, 80, 111, 586cc, 697ccc

Badness (Sintel): 14.8

Mowgli

For extensions, see Hemimean clan #Mowglic.

Subgroup: 2.3.5

Comma list: 31381059609/30517578125

Mapping[1 0 0], 0 15 22]]

Optimal tunings:

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

Optimal ET sequence19, 85c, 104c, 123, 142, 161, 303

Badness (Sintel): 15.3

Septimin

For extensions, see Marvel temperaments #Septimin.

Subgroup: 2.3.5

Comma list: 35595703125/34359738368

Mapping[1 4 1], 0 -11 6]]

Optimal tunings:

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

Optimal ET sequence9, 23b, 32, 41, 91, 132, 223c, 355bcc

Badness (Sintel): 15.7

Slurpee

For extensions, see Mint temperaments #Slurpee.

Subgroup: 2.3.5

Comma list: 177147/156250

Mapping[1 2 3], 0 -7 -11]]

Optimal tunings:

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

Optimal ET sequence16, 17c, 33

Badness (Sintel): 16.2

Pentadecal

For extensions, see Cloudy clan #Pentadecal.

Subgroup: 2.3.5

Comma list: 30517578125/29386561536

Mapping[15 0 11], 0 1 1]]

Optimal tunings:

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

Optimal ET sequence15, 45, 60, 75, 135, 210c

Badness (Sintel): 16.2

Sentinel

For extensions, see Orwellismic temperaments #Sentinel.

Subgroup: 2.3.5

Comma list: 8968066875/8589934592

Mapping[1 3 -3], 0 -4 15]]

Optimal tunings:

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

Optimal ET sequence14, 17, 31, 79, 110, 361bbcc

Badness (Sintel): 17.0

Kumonga

For extensions, see Starling temperaments #Kumonga.

Subgroup: 2.3.5

Comma list: 1289945088/1220703125

Mapping[1 4 4], 0 -13 -9]]

Optimal tunings:

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

Optimal ET sequence16, 27, 43, 70, 183cc

Badness (Sintel): 17.1

Mirkat

For extensions, see Mirkwai clan #Mirkat.

Subgroup: 2.3.5

Comma list: [20 -39 18

Mapping[3 2 1], 0 6 13]]

Optimal tunings:

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

Optimal ET sequence33c, 39, 72, 111, 183, 438, 621, 1425b

Badness (Sintel): 17.6

Semidimi

For extensions, see Ragismic microtemperaments #Semidimi.

Subgroup: 2.3.5

Comma list: [-12 -73 55

Mapping[1 36 48], 0 -55 -73]]

Optimal tunings:

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

Optimal ET sequence8, …, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419

Badness (Sintel): 17.7

Slender

For extensions, see Marvel temperaments #Slender.

Subgroup: 2.3.5

Comma list: [-46 10 13

Mapping[1 2 2], 0 -13 10]]

Optimal tunings:

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

Optimal ET sequence31, 94, 125, 781bcc

Badness (Sintel): 17.8

Quasitemp

For extensions, see Keemic temperaments #Quasitemp.

Subgroup: 2.3.5

Comma list: 6103515625/5804752896

Mapping[1 5 5], 0 -14 -11]]

Optimal tunings:

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

Optimal ET sequence4, …, 37, 41

Badness (Sintel): 18.0

Cypress

For extensions, see Starling temperaments #Cypress.

Subgroup: 2.3.5

Comma list: 258280326/244140625

Mapping[1 7 10], 0 -12 -17]]

Optimal tunings:

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

Optimal ET sequence11c, 20c, 31, 113c, 144c, 175c

Badness (Sintel): 19.2

Chromo

For extensions, see Keemic temperaments #Chromo.

Subgroup: 2.3.5

Comma list: 1220703125/1146617856

Mapping[1 1 2], 0 13 7]]

Optimal tunings:

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

Optimal ET sequence22, 45, 67c, 89c

Badness (Sintel): 19.8

Tertiosec

For extensions, see Marvel temperaments #Tertiosec.

Subgroup: 2.3.5

Comma list: [-89 21 24

Mapping[3 7 5], 0 -8 7]]

Optimal tunings:

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

Optimal ET sequence21, 54, 75, 96, 171

Badness (Sintel): 20.0

Fervor

For extensions, see Archytas clan #Fervor.

Subgroup: 2.3.5

Comma list: 67108864/61509375

Mapping[1 4 -2], 0 -5 9]]

Optimal tunings:

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

Optimal ET sequence2, …, 25, 27

Badness (Sintel): 20.0

Bohpier

For extensions, see Sensamagic clan #Bohpier.

Subgroup: 2.3.5

Comma list: 1220703125/1162261467

Mapping[1 0 0], 0 13 19]]

Optimal tunings:

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

Optimal ET sequence8, …, 41, 131, 172, 213c

Badness (Sintel): 20.2

Elvis

For extensions, see Jubilismic clan #Elvis.

Subgroup: 2.3.5

Comma list: 36905625/33554432

Mapping[2 1 10], 0 2 -5]]

Optimal tunings:

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

Optimal ET sequence26, 80bc, 106bbcc, 132bbcc

Badness (Sintel): 20.7

Enneadecacot

Subgroup: 2.3.5

Comma list: [79 -22 -19

Mapping[1 1 3], 0 19 -22]]

Optimal tunings:

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

Optimal ET sequence32, 65, 292, 357, 422, 487, 1396c

Badness (Sintel): 20.9

Vinegar

For extensions, see Starling temperaments #Vinegar.

Subgroup: 2.3.5

Comma list: 16000000/14348907

Mapping[3 0 -5], 0 2 5]]

Optimal tunings:

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

Optimal ET sequence15, 39c, 54, 69b

Badness (Sintel): 21.2

Oolong

For extensions, see Starling temperaments #Oolong.

Subgroup: 2.3.5

Comma list: 793437161472/762939453125

Mapping[1 6 7], 0 -17 -18]]

Optimal tunings:

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

Optimal ET sequence23, 27, 50, 77

Badness (Sintel): 22.1

Oncle

For extensions, see Gamelismic clan #Oncle.

Subgroup: 2.3.5

Comma list: 145282683375/137438953472

Mapping[1 1 6], 0 3 -19]]

Optimal tunings:

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

Optimal ET sequence31, 98c, 129c, 160bc, 289bbcc

Badness (Sintel): 29.2

Quasiorwell

For extensions, see Breedsmic temperaments #Quasiorwell.

Subgroup: 2.3.5

Comma list: [-93 3 38

Mapping[1 31 0], 0 -38 3]]

Optimal tunings:

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

Optimal ET sequence31, …, 177, 208, 239, 270, 841, 1111, 1381, 2492c

Badness (Sintel): 30.6

Diesic

For extensions, see Orwellismic temperaments #Diesic.

Subgroup: 2.3.5

Comma list: 10460353203/9765625000

Mapping[1 2 3], 0 -13 -21]]

Optimal tunings:

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

Optimal ET sequence31, 156c

Badness (Sintel): 31.5

Quartemka

For extensions, see Gamelismic clan #Quartemka.

Subgroup: 2.3.5

Comma list: [2 -32 21

Mapping[1 4 6], 0 -21 -32]]

Optimal tunings:

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

Optimal ET sequence26, 61, 87, 287, 374, 461

Badness (Sintel): 32.4

Genocchi

Subgroup: 2.3.5

Comma list: 2359296/1953125

Mapping[1 0 2], 0 9 2]]

Optimal tunings:

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

Optimal ET sequence6b, 11b, 17c

Badness (Sintel): 33.0

Casablanca

For extensions, see Starling temperaments #Casablanca.

Subgroup: 2.3.5

Comma list: [22 14 -19

Mapping[1 -7 -14], 0 19 14]]

Optimal tunings:

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

Optimal ET sequence11b, 20b, 31, 73, 104c, 135c

Badness (Sintel): 33.4

Archaeotherium

For extensions, see Gamelismic clan #Archaeotherium.

Subgroup: 2.3.5

Comma list: 597871125/536870912

Mapping[1 1 5], 0 3 -14]]

Optimal tunings:

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

Optimal ET sequence21, 26, 73bc, 99bc

Badness (Sintel): 33.7

Octacoid

Subgroup: 2.3.5

Comma list: 8589934592/7688671875

Mapping[1 1 3], 0 8 -9]]

Mapping generators: ~2, ~16/15

Optimal tunings:

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

Optimal ET sequence13, 14, 27

Badness (Sintel): 41.1

Quasimoha

For extensions, see Breedsmic temperaments #Quasimoha.

Subgroup: 2.3.5

Comma list: [-41 23 2

Mapping[1 1 9], 0 2 -23]]

Optimal tunings:

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

Optimal ET sequence31, 117c, 148bc, 179bc

Badness (Sintel): 46.6

Phillips

For extensions, see Orwellismic temperaments #Phillips.

Subgroup: 2.3.5

Comma list: 9685512225/8589934592

Mapping[2 0 33], 0 1 -9]]

Optimal tunings:

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

Optimal ET sequence14, 26, 66b, 92bc, 118bbc

Badness (Sintel): 52.3

Triskaidekic

For extensions, see Orwellismic temperaments #Triskaidekic.

Subgroup: 2.3.5

Comma list: 1220703125/1073741824

Mapping[13 0 30], 0 1 0]]

Optimal tunings:

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

Optimal ET sequence13, 26, 91cc

Badness (Sintel): 52.6

Satin

For extensions, see Canousmic temperaments #Satin.

Subgroup: 2.3.5

Comma list: [104 -70 3

Mapping[1 2 12], 0 -3 -70]]

Optimal tunings:

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

Optimal ET sequence94, 217, 528, 745, 1273

Badness (Sintel): 66.9

Lockerbie

For extensions, see Breedsmic temperaments #Lockerbie.

Subgroup: 2.3.5

Comma list: [91 51 -74

Mapping[1 -25 -16], 0 74 51]]

mapping generators: ~2, ~[36 20 -29

Optimal tunings:

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

Optimal ET sequence103, 167, 270, 643, 913, 1183, 2636, 3819c, 5002c

Badness (Sintel): 72.4

Rarity

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

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

Subgroup: 2.3.5

Comma list: [-57 17 13

Mapping[1 11 -10], 0 -13 17]]

Mapping generators: ~2, ~16384/10125

Optimal tunings:

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

Optimal ET sequence11, 29, 69, 98c

Badness (Sintel): 99.2