Porwell temperaments

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.

This is a collection of temperaments that tempers out the porwell comma, [11 1 -3 -2⟩ (6144/6125).

Temperaments discussed elsewhere are:

Armodue (+36/35) → Mavila family
Porcupine (+64/63) → Porcupine family
Mohajira (+81/80) → Meantone family
Valentine (+126/125) → Starling temperaments
Orwell (+225/224) → Semicomma family
Shrutar (+245/243) → Diaschismic family
Quinkee (+1029/1000) → Cloudy clan
Hemiwürschmidt (+2401/2400 or 3136/3125) → Hemimean clan
Hemikleismic (+4000/3969) → Kleismic family
Amity (+4375/4374 or 5120/5103) → Amity family
Freivald (+6272/6075) → Passion family
Grendel (+16875/16807) → Mirkwai clan
Hemischis (+19683/19600) → Schismatic family
Bison (+78732/78125) → Sensipent family
Hemimabila (+117649/116640) → Mabila family
Septisuperfourth (+118098/117649) → Escapade family
Alphatrident (+14348907/14336000) → Alphatricot family
Hemimaquila (+[-5 10 5 -8⟩) → Maquila family
Decimaleap (+[15 -18 1 4⟩) → Quintaleap family
Twilight (+[19 -22 2 4⟩) → Undim family
Countermiracle (+823543/819200) → Quince clan

Considered below are hendecatonic, twothirdtonic, nessafof, aufo, whoops, polypyth, icositritonic, absurdity, and dodifo.

Hendecatonic

For the 5-limit version, see 11th-octave temperaments #Hendecapent.

The hendecatonic temperament has a period of 1/11 octave, which represents 16/15 and four times of which represent 9/7. It tempers out 10976/10935, the hemimage comma, and may be described as the 22 & 99 temperament, with 99edo giving an almost perfect tuning.

Subgroup: 2.3.5.7

Comma list: 6144/6125, 10976/10935

Mapping: [⟨11 0 43 -4], ⟨0 1 -1 2]]

mapping generators: ~16/15, ~3

Optimal tunings:

WE: ~16/15 = 109.0526 ¢, ~3/2 = 702.8069 ¢

error map: ⟨-0.421 +0.431 +0.563 -0.265]

CWE: ~16/15 = 109.0909 ¢, ~3/2 = 702.9705 ¢

error map: ⟨0.000 +1.015 +1.625 +0.751]

Optimal ET sequence: 22, 55, 77, 99

Badness (Sintel): 1.04

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 176/175, 10976/10935

Mapping: [⟨11 0 43 -4 38], ⟨0 1 -1 2 0]]

Optimal tunings:

WE: ~16/15 = 109.0977 ¢, ~3/2 = 702.6801 ¢
CWE: ~16/15 = 109.0909 ¢, ~3/2 = 702.6484 ¢

Optimal ET sequence: 22, 55, 77, 99

Badness (Sintel): 1.52

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 176/175, 351/350, 4459/4455

Mapping: [⟨11 0 43 -4 38 93], ⟨0 1 -1 2 0 -3]]

Optimal tunings:

WE: ~16/15 = 109.1092 ¢, ~3/2 = 702.4093 ¢
CWE: ~16/15 = 109.0909 ¢, ~3/2 = 702.2930 ¢

Optimal ET sequence: 22, 55, 77, 99

Badness (Sintel): 1.66

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 121/120, 154/153, 176/175, 273/272, 2025/2023

Mapping: [⟨11 0 43 -4 38 93 45], ⟨0 1 -1 2 0 -3 0]]

Optimal tunings:

WE: ~16/15 = 109.0933 ¢, ~3/2 = 702.3170 ¢
CWE: ~16/15 = 109.0909 ¢, ~3/2 = 702.3017 ¢

Optimal ET sequence: 22, 55, 77, 99, 176eg

Badness (Sintel): 1.48

Cohendecatonic

Subgroup: 2.3.5.7.11

Comma list: 540/539, 896/891, 4375/4356

Mapping: [⟨11 0 43 -4 73], ⟨0 1 -1 2 -2]]

Optimal tunings:

WE: ~16/15 = 109.0237 ¢, ~3/2 = 703.2522 ¢
CWE: ~16/15 = 109.0909 ¢, ~3/2 = 703.6563 ¢

Optimal ET sequence: 22, 77e, 99e, 121, 220e

Badness (Sintel): 1.26

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 364/363, 540/539, 625/624

Mapping: [⟨11 0 43 -4 73 128], ⟨0 1 -1 2 -2 -5]]

Optimal tunings:

WE: ~16/15 = 109.0189 ¢, ~3/2 = 703.4228 ¢
CWE: ~16/15 = 109.0909 ¢, ~3/2 = 703.9248 ¢

Optimal ET sequence: 22, 99ef, 121, 341bdeeff

Badness (Sintel): 1.49

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 256/255, 352/351, 364/363, 375/374, 540/539

Mapping: [⟨11 0 43 -4 73 128 45], ⟨0 1 -1 2 -2 -5 0]]

Optimal tunings:

WE: ~16/15 = 109.0159 ¢, ~3/2 = 703.3932 ¢
CWE: ~16/15 = 109.0909 ¢, ~3/2 = 703.9110 ¢

Optimal ET sequence: 22, 99ef, 121, 220efg, 341bdeeffgg

Badness (Sintel): 1.15

Icosidillic

Subgroup: 2.3.5.7.11

Comma list: 3388/3375, 6144/6125, 9801/9800

Mapping: [⟨22 0 86 -8 111], ⟨0 1 -1 2 -1]]

mapping generators: ~33/32, ~3

Optimal tunings:

WE: ~33/32 = 54.5305 ¢, ~3/2 = 702.7206 ¢
CWE: ~33/32 = 54.5455 ¢, ~3/2 = 702.8829 ¢

Optimal ET sequence: 22, 154, 176, 198

Badness (Sintel): 1.84

Twothirdtonic

Twothirdtonic tempers out 686/675, the senga, in addition to the porwell comma, and may be described as the 37 & 46 temperament, generated by one third of a classical major third that represents 15/14, 14/13, and 13/12 in the 13-limit interpretation. Note that in the data below, the generator is taken to be its octave complement, thirteen of which octave reduced make the perfect fifth; it follows that the ploidacot for this temperament is 11-sheared 13-cot. 46edo may be recommended as a tuning.

Subgroup: 2.3.5.7

Comma list: 686/675, 6144/6125

Mapping: [⟨1 -10 5 -7], ⟨0 13 -3 11]]

mapping generators: ~2, ~28/15

Optimal tunings:

WE: ~2 = 1199.3074 ¢, ~28/15 = 1068.9820 ¢

error map: ⟨-0.693 +1.736 +3.278 -5.176]

CWE: ~2 = 1200.0000 ¢, ~28/15 = 1069.5746 ¢

error map: ⟨0.000 +2.515 +4.962 -3.505]

Optimal ET sequence: 9, 28b, 37, 46

Badness (Sintel): 2.52

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 176/175, 686/675

Mapping: [⟨1 -10 5 -7 -1], ⟨0 13 -3 11 5]]

Optimal tunings:

WE: ~2 = 1199.7068 ¢, ~28/15 = 1069.3084 ¢
CWE: ~2 = 1200.0000 ¢, ~28/15 = 1069.5600 ¢

Optimal ET sequence: 9, 28b, 37, 46

Badness (Sintel): 1.35

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 121/120, 169/168, 176/175

Mapping: [⟨1 -10 5 -7 -1 -7], ⟨0 13 -3 11 5 12]]

Optimal tunings:

WE: ~2 = 1199.9531 ¢, ~13/7 = 1069.5492 ¢
CWE: ~2 = 1200.0000 ¢, ~13/7 = 1069.5893 ¢

Optimal ET sequence: 9, 28b, 37, 46

Badness (Sintel): 1.07

Semaja

Cryptically named by Petr Pařízek in 2011, semaja adds the gariboh comma to the comma list, and may be described as the 37 & 53 temperament. Its ploidacot is gamma-19-cot. The name actually refers to the fact that two of its ~8/7 generator steps reach a ~13/10^[1].

Subgroup: 2.3.5.7

Comma list: 3125/3087, 6144/6125

Mapping: [⟨1 -2 1 3], ⟨0 19 7 -1]]

mapping generators: ~2, ~8/7

Optimal tunings:

WE: ~2 = 1199.4860 ¢, ~8/7 = 226.3864 ¢

error map: ⟨-0.514 +0.415 -2.123 +3.246]

CWE: ~2 = 1200.0000 ¢, ~8/7 = 226.4697 ¢

error map: ⟨0.000 +0.970 -1.026 +4.704]

Optimal ET sequence: 16, 37, 53, 196d

Badness (Sintel): 2.71

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 176/175, 3125/3087

Mapping: [⟨1 -2 1 3 1], ⟨0 19 7 -1 13]]

Optimal tunings:

WE: ~2 = 1199.9818 ¢, ~8/7 = 226.4821 ¢
CWE: ~2 = 1200.0000 ¢, ~8/7 = 226.4851 ¢

Optimal ET sequence: 16, 37, 53

Badness (Sintel): 1.98

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 169/168, 176/175, 275/273

Mapping: [⟨1 -2 1 3 1 2], ⟨0 19 7 -1 13 9]]

Optimal tunings:

WE: ~2 = 1200.1020 ¢, ~8/7 = 226.4987 ¢
CWE: ~2 = 1200.0000 ¢, ~8/7 = 226.4822 ¢

Optimal ET sequence: 16, 37, 53

Badness (Sintel): 1.35

Nessafof

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

Cryptically named by Petr Pařízek in 2011^[2], nessafof adds the landscape comma and has a third-octave period. The name actually refers to the fact that it has a neutral-second generator, and that a semi-augmented fourth, stacked five times, makes 5/1^[1].

Subgroup: 2.3.5.7

Comma list: 6144/6125, 250047/250000

Mapping: [⟨3 2 5 10], ⟨0 7 5 -4]]

mapping generators: ~63/50, ~35/32

Optimal tunings:

WE: ~63/50 = 399.9023 ¢, ~35/32 = 157.4418 ¢

error map: ⟨-0.293 -0.057 +0.407 +0.430]

CWE: ~63/50 = 400.0000 ¢, ~35/32 = 157.4658 ¢

error map: ⟨0.000 +0.306 1.016 +1.311]

Optimal ET sequence: 15, 54b, 69, 84, 99, 282, 381

Badness (Sintel): 1.14

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 176/175, 250047/250000

Mapping: [⟨3 2 5 10 8], ⟨0 7 5 -4 6]]

Optimal tunings:

WE: ~63/50 = 400.0266 ¢, ~12/11 = 157.5301 ¢
CWE: ~63/50 = 400.0000 ¢, ~12/11 = 157.5240 ¢

Optimal ET sequence: 15, 69e, 84e, 99

Badness (Sintel): 2.26

Nessa

Subgroup: 2.3.5.7.11

Comma list: 441/440, 1344/1331, 4375/4356

Mapping: [⟨3 2 5 10 10], ⟨0 7 5 -4 1]]

Optimal tunings:

WE: ~44/35 = 399.7815 ¢, ~35/32 = 157.4527 ¢
CWE: ~44/35 = 400.0000 ¢, ~35/32 = 157.5109 ¢

Optimal ET sequence: 15, 69, 84, 99e

Badness (Sintel): 1.61

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 364/363, 441/440, 625/624

Mapping: [⟨3 2 5 10 10 6], ⟨0 7 5 -4 1 13]]

Optimal tunings:

WE: ~44/35 = 399.7595 ¢, ~35/32 = 157.3348 ¢
CWE: ~44/35 = 400.0000 ¢, ~35/32 = 157.3955 ¢

Optimal ET sequence: 15, 54bf, 69, 84, 99ef, 183ef, 282eeff

Badness (Sintel): 1.55

Aufo

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

Also named by Petr Pařízek in 2011, aufo refers to the augmented fourth, which is a generator of this temperament^[1].

Subgroup: 2.3.5.7

Comma list: 6144/6125, 177147/175616

Mapping: [⟨1 6 -7 19], ⟨0 -9 19 -33]]

mapping generators: ~2, ~45/32

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~45/32 = 588.782 ¢

Optimal ET sequence: 53, 161, 214

Badness (Smith): 0.121428

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 176/175, 177147/175616

Mapping: [⟨1 6 -7 19 1], ⟨0 -9 19 -33 5]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~45/32 = 588.811 ¢

Optimal ET sequence: 53, 108e, 161e

Badness (Smith): 0.088631

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 176/175, 351/350, 58806/57967

Mapping: [⟨1 6 -7 19 1 -12], ⟨0 -9 19 -33 5 32]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~45/32 = 588.788 ¢

Optimal ET sequence: 53, 108e, 161e, 214ee

Badness (Smith): 0.058507

Aufic

Subgroup: 2.3.5.7.11

Comma list: 540/539, 5632/5625, 72171/71680

Mapping: [⟨1 6 -7 19 -25], ⟨0 -9 19 -33 58]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~45/32 = 588.800 ¢

Optimal ET sequence: 53, 108, 161, 214, 375

Badness (Smith): 0.075149

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 540/539, 847/845, 4096/4095

Mapping: [⟨1 6 -7 19 -25 -12], ⟨0 -9 19 -33 58 32]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~45/32 = 588.796 ¢

Optimal ET sequence: 53, 108, 161, 214, 375, 589be

Badness (Smith): 0.039050

Whoops

For the 5-limit version, see Very high accuracy temperaments #Whoosh.

Also named by Petr Pařízek in 2011, whoops is a relatively simple extension to the otherwise very accurate microtemperament known as whoosh^[1].

Subgroup: 2.3.5.7

Comma list: 6144/6125, 244140625/243045684

Mapping: [⟨1 17 14 -7], ⟨0 -33 -25 21]]

mapping generators: ~2, ~441/320

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~441/320 = 560.519 ¢

Optimal ET sequence: 15, 122d, 137, 152, 608d, 623bd, 775bcd

Badness (Smith): 0.175840

11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 4000/3993, 6144/6125

Mapping: [⟨1 17 14 -7 10], ⟨0 -33 -25 21 -14]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~242/175 = 560.519 ¢

Optimal ET sequence: 15, 122d, 137, 152, 608de, 623bde, 775bcde

Badness (Smith): 0.043743

Polypyth

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

Polypyth (46 & 121) tempers out the same 5-limit comma as the leapday temperament (29 & 46), but with the porwell (6144/6125) rather than the hemifamity (5120/5103) tempered out.

Subgroup: 2.3.5.7

Comma list: 6144/6125, 179200/177147

Mapping: [⟨1 0 -31 52], ⟨0 1 21 -31]]

mapping generators: ~2, ~3

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~3/2 = 704.174 ¢

Optimal ET sequence: 46, 121, 167, 288b, 455bcd, 743bcd

Badness (Smith): 0.137995

11-limit

Subgroup: 2.3.5.7.11

Comma list: 896/891, 2200/2187, 6144/6125

Mapping: [⟨1 0 -31 52 59], ⟨0 1 21 -31 -35]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~3/2 = 704.177 ¢

Optimal ET sequence: 46, 121, 167, 288be, 455bcde

Badness (Smith): 0.051131

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 352/351, 364/363, 1716/1715

Mapping: [⟨1 0 -31 52 59 64], ⟨0 1 21 -31 -35 -38]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~3/2 = 704.168 ¢

Optimal ET sequence: 46, 121, 167, 288be

Badness (Smith): 0.030292

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 256/255, 325/324, 352/351, 364/363, 1716/1715

Mapping: [⟨1 0 -31 52 59 64 39], ⟨0 1 21 -31 -35 -38 -22]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~3/2 = 704.168 ¢

Optimal ET sequence: 46, 121, 167, 288beg

Badness (Smith): 0.019051

Icositritonic

See also: 23rd-octave temperaments

The icositritonic temperament (46 & 161) has a period of 1/23 octave, so six period represents 6/5 and nine period represents 21/16.

Subgroup: 2.3.5.7

Comma list: 6144/6125, 9920232/9765625

Mapping: [⟨23 0 17 101], ⟨0 1 1 -1]]

mapping generators: ~1323/1280, ~3

Optimal tuning (POTE): ~1323/1280 = 52.1739 ¢, ~64/63 = 29.3586 ¢

Optimal ET sequence: 46, 115, 161, 207, 368c

Badness (Smith): 0.196622

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 6144/6125, 35937/35840

Mapping: [⟨23 0 17 101 116], ⟨0 1 1 -1 -1]]

Optimal tuning (POTE): ~33/32 = 52.1739 ¢, ~64/63 = 29.3980 ¢

Optimal ET sequence: 46, 115, 161, 207, 368c

Badness (Smith): 0.064613

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 441/440, 847/845, 3584/3575

Mapping: [⟨23 0 17 101 116 158], ⟨0 1 1 -1 -1 -2]]

Optimal tuning (POTE): ~33/32 = 52.1739 ¢, ~64/63 = 29.2830 ¢

Optimal ET sequence: 46, 115, 161, 207, 368c

Badness (Smith): 0.040484

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 351/350, 441/440, 561/560, 847/845, 1089/1088

Mapping: [⟨23 0 17 101 116 158 94], ⟨0 1 1 -1 -1 -2 0]]

Optimal tuning (POTE): ~33/32 = 52.1739 ¢, ~64/63 = 29.2800 ¢

Optimal ET sequence: 46, 115, 161, 207, 368c

Badness (Smith): 0.024676

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 351/350, 441/440, 456/455, 476/475, 513/512, 847/845

Mapping: [⟨23 0 17 101 116 158 94 207], ⟨0 1 1 -1 -1 -2 0 -3]]

Optimal tuning (POTE): ~33/32 = 52.1739 ¢, ~64/63 = 29.3760 ¢

Optimal ET sequence: 46, 115, 161, 207, 368c

Badness (Smith): 0.021579

23-limit

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 276/275, 351/350, 391/390, 441/440, 456/455, 476/475, 847/845

Mapping: [⟨23 0 17 101 116 158 94 207 104], ⟨0 1 1 -1 -1 -2 0 -3 0]]

Optimal tuning (POTE): ~33/32 = 52.1739 ¢, ~64/63 = 29.3471 ¢

Optimal ET sequence: 46, 115, 161, 207, 368ci

Badness (Smith): 0.017745

Absurdity

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

Subgroup: 2.3.5.7

Comma list: 6144/6125, 177147/175000

Mapping: [⟨7 0 -17 64], ⟨0 1 3 -4]]

mapping generators: ~972/875, ~3

Optimal tuning (POTE): ~972/875 = 171.4286 ¢, ~3/2 = 700.5854 ¢ (or ~10/9 = 186.2997 ¢)

Optimal ET sequence: 77, 84, 161

Badness (Smith): 0.133520

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 6144/6125, 72171/71680

Mapping: [⟨7 0 -17 64 124], ⟨0 1 3 -4 -9]]

Optimal tuning (POTE): ~495/448 = 171.4286 ¢, ~3/2 = 700.6354 ¢ (or ~10/9 = 186.3497 ¢)

Optimal ET sequence: 77, 84, 161

Badness (Smith): 0.081564

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 441/440, 1188/1183, 3584/3575

Mapping: [⟨7 0 -17 64 124 37], ⟨0 1 3 -4 -9 -1]]

Optimal tuning (POTE): ~72/65 = 171.4286 ¢, ~3/2 = 700.6291 ¢ (or ~10/9 = 186.3434 ¢)

Optimal ET sequence: 77, 84, 161

Badness (Smith): 0.041600

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 351/350, 441/440, 561/560, 1188/1183, 1632/1625

Mapping: [⟨7 0 -17 64 124 37 -49], ⟨0 1 3 -4 -9 -1 7]]

Optimal tuning (POTE): ~72/65 = 171.4286 ¢, ~3/2 = 700.6524 ¢ (or ~10/9 = 186.3667 ¢)

Optimal ET sequence: 77, 161

Badness (Smith): 0.031783

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 324/323, 351/350, 441/440, 456/455, 476/475, 495/494

Mapping: [⟨7 0 -17 64 124 37 -49 63], ⟨0 1 3 -4 -9 -1 7 -3]]

Optimal tuning (POTE): ~21/19 = 171.4286 ¢, ~3/2 = 700.6565 ¢ (or ~10/9 = 186.3708 ¢)

Optimal ET sequence: 77, 161

Badness (Smith): 0.022291

23-limit

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 276/275, 324/323, 351/350, 441/440, 456/455, 476/475, 495/494

Mapping: [⟨7 0 -17 64 124 37 -49 63 76], ⟨0 1 3 -4 -9 -1 7 -3 -4]]

Optimal tuning (CTE): ~21/19 = 171.429 ¢, ~3/2 = 700.629 ¢ (or ~10/9 = 186.343 ¢)

Optimal ET sequence: 77, 84, 161

29-limit

See also: Fifth-chroma temperaments

Subgroup: 2.3.5.7.11.13.17.19.23.29

Comma list: 261/260, 276/275, 324/323, 351/350, 441/440, 456/455, 476/475, 495/494

Mapping: [⟨7 0 -17 64 124 37 -49 63 76 34], ⟨0 1 3 -4 -9 -1 7 -3 -4 0]]

Optimal tuning (CTE): ~21/19 = 171.429 ¢, ~3/2 = 700.629 ¢ (or ~10/9 = 186.343 ¢)

Optimal ET sequence: 77, 84, 161

Dodifo

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

Also named by Petr Pařízek in 2011, dodifo refers to the (tetraptolemaic) double-diminished fourth, which is a generator of this temperament^[1]. The extension here is a less accurate 7-limit intepretation.

Subgroup: 2.3.5.7

Comma list: 6144/6125, 2500000/2470629

Mapping: [⟨1 12 5 4], ⟨0 -35 -9 -4]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~49/40 = 357.070 ¢

Optimal ET sequence: 37, 84, 121, 205

Badness (Smith): 0.179692

11-limit

Subgroup: 2.3.5.7.11

Comma list: 1375/1372, 2560/2541, 4375/4356

Mapping: [⟨1 12 5 4 -1], ⟨0 -35 -9 -4 15]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~49/40 = 357.048 ¢

Optimal ET sequence: 37, 84, 121, 326dee

Badness (Smith): 0.081923

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 364/363, 625/624, 640/637, 1375/1372

Mapping: [⟨1 12 5 4 -1 4], ⟨0 -35 -9 -4 15 -1]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~16/13 = 357.049 ¢

Optimal ET sequence: 37, 84, 121, 326deef

Badness (Smith): 0.039533

References

[petr's_long_post-1] 1.0 ^1.1 ^1.2 ^1.3 ^1.4 Yahoo! Tuning Group | Suggested names for the unclasified temperaments

[petr's_short_post-2] Yahoo! Tuning Group | Some more unclassified temperaments

[1]

[2]