Marvel temperaments
This page discusses miscellaneous rank-2 temperaments tempering out [-5 2 2 -1⟩ = 225/224, the marvel comma or septimal kleisma.
Temperaments considered in families and clans are:
- Sharp, {25/24, 28/27} → Dicot family
- Pelogic, {21/20, 135/128} → Pelogic family
- August, {36/35, 128/125} → Augmented family
- Pajara, {50/49, 64/63} → Diaschismic family
- Meantone, {81/80, 126/125} → Meantone family
- Magic, {225/224, 245/243} → Magic family
- Passive, {225/224, 256/245} → Passion family
- Miracle, {225/224, 1029/1024} → Gamelismic clan
- Orwell, {225/224, 1728/1715} → Semicomma family
- Garibaldi, {225/224, 3125/3087} → Schismatic family
- Catakleismic, {225/224, 4375/4374} → Kleismic family
- Snipes, {225/224, 6125/5832} → Wesley family
- Decic, {225/224, 16807/16384} → Cloudy clan
- Amavil, {225/224, 17496/16807} → Mabila family
- Escapade, {225/224, 65625/65536} → Escapade family
- Fog, {225/224, 156250/151263} → Misty family
- Compton, {225/224, 250047/250000} → Compton family
- Immune, {225/224, 781250/750141} → Immunity family
- Betic, {225/224, 1071875/1062882} → Sycamore family
- Houborizic {225/224, 1250000/1240029} → Amity family
- Qintosec, {225/224, 2560000/2470629} → Qintosec family
- Quintapole, {225/224, 7812500/7411887} → Quintaleap family
- Maquila, {225/224, 30233088/28824005} → Maquila family
- Marvo, {225/224, 78125000/78121827} → Gravity family
- Gammy, {225/224, 94143178827/91913281250} → Gammic family
Considered below are negri, wizard, tritonic, septimin, slender, triton, merman, marvolo, amavil, enneaportent, submajor, alphorn, tertiosec, gwazy, and gracecordial.
Since (5/4)2 = 225/224 × 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.
The melodic signature of marvel temperaments is that 16/15 and 15/14 are tempered to be equal. Hence 8/7 can be divided into two equal parts.
Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is (16/9)/(5/4) = 64/45. Setting this equal to 10/7 gives (10/7)/(64/45) = 225/224.)
Negri
- Main article: Negri
Negri tempers out the negri comma in the 5-limit, 49/48 and 225/224 in the 7-limit. It can be extended naturally to the 2.3.5.7.13 subgroup by adding 91/90 to the comma list; this will be discussed below under the title of negra.
Subgroup: 2.3.5
Comma list: 16875/16384
Mapping: [⟨1 2 2], ⟨0 -4 3]]
Wedgie: ⟨⟨4 -3 -14]]
POTE generator: ~16/15 = 125.7549
Optimal GPV sequence: 9, 10, 19, 67c, 86c, 105c
Badness: 0.086856
7-limit
Subgroup: 2.3.5.7
Comma list: 49/48, 225/224
Mapping: [⟨1 2 2 3], ⟨0 -4 3 -2]]
Wedgie: ⟨⟨4 -3 2 -14 -8 13]]
POTE generator: ~15/14 = 125.608
Optimal GPV sequence: 9, 10, 19, 48d, 67cdd, 86cdd
Badness: 0.026483
Negra
This is the 2.3.5.7.13 extension of negri.
Subgroup: 2.3.5.7.13
Comma list: 49/48, 65/64, 91/90
Sval mapping: [⟨1 2 2 3 4], ⟨0 -4 3 -2 -3]]
Gencom mapping: [⟨1 2 2 3 0 4], ⟨0 -4 3 -2 0 -3]]
Gencom: [2 14/13; 49/48 65/64 91/90]
POTE generator: ~14/13 = 125.567
Optimal GPV sequence: 9, 10, 19, 48df, 67cddf, 86cddff
11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 49/48, 56/55
Mapping: [⟨1 2 2 3 4], ⟨0 -4 3 -2 -5]]
POTE generator: ~15/14 = 126.474
Optimal GPV sequence: 9, 10, 19
Badness: 0.026190
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 49/48, 56/55, 78/77
Mapping: [⟨1 2 2 3 4 4], ⟨0 -4 3 -2 -5 -3]]
POTE generator: ~14/13 = 126.431
Optimal GPV sequence: 9, 10, 19
Badness: 0.017833
Negril
Subgroup: 2.3.5.7.11
Comma list: 49/48, 100/99, 225/224
Mapping: [⟨1 2 2 3 2], ⟨0 -4 3 -2 14]]
POTE generator: ~15/14 = 124.767
Optimal GPV sequence: 19, 29, 48d, 77cdd
Badness: 0.038679
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 65/64, 91/90, 875/858
Mapping: [⟨1 2 2 3 2 4], ⟨0 -4 3 -2 14 -3]]
POTE generator: ~14/13 = 124.716
Optimal GPV sequence: 19, 29, 48df, 77cddf
Badness: 0.024383
Negric
Subgroup: 2.3.5.7.11
Comma list: 33/32, 49/48, 77/75
Mapping: [⟨1 2 2 3 3], ⟨0 -4 3 -2 4]]
POTE generator: ~15/14 = 127.039
Badness: 0.030617
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 33/32, 49/48, 65/64, 91/90
Mapping: [⟨1 2 2 3 3 4], ⟨0 -4 3 -2 4 -3]]
POTE generator: ~14/13 = 127.039
Badness: 0.020205
Negroni
Subgroup: 2.3.5.7.11
Comma list: 49/48, 55/54, 225/224
Mapping: [⟨1 2 2 3 5], ⟨0 -4 3 -2 -15]]
POTE generator: ~15/14 = 124.539
Optimal GPV sequence: 10, 19e, 29, 77cddee
Badness: 0.035296
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 55/54, 65/64, 91/90
Mapping: [⟨1 2 2 3 5 4], ⟨0 -4 3 -2 -15 -3]]
POTE generator: ~14/13 = 124.545
Optimal GPV sequence: 10, 19e, 29, 77cddeef
Badness: 0.021559
Wilsec
Subgroup: 2.3.5.7.11
Comma list: 49/48, 121/120, 225/224
Mapping: [⟨1 6 -1 5 4], ⟨0 -8 6 -4 -1]]
POTE generator: ~11/8 = 537.186
Optimal GPV sequence: 9, 20, 29, 38d, 67cdde
Badness: 0.041886
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 65/64, 91/90, 121/120
Mapping: [⟨1 6 -1 5 4 7], ⟨0 -8 6 -4 -1 -6]]
POTE generator: ~11/8 = 537.208
Optimal GPV sequence: 9, 20, 29, 38df, 67cddef
Badness: 0.025192
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 49/48, 65/64, 91/90, 121/120, 154/153
Mapping: [⟨1 6 -1 5 4 7 -2], ⟨0 -8 6 -4 -1 -6 11]]
POTE generator: ~11/8 = 537.230
Optimal GPV sequence: 9, 20g, 29g, 38df, 67cddefg
Badness: 0.021778
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 49/48, 65/64, 77/76, 91/90, 121/120, 154/153
Mapping: [⟨1 6 -1 5 4 7 -2 7], ⟨0 -8 6 -4 -1 -6 11 -5]]
POTE generator: ~11/8 = 537.214
Optimal GPV sequence: 9, 20g, 29g, 38df, 67cddefgh
Badness: 0.016828
Wizard
- Main article: Wizard
- For the 5-limit version of this temperament, see High badness temperaments #Wizard.
Subgroup: 2.3.5.7
Comma list: 225/224, 118098/117649
Mapping: [⟨2 1 5 2], ⟨0 6 -1 10]]
Mapping generators: ~1225/864, ~245/216
POTE generator: ~5/4 = 383.256
Wedgie: ⟨⟨12 -2 20 -31 -2 52]]
Optimal GPV sequence: 22, 50, 72, 166, 238c, 310c, 382c
Badness: 0.040846
Scales: wizard22
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 4000/3993
Mapping: [⟨2 1 5 2 8], ⟨0 6 -1 10 -3]]
Mapping generators: ~99/70, ~25/22
POTE generator: ~5/4 = 383.232
Optimal GPV sequence: 22, 50, 72, 166, 238c, 310c
Badness: 0.018539
Scales: wizard22
Lizard
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 351/350, 364/363, 385/384
Mapping: [⟨2 1 5 2 8 11], ⟨0 6 -1 10 -3 -10]]
Mapping generators: ~99/70, ~25/22
POTE generator: ~5/4 = 383.389
Optimal GPV sequence: 22, 50, 72, 122, 194df
Badness: 0.021781
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 221/220, 273/272, 289/288, 351/350, 375/374
Mapping: [⟨2 1 5 2 8 11 6], ⟨0 6 -1 10 -3 -10 6]]
Mapping generators: ~17/12, ~17/15
POTE generator: ~5/4 = 383.381
Optimal GPV sequence: 22, 50, 72, 122g, 194dfg
Badness: 0.014536
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342
Mapping: [⟨2 1 5 2 8 11 6 2], ⟨0 6 -1 10 -3 -10 6 18]]
Mapping generators: ~17/12, ~17/15
POTE generator: ~5/4 = 383.477
Optimal GPV sequence: 22h, 50, 72, 122g, 194dfg
Badness: 0.015702
Gizzard
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 325/324, 385/384, 1573/1568
Mapping: [⟨2 1 5 2 8 -2], ⟨0 6 -1 10 -3 26]]
Mapping generators: ~99/70, ~25/22
POTE generator: ~5/4 = 383.170
Optimal GPV sequence: 72, 166, 238cf
Badness: 0.020252
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 289/288, 325/324, 375/374, 385/384
Mapping: [⟨2 1 5 2 8 -2 6], ⟨0 6 -1 10 -3 26 6]]
Mapping generators: ~17/12, ~17/15
POTE generator: ~5/4 = 383.175
Optimal GPV sequence: 72, 166g, 238cfg
Badness: 0.013624
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 225/224, 325/324, 375/374, 385/384, 400/399, 595/594
Mapping: [⟨2 1 5 2 8 -2 6 15], ⟨0 6 -1 10 -3 26 6 -18]]
Mapping generators: ~17/12, ~17/15
POTE generator: ~5/4 = 383.138
Optimal GPV sequence: 72, 94, 166g
Badness: 0.014810
Mage
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 1331/1296
Mapping: [⟨2 1 5 2 4], ⟨0 6 -1 10 8]]
Mapping generators: ~77/54, ~55/48
POTE generator: ~5/4 = 383.124
Optimal GPV sequence: 22, 50e, 72ee, 94ee
Badness: 0.057799
Tritonic
- For the 5-limit version of this temperament, see High badness temperaments #Tritonic.
Subgroup: 2.3.5.7
Comma list: 225/224, 50421/50000
Mapping: [⟨1 4 -3 -3], ⟨0 -5 11 12]]
Wedgie: ⟨⟨5 -11 -12 -29 -33 3]]
POTE generator: ~7/5 = 580.286
Optimal GPV sequence: 29, 31, 60, 91, 122, 213bcd
Badness: 0.047578
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 225/224, 441/440
Mapping: [⟨1 4 -3 -3 2], ⟨0 -5 11 12 3]]
POTE generator: ~7/5 = 580.267
Optimal GPV sequence: 29, 31, 60e
Badness: 0.023659
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 121/120, 196/195, 275/273
Mapping: [⟨1 4 -3 -3 2 -5], ⟨0 -5 11 12 3 18]]
POTE generator: ~7/5 = 580.108
Optimal GPV sequence: 29, 31, 60e, 151cde
Badness: 0.022993
Tritoni
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 27783/27500
Mapping: [⟨1 4 -3 -3 17], ⟨0 -5 11 12 -28]]
POTE generator: ~7/5 = 580.389
Optimal GPV sequence: 31, 91, 122, 153d
Badness: 0.045456
Septimin
- For the 5-limit version of this temperament, see High badness temperaments #Septimin.
Subgroup: 2.3.5.7
Comma list: 225/224, 84035/82944
Mapping: [⟨1 4 1 5], ⟨0 -11 6 -10]]
Wedgie: ⟨⟨11 -6 10 -35 -15 40]]
POTE generator: ~7/6 = 263.632
Optimal GPV sequence: 41, 91, 132d
Badness: 0.054502
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 2401/2376
Mapping: [⟨1 4 1 5 5], ⟨0 -11 6 -10 -7]]
POTE generator: ~7/6 = 263.634
Optimal GPV sequence: 41, 91, 223cdef
Badness: 0.031309
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 144/143, 196/195, 245/242
Mapping: [⟨1 4 1 5 5 7], ⟨0 -11 6 -10 -7 -15]]
POTE generator: ~7/6 = 263.700
Badness: 0.023117
Merman
- For the 5-limit version of this temperament, see High badness temperaments #Merman.
Subgroup: 2.3.5.7
Comma list: 225/224, 2500000/2470629
Mapping: [⟨1 5 -5 -5], ⟨0 -7 15 16]]
Wedgie: ⟨⟨7 -15 -16 -40 -45 5]]
POTE generator: ~7/5 = 585.585
Optimal GPV sequence: 41, 84, 125
Badness: 0.055078
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 441/440, 1344/1331
Mapping: [⟨1 5 -5 -5 2], ⟨0 -7 15 16 3]]
POTE generator: ~7/5 = 585.606
Optimal GPV sequence: 41, 84, 125e
Badness: 0.036383
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 225/224, 364/363, 441/440
Mapping: [⟨1 5 -5 -5 2 12], ⟨0 -7 15 16 3 -17]]
POTE generator: ~7/5 = 585.657
Optimal GPV sequence: 41, 84, 125e, 209ef, 293ef
Badness: 0.027544
Slender
Slender (31&32) tempers out the hewuermera comma in addition to the marvel comma, this has a generator 49/48, 3 of which equal marvel's 16/15 - 15/14, and 10 generators is 5/4.
Subgroup: 2.3.5.7
Comma list: 225/224, 589824/588245
Mapping: [⟨1 2 2 3], ⟨0 -13 10 -6]]
Wedgie: ⟨⟨13 -10 6 -46 -27 42]]
POTE generator: ~49/48 = 38.413
Optimal GPV sequence: 31, 94, 125
Badness: 0.056934
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 1331/1323
Mapping: [⟨1 2 2 3 4], ⟨0 -13 10 -6 -17]]
POTE generator: ~49/48 = 38.387
Optimal GPV sequence: 31, 63, 94, 125
Badness: 0.025342
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 275/273, 385/384, 1331/1323
Mapping: [⟨1 2 2 3 4 3], ⟨0 -13 10 -6 -17 22]]
POTE generator: ~49/48 = 38.314
Optimal GPV sequence: 31, 63, 94
Badness: 0.025913
Triton
- For the 5-limit version of this temperament, see High badness temperaments #Stump.
Subgroup: 2.3.5.7
Comma list: 225/224, 1029/1000
Mapping: [⟨1 0 6 7], ⟨0 3 -7 -8]]
Wedgie: ⟨⟨3 -7 -8 -18 -21 1]]
POTE generator: ~7/5 = 568.865
Optimal GPV sequence: 2, 17d, 19, 78bd, 97bd
Badness: 0.059245
11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 56/55, 1029/1000
Mapping: [⟨1 0 6 7 4], ⟨0 3 -7 -8 -1]]
POTE generator: ~7/5 = 569.144
Optimal GPV sequence: 2, 17d, 19, 59bde, 78bde, 97bde
Badness: 0.045675
Submajor
Subgroup: 2.3.5
Comma list: 69198046875/68719476736
Mapping: [⟨1 4 -1], ⟨0 -8 11]]
POTE generator: ~10125/8192 = 362.321
Optimal GPV sequence: 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc
Badness: 0.130236
7-limit
Subgroup: 2.3.5.7
Comma list: 225/224, 51200/50421
Mapping: [⟨1 4 -1 1], ⟨0 -8 11 6]]
Wedgie: ⟨⟨8 -11 -6 -36 -32 17]]
POTE generator: ~49/40 = 362.255
Optimal GPV sequence: 10, 33, 43, 53
Badness: 0.060533
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 6655/6561
Mapping: [⟨1 4 -1 1 11], ⟨0 -8 11 6 -25]]
POTE generator: ~27/22 = 362.101
Optimal GPV sequence: 10, 43e, 53, 116, 169de, 285cde
Badness: 0.050582
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 225/224, 275/273, 385/384
Mapping: [⟨1 4 -1 1 11 4], ⟨0 -8 11 6 -25 -1]]
POTE generator: ~16/13 = 362.105
Optimal GPV sequence: 10, 43e, 53, 116, 169de, 285cdef
Badness: 0.027689
Interpental
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 51200/50421
POTE generator: ~49/40 = 362.418
Mapping: [⟨1 4 -1 1 -5], ⟨0 -8 11 6 28]]
POTE generator: ~49/40 = 362.418
Optimal GPV sequence: 43, 53, 96, 149d
Badness: 0.051806
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 169/168, 176/175, 640/637
POTE generator: ~16/13 = 362.402
Mapping: [⟨1 4 -1 1 -5 4], ⟨0 -8 11 6 28 -1]]
POTE generator: ~16/13 = 362.402
Optimal GPV sequence: 43, 53, 96, 149d
Badness: 0.029680
Marvolo
Subgroup: 2.3.5.7
Comma list: 225/224, 156250000/155649627
Mapping: [⟨1 2 1 1], ⟨0 -6 19 26]]
Wedgie: ⟨⟨6 -19 -26 -44 -58 -7]]
POTE generator: ~21/20 = 83.348
Optimal GPV sequence: 29, 43, 72, 619bcd, 691bcd
Badness: 0.083338
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 441/440, 4000/3993
Mapping: [⟨1 2 1 1 2], ⟨0 -6 19 26 21]]
POTE generator: ~21/20 = 83.340
Optimal GPV sequence: 29, 43, 72
Badness: 0.028965
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 225/224, 364/363, 441/440
Mapping: [⟨1 2 1 1 2 3], ⟨0 -6 19 26 21 10]]
POTE generator: ~21/20 = 83.330
Optimal GPV sequence: 29, 43, 72, 115f
Badness: 0.021470
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 169/168, 221/220, 225/224, 364/363, 441/440
Mapping: [⟨1 2 1 1 2 3 2], ⟨0 -6 19 26 21 10 30]]
POTE generator: ~21/20 = 83.330
Optimal GPV sequence: 29g, 43, 72
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 169/168, 210/209, 221/220, 225/224, 364/363, 441/440
Mapping: [⟨1 2 1 1 2 3 2 3], ⟨0 -6 19 26 21 10 30 18]]
POTE generator: ~21/20 = 83.330
Optimal GPV sequence: 29g, 43, 72
Enneaportent
Subgroup: 2.3.5.7
Comma list: 225/224, 40353607/40310784
Mapping: [⟨9 0 28 11], ⟨0 2 -1 2]]
Wedgie: ⟨⟨18 -9 18 -56 -22 67]]
POTE generator: ~5/4 = 383.165
Optimal GPV sequence: 9, 63, 72, 495bcd
Badness: 0.093679
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 12005/11979
Mapping: [⟨9 0 28 11 24], ⟨0 2 -1 2 1]]
POTE generator: ~5/4 = 383.146
Optimal GPV sequence: 9, 63, 72, 423cd, 495bcd
Badness: 0.030426
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 225/224, 364/363, 1716/1715
Mapping: [⟨9 0 28 11 24 19], ⟨0 2 -1 2 1 2]]
POTE generator: ~5/4 = 383.047
Optimal GPV sequence: 9, 63, 72, 279cf
Badness: 0.022322
Gracecordial
- For the 5-limit version of this temperament, see High badness temperaments #Gracecordial.
Subgroup: 2.3.5.7
Comma list: 225/224, 781250000/771895089
Mapping: [⟨1 0 34 63], ⟨0 1 -20 -38]]
Wedgie: ⟨⟨1 -20 -38 -34 -63 -32]]
POTE generator: ~3/2 = 700.824
Optimal GPV sequence: 12, 113, 125, 238c, 363c
Badness: 0.096279
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 236328125/234365481
Mapping: [⟨1 0 34 63 -90], ⟨0 1 -20 -38 59]]
POTE generator: ~3/2 = 700.834
Optimal GPV sequence: 12e, 101cde, 113, 125, 238c
Badness: 0.089588
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 325/324, 385/384, 831875/830466
Mapping: [⟨1 0 34 63 -90 -66], ⟨0 1 -20 -38 59 44]]
POTE generator: ~3/2 = 700.841
Optimal GPV sequence: 12e, 101cde, 113, 125f, 238cf
Badness: 0.052235
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 273/272, 325/324, 385/384, 4928/4913
Mapping: [⟨1 0 34 63 -90 -66 -7], ⟨0 1 -20 -38 59 44 7]]
POTE generator: ~3/2 = 700.841
Optimal GPV sequence: 12e, 101cde, 113, 125f, 238cf
Badness: 0.038565
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 1445/1444
Mapping: [⟨1 0 34 63 -90 -66 -7 9], ⟨0 1 -20 -38 59 44 7 -3]]
POTE generator: ~3/2 = 700.842
Optimal GPV sequence: 12e, 101cde, 113, 125f, 238cf
Badness: 0.028165
23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 460/459, 529/528
Mapping: [⟨1 0 34 63 -90 -66 -7 9 -43], ⟨0 1 -20 -38 59 44 7 -3 30]]
POTE generator: ~3/2 = 700.843
Optimal GPV sequence: 12e, 101cde, 113, 238cfi
Badness: 0.021879
29-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 494/493
Mapping: [⟨1 0 34 63 -90 -66 -7 9 -43 -49], ⟨0 1 -20 -38 59 44 7 -3 30 34]]
POTE generator: ~3/2 = 700.842
Optimal GPV sequence: 12e, 101cde, 113, 125f, 238cfi
Badness: 0.018011
31-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29.31
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 465/464, 494/493
Mapping: [⟨1 0 34 63 -90 -66 -7 9 -43 -49 -79], ⟨0 1 -20 -38 59 44 7 -3 30 34 53]]
POTE generator: ~3/2 = 700.838
Optimal GPV sequence: 12e, 101cdek, 113, 125f, 238cfi
Badness: 0.016007
Gracecord
Subgroup: 2.3.5.7.11
Comma list: 225/224, 441/440, 109375/107811
Mapping: [⟨1 0 34 63 89], ⟨0 1 -20 -38 -54]]
POTE generator: ~3/2 = 700.885
Optimal GPV sequence: 12, 101cd, 113
Badness: 0.066964
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 364/363, 441/440, 6125/6084
Mapping: [⟨1 0 34 63 89 113], ⟨0 1 -20 -38 -54 -69]]
POTE generator: ~3/2 = 700.890
Optimal GPV sequence: 12f, 101cdf, 113
Badness: 0.044196
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 364/363, 441/440, 595/594, 2000/1989
Mapping: [⟨1 0 34 63 89 113 -7], ⟨0 1 -20 -38 -54 -69 7]]
POTE generator: ~3/2 = 700.870
Optimal GPV sequence: 12f, 101cdf, 113
Badness: 0.036637
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 210/209, 225/224, 324/323, 364/363, 400/399, 665/663
Mapping: [⟨1 0 34 63 89 113 -7 9], ⟨0 1 -20 -38 -54 -69 7 -3]]
POTE generator: ~3/2 = 700.866
Optimal GPV sequence: 12f, 101cdf, 113
Badness: 0.027559
Alphorn
Subgroup: 2.3.5.7
Comma list: 225/224, 5764801/5668704
Mapping: [⟨1 9 0 13], ⟨0 -16 5 -22]]
Wedgie: ⟨⟨16 -5 22 -45 -10 65]]
POTE generator: ~48/35 = 556.221
Optimal GPV sequence: 28d, 41, 151cd, 192cd, 233cd
Badness: 0.129258
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 12250/11979
Mapping: [⟨1 9 0 13 3], ⟨0 -16 5 -22 1]]
POTE generator: ~11/8 = 556.144
Optimal GPV sequence: 28d, 41, 315cde
Badness: 0.073459
Misneb
- For the 5-limit version of this temperament, see High badness temperaments #Misneb.
Subgroup: 2.3.5.7
Comma list: 225/224, 4194304/4117715
Mapping: [⟨1 3 1 3], ⟨0 -15 14 -2]]
Wedgie: ⟨⟨15 -14 2 -57 -39 44]]
POTE generator: ~16/15 = 113.235
Optimal GPV sequence: 21, 32, 53
Badness: 0.140970
11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 1310720/1294139
Mapping: [⟨1 3 1 3 1], ⟨0 -15 14 -2 26]]
POTE generator: ~16/15 = 113.323
Optimal GPV sequence: 21, 32e, 53, 127, 180de
Badness: 0.085390
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 176/175, 640/637, 847/845
Mapping: [⟨1 3 1 3 1 2], ⟨0 -15 14 -2 26 18]]
POTE generator: ~16/15 = 113.323
Optimal GPV sequence: 21, 32e, 53, 127, 180de
Badness: 0.045569
Musneb
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 66550/64827
Mapping: [⟨1 3 1 3 6], ⟨0 -15 14 -2 -27]]
POTE generator: ~16/15 = 113.142
Optimal GPV sequence: 32, 53, 191de, 244cddee, 297cddee
Badness: 0.087333
Untriton
- For the 5-limit version of this temperament, see High badness temperaments #Untriton.
Subgroup: 2.3.5.7
Comma list: 225/224, 125000000/121060821
Mapping: [⟨1 6 -7 -7], ⟨0 -9 19 20]]
Wedgie: ⟨⟨9 -19 -20 -51 -57 7]]
POTE generator: ~7/5 = 588.641
Optimal GPV sequence: 51, 53, 316cd, 369cdd, 422cdd
Badness: 0.143976
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 225/224, 22000/21609
Mapping: [⟨1 6 -7 -7 1], ⟨0 -9 19 20 5]]
POTE generator: ~7/5 = 588.626
Badness: 0.074295
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 225/224, 275/273, 1040/1029
Mapping: [⟨1 6 -7 -7 1 -12], ⟨0 -9 19 20 5 32]]
POTE generator: ~7/5 = 588.654
Badness: 0.047441
Quintannic
Subgroup: 2.3.5.7
Comma list: 225/224, 9805926501/9765625000
Mapping: [⟨1 1 5 7], ⟨0 5 -23 -36]]
Wedgie: ⟨⟨5 -23 -36 -48 -71 -19]]
POTE generator: ~10000/9261 = 139.838
Optimal GPV sequence: 43, 60, 103, 266bcd, 369bcd
Badness: 0.150565
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 441/440, 43923/43750
Mapping: [⟨1 1 5 7 8], ⟨0 5 -23 -36 -39]]
POTE generator: ~320/297 = 139.827
Optimal GPV sequence: 43, 60e, 103
Badness: 0.052590
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 441/440, 1001/1000, 1188/1183
Mapping: [⟨1 1 5 7 8 3], ⟨0 5 -23 -36 -39 6]]
POTE generator: ~13/12 = 139.812
Optimal GPV sequence: 43, 60e, 103
Badness: 0.032730
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 273/272, 375/374, 441/440, 891/884
Mapping: [⟨1 1 5 7 8 3 7], ⟨0 5 -23 -36 -39 6 -25]]
POTE generator: ~13/12 = 139.815
Optimal GPV sequence: 43, 60e, 103
Badness: 0.023038
Gwazy
- See also: Very high accuracy temperaments #Kwazy
Subgroup: 2.3.5.7
Comma list: 225/224, 5971968/5764801
Mapping: [⟨2 1 6 4], ⟨0 8 -5 6]]
Wedgie: ⟨⟨16 -10 12 -53 -26 56]]
POTE generator: ~35/32 = 162.658
Optimal GPV sequence: 22, 74, 96, 118d
Badness: 0.178826
11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 65536/65219
Mapping: [⟨2 1 6 4 8], ⟨0 8 -5 6 -4]]
POTE generator: ~11/10 = 162.592
Optimal GPV sequence: 22, 74, 96, 118d
Badness: 0.068410
Tertiosec
- For the 5-limit version of this temperament, see High badness temperaments #Tertiosec.
Subgroup: 2.3.5.7
Comma list: 225/224, 14495514624/13841287201
Mapping: [⟨3 7 5 9], ⟨0 -8 7 -2]]
Wedgie: ⟨⟨24 -21 6 -89 -58 73]]
POTE generator: ~15/14 = 112.283
Optimal GPV sequence: 21, 54, 75, 96, 171d
Badness: 0.431636
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 3840/3773, 12005/11979
Mapping: [⟨3 7 5 9 9], ⟨0 -8 7 -2 5]]
POTE generator: ~15/14 = 112.171
Optimal GPV sequence: 21, 54, 75e
Badness: 0.173485