Xenharmonic Wiki

Jubilismic clan

Revision as of 14:16, 21 July 2025 by FloraC (talk | contribs) (- CTE & POTE tunings)
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.

The jubilismic clan tempers out the jubilisma, 50/49, which means 7/5 and 10/7 are both equated to the 600-cent tritone and the octave is divided in two.

Jubilic

The head of this clan, jubilic, is generated by ~5/4. That and a semioctave give ~7/4.

Subgroup: 2.5.7

Comma list: 50/49

Sval mapping: [⟨2 0 1], ⟨0 1 1]]

sval mapping generators: ~7/5, ~5

Gencom mapping: [⟨2 0 0 1], ⟨0 0 1 1]]

Optimal tunings:

  • WE: ~7/5 = 599.6673 ¢, ~5/4 = 380.6287 ¢ (~8/7 = 219.0386 ¢)
error map: ⟨-0.665 -7.016 +10.139]
  • CWE: ~7/5 = 600.0000 ¢, ~5/4 = 380.0086 ¢ (~8/7 = 219.9914 ¢)
error map: ⟨0.000 -6.305 +11.183]

Optimal ET sequence: 2, 4, 6, 16, 22, 60d

Badness (Sintel): 0.140

Overview to extensions

Lemba finds the perfect fifth three steps away by tempering out 1029/1024. Astrology, five steps away by tempering out 3125/3072. Decimal, two steps away by tempering out 25/24 and 49/48. Walid merges ~5/4 and ~4/3 by tempering out 16/15.

Diminished adds 36/35 and splits the ~7/5 period in a further two. Pajara adds 64/63 and slices the ~7/4 in two, with antikythera being every other step thereof. Dubbla adds 78125/73728 and slices the ~5/4 in two. Injera adds 81/80 and slices the ~5/1 in four. Octokaidecal adds 28/27. Bipelog adds 135/128. Those splits the generator into three in various ways. Hexe adds 128/125 and slices the period in three. Hedgehog adds 250/243. Elvis adds 8505/8192. Those slice the generator in five. Comic adds 2240/2187. Crepuscular adds 4375/4374. Those slice the generator in seven. Byhearted adds 19683/19208. Bipyth adds 20480/19683. Those slice the generator in nine.

Temperaments discussed elsewhere are:

Considered below are lemba, astrology, walid, antikythera, doublewide, elvis, comic, and bipyth.

Lemba

Main article: Lemba
For the 5-limit version, see Miscellaneous 5-limit temperaments #Lemba.

Lemba tempers out 1029/1024, the gamelisma, and a stack of three ~8/7 generators gives an approximate perfect fifth.

Subgroup: 2.3.5.7

Comma list: 50/49, 525/512

Mapping: [⟨2 2 5 6], ⟨0 3 -1 -1]]

mapping generators: ~7/5, ~8/7

Optimal tunings:

  • WE: ~7/5 = 601.4623 ¢, ~8/7 = 232.6544 ¢
error map: ⟨+2.925 -1.067 -11.656 +7.294]
  • CWE: ~7/5 = 600.0000 ¢, ~8/7 = 232.2655 ¢
error map: ⟨0.000 -5.158 -18.579 -1.091]

Optimal ET sequence: 10, 16, 26, 36c, 62c

Badness (Sintel): 1.57

11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 50/49, 385/384

Mapping: [⟨2 2 5 6 5], ⟨0 3 -1 -1 5]]

Optimal tunings:

  • WE: ~7/5 = 601.1769 ¢, ~8/7 = 231.4273 ¢
  • CWE: ~7/5 = 600.0000 ¢, ~8/7 = 231.1781 ¢

Optimal ET sequence: 10, 16, 26

Badness (Sintel): 1.37

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 50/49, 65/64, 78/77

Mapping: [⟨2 2 5 6 5 7], ⟨0 3 -1 -1 5 1]]

Optimal tunings:

  • WE: ~7/5 = 601.1939 ¢, ~8/7 = 231.4261 ¢
  • CWE: ~7/5 = 600.0000 ¢, ~8/7 = 231.1617 ¢

Optimal ET sequence: 10, 16, 26

Badness (Sintel): 1.05

Astrology

Astrology tempers out 3125/3072, the magic comma, and a stack of five ~5/4 generators gives an approximate harmonic 3.

Subgroup: 2.3.5.7

Comma list: 50/49, 3125/3072

Mapping: [⟨2 0 4 5], ⟨0 5 1 1]]

mapping geenerators: ~7/5, ~5/4

Optimal tunings:

  • WE: ~7/5 = 599.6999 ¢, ~5/4 = 380.3881 ¢ (~8/7 = 219.3119 ¢)
error map: ⟨-0.600 -0.015 -7.126 +10.062]
  • CWE: ~7/5 = 600.0000 ¢, ~5/4 = 380.5123 ¢ (~8/7 = 219.4877 ¢)
error map: ⟨0.000 +0.606 -5.801 +11.686]

Optimal ET sequence: 6, 16, 22, 60d

Badness (Sintel): 2.09

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 121/120, 176/175

Mapping: [⟨2 0 4 5 5], ⟨0 5 1 1 3]]

Optimal tunings:

  • WE: ~7/5 = 600.0538 ¢, ~5/4 = 380.5640 ¢ (~8/7 = 219.4897 ¢)
  • CWE: ~7/5 = 600.0000 ¢, ~5/4 = 380.5419 ¢ (~8/7 = 219.4581 ¢)

Optimal ET sequence: 6, 16, 22

Badness (Sintel): 1.29

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 65/64, 78/77, 121/120

Mapping: [⟨2 0 4 5 5 8], ⟨0 5 1 1 3 -1]]

Optimal tunings:

  • WE: ~7/5 = 600.7886 ¢, ~5/4 = 380.2857 ¢ (~8/7 = 220.5028 ¢)
  • CWE: ~7/5 = 600.0000 ¢, ~5/4 = 379.9119 ¢ (~8/7 = 220.0881 ¢)

Optimal ET sequence: 6, 16, 22, 38f

Badness (Sintel): 1.42

Music

Horoscope

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 66/65, 105/104, 121/120

Mapping: [⟨2 0 4 5 5 3], ⟨0 5 1 1 3 7]]

Optimal tunings:

  • WE: ~7/5 = 599.8927 ¢, ~5/4 = 379.7688 ¢ (~8/7 = 220.1239 ¢)
  • CWE: ~7/5 = 600.0000 ¢, ~5/4 = 379.8117 ¢ (~8/7 = 220.1883 ¢)

Optimal ET sequence: 6f, 16, 22f, 38

Badness (Sintel): 1.46

Walid

Subgroup: 2.3.5.7

Comma list: 16/15, 50/49

Mapping: [⟨2 0 8 9], ⟨0 1 -1 -1]]

mapping generators: ~7/5, ~3

Optimal tunings:

  • WE: ~7/5 = 589.0384 ¢, ~3/2 = 735.7242 ¢ (~15/14 = 146.6857 ¢)
error map: ⟨-21.923 +11.846 +12.193 +18.719]
  • CWE: ~7/5 = 600.0000 ¢, ~3/2 = 750.4026 ¢ (~15/14 = 150.4026 ¢)
error map: ⟨0.000 +48.448 +63.284 +80.771]

Optimal ET sequence: 2, 6, 8d

Badness (Sintel): 1.24

11-limit

Subgroup: 2.3.5.7.11

Comma list: 16/15, 22/21, 50/49

Mapping: [⟨2 0 8 9 7], ⟨0 1 -1 -1 0]]

Optimal tunings:

  • WE: ~7/5 = 589.7684 ¢, ~3/2 = 736.9708 ¢ (~12/11 = 147.2023 ¢)
  • CWE: ~7/5 = 600.0000 ¢, ~3/2 = 750.5221 ¢ (~12/11 = 150.5221 ¢)

Optimal ET sequence: 2, 6, 8d

Badness (Sintel): 0.965

Antikythera

Named by Gene Ward Smith in 2011[1], antikythera is every other step of pajara.

Subgroup: 2.9.5.7

Comma list: 50/49, 64/63

Sval mapping: [⟨2 0 11 12], ⟨0 1 -1 -1]]

mapping generators: ~7/5, ~9

Gencom mapping: [⟨2 3 5 6], ⟨0 1/2 -1 -1]]

gencom: [7/5 8/7; 50/49 64/63]

Optimal tunings:

  • WE: ~7/5 = 598.8483 ¢, ~9/8 = 213.6844 ¢
error map: ⟨-2.303 +2.864 -5.756 +10.580]
  • CWE: ~7/5 = 600.0000 ¢, ~9/8 = 214.6875 ¢
error map: ⟨0.000 +10.778 -1.001 +16.487]

Optimal ET sequence: 2, 4, 6, 16, 22, 28

RMS error: 2.572 cents

Badness (Sintel): 0.253

Doublewide

For the 5-limit version, see Superpyth–22 equivalence continuum #Doublewide (5-limit).

Subgroup: 2.3.5.7

Comma list: 50/49, 875/864

Mapping: [⟨2 1 3 4], ⟨0 4 3 3]]

mapping generators: ~7/5, ~6/5

Optimal tunings:

  • WE: ~7/5 = 600.0365 ¢, ~6/5 = 325.7389 ¢ (~7/6 = 274.2975 ¢)
error map: ⟨-2.303 +2.864 -5.756 +10.580]
  • CWE: ~7/5 = 600.0000 ¢, ~6/5 = 325.7353 ¢ (~7/6 = 274.2647 ¢)
error map: ⟨0.000 +10.778 -1.001 +16.487]

Optimal ET sequence: 4, 14bd, 18, 22, 48

Badness (Sintel): 1.10

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 99/98, 875/864

Mapping: [⟨2 1 3 4 8], ⟨0 4 3 3 -2]]

Optimal tunings:

  • WE: ~7/5 = 600.1818 ¢, ~6/5 = 325.6434 ¢ (~7/6 = 274.5384 ¢)
  • CWE: ~7/5 = 600.0000 ¢, ~6/5 = 325.5854 ¢ (~7/6 = 274.4146 ¢)

Optimal ET sequence: 4, 18, 22, 48

Badness (Sintel): 1.06

Fleetwood

Subgroup: 2.3.5.7.11

Comma list: 50/49, 55/54, 176/175

Mapping: [⟨2 1 3 4 2], ⟨0 4 3 3 9]]

Optimal tunings:

  • WE: ~7/5 = 599.6049 ¢, ~6/5 = 326.8229 ¢ (~7/6 = 272.7819 ¢)
  • CWE: ~7/5 = 600.0000 ¢, ~6/5 = 326.8890 ¢ (~7/6 = 273.1110 ¢)

Optimal ET sequence: 4e, …, 18e, 22

Badness (Sintel): 1.16

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 55/54, 65/63, 176/175

Mapping: [⟨2 1 3 4 2 3], ⟨0 4 3 3 9 8]]

Optimal tunings:

  • WE: ~7/5 = 599.5482 ¢, ~6/5 = 327.5939 ¢ (~7/6 = 271.9543 ¢)
  • CWE: ~7/5 = 600.0000 ¢, ~6/5 = 327.6706 ¢ (~7/6 = 272.3294 ¢)

Optimal ET sequence: 4ef, …, 18e, 22

Badness (Sintel): 1.32

Cavalier

Subgroup: 2.3.5.7.11

Comma list: 45/44, 50/49, 875/864

Mapping: [⟨2 1 3 4 1], ⟨0 4 3 3 11]]

Optimal tunings:

  • WE: ~7/5 = 600.9467 ¢, ~6/5 = 323.9369 ¢ (~7/6 = 277.0098 ¢)
  • CWE: ~7/5 = 600.0000 ¢, ~6/5 = 323.7272 ¢ (~7/6 = 276.2728 ¢)

Optimal ET sequence: 4e, 22e, 26

Badness (Sintel): 1.75

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 50/49, 78/77, 325/324

Mapping: [⟨2 1 3 4 1 2], ⟨0 4 3 3 11 10]]

Optimal tunings:

  • WE: ~7/5 = 600.9537 ¢, ~6/5 = 323.9097 ¢ (~7/6 = 277.0440 ¢)
  • CWE: ~7/5 = 600.0000 ¢, ~6/5 = 323.6876 ¢ (~7/6 = 276.3124 ¢)

Optimal ET sequence: 4ef, 22ef, 26

Badness (Sintel): 1.45

Elvis

For the 5-limit version, see Miscellaneous 5-limit temperaments #Elvis.

Subgroup: 2.3.5.7

Comma list: 50/49, 8505/8192

Mapping: [⟨2 1 10 11], ⟨0 2 -5 -5]]

mapping generators: ~7/5, ~64/45

Optimal tunings:

  • WE: ~7/5 = 601.6846 ¢, ~64/45 = 648.0937 ¢ (~64/63 = 46.4091 ¢)
error map: ⟨+3.369 -4.083 -9.936 +9.236]
  • CWE: ~7/5 = 600.0000 ¢, ~64/45 = 646.0539 ¢ (~64/63 = 46.0539 ¢)
error map: ⟨0.000 -9.847 -16.583 +0.904]

Optimal ET sequence: 2, 24c, 26

Badness (Sintel): 3.58

11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 50/49, 1344/1331

Mapping: [⟨2 1 10 11 8], ⟨0 2 -5 -5 -1]]

Optimal tunings:

  • WE: ~7/5 = 601.2186 ¢, ~16/11 = 647.4300 ¢ (~56/55 = 46.2114 ¢)
  • CWE: ~7/5 = 600.0000 ¢, ~16/11 = 645.9681 ¢ (~56/55 = 45.9681 ¢)

Optimal ET sequence: 2, 24c, 26

Badness (Sintel): 2.09

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 50/49, 78/77, 1053/1024

Mapping: [⟨2 1 10 11 8 16], ⟨0 2 -5 -5 -1 -8]]

Optimal tunings:

  • WE: ~7/5 = 601.2206 ¢, ~16/11 = 647.4219 ¢ (~56/55 = 46.2013 ¢)
  • CWE: ~7/5 = 600.0000 ¢, ~16/11 = 645.9362 ¢ (~56/55 = 45.9362 ¢)

Optimal ET sequence: 2f, 24cf, 26

Badness (Sintel): 1.82

Comic

For the 5-limit version, see Superpyth–22 equivalence continuum #Comic (5-limit).

Subgroup: 2.3.5.7

Comma list: 50/49, 2240/2187

Mapping: [⟨2 1 -3 -2], ⟨0 2 7 7]]

mapping generators: ~7/5, ~40/27

Optimal tunings:

  • WE: ~7/5 = 598.9554 ¢, ~40/27 = 653.5596 ¢ (~28/27 = 54.6042 ¢)
error map: ⟨+3.369 -4.083 -9.936 +9.236]
  • CWE: ~7/5 = 600.0000 ¢, ~40/27 = 654.3329 ¢ (~28/27 = 54.3329 ¢)
error map: ⟨0.000 -9.847 -16.583 +0.904]

Optimal ET sequence: 2cd, …, 20cd, 22

Badness (Sintel): 2.14

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 99/98, 2662/2625

Mapping: [⟨2 1 -3 -2 -4], ⟨0 2 7 7 10]]

Optimal tunings:

  • WE: ~7/5 = 598.8161 ¢, ~22/15 = 653.8909 ¢ (~28/27 = 55.0747 ¢)
  • CWE: ~7/5 = 600.0000 ¢, ~22/15 = 654.7898 ¢ (~28/27 = 54.7898 ¢)

Optimal ET sequence: 2cde, …, 20cde, 22

Badness (Sintel): 1.49

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 65/63, 99/98, 968/945

Mapping: [⟨2 1 -3 -2 -4 3], ⟨0 2 7 7 10 4]]

Optimal tunings:

  • WE: ~7/5 = 600.1030 ¢, ~22/15 = 654.5470 ¢ (~28/27 = 54.4440 ¢)
  • CWE: ~7/5 = 600.0000 ¢, ~22/15 = 654.4665 ¢ (~28/27 = 54.4665 ¢)

Optimal ET sequence: 2cde, 20cde, 22

Badness (Sintel): 1.71

Bipyth

For the 5-limit version, see Syntonic–diatonic equivalence continuum #Superpyth (5-limit).

Subgroup: 2.3.5.7

Comma list: 50/49, 20480/19683

Mapping: [⟨2 0 -24 -23], ⟨0 1 9 9]]

mapping generators: ~7/5, ~3

Optimal tunings:

  • WE: ~7/5 = 598.7533 ¢, ~3/2 = 707.9630 ¢ (~15/14 = 109.2098 ¢)
error map: ⟨+3.369 -4.083 -9.936 +9.236]
  • CWE: ~7/5 = 600.0000 ¢, ~3/2 = 709.1579 ¢ (~15/14 = 109.1579 ¢)
error map: ⟨0.000 -9.847 -16.583 +0.904]

Optimal ET sequence: 10cd, 12cd, 22

Badness (Sintel): 4.18

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 121/120, 896/891

Mapping: [⟨2 0 -24 -23 -9], ⟨0 1 9 9 5]]

Optimal tunings:

  • WE: ~7/5 = 599.2296 ¢, ~3/2 = 708.3992 ¢ (~15/14 = 109.1697 ¢)
  • CWE: ~7/5 = 600.0000 ¢, ~3/2 = 709.1395 ¢ (~15/14 = 109.1395 ¢)

Optimal ET sequence: 10cd, 12cde, 22

Badness (Sintel): 2.34

Sedecic

Subgroup: 2.3.5.7

Comma list: 50/49, 546875/524288

Mapping: [⟨16 0 37 45], ⟨0 1 0 0]]

Optimal tunings:

  • WE: ~128/125 = 75.0539 ¢, ~3/2 = 701.0578 ¢ (~525/512 = 25.5726 ¢)
error map: ⟨0.000 0.000 -11.314 +6.174]
  • CWE: ~128/125 = 75.0000 ¢, ~3/2 = 700.8957 ¢ (~525/512 = 25.8957 ¢)
error map: ⟨0.000 -1.401 -11.314 +6.174]

Optimal ET sequence: 16, 32, 48

Badness (Sintel): 6.73

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 385/384, 1331/1323

Mapping: [⟨16 0 37 45 30], ⟨0 1 0 0 1]]

Optimal tunings:

  • WE: ~22/21 = 75.0000 ¢, ~3/2 = 700.7810 ¢ (~45/44 = 25.3476 ¢)
  • CWE: ~22/21 = 75.0000 ¢, ~3/2 = 700.6780 ¢ (~45/44 = 25.6780 ¢)

Optimal ET sequence: 16, 32, 48

Badness (Sintel): 3.07

Notes

  1. ↑ Yahoo! Tuning Group | Antikythera
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