Jubilismic clan
- 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]]
- 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:
- Decimal (+25/24) → Dicot family
- Diminished (+36/35) → Dimipent family
- Pajara (+64/63) → Diaschismic family
- Dubbla (+78125/73728) → Wesley family
- Injera (+81/80) → Meantone family
- Octokaidecal (+28/27) → Trienstonic clan
- Bipelog (+135/128) → Mavila family
- Hexe (+128/125) → Augmented family
- Hedgehog (+250/243) → Porcupine family
- Crepuscular (+4375/4374) → Fifive family
- Byhearted (+19683/19208) → Tetracot family
Considered below are lemba, astrology, walid, antikythera, doublewide, elvis, comic, and bipyth.
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. It may be described as the 10 & 16 temperament; its ploidacot is diploid tricot.
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
- 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. It may be described as the 16 & 22 temperament; its ploidacot is diploid pentacot.
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
- 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
This low-accuracy extension tempers out 16/15, so the perfect fifth stands in for ~8/5 as in father. Its ploidacot is diploid monocot.
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
- 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 ¢)
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]
- 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
Badness (Sintel): 0.253
Doublewide
- For the 5-limit version, see Superpyth–22 equivalence continuum #Doublewide (5-limit).
Doublewide is generated by a sharply tuned ~6/5 minor third, four of which and a semi-octave period give the 3rd harmonic. It may be described as the 22 & 26 temperament; its ploidacot is diploid alpha-tetracot. An 11-limit extension is immediately available by identifying two generator steps as ~16/11. 48edo makes for an excellent tuning.
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
- 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, 385/384
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.
Elvis is generated by a ptolemaic diminished fifth, tuned sharp such that two generators and a semi-octave period give the 3rd harmonic. Its ploidacot is diploid alpha-dicot. 26edo makes for an obvious tuning.
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
- 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).
Comic is generated by a grave fifth, tuned flat such that two generators and a semi-octave period give the 3rd harmonic. Its ploidacot is diploid alpha-dicot. 22edo makes for an obvious tuning.
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
- 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
Bipyth tempers out the 5-limit superpyth comma, 20480/19683, making it an alternative extension of 5-limit superpyth. Its ploidacot is diploid monocot.
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
- 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
Sedecic has 1/16-octave period and may be thought of as 16edo with an independent generator for prime 3. Its ploidacot is 16-ploid monocot.
Subgroup: 2.3.5.7
Comma list: 50/49, 546875/524288
Mapping: [⟨16 0 37 45], ⟨0 1 0 0]]
- 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