Marvel temperaments

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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, gracecordial, and quintapole.

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

Vals9, 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

Vals9, 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

Vals9, 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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]]

Vals22, 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 22, 50e, 72ee, 94ee

Badness: 0.057799

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

Vals2, 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

Vals: 2, 17d, 19, 59bde, 78bde, 97bde

Badness: 0.045675

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

Vals29, 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

Vals: 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

Vals: 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

Vals: 31, 91, 122, 153d

Badness: 0.045456

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

Vals41, 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

Vals: 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

Vals: 41, 84, 125e, 209ef, 293ef

Badness: 0.027544

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

Vals51, 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

Vals: 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

Vals: 51f, 53

Badness: 0.047441

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

Vals41, 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

Vals: 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

Vals: 41, 91

Badness: 0.023117

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

Vals21, 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

Vals: 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

Vals: 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

Vals: 32, 53, 191de, 244cddee, 297cddee

Badness: 0.087333

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

Vals31, 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

Vals: 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

Vals: 31, 63, 94

Badness: 0.025913

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

Vals29, 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

Vals: 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

Vals: 29, 43, 72, 115f

Badness: 0.021470

Amavil

For the 5-limit version of this temperament, see High badness temperaments #Mabila.

Subgroup: 2.3.5.7

Comma list: 225/224, 17496/16807

Mapping: [1 6 1 9], 0 -10 3 -14]]

Wedgie⟨⟨10 -3 14 -28 -6 41]]

POTE generator: ~48/35 = 529.979

Vals9, 25d, 34d, 43, 77d

Badness: 0.109625

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 864/847

Mapping: [1 6 1 9 7], 0 -10 3 -14 -8]]

POTE generator: ~15/11 = 529.974

Vals: 9, 34d, 43, 77de

Badness: 0.042649

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 78/77, 99/98, 144/143, 176/175

Mapping: [1 6 1 9 7 9], 0 -10 3 -14 -8 -12]]

POTE generator: ~15/11 = 529.951

Vals: 9, 34d, 43, 77de

Badness: 0.025791

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

Vals9, 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

Vals: 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

Vals: 9, 63, 72, 279cf

Badness: 0.022322

Submajor

Subgroup: 2.3.5

Comma list: 69198046875/68719476736

Mapping: [1 4 -1], 0 -8 11]]

POTE generator: ~10125/8192 = 362.321

Vals10, 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

Vals10, 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

Vals: 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

Vals: 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

Vals: 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

Vals: 43, 53, 96, 149d

Badness: 0.029680

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

Vals28d, 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

Vals: 28d, 41, 315cde

Badness: 0.073459

Tertiosec

Subgroup: 2.3.5

Comma list: [-89 21 24

Mapping: [3 7 5], 0 -8 7]]

POTE generator: ~16/15 = 112.281

Vals21, 54, 75, 96, 171

Badness: 0.851003

7-limit

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

Vals21, 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

Vals: 21, 54, 75e

Badness: 0.173485

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

Vals22, 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

Vals: 22, 74, 96, 118d

Badness: 0.068410

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

Vals12, 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

Vals: 12e, 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

Vals: 12e, 113, 125f, 238cf

Badness: 0.052235

Quintapole

See also: 16ed5/2 #Regular temperaments or 42ed11 #Regular temperaments

Aside from the marvel comma, the quintapole temperament (12&85) tempers out 7812500/7411887 (sepru-atritriyo). In the 11-limit, it tempers out the ptolemisma (100/99) as well as 85184/84035 (trilo-aquinru-agu). It is so named for the following reasons - it has the same commas as the apollo temperament, and its generator is a semitone five of which gives a flat fourth (~4/3, about 495 cents). Proper pronunciation of the word "quintapole" is /'kwɪntəpəʊl/ or /'kwɪntəpoʊl/, like as "quint-a-pole". Not to be confused with quintupole temperament (12&121).


Subgroup: 2.3.5.7

Comma list: 225/224, 7812500/7411887

Mapping: [1 2 1 1], 0 -5 16 22]]

POTE generator: ~21/20 = 98.994

Vals12, 73c, 85, 97d

Badness: 0.192498

11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 225/224, 85184/84035

Mapping: [1 2 1 1 0], 0 -5 16 22 42]]

POTE generator: ~21/20 = 98.954

Vals: 12, 73ce, 85, 97d

Badness: 0.104353