Marvel temperaments

From Xenharmonic Wiki
(Redirected from Negril)
Jump to navigation Jump to search

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:

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 sequence9, 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 sequence9, 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 sequence9, 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

Optimal GPV sequence: 9, 19e

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

Optimal GPV sequence: 9, 19e

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 sequence22, 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 sequence29, 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 sequence41, 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

Optimal GPV sequence: 41, 91

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 sequence41, 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 sequence31, 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 sequence2, 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 sequence10, 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 sequence10, 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 sequence29, 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 sequence9, 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 sequence12, 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 sequence28d, 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 sequence21, 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 sequence51, 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

Optimal GPV sequence: 51, 53

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

Optimal GPV sequence: 51f, 53

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 sequence43, 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 sequence22, 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 sequence21, 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