Miscellaneous 5-limit temperaments: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
the article's no longer called "high badness temperaments", so updated the header to reflect this
mNo edit summary
Line 1: Line 1:
{{Technical data page}}
{{Technical data page}}
Below are listed some 5-limit temperaments that do not belong to some other temperament collection, the majority of which are [[restriction]]s to the 5-limit of temperaments that emerge more fully in higher [[prime limit|limits]] or [[subgroup]]s; they are sorted by Smith [[TE logflat badness]], of which most have > 0.2. Most of these temperaments have low accuracy, high-complexity generators, or large number of generators for simple consonances. This is not an exhaustive list. Only expect to find a temperament here if you have not found it in:  
Below are listed some [[5-limit]] temperaments that do not belong to some other temperament collection, the majority of which are [[restriction]]s to the 5-limit of temperaments that emerge more fully in higher [[prime limit|limits]] or [[subgroup]]s; they are sorted by Smith [[TE logflat badness]], of which most have > 0.2. Most of these temperaments have low accuracy, high-complexity generators, or large number of generators for simple consonances. This is not an exhaustive list. Only expect to find a temperament here if you have not found it in:  
* Individual [[temperament families and clans]]
* Individual [[temperament families and clans]]
* Individual [[equivalence continuum|equivalence continua]]
* Individual [[equivalence continuum|equivalence continua]]

Revision as of 17:07, 16 April 2025

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 Smith TE logflat badness, of which most have > 0.2. Most of these temperaments have low accuracy, high-complexity generators, or large number of generators for simple consonances. This is not an exhaustive list. Only expect to find a temperament here if you have not found it in:

Lafayette

For extensions, see Mint temperaments #Progression.

Subgroup: 2.3.5

Comma list: 3456/3125

Mapping: [⟨1 1 2], ⟨0 5 3]]

Optimal tunings:

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

Optimal ET sequence: 8, 9, 17c

Badness: 0.200483

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:

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

Optimal ET sequence: 17, 19

Badness: 0.200600

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:

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

Optimal ET sequence: 37, 84, 205, 289, 494, 783, 2060, 2843, 3626

Badness: 0.213112

Mabila

For extensions, see Mabila family.

Subgroup: 2.3.5

Comma list: 268435456/263671875

Mapping: [⟨1 6 1], ⟨0 -10 3]]

Optimal tunings:

  • POTE: ~2 = 1200.000, ~512/375 = 529.685

Optimal ET sequence: 9, 25, 34, 77, 111, 145, 256c

Badness: 0.232481

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:

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

Optimal ET sequence: 8, 91, 99, 190, 289, 388, 677, 3674, 4351, 5028, 5705, 6382, 13441c, 19823bcc

Badness: 0.233376

Undim

See also: Undim family

Subgroup: 2.3.5

Comma list: 2199023255552/2179240250625

Mapping: [⟨4 6 11], ⟨0 1 -5]]

Optimal tunings:

  • POTE: ~300.000, ~3/2 = 702.605

Optimal ET sequence: 12, 140, 152, 164, 1076bc, 1228bc

Badness: 0.241703

Mynic

For extensions, see Starling temperaments #Myna.

Subgroup: 2.3.5

Comma list: 10077696/9765625

Mapping: [⟨1 9 9], ⟨0 -10 -9]]

Optimal tunings:

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

Optimal ET sequence: 27, 31, 58, 89, 325cc

Badness: 0.249965

Progress

For extensions, see Archytas clan #Progress.

Subgroup: 2.3.5

Comma list: 32768/30375

Mapping: [⟨1 0 5], ⟨0 3 -5]]

Optimal tunings:

  • POTE: ~2 = 1200.000, ~64/45 = 561.264

Optimal ET sequence: 2, 13, 15, 32c, 47bc, 62bc

Badness: 0.246073

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:

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

Optimal ET sequence: 46, 132, 178, 224, 270, 494, 1752, 2246, 2740, 4986, 7726b

Badness:

  • Smith: 0.255
  • Dirichlet: 5.970

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:

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

Optimal ET sequence: 80, 171, 593, 764, 935, 1106, 3489, 4595, 5701

Badness:

  • Smith: 0.264
  • Dirichlet: 6.185

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 sequence: 26, 73, 99, 224, 323, 547, 870

Badness:

  • Smith: 0.273
  • Dirichlet: 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:

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

Optimal ET sequence: 15, 88, 103, 118, 959, 1077

Badness: 0.283570

Kangaroo

For extensions, see Trienstonic clan #Parakangaroo.

Subgroup: 2.3.5

Comma list: 64000/59049

Mapping: [⟨1 0 -3], ⟨0 3 10]]

Optimal tunings:

  • POTE: ~2 = 1200.000, ~27/20 = 561.195

Optimal ET sequence: 15, 47b, 62b

Badness: 0.295767

Tertiaseptal

For extensions, see Breedsmic temperaments #Tertiaseptal.

Subgroup: 2.3.5

Comma list: 579357147216796875/576460752303423488

Mapping: [⟨1 3 2], ⟨0 -22 5]]

Optimal tunings:

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

Optimal ET sequence: 31, 109, 140, 171, 1679c, 1850c, 2021c, 2192c, 2363c, 2534c, 2705c, 2876c, 3047c

Badness: 0.297544

Gracecordial

For extensions, see Marvel temperaments #Gracecordial.

Subgroup: 2.3.5

Comma list: 17433922005/17179869184

Mapping: [⟨1 0 34], ⟨0 1 -20]]

Optimal tunings:

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

Optimal ET sequence: 12, 113, 125, 137

Badness: 0.306809

Untriton

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

Subgroup: 2.3.5

Comma list: 2270041927734375/2251799813685248

Mapping: [⟨1 6 -7], ⟨0 -9 19]]

Optimal tunings:

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

Optimal ET sequence: 51, 53, 267, 320, 373, 426, 479, 532, 2607bc

Badness: 0.307073

Counterhanson

For extensions, see Ragismic microtemperaments #Counterkleismic.

Subgroup: 2.3.5

Comma list: [-20 -24 25⟩ = 298023223876953125/296148833645101056

Mapping: [⟨1 -5 -4], ⟨0 25 24]]

Optimal tunings:

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

Optimal ET sequence: 19, 148, 167, 186, 205, 224, 429, 653, 1082, 1735c

Badness: 0.317551

Nessafof

For extensions, see Porwell temperaments #Nessafof.

Subgroup: 2.3.5

Comma list: 481469424205824/476837158203125

Mapping: [⟨3 2 5], ⟨0 7 5]]

Optimal tunings:

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

Optimal ET sequence: 15, 54b, 69, 84, 99, 183, 282, 465, 1212c, 1677cc

Badness:

  • Smith: 0.333
  • Dirichlet: 7.807

Lemba

For extensions, see Jubilismic clan #Lemba.

Subgroup: 2.3.5

Comma list: 140625/131072

Mapping: [⟨2 2 5], ⟨0 3 -1]]

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

Optimal tunings:

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

Optimal ET sequence: 10, 16, 26, 88cc

Badness:

  • Smith: 0.335
  • Dirichlet: 7.85

Wronecki

Subgroup: 2.3.5

Comma list: 531441/500000

Mapping: [⟨6 0 -5], ⟨0 1 2]]

Optimal tunings:

  • POTE: ~200.000, ~3/2 = 695.040

Optimal ET sequence: 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bbc

Badness: 0.341757

Delorean

For extensions, see Mint temperaments #Subklei.

Subgroup: 2.3.5

Comma list: 17496/15625

Mapping: [⟨1 3 4], ⟨0 -6 -7]]

Optimal tunings:

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

Optimal ET sequence: 4, 17c, 21, 38c

Badness: 0.355937

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:

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

Optimal ET sequence: 34, 115, 149, 183, 217, 400, 617

Badness: 0.356948

Beatles

For extensions, see Archytas clan #Beatles.

Subgroup: 2.3.5

Comma list: 524288/492075

Mapping: [⟨1 1 5], ⟨0 2 -9]]

Optimal tunings:

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

Optimal ET sequence: 10, 17c, 27, 64b, 91bc, 118bc

Badness: 0.358542

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:

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

Optimal ET sequence: 3, 40, 43, 46, 181c, 227c, 273c, 319c

Badness: 0.360162

Countermeantone

Subgroup: 2.3.5

Comma list: [10 23 -20⟩ = 96402615118848/95367431640625

Mapping: [⟨1 10 12], ⟨0 -20 -23]]

Optimal tunings:

  • POTE: ~2 = 1200.000, ~104976/78125 = 504.913

Optimal ET sequence: 19, 126, 145, 164, 183, 713, 896c, 1079c, 1262c

Badness: 0.373477

Tritonic

For extensions, see Marvel temperaments #Tritonic.

Subgroup: 2.3.5

Comma list: 553584375/536870912

Mapping: [⟨1 4 -3], ⟨0 -5 11]]

Optimal tunings:

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

Optimal ET sequence: 29, 31, 60, 91

Badness: 0.378527

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:

  • POTE: ~42875/32768 = 600.000, ~5/4 = 383.212

Optimal ET sequence: 22, 50, 72, 166, 238c, 310c, 548bc

Badness: 0.386367

Scales (Scala files): wizard22

Quindromeda

See also: Quindromeda family

Subgroup: 2.3.5

Comma list: 72057594037927936/71489976421753125

Mapping: [⟨1 2 0], ⟨0 -5 28]]

Optimal tunings:

  • POTE: ~2 = 1200.000, ~4428675/4194304 = 99.526

Optimal ET sequence: 12, 193, 205, 217, 422

Badness: 0.399849

Hogzilla

For extensions, see Semaphoresmic clan #Helayo.

Subgroup: 2.3.5

Comma list: 4428675/4194304

Mapping: [⟨1 0 11], ⟨0 2 -11]]

Optimal tunings:

  • POTE: ~2 = 1200.000, ~1215/1024 = 252.649

Optimal ET sequence: 14, 19

Badness: 0.424685

Quintaleap

See also: Quintaleap family

Subgroup: 2.3.5

Comma list: 137438953472/134521003125

Mapping: [⟨1 2 1], ⟨0 -5 16]]

Optimal tunings:

  • POTE: ~2 = 1200.000, ~135/128 = 99.267

Optimal ET sequence: 12, 109, 121, 133

Badness: 0.444506

Merman

For extensions, see Marvel temperaments #Merman.

Subgroup: 2.3.5

Comma list: 1121008359375/1099511627776

Mapping: [⟨1 5 -5], ⟨0 -7 15]]

Optimal tunings:

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

Optimal ET sequence: 41, 84, 125, 209, 334c, 543bc

Badness: 0.453848

Unsmate

Subgroup: 2.3.5

Comma list: 17578125/16777216

Mapping: [⟨1 3 2], ⟨0 -9 2]]

Optimal tunings:

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

Optimal ET sequence: 13, 19, 89c, 108c, 127c, 146cc

Badness: 0.460168

Nusecond

For extensions, see Starling temperaments #Nusecond.

Subgroup: 2.3.5

Comma list: 51018336/48828125

Mapping: [⟨1 3 4], ⟨0 -11 -13]]

Optimal tunings:

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

Optimal ET sequence: 8, 23, 31, 70, 101, 132c, 233c, 365bcc

Badness: 0.466493

Sfourth

For extensions, see Ragismic microtemperaments #Sfourth.

Subgroup: 2.3.5

Comma list: 617673396283947/610351562500000

Mapping: [⟨1 2 3], ⟨0 -19 -31]]

Optimal tunings:

  • POTE: ~2 = 1200.000, ~1594323/1562500 = 26.2342

Optimal ET sequence: 45, 46, 91, 137, 183

Badness: 0.504555

Thuja

For extensions, see Buzzardsmic clan #Thuja.

Subgroup: 2.3.5

Comma list: 254803968/244140625

Mapping: [⟨1 -4 0], ⟨0 12 5]]

Optimal tunings:

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

Optimal ET sequence: 15, 43, 58

Badness: 0.511109

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:

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

Optimal ET sequence: 29, 46, 121, 167, 455bc, 622bbc

Badness: 0.523182

Vines

For extensions, see Starling temperaments #Vines.

Subgroup: 2.3.5

Comma list: 156728328192/152587890625

Mapping: [⟨2 7 8], ⟨0 -8 -7]]

Optimal tunings:

  • POTE: ~600.000, ~6/5 = 312.713

Optimal ET sequence: 4, 42, 46, 96, 142

Badness: 0.541831

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:

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

Optimal ET sequence: 37, 50, 87, 137, 224

Badness: 0.544752

Misneb

For extensions, see Marvel temperaments #Misneb.

Subgroup: 2.3.5

Comma list: 145964630126953125/144115188075855872

Mapping: [⟨1 3 1], ⟨0 -15 14]]

Optimal tunings:

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

Optimal ET sequence: 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc

Badness: 0.609540

Semisept

For extensions, see Hemimean clan #Semisept.

Subgroup: 2.3.5

Comma list: 782757789696/762939453125

Mapping: [⟨1 12 6], ⟨0 -17 -6]]

Optimal tunings:

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

Optimal ET sequence: 18, 31, 80, 111

Badness: 0.630576

Mowgli

For extensions, see Hemimean clan #Mowglic.

Subgroup: 2.3.5

Comma list: [0 22 -15⟩ = 31381059609/30517578125

Mapping: [⟨1 0 0], ⟨0 15 22]]

Optimal tunings:

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

Optimal ET sequence: 19, 85c, 104c, 123, 142, 161

Badness: 0.653871

Septimin

For extensions, see Marvel temperaments #Septimin.

Subgroup: 2.3.5

Comma list: 35595703125/34359738368

Mapping: [⟨1 4 1], ⟨0 -11 6]]

Optimal tunings:

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

Optimal ET sequence: 9, 23b, 32, 41, 91, 132, 223c, 355bc

Badness: 0.670947

Slurpee

For extensions, see Mint temperaments #Slurpee.

Subgroup: 2.3.5

Comma list: 177147/156250

Mapping: [⟨1 2 3], ⟨0 -7 -11]]

Optimal tunings:

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

Optimal ET sequence: 16, 17c, 33

Badness: 0.689274

Pentadecal

For extensions, see Cloudy clan #Pentadecal.

Subgroup: 2.3.5

Comma list: 30517578125/29386561536

Mapping: [⟨15 0 11], ⟨0 1 1]]

Optimal tunings:

  • POTE: ~80.000, ~3/2 = 702.652

Optimal ET sequence: 15, 45, 60, 75, 135, 210c, 345cc

Badness: 0.692042

Sentinel

For extensions, see Orwellismic temperaments #Sentinel.

Subgroup: 2.3.5

Comma list: 8968066875/8589934592

Mapping: [⟨1 3 -3], ⟨0 -4 15]]

Optimal tunings:

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

Optimal ET sequence: 14, 17, 31, 79, 110, 361bc

Badness: 0.723413

Kumonga

For extensions, see Starling temperaments #Kumonga.

Subgroup: 2.3.5

Comma list: 1289945088/1220703125

Mapping: [⟨1 4 4], ⟨0 -13 -9]]

Optimal tunings:

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

Optimal ET sequence: 16, 27, 43, 70, 183cc

Badness: 0.729609

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 = 183.583
  • CWE: ~2000000/1594323 = 400.000, ~10/9 = 183.585

Optimal ET sequence: 33c, 39, 72, 111, 183, 438, 621, 1425b

Badness:

  • Smith: 0.752
  • Dirichlet: 17.631

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:

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

Optimal ET sequence: 8, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419

Badness: 0.754866

Slender

For extensions, see Marvel temperaments #Slender.

Subgroup: 2.3.5

Comma list: 72081298828125/70368744177664

Mapping: [⟨1 2 2], ⟨0 -13 10]]

Optimal tunings:

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

Optimal ET sequence: 31, 94, 125, 781bcc

Badness:

  • Smith: 0.761
  • Dirichlet: 17.842

Quasitemp

For extensions, see Keemic temperaments #Quasitemp.

Subgroup: 2.3.5

Comma list: 6103515625/5804752896

Mapping: [⟨1 5 5], ⟨0 -14 -11]]

Optimal tunings:

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

Optimal ET sequence: 4, 37, 41

Badness: 0.767824

Cypress

For extensions, see Starling temperaments #Cypress.

Subgroup: 2.3.5

Comma list: 258280326/244140625

Mapping: [⟨1 7 10], ⟨0 -12 -17]]

Optimal tunings:

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

Optimal ET sequence: 11c, 20c, 31, 113c, 144c, 175c, 381bcc

Badness: 0.816635

Chromo

For extensions, see Keemic temperaments #Chromo.

Subgroup: 2.3.5

Comma list: 1220703125/1146617856

Mapping: [⟨1 1 2], ⟨0 13 7]]

Optimal tunings:

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

Optimal ET sequence: 22, 45, 67c, 89c

Badness: 0.842835

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:

  • POTE: ~400.000, ~16/15 = 112.281

Optimal ET sequence: 21, 54, 75, 96, 171

Badness: 0.851003

Fervor

For extensions, see Archytas clan #Fervor.

Subgroup: 2.3.5

Comma list: 67108864/61509375

Mapping: [⟨1 4 -2], ⟨0 -5 9]]

Optimal tunings:

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

Optimal ET sequence: 2, 25, 27

Badness: 0.852612

Bohpier

For extensions, see Sensamagic clan #Bohpier.

Subgroup: 2.3.5

Comma list: 1220703125/1162261467

Mapping: [⟨1 0 0], ⟨0 13 19]]

Optimal tunings:

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

Optimal ET sequence: 8, 41, 131, 172, 213c

Badness: 0.860534

Elvis

For extensions, see Jubilismic clan #Elvis.

Subgroup: 2.3.5

Comma list: 36905625/33554432

Mapping: [⟨2 1 10], ⟨0 2 -5]]

Optimal tunings:

  • POTE: ~600.000, ~45/32 = 554.546

Optimal ET sequence: 26, 80bc, 106bc, 132bc

Badness: 0.884000

Vinegar

For extensions, see Starling temperaments #Vinegar.

Subgroup: 2.3.5

Comma list: 16000000/14348907

Mapping: [⟨3 0 -5], ⟨0 2 5]]

Optimal tunings:

  • POTE: ~400.000, ~10/9 = 156.861

Optimal ET sequence: 15, 39c, 54, 69b, 84b

Badness: 0.903002

Oolong

For extensions, see Starling temperaments #Oolong.

Subgroup: 2.3.5

Comma list: 793437161472/762939453125

Mapping: [⟨1 6 7], ⟨0 -17 -18]]

Optimal tunings:

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

Optimal ET sequence: 23, 27, 50, 77

Badness: 0.942789

Oncle

For extensions, see Gamelismic clan #Oncle.

Subgroup: 2.3.5

Comma list: 145282683375/137438953472

Mapping: [⟨1 1 6], ⟨0 3 -19]]

Optimal tunings:

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

Optimal ET sequence: 31, 98c, 129c, 160bc, 289bbcc

Badness: 1.244699

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, ~3662109375/2147483648 = 928.896
  • CWE: ~2 = 1200.000, ~3662109375/2147483648 = 928.893

Optimal ET sequence: 31, …, 177, 208, 239, 270, 841, 1111, 1381, 2492c

Badness:

  • Smith: 1.30
  • Dirichlet: 30.581

Diesic

For extensions, see Orwellismic temperaments #Diesic.

Subgroup: 2.3.5

Comma list: 10460353203/9765625000

Mapping: [⟨1 2 3], ⟨0 -13 -21]]

Optimal tunings:

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

Optimal ET sequence: 31, 156c, 187c, 218bc, 249bc, 280bc

Badness: 1.344681

Quartemka

For extensions, see Gamelismic clan #Quartemka.

Subgroup: 2.3.5

Comma list: 1907348632812500/1853020188851841

Mapping: [⟨1 4 6], ⟨0 -21 -32]]

Optimal tunings:

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

Optimal ET sequence: 26, 61, 87, 287, 374, 461

Badness: 1.381216

Genocchi

Subgroup: 2.3.5

Comma list: 2359296/1953125

Mapping: [⟨1 0 2], ⟨0 9 2]]

Optimal tunings:

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

Optimal ET sequence: 6b, 11b, 17c

Badness: 1.404977

Casablanca

For extensions, see Starling temperaments #Casablanca.

Subgroup: 2.3.5

Comma list: 20061226008576/19073486328125

Mapping: [⟨1 -7 -14], ⟨0 19 14]]

Optimal tunings:

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

Optimal ET sequence: 11b, 20b, 31, 73, 104c, 135c

Badness: 1.423736

Archaeotherium

For extensions, see Gamelismic clan #Archaeotherium.

Subgroup: 2.3.5

Comma list: 597871125/536870912

Mapping: [⟨1 1 5], ⟨0 3 -14]]

Optimal tunings:

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

Optimal ET sequence: 21, 26, 73bc, 99bc

Badness: 1.434855

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 = 1200.000, ~16/15 = 88.7331
  • CWE: ~2 = 1200.000, ~16/15 = 88.8168

Optimal ET sequence: 13, 14, 27

Badness: 1.75

Quasimoha

For extensions, see Breedsmic temperaments #Quasimoha.

Subgroup: 2.3.5

Comma list: 2353579470675/2199023255552

Mapping: [⟨1 1 9], ⟨0 2 -23]]

Optimal tunings:

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

Optimal ET sequence: 31, 117c, 148bc, 179bc

Badness: 1.986675

Phillips

For extensions, see Orwellismic temperaments #Phillips.

Subgroup: 2.3.5

Comma list: 9685512225/8589934592

Mapping: [⟨2 0 33], ⟨0 1 -9]]

Optimal tunings:

  • POTE: ~600.000, ~3/2 = 691.455

Optimal ET sequence: 14, 26, 66b, 92bc, 118bbc

Badness: 2.228904

Triskaidekic

For extensions, see Orwellismic temperaments #Triskaidekic.

Subgroup: 2.3.5

Comma list: 1220703125/1073741824

Mapping: [⟨13 0 30], ⟨0 1 0]]

Optimal tunings:

  • POTE: ~92.308, ~3/2 = 696.142

Optimal ET sequence: 13, 26, 91c

Badness: 2.241568

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:

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

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

Badness: 2.853049

Rarity

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

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

Subgroup: 2.3.5

Comma list: [-57 17 13⟩

Mapping: [⟨1 11 -10], ⟨0 -13 17]]

mapping generators: ~2, ~16384/10125

Optimal tunings:

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

Optimal ET sequence: 11, 29, 69, 98c

Badness: 4.229300

Retrieved from "https://en.xen.wiki/index.php?title=Miscellaneous_5-limit_temperaments&oldid=192479"