Marvel temperaments: Difference between revisions

Revision as of 13:45, 22 February 2026

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 page discusses miscellaneous rank-2 temperaments tempering out 225/224, the marvel comma or septimal kleisma.

Temperaments considered in families and clans are:

Pelogic → Mavila family (+21/20 or 135/128, generated by the fifth with 5/4 mapped to the m3)
Meantone → Meantone family (+81/80 or 126/125, generated by the fifth with 5/4 mapped to the M3)
Garibaldi → Schismatic family (+3125/3087, generated by the fifth with 5/4 mapped to the d4)
Pajara → Diaschismic family (+50/49 or 64/63, generated by the fifth with a semioctave period)
Sharpie → Dicot family (+25/24 or 28/27, fifth sliced in two)
Immune → Immunity family (+781250/750141, twelfth sliced in two)
August → Augmented family (+36/35 or 128/125, generated by the fifth with a 1/3-octave period)
Fog → Misty family (+156250/151263, generated by the fifth with a 1/3-octave period)
Negri → Slendro clan (+49/48, fourth sliced in four)
Magic → Magic family (+245/243, twelfth sliced in five)
Passive → Passion family (+256/245, fourth sliced in five)
Quintapole → Quintaleap family (+7812500/7411887, fourth sliced in five)
Houborizic → Amity family (+1250000/1240029, eleventh sliced in five)
Qintosec → Quintosec family (+2560000/2470629, generated by the classical minor second with a 1/5-octave period)
Miracle → Gamelismic clan (+1029/1024, fifth sliced in six)
Catakleismic → Kleismic family (+4375/4374, twelfth sliced in six)
Marvo → Gravity family (+78125000/78121827, two octaves and a fifth sliced in six)
Orwell → Semicomma family (+1728/1715, twelfth sliced in seven)
Snipes → Wesley family (+6125/5832, two octaves and a fourth sliced in seven)
Submajor → Buzzardsmic clan (+65536/64827, two octaves and a fourth sliced in eight)
Escapist → Escapade family (+65625/65536, fourth sliced in nine)
Decic → Cloudy clan (+16807/16384, generated by the fifth with a 1/10-octave period)
Amavil → Mabila family (+17496/16807, four octaves and a fourth sliced in ten)
Betic → Sycamore family (+1071875/1062882, fifth sliced in eleven)
Hendeca → 11th-octave temperaments (+122880/117649, generated by the fifth with a 1/11-octave period)
Compton → Compton family (+250047/250000, generated by the classical major third with a 1/12-octave period)
Raccoon → Vavoom family (+41943040/40353607, twelfth sliced in seventeen)
Maquila → Maquila family (+30233088/28824005, seven octaves and a fifth sliced in seventeen)
Gammy → Gammic family (+94143178827/91913281250, fifth sliced in twenty)

Considered below are wizard, tritonic, septimin, slender, triton, merman, marvolo, amavil, enneaportent, 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.)

Wizard

Main article: Wizard

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

Wizard has a semi-octave period and is generated by an interval that is best treated as ~17/15. The semi-octave complement of this interval is ~5/4. Wizard can be described as 22 & 72. Its ploidacot is diploid alpha-hexacot, so six generator steps plus a semi-octave period gives the perfect twelfth. 72edo, 94edo, and especially 166edo are good tunings for it.

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

Optimal tunings:

WE: ~1225/864 = 600.3438 ¢, ~245/216 = 216.8680 ¢

error map: ⟨+0.688 -0.403 -1.463 +0.541]

CWE: ~1225/864 = 600.0000 ¢, ~245/216 = 216.7977 ¢

error map: ⟨0.000 -1.169 -3.111 -0.849]

Optimal ET sequence: 22, 50, 72, 238c, 310c, 382c, 454bccd

Badness (Sintel): 1.03

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]]

Optimal tunings:

WE: ~99/70 = 600.3051 ¢, ~25/22 = 216.8782 ¢
CWE: ~99/70 = 600.0000 ¢, ~25/22 = 216.7961 ¢

Optimal ET sequence: 22, 50, 72, 166, 238c, 310c

Badness (Sintel): 0.613

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]]

Optimal tunings:

WE: ~55/39 = 600.4824 ¢, ~25/22 = 216.7852 ¢
CWE: ~55/39 = 600.0000 ¢, ~25/22 = 216.6247 ¢

Optimal ET sequence: 22, 50, 72

Badness (Sintel): 0.900

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]]

Optimal tunings:

WE: ~17/12 = 600.5032 ¢, ~17/15 = 216.8002 ¢
CWE: ~17/12 = 600.0000 ¢, ~17/15 = 216.6361 ¢

Optimal ET sequence: 22, 50, 72

Badness (Sintel): 0.741

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]]

Optimal tunings:

WE: ~17/12 = 600.4698 ¢, ~17/15 = 216.6925 ¢
CWE: ~17/12 = 600.0000 ¢, ~17/15 = 216.5434 ¢

Optimal ET sequence: 22h, 50, 72, 122g, 194dfg

Badness (Sintel): 0.955

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]]

Optimal tunings:

WE: ~99/70 = 600.2896 ¢, ~25/22 = 216.9343 ¢
CWE: ~99/70 = 600.0000 ¢, ~25/22 = 216.8501 ¢

Optimal ET sequence: 22f, 72, 166, 238cf

Badness (Sintel): 0.837

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]]

Optimal tunings:

WE: ~17/12 = 600.3227 ¢, ~17/15 = 216.9414 ¢
CWE: ~17/12 = 600.0000 ¢, ~17/15 = 216.8469 ¢

Optimal ET sequence: 22f, 72, 166g, 238cfg

Badness (Sintel): 0.694

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]]

Optimal tunings:

WE: ~17/12 = 600.2637 ¢, ~17/15 = 216.9570 ¢
CWE: ~17/12 = 600.0000 ¢, ~17/15 = 216.8687 ¢

Optimal ET sequence: 72, 94, 166g

Badness (Sintel): 0.901

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]]

Optimal tunings:

WE: ~77/54 = 600.6486 ¢, ~55/48 = 217.1099 ¢
CWE: ~77/54 = 600.0000 ¢, ~55/48 = 216.9841 ¢

Optimal ET sequence: 22, 50e, 72ee

Badness (Sintel): 1.91

Tritonic

For the 5-limit version of this temperament, see Miscellaneous 5-limit temperaments #Tritonic.

Subgroup: 2.3.5.7

Comma list: 225/224, 50421/50000

Mapping: [⟨1 -1 8 9], ⟨0 5 -11 -12]]

mapping generators: ~2, ~10/7

Optimal tunings:

WE: ~2 = 1201.3539 ¢, ~10/7 = 620.4131 ¢

error map: ⟨+1.354 -1.243 -0.027 -1.598]

CWE: ~2 = 1200.0000 ¢, ~10/7 = 619.6778 ¢

error map: ⟨0.000 -3.566 -2.769 -4.959]

Optimal ET sequence: 29, 31, 60, 91, 122, 213bcd

Badness (Sintel): 1.20

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 225/224, 441/440

Mapping: [⟨1 -1 8 9 5], ⟨0 5 -11 -12 -3]]

Optimal tunings:

WE: ~2 = 1201.7116 ¢, ~10/7 = 620.6166 ¢
CWE: ~2 = 1200.0000 ¢, ~10/7 = 619.6890 ¢

Optimal ET sequence: 29, 31, 60e, 91e, 213bcdeee

Badness (Sintel): 0.782

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 121/120, 196/195, 275/273

Mapping: [⟨1 -1 8 9 5 13], ⟨0 5 -11 -12 -3 -18]]

Optimal tunings:

WE: ~2 = 1201.5355 ¢, ~10/7 = 620.6855 ¢
CWE: ~2 = 1200.0000 ¢, ~10/7 = 619.8469 ¢

Optimal ET sequence: 29, 31, 60e

Badness (Sintel): 0.950

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 105/104, 121/120, 154/153, 196/195, 273/272

Mapping: [⟨1 -1 8 9 5 13 17], ⟨0 5 -11 -12 -3 -18 -25]]

Optimal tunings:

WE: ~2 = 1201.5260 ¢, ~10/7 = 620.7330 ¢
CWE: ~2 = 1200.0000 ¢, ~10/7 = 619.8986 ¢

Optimal ET sequence: 29g, 31, 60e

Badness (Sintel): 0.973

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 77/76, 105/104, 121/120, 153/152, 196/195, 273/272

Mapping: [⟨1 -1 8 9 5 13 17 12], ⟨0 5 -11 -12 -3 -18 -25 -15]]

Optimal tunings:

WE: ~2 = 1201.3100 ¢, ~10/7 = 620.6509 ¢
CWE: ~2 = 1200.0000 ¢, ~10/7 = 619.9328 ¢

Optimal ET sequence: 29g, 31, 60e

Badness (Sintel): 1.03

23-limit

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 77/76, 105/104, 115/114, 121/120, 153/152, 161/160, 196/195

Mapping: [⟨1 -1 8 9 5 13 17 12 4], ⟨0 5 -11 -12 -3 -18 -25 -15 1]]

Optimal tunings:

WE: ~2 = 1201.4074 ¢, ~10/7 = 620.7185 ¢
CWE: ~2 = 1200.0000 ¢, ~10/7 = 619.9548 ¢

Optimal ET sequence: 29g, 31, 60e

Badness (Sintel): 1.04

Tritoni

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 27783/27500

Mapping: [⟨1 -1 8 9 -11], ⟨0 5 -11 -12 28]]

Optimal tunings:

WE: ~2 = 1201.0888 ¢, ~10/7 = 620.1733 ¢
CWE: ~2 = 1200.0000 ¢, ~10/7 = 619.6146 ¢

Optimal ET sequence: 31, 91, 122, 153d

Badness (Sintel): 1.50

Septimin

For the 5-limit version of this temperament, see Miscellaneous 5-limit temperaments #Septimin.

Subgroup: 2.3.5.7

Comma list: 225/224, 84035/82944

Mapping: [⟨1 -7 7 -5], ⟨0 11 -6 10]]

mapping generators: ~2, ~12/7

Optimal tunings:

WE: ~2 = 1201.2452 ¢, ~12/7 = 937.3394 ¢

error map: ⟨+1.245 +0.062 -1.633 -1.658]

CWE: ~2 = 1200.0000 ¢, ~12/7 = 936.4036 ¢

error map: ⟨0.000 -1.516 -4.735 -4.790]

Optimal ET sequence: 41, 91, 132d

Badness (Sintel): 1.38

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 245/242, 385/384

Mapping: [⟨1 -7 7 -5 -2], ⟨0 11 -6 10 7]]

Optimal tunings:

WE: ~2 = 1200.8059 ¢, ~12/7 = 936.9952 ¢
CWE: ~2 = 1200.0000 ¢, ~12/7 = 936.3906 ¢

Optimal ET sequence: 41, 91, 223cdef

Badness (Sintel): 1.04

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 144/143, 196/195, 245/242

Mapping: [⟨1 -7 7 -5 -2 -8], ⟨0 11 -6 10 7 15]]

Optimal tunings:

WE: ~2 = 1200.5990 ¢, ~12/7 = 936.7670 ¢
CWE: ~2 = 1200.0000 ¢, ~12/7 = 936.3196 ¢

Optimal ET sequence: 41, 91

Badness (Sintel): 0.955

Merman

For the 5-limit version of this temperament, see Miscellaneous 5-limit temperaments #Merman.

Subgroup: 2.3.5.7

Comma list: 225/224, 2500000/2470629

Mapping: [⟨1 -2 10 11], ⟨0 7 -15 -16]]

mapping generators: ~2, ~10/7

Optimal tunings:

WE: ~2 = 1200.3898 ¢, ~10/7 = 614.6413 ¢

error map: ⟨+0.390 -0.435 -1.630 +1.634]

CWE: ~2 = 1200.0000 ¢, ~10/7 = 614.4073 ¢

error map: ⟨0.000 -1.104 -2.423 +0.657]

Optimal ET sequence: 41, 84, 125

Badness (Sintel): 1.39

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 441/440, 1344/1331

Mapping: [⟨1 -2 10 11 5], ⟨0 7 -15 -16 -3]]

Optimal tunings:

WE: ~2 = 1199.9578 ¢, ~10/7 = 614.3720 ¢
CWE: ~2 = 1200.0000 ¢, ~10/7 = 614.3943 ¢

Optimal ET sequence: 41, 84, 125e

Badness (Sintel): 1.20

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 225/224, 364/363, 441/440

Mapping: [⟨1 -2 10 11 5 -5], ⟨0 7 -15 -16 -3 17]]

Optimal tunings:

WE: ~2 = 1199.7422 ¢, ~10/7 = 614.2110 ¢
CWE: ~2 = 1200.0000 ¢, ~10/7 = 614.3442 ¢

Optimal ET sequence: 41, 84, 125e, 209ef, 293ef

Badness (Sintel): 1.14

Slender

Slender (31 & 32) tempers out the hewuermera comma in addition to the marvel comma. This temperament has a generator of 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]]

mapping generators: ~2, ~49/48

Optimal tunings:

WE: ~2 = 1200.3816 ¢, ~49/48 = 38.4256 ¢

error map: ⟨+0.382 -0.725 -1.295 +1.765]

CWE: ~2 = 1200.0000 ¢, ~49/48 = 38.4079 ¢

error map: ⟨0.000 -1.257 -2.235 +0.727]

Optimal ET sequence: 31, 94, 125, 406c

Badness (Sintel): 1.44

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]]

Optimal tunings:

WE: ~2 = 1199.4983 ¢, ~49/48 = 38.4030 ¢
CWE: ~2 = 1200.0000 ¢, ~49/48 = 38.3775 ¢

Optimal ET sequence: 31, 63, 94, 125

Badness (Sintel): 0.838

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]]

Optimal tunings:

WE: ~2 = 1200.1728 ¢, ~49/48 = 38.3192 ¢
CWE: ~2 = 1200.0000 ¢, ~49/48 = 38.3129 ¢

Optimal ET sequence: 31, 63, 94

Badness (Sintel): 1.07

Triton

For the 5-limit version of this temperament, see Miscellaneous 5-limit temperaments #Stump.

Subgroup: 2.3.5.7

Comma list: 225/224, 1029/1000

Mapping: [⟨1 0 6 7], ⟨0 3 -7 -8]]

mapping generators: ~2, ~10/7

Optimal tunings:

WE: ~2 = 1203.3828 ¢, ~10/7 = 632.9137 ¢

error map: ⟨+3.383 -3.214 +3.587 -8.457]

CWE: ~2 = 1200.0000 ¢, ~10/7 = 630.9827 ¢

error map: ⟨0.000 -9.007 -3.192 -16.687]

Optimal ET sequence: 2, 17d, 19, 78bd, 97bd

Badness (Sintel): 1.50

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]]

Optimal tunings:

WE: ~2 = 1201.3875 ¢, ~10/7 = 631.5852 ¢
CWE: ~2 = 1200.0000 ¢, ~10/7 = 630.8007 ¢

Optimal ET sequence: 2, 17d, 19

Badness (Sintel): 1.51

Marvolo

Subgroup: 2.3.5.7

Comma list: 225/224, 156250000/155649627

Mapping: [⟨1 2 1 1], ⟨0 -6 19 26]]

mapping generators: ~2, ~21/20

Optimal tunings:

WE: ~2 = 1200.7714 ¢, ~21/20 = 83.4014 ¢

error map: ⟨+0.772 -0.820 -0.916 +0.381]

CWE: ~2 = 1200.0000 ¢, ~21/20 = 83.3640 ¢

error map: ⟨0.000 -2.139 -2.398 -1.362]

Optimal ET sequence: 29, 43, 72, 619bbccd, 691bbccd

Badness (Sintel): 2.11

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]]

Optimal tunings:

WE: ~2 = 1200.7075 ¢, ~21/20 = 83.3888 ¢
CWE: ~2 = 1200.0000 ¢, ~21/20 = 83.3564 ¢

Optimal ET sequence: 29, 43, 72

Badness (Sintel): 0.958

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]]

Optimal tunings:

WE: ~2 = 1200.9467 ¢, ~21/20 = 83.3956 ¢
CWE: ~2 = 1200.0000 ¢, ~21/20 = 83.3516 ¢

Optimal ET sequence: 29, 43, 72

Badness (Sintel): 0.887

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]]

Optimal tunings:

WE: ~2 = 1200.9606 ¢, ~21/20 = 83.4030 ¢
CWE: ~2 = 1200.0000 ¢, ~21/20 = 83.3594 ¢

Optimal ET sequence: 29g, 43, 72

Badness (Sintel): 0.760

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]]

Optimal tunings:

WE: ~2 = 1200.7625 ¢, ~21/20 = 83.3895 ¢
CWE: ~2 = 1200.0000 ¢, ~21/20 = 83.3551 ¢

Optimal ET sequence: 29g, 43, 72

Badness (Sintel): 0.895

Enneaportent

Subgroup: 2.3.5.7

Comma list: 225/224, 40353607/40310784

Mapping: [⟨9 0 28 11], ⟨0 2 -1 2]]

mapping generators: ~2592/2401, ~12005/6912

Optimal tunings:

WE: ~2592/2401 = 133.4174 ¢, ~12005/6912 = 950.7667 ¢ (~1728/1715 = 16.8452 ¢)

error map: ⟨+0.756 -0.422 -1.395 +0.298]

CWE: ~2592/2401 = 133.3333 ¢, ~12005/6912 = 950.2969 ¢ (~1728/1715 = 16.9636 ¢)

error map: ⟨0.000 -1.361 -3.277 -1.565]

Optimal ET sequence: 9, 54, 63, 72, 495bccd, 567bcccd

Badness (Sintel): 2.37

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]]

Optimal tunings:

WE: ~121/112 = 133.4071 ¢, ~210/121 = 950.7131 ¢ (~99/98 = 16.8633 ¢)
CWE: ~121/112 = 133.3333 ¢, ~210/121 = 950.2994 ¢ (~99/98 = 16.9661 ¢)

Optimal ET sequence: 9, 54, 63, 72

Badness (Sintel): 1.01

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]]

Optimal tunings:

WE: ~14/13 = 133.4245 ¢, ~26/15 = 950.9362 ¢ (~105/104 = 16.9650 ¢)
CWE: ~14/13 = 133.3333 ¢, ~26/15 = 950.4364 ¢ (~99/98 = 17.1031 ¢)

Optimal ET sequence: 9, 54, 63, 72

Badness (Sintel): 0.922

Gracecordial

For the 5-limit version of this temperament, see Schismic–Pythagorean equivalence continuum #Gracecordial (5-limit).

Subgroup: 2.3.5.7

Comma list: 225/224, 781250000/771895089

Mapping: [⟨1 0 34 63], ⟨0 1 -20 -38]]

mapping generators: ~2, ~3

Optimal tunings:

WE: ~2 = 1200.4904 ¢, ~3/2 = 701.1103 ¢

error map: ⟨+0.490 -0.354 -1.655 +1.241]

CWE: ~2 = 1200.3333 ¢, ~3/2 = 700.8112 ¢

error map: ⟨0.000 -1.144 -2.537 +0.349]

Optimal ET sequence: 12, …, 113, 125, 238c, 363c

Badness (Sintel): 2.44

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]]

Optimal tunings:

WE: ~2 = 1200.5571 ¢, ~3/2 = 701.1589 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 700.8328 ¢

Optimal ET sequence: 12e, 113, 125, 238c

Badness (Sintel): 2.96

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]]

Optimal tunings:

WE: ~2 = 1200.6282 ¢, ~3/2 = 701.2080 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 700.8421 ¢

Optimal ET sequence: 12e, 113, 125f, 238cf

Badness (Sintel): 2.16

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]]

Optimal tunings:

WE: ~2 = 1200.5058 ¢, ~3/2 = 701.1360 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 700.8414 ¢

Optimal ET sequence: 12e, 113, 125f, 238cf

Badness (Sintel): 1.96

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]]

Optimal tunings:

WE: ~2 = 1200.4418 ¢, ~3/2 = 701.0999 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 700.8425 ¢

Optimal ET sequence: 12e, 113, 125f, 238cf

Badness (Sintel): 1.71

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]]

Optimal tunings:

WE: ~2 = 1200.4641 ¢, ~3/2 = 701.1145 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 700.8444 ¢

Optimal ET sequence: 12e, 113, 238cfi

Badness (Sintel): 1.57

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]]

Optimal tunings:

WE: ~2 = 1200.4400 ¢, ~3/2 = 701.0986 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 700.8428 ¢

Optimal ET sequence: 12e, 113, 125f, 238cfi

Badness (Sintel): 1.50

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]]

Optimal tunings:

WE: ~2 = 1200.4178 ¢, ~3/2 = 701.0822 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 700.8396 ¢

Optimal ET sequence: 12e, 113, 125f, 238cfi

Badness (Sintel): 1.53

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]]

Optimal tunings:

WE: ~2 = 1200.6064 ¢, ~3/2 = 701.2398 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 700.8718 ¢

Optimal ET sequence: 12, …, 101cd, 113

Badness (Sintel): 2.21

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]]

Optimal tunings:

WE: ~2 = 1200.6225 ¢, ~3/2 = 701.2539 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 700.8781 ¢

Optimal ET sequence: 12f, …, 101cdf, 113

Badness (Sintel): 1.83

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]]

Optimal tunings:

WE: ~2 = 1200.3308 ¢, ~3/2 = 701.0632 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 700.8654 ¢

Optimal ET sequence: 12f, 101cdf, 113

Badness (Sintel): 1.87

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]]

Optimal tunings:

WE: ~2 = 1200.2658 ¢, ~3/2 = 701.0213 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 700.8629 ¢

Optimal ET sequence: 12f, 101cdf, 113

Badness (Sintel): 1.68

Alphorn

Subgroup: 2.3.5.7

Comma list: 225/224, 5764801/5668704

Mapping: [⟨1 -7 5 -9], ⟨0 16 -5 22]]

mapping generators: ~2, ~35/24

Optimal tunings:

WE: ~2 = 1201.3004 ¢, ~35/24 = 644.4767 ¢

error map: ⟨+1.300 +0.569 -2.195 -2.043]

CWE: ~2 = 1200.3333 ¢, ~35/24 = 643.8137 ¢

error map: ⟨0.000 -0.936 -5.382 -4.924]

Optimal ET sequence: 13d, 28d, 41, 151cd, 192cdd, 233ccdd

Badness (Sintel): 3.27

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 12250/11979

Mapping: [⟨1 -7 5 -9 4], ⟨0 16 -5 22 -1]]

Optimal tunings:

WE: ~2 = 1200.5123 ¢, ~16/11 = 644.1307 ¢
CWE: ~2 = 1200.0000 ¢, ~16/11 = 643.8662 ¢

Optimal ET sequence: 13d, 28d, 41

Badness (Sintel): 2.43

Misneb

For the 5-limit version of this temperament, see Miscellaneous 5-limit temperaments #Misneb.

Subgroup: 2.3.5.7

Comma list: 225/224, 4194304/4117715

Mapping: [⟨1 -12 15 1], ⟨0 15 -14 2]]

mapping generators: ~2, ~15/8

Optimal tunings:

WE: ~2 = 1199.7642 ¢, ~15/8 = 1086.5513 ¢

error map: ⟨-0.236 -0.856 -1.569 +4.041]

CWE: ~2 = 1200.0000 ¢, ~15/8 = 1086.7633 ¢

error map: ⟨0.000 -0.506 -0.999 +4.701]

Optimal ET sequence: 21, 32, 53

Badness (Sintel): 3.57

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 1310720/1294139

Mapping: [⟨1 -12 15 1 27], ⟨0 15 -14 2 -26]]

Optimal tunings:

WE: ~2 = 1200.1654 ¢, ~15/8 = 1086.8269 ¢
CWE: ~2 = 1200.0000 ¢, ~15/8 = 1086.6766 ¢

Optimal ET sequence: 21, 32e, 53, 127

Badness (Sintel): 2.82

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 176/175, 640/637, 847/845

Mapping: [⟨1 -12 15 1 27 20], ⟨0 15 -14 2 -26 -18]]

Optimal tunings:

WE: ~2 = 1200.1687 ¢, ~15/8 = 1086.8295 ¢
CWE: ~2 = 1200.0000 ¢, ~15/8 = 1086.6757 ¢

Optimal ET sequence: 21, 32e, 53, 127

Badness (Sintel): 1.88

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]]

Optimal tunings:

WE: ~2 = 1200.0839 ¢, ~15/8 = 1086.9343 ¢
CWE: ~2 = 1200.0000 ¢, ~15/8 = 1086.8593 ¢

Optimal ET sequence: 21e, 32, 53

Badness (Sintel): 2.89

Untriton

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

Subgroup: 2.3.5.7

Comma list: 225/224, 125000000/121060821

Mapping: [⟨1 -3 12 13], ⟨0 9 -19 -20]]

mapping generators: ~2, ~10/7

Optimal tunings:

WE: ~2 = 1199.8275 ¢, ~10/7 = 611.2710 ¢

error map: ⟨-0.172 +0.002 -2.533 +3.511]

CWE: ~2 = 1200.0000 ¢, ~10/7 = 611.3614 ¢

error map: ⟨0.000 +0.298 -2.181 +3.946]

Optimal ET sequence: 51, 53

Badness (Sintel): 3.64

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 225/224, 22000/21609

Mapping: [⟨1 -3 12 13 6], ⟨0 9 -19 -20 -5]]

Optimal tunings:

WE: ~2 = 1200.3591 ¢, ~10/7 = 611.5569 ¢
CWE: ~2 = 1200.0000 ¢, ~10/7 = 611.3690 ¢

Optimal ET sequence: 51, 53

Badness (Sintel): 2.46

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 225/224, 275/273, 1040/1029

Mapping: [⟨1 -3 12 13 6 20], ⟨0 9 -19 -20 -5 -32]]

Optimal tunings:

WE: ~2 = 1200.4078 ¢, ~10/7 = 611.5536 ¢
CWE: ~2 = 1200.0000 ¢, ~10/7 = 611.3392 ¢

Optimal ET sequence: 51f, 53

Badness (Sintel): 1.96

Naiadical

Subgroup: 2.3.5.7

Comma list: 225/224, 823543/800000

Mapping: [⟨1 -4 11 9], ⟨0 9 -14 -10]]

mapping generators: ~2, ~32/21

Optimal tunings:

WE: ~2 = 1202.1198 ¢, ~32/21 = 745.4675 ¢

error map: ⟨+2.120 -1.227 +0.459 -4.423]

CWE: ~2 = 1200.0000 ¢, ~32/21 = 744.1318 ¢

error map: ⟨0.000 -4.769 -4.159 -10.144]

Optimal ET sequence: 21, 29, 50, 79d, 129cdd, 179bcddd

Badness (Sintel): 3.67

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 245/242, 1617/1600

Mapping: [⟨1 -4 11 9 14], ⟨0 9 -14 -10 -17]]

Optimal tunings:

WE: ~2 = 1201.9008 ¢, ~21/16 = 745.3867 ¢
CWE: ~2 = 1200.0000 ¢, ~32/21 = 744.1777 ¢

Optimal ET sequence: 21, 29, 50, 79d

Badness (Sintel): 2.00

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 196/195, 245/242, 1001/1000

Mapping: [⟨1 -4 11 9 14 13], ⟨0 9 -14 -10 -17 -15]]

Optimal tunings:

WE: ~2 = 1201.7863 ¢, ~20/13 = 745.3344 ¢
CWE: ~2 = 1200.0000 ¢, ~20/13 = 744.1931 ¢

Optimal ET sequence: 21, 29, 50, 79d

Badness (Sintel): 1.43

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 105/104, 170/169, 196/195, 221/220, 245/242

Mapping: [⟨1 -4 11 9 14 13 14], ⟨0 9 -14 -10 -17 -15 -16]]

Optimal tunings:

WE: ~2 = 1201.9208 ¢, ~20/13 = 745.3976 ¢
CWE: ~2 = 1200.0000 ¢, ~20/13 = 744.1669 ¢

Optimal ET sequence: 21, 29g, 50, 79dg

Badness (Sintel): 1.26

Quintannic

Subgroup: 2.3.5.7

Comma list: 225/224, 9805926501/9765625000

Mapping: [⟨1 1 5 7], ⟨0 5 -23 -36]]

mapping generators: ~2, ~10000/9261

Optimal tunings:

WE: ~2 = 1200.9803 ¢, ~10000/9261 = 139.9522 ¢

error map: ⟨+0.980 -1.214 -0.313 -0.243]

CWE: ~2 = 1200.0000 ¢, ~10000/9261 = 139.8184 ¢

error map: ⟨0.000 -2.863 -2.136 -2.287]

Optimal ET sequence: 43, 60, 103, 266bcd, 369bcd

Badness (Sintel): 3.81

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]]

Optimal tunings:

WE: ~2 = 1201.0031 ¢, ~320/297 = 139.9435 ¢
CWE: ~2 = 1200.0000 ¢, ~320/297 = 139.8053 ¢

Optimal ET sequence: 43, 60e, 103, 369bcdeee, 472bbcddeee

Badness (Sintel): 1.74

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]]

Optimal tunings:

WE: ~2 = 1200.8354 ¢, ~13/12 = 139.9095 ¢
CWE: ~2 = 1200.0000 ¢, ~13/12 = 139.7997 ¢

Optimal ET sequence: 43, 60e, 103

Badness (Sintel): 1.35

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]]

Optimal tunings:

WE: ~2 = 1200.7402 ¢, ~13/12 = 139.9015 ¢
CWE: ~2 = 1200.0000 ¢, ~13/12 = 139.8038 ¢

Optimal ET sequence: 43, 60e, 103

Badness (Sintel): 1.17

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]]

mapping generators: ~2401/1728, ~35/32

Optimal tunings:

WE: ~2401/1728 = 599.7132 ¢, ~35/32 = 162.5806 ¢

error map: ⟨-0.574 -1.597 -0.937 +5.510]

CWE: ~2401/1728 = 600.0000 ¢, ~35/32 = 162.6388 ¢

error map: ⟨0.000 -0.844 +0.492 +7.007]

Optimal ET sequence: 22, 74, 96, 118d

Badness (Sintel): 4.53

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]]

Optimal tunings:

WE: ~363/256 = 599.8517 ¢, ~11/10 = 162.5518 ¢
CWE: ~363/256 = 600.0000 ¢, ~11/10 = 162.5863 ¢

Optimal ET sequence: 22, 74, 96

Badness (Sintel): 2.26

Tertiosec

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

Subgroup: 2.3.5.7

Comma list: 225/224, 14495514624/13841287201

Mapping: [⟨3 -1 12 7], ⟨0 8 -7 2]]

mapping generators: ~3072/2401, ~2048/1715

Optimal tunings:

WE: ~3072/2401 = 399.8257 ¢, ~2048/1715 = 287.5920 ¢

error map: ⟨-0.523 -1.044 -1.549 +5.138]

CWE: ~3072/2401 = 400.0000 ¢, ~2048/1715 = 287.7088 ¢

error map: ⟨0.000 -0.284 -0.276 +6.592]

Optimal ET sequence: 21, 54, 75, 96, 171d

Badness (Sintel): 10.9

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 3840/3773, 12005/11979

Mapping: [⟨3 -1 12 7 14], ⟨0 8 -7 2 -5]]

Optimal tunings:

WE: ~44/35 = 399.6550 ¢, ~33/28 = 287.5803 ¢
CWE: ~44/35 = 400.0000 ¢, ~33/28 = 287.8224 ¢

Optimal ET sequence: 21, 54, 75e

Badness (Sintel): 5.74

@@ Line 55: / Line 55: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~1225/864 = 600.000{{c}}, ~245/216 = 216.919{{c}}
+* [[WE]]: ~1225/864 = 600.3438{{c}}, ~245/216 = 216.8680{{c}}
+: [[error map]]: {{val| +0.688 -0.403 -1.463 +0.541 }}
+* [[CWE]]: ~1225/864 = 600.0000{{c}}, ~245/216 = 216.7977{{c}}
+: error map: {{val| 0.000 -1.169 -3.111 -0.849 }}
+<!-- * [[CTE]]: ~1225/864 = 600.000{{c}}, ~245/216 = 216.919{{c}}
 : [[error map]]: {{val| 0.000 -0.443 -3.232 +0.361 }}
 * [[POTE]]: ~1225/864 = 600.000{{c}}, ~245/216 = 216.744{{c}}
-: error map: {{val| 0.000 -1.492 -3.057 -1.388 }}
+: error map: {{val| 0.000 -1.492 -3.057 -1.388 }} -->
-{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 382c }}
+{{Optimal ET sequence|legend=1| 22, 50, 72, 238c, 310c, 382c, 454bccd }}
-[[Badness]] (Smith): 0.040846
+[[Badness]] (Sintel): 1.03
 === 11-limit ===
@@ Line 72: / Line 76: @@
 Optimal tunings:
-* CTE: ~99/70 = 600.000{{c}}, ~25/22 = 216.900{{c}}
+* WE: ~99/70 = 600.3051{{c}}, ~25/22 = 216.8782{{c}}
-* POTE: ~99/70 = 600.000{{c}}, ~25/22 = 216.768{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~25/22 = 216.7961{{c}}
+<!-- * CTE: ~99/70 = 600.000{{c}}, ~25/22 = 216.900{{c}}
+* POTE: ~99/70 = 600.000{{c}}, ~25/22 = 216.768{{c}} -->
 {{Optimal ET sequence|legend=0| 22, 50, 72, 166, 238c, 310c }}
-Badness (Smith): 0.018539
+Badness (Sintel): 0.613
 ==== Lizard ====
@@ Line 87: / Line 93: @@
 Optimal tunings:
-* CTE: ~55/39 = 600.000{{c}}, ~25/22 = 216.703{{c}}
+* WE: ~55/39 = 600.4824{{c}}, ~25/22 = 216.7852{{c}}
-* POTE: ~55/39 = 600.000{{c}}, ~25/22 = 216.711{{c}}
+* CWE: ~55/39 = 600.0000{{c}}, ~25/22 = 216.6247{{c}}
+<!-- * CTE: ~55/39 = 600.000{{c}}, ~25/22 = 216.703{{c}}
+* POTE: ~55/39 = 600.000{{c}}, ~25/22 = 216.711{{c}} -->
-{{Optimal ET sequence|legend=0| 22, 50, 72, 122, 194df }}
+{{Optimal ET sequence|legend=0| 22, 50, 72 }}
-Badness (Smith): 0.021781
+Badness (Sintel): 0.900
 ===== 17-limit =====
@@ Line 102: / Line 110: @@
 Optimal tunings:
-* CTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.748{{c}}
+* WE: ~17/12 = 600.5032{{c}}, ~17/15 = 216.8002{{c}}
-* POTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.619{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.6361{{c}}
+<!-- * CTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.748{{c}}
+* POTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.619{{c}} -->
-{{Optimal ET sequence|legend=0| 22, 50, 72, 122g, 194dfg }}
+{{Optimal ET sequence|legend=0| 22, 50, 72 }}
-Badness (Smith): 0.014536
+Badness (Sintel): 0.741
 ===== 19-limit =====
@@ Line 117: / Line 127: @@
 Optimal tunings:
-* CTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.677{{c}}
+* WE: ~17/12 = 600.4698{{c}}, ~17/15 = 216.6925{{c}}
-* POTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.523{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.5434{{c}}
+<!-- * CTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.677{{c}}
+* POTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.523{{c}} -->
 {{Optimal ET sequence|legend=0| 22h, 50, 72, 122g, 194dfg }}
-Badness (Smith): 0.015702
+Badness (Sintel): 0.955
 ==== Gizzard ====
@@ Line 132: / Line 144: @@
 Optimal tunings:
-* CTE: ~99/70 = 600.000{{c}}, ~25/22 = 216.928{{c}}
+* WE: ~99/70 = 600.2896{{c}}, ~25/22 = 216.9343{{c}}
-* POTE: ~99/70 = 600.000{{c}}, ~25/22 = 216.830{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~25/22 = 216.8501{{c}}
+<!-- * CTE: ~99/70 = 600.000{{c}}, ~25/22 = 216.928{{c}}
+* POTE: ~99/70 = 600.000{{c}}, ~25/22 = 216.830{{c}} -->
 {{Optimal ET sequence|legend=0| 22f, 72, 166, 238cf }}
-Badness (Smith): 0.020252
+Badness (Sintel): 0.837
 ===== 17-limit =====
@@ Line 147: / Line 161: @@
 Optimal tunings:
-* CTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.943{{c}}
+* WE: ~17/12 = 600.3227{{c}}, ~17/15 = 216.9414{{c}}
-* POTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.825{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.8469{{c}}
+<!-- * CTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.943{{c}}
+* POTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.825{{c}} -->
 {{Optimal ET sequence|legend=0| 22f, 72, 166g, 238cfg }}
-Badness (Smith): 0.013624
+Badness (Sintel): 0.694
 ===== 19-limit =====
@@ Line 162: / Line 178: @@
 Optimal tunings:
-* CTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.918{{c}}
+* WE: ~17/12 = 600.2637{{c}}, ~17/15 = 216.9570{{c}}
-* POTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.862{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.8687{{c}}
+<!-- * CTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.918{{c}}
+* POTE: ~17/12 = 600.000{{c}}, ~17/15 = 216.862{{c}} -->
 {{Optimal ET sequence|legend=0| 72, 94, 166g }}
-Badness (Smith): 0.014810
+Badness (Sintel): 0.901
 === Mage ===
@@ Line 177: / Line 195: @@
 Optimal tunings:
-* CTE: ~77/54 = 600.000{{c}}, ~55/48 = 217.247{{c}}
+* WE: ~77/54 = 600.6486{{c}}, ~55/48 = 217.1099{{c}}
-* POTE: ~77/54 = 600.000{{c}}, ~55/48 = 216.876{{c}}
+* CWE: ~77/54 = 600.0000{{c}}, ~55/48 = 216.9841{{c}}
+<!-- * CTE: ~77/54 = 600.000{{c}}, ~55/48 = 217.247{{c}}
+* POTE: ~77/54 = 600.000{{c}}, ~55/48 = 216.876{{c}} -->
 {{Optimal ET sequence|legend=0| 22, 50e, 72ee }}
-Badness (Smith): 0.057799
+Badness (Sintel): 1.91
 == Tritonic ==
@@ Line 191: / Line 211: @@
 [[Comma list]]: 225/224, 50421/50000
-{{Mapping|legend=1| 1 4 -3 -3 | 0 -5 11 12 }}
+{{Mapping|legend=1| 1 -1 8 9 | 0 5 -11 -12 }}
+: mapping generators: ~2, ~10/7
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~7/5 = 580.286{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1201.3539{{c}}, ~10/7 = 620.4131{{c}}
+: [[error map]]: {{val| +1.354 -1.243 -0.027 -1.598 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 619.6778{{c}}
+: error map: {{val| 0.000 -3.566 -2.769 -4.959 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~10/7 = 619.714{{c}} -->
 {{Optimal ET sequence|legend=1| 29, 31, 60, 91, 122, 213bcd }}
-[[Badness]] (Smith): 0.047578
+[[Badness]] (Sintel): 1.20
 === 11-limit ===
@@ Line 204: / Line 230: @@
 Comma list: 121/120, 225/224, 441/440
-Mapping: {{mapping| 1 4 -3 -3 2 | 0 -5 11 12 3 }}
+Mapping: {{mapping| 1 -1 8 9 5 | 0 5 -11 -12 -3 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 580.267{{c}}
+Optimal tunings:
+* WE: ~2 = 1201.7116{{c}}, ~10/7 = 620.6166{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.6890{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~10/7 = 619.733{{c}} -->
-{{Optimal ET sequence|legend=0| 29, 31, 60e }}
+{{Optimal ET sequence|legend=0| 29, 31, 60e, 91e, 213bcdeee }}
-Badness (Smith): 0.023659
+Badness (Sintel): 0.782
 ==== 13-limit ====
@@ Line 217: / Line 246: @@
 Comma list: 105/104, 121/120, 196/195, 275/273
-Mapping: {{mapping| 1 4 -3 -3 2 -5 | 0 -5 11 12 3 18 }}
+Mapping: {{mapping| 1 -1 8 9 5 13 | 0 5 -11 -12 -3 -18 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 580.108{{c}}
+Optimal tunings:
+* WE: ~2 = 1201.5355{{c}}, ~10/7 = 620.6855{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.8469{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~10/7 = 619.892{{c}} -->
 {{Optimal ET sequence|legend=0| 29, 31, 60e }}
-Badness (Smith): 0.022993
+Badness (Sintel): 0.950
 ==== 17-limit ====
@@ Line 230: / Line 262: @@
 Comma list: 105/104, 121/120, 154/153, 196/195, 273/272
-Mapping: {{mapping| 1 4 -3 -3 2 -5 -8 | 0 -5 11 12 3 18 25 }}
+Mapping: {{mapping| 1 -1 8 9 5 13 17 | 0 5 -11 -12 -3 -18 -25 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 580.055{{c}}
+Optimal tunings:
+* WE: ~2 = 1201.5260{{c}}, ~10/7 = 620.7330{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.8986{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~10/7 = 619.945{{c}} -->
 {{Optimal ET sequence|legend=0| 29g, 31, 60e }}
-Badness (Smith): 0.019093
+Badness (Sintel): 0.973
 ==== 19-limit ====
@@ Line 243: / Line 278: @@
 Comma list: 77/76, 105/104, 121/120, 153/152, 196/195, 273/272
-Mapping: {{mapping| 1 4 -3 -3 2 -5 -8 -3 | 0 -5 11 12 3 18 25 15 }}
+Mapping: {{mapping| 1 -1 8 9 5 13 17 12 | 0 5 -11 -12 -3 -18 -25 -15 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 580.026{{c}}
+Optimal tunings:
+* WE: ~2 = 1201.3100{{c}}, ~10/7 = 620.6509{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.9328{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~10/7 = 619.974{{c}} -->
 {{Optimal ET sequence|legend=0| 29g, 31, 60e }}
-Badness (Smith): 0.017010
+Badness (Sintel): 1.03
 ==== 23-limit ====
@@ Line 256: / Line 294: @@
 Comma list: 77/76, 105/104, 115/114, 121/120, 153/152, 161/160, 196/195
-Mapping: {{mapping| 1 4 -3 -3 2 -5 -8 -3 5 | 0 -5 11 12 3 18 25 15 -1 }}
+Mapping: {{mapping| 1 -1 8 9 5 13 17 12 4 | 0 5 -11 -12 -3 -18 -25 -15 1 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 580.009{{c}}
+Optimal tunings:
+* WE: ~2 = 1201.4074{{c}}, ~10/7 = 620.7185{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.9548{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~10/7 = 619.991{{c}} -->
 {{Optimal ET sequence|legend=0| 29g, 31, 60e }}
-Badness (Smith): 0.014471
+Badness (Sintel): 1.04
 === Tritoni ===
@@ Line 269: / Line 310: @@
 Comma list: 225/224, 385/384, 27783/27500
-Mapping: {{mapping| 1 4 -3 -3 17 | 0 -5 11 12 -28 }}
+Mapping: {{mapping| 1 -1 8 9 -11 | 0 5 -11 -12 28 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 580.389{{c}}
+Optimal tunings:
+* WE: ~2 = 1201.0888{{c}}, ~10/7 = 620.1733{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.6146{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~10/7 = 619.611{{c}} -->
 {{Optimal ET sequence|legend=0| 31, 91, 122, 153d }}
-Badness (Smith): 0.045456
+Badness (Sintel): 1.50
 == Septimin ==
@@ Line 284: / Line 328: @@
 [[Comma list]]: 225/224, 84035/82944
-{{Mapping|legend=1| 1 4 1 5 | 0 -11 6 -10 }}
+{{Mapping|legend=1| 1 -7 7 -5 | 0 11 -6 10 }}
+: mapping generators: ~2, ~12/7
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~7/6 = 263.632{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1201.2452{{c}}, ~12/7 = 937.3394{{c}}
+: [[error map]]: {{val| +1.245 +0.062 -1.633 -1.658 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~12/7 = 936.4036{{c}}
+: error map: {{val| 0.000 -1.516 -4.735 -4.790 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~12/7 = 936.368{{c}} -->
 {{Optimal ET sequence|legend=1| 41, 91, 132d }}
-[[Badness]] (Smith): 0.054502
+[[Badness]] (Sintel): 1.38
 === 11-limit ===
@@ Line 297: / Line 347: @@
 Comma list: 225/224, 245/242, 385/384
-Mapping: {{mapping| 1 4 1 5 5 | 0 -11 6 -10 -7 }}
+Mapping: {{mapping| 1 -7 7 -5 -2 | 0 11 -6 10 7 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/6 = 263.634{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.8059{{c}}, ~12/7 = 936.9952{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3906{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~12/7 = 936.366{{c}} -->
 {{Optimal ET sequence|legend=0| 41, 91, 223cdef }}
-Badness (Smith): 0.031309
+Badness (Sintel): 1.04
 === 13-limit ===
@@ Line 310: / Line 363: @@
 Comma list: 105/104, 144/143, 196/195, 245/242
-Mapping: {{mapping| 1 4 1 5 5 7 | 0 -11 6 -10 -7 -15 }}
+Mapping: {{mapping| 1 -7 7 -5 -2 -8 | 0 11 -6 10 7 15 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/6 = 263.700{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.5990{{c}}, ~12/7 = 936.7670{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3196{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~12/7 = 936.300{{c}} -->
 {{Optimal ET sequence|legend=0| 41, 91 }}
-Badness (Smith): 0.023117
+Badness (Sintel): 0.955
 == Merman ==
@@ Line 325: / Line 381: @@
 [[Comma list]]: 225/224, 2500000/2470629
-{{Mapping|legend=1| 1 5 -5 -5 | 0 -7 15 16 }}
+{{Mapping|legend=1| 1 -2 10 11 | 0 7 -15 -16 }}
+: mapping generators: ~2, ~10/7
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~7/5 = 585.585{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.3898{{c}}, ~10/7 = 614.6413{{c}}
+: [[error map]]: {{val| +0.390 -0.435 -1.630 +1.634 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 614.4073{{c}}
+: error map: {{val| 0.000 -1.104 -2.423 +0.657 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~10/7 = 614.415{{c}} -->
 {{Optimal ET sequence|legend=1| 41, 84, 125 }}
-[[Badness]] (Smith): 0.055078
+[[Badness]] (Sintel): 1.39
 === 11-limit ===
@@ Line 338: / Line 400: @@
 Comma list: 225/224, 441/440, 1344/1331
-Mapping: {{mapping| 1 5 -5 -5 2 | 0 -7 15 16 3 }}
+Mapping: {{mapping| 1 -2 10 11 5 | 0 7 -15 -16 -3 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 585.606{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9578{{c}}, ~10/7 = 614.3720{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.3943{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~10/7 = 614.394{{c}} -->
 {{Optimal ET sequence|legend=0| 41, 84, 125e }}
-Badness (Smith): 0.036383
+Badness (Sintel): 1.20
 === 13-limit ===
@@ Line 351: / Line 416: @@
 Comma list: 144/143, 225/224, 364/363, 441/440
-Mapping: {{mapping| 1 5 -5 -5 2 12 | 0 -7 15 16 3 -17 }}
+Mapping: {{mapping| 1 -2 10 11 5 -5 | 0 7 -15 -16 -3 17 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 585.657{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.7422{{c}}, ~10/7 = 614.2110{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.3442{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~10/7 = 614.343{{c}} -->
 {{Optimal ET sequence|legend=0| 41, 84, 125e, 209ef, 293ef }}
-Badness (Smith): 0.027544
+Badness (Sintel): 1.14
 == Slender ==
@@ Line 367: / Line 435: @@
 {{Mapping|legend=1| 1 2 2 3 | 0 -13 10 -6 }}
+: mapping generators: ~2, ~49/48
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~49/48 = 38.413{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.3816{{c}}, ~49/48 = 38.4256{{c}}
+: [[error map]]: {{val| +0.382 -0.725 -1.295 +1.765 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/48 = 38.4079{{c}}
+: error map: {{val| 0.000 -1.257 -2.235 +0.727 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~49/48 = 38.413{{c}} -->
-{{Optimal ET sequence|legend=1| 31, 94, 125 }}
+{{Optimal ET sequence|legend=1| 31, 94, 125, 406c }}
-[[Badness]] (Smith): 0.056934
+[[Badness]] (Sintel): 1.44
 === 11-limit ===
@@ Line 381: / Line 455: @@
 Mapping: {{mapping| 1 2 2 3 4 | 0 -13 10 -6 -17 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~49/48 = 38.387{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.4983{{c}}, ~49/48 = 38.4030{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 38.3775{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~49/48 = 38.387{{c}} -->
 {{Optimal ET sequence|legend=0| 31, 63, 94, 125 }}
-Badness (Smith): 0.025342
+Badness (Sintel): 0.838
 === 13-limit ===
@@ Line 394: / Line 471: @@
 Mapping: {{mapping| 1 2 2 3 4 3 | 0 -13 10 -6 -17 22 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~49/48 = 38.314{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.1728{{c}}, ~49/48 = 38.3192{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 38.3129{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~49/48 = 38.314{{c}} -->
 {{Optimal ET sequence|legend=0| 31, 63, 94 }}
-Badness (Smith): 0.025913
+Badness (Sintel): 1.07
 == Triton ==
@@ Line 408: / Line 488: @@
 {{Mapping|legend=1| 1 0 6 7 | 0 3 -7 -8 }}
+: mapping generators: ~2, ~10/7
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~7/5 = 568.865{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1203.3828{{c}}, ~10/7 = 632.9137{{c}}
+: [[error map]]: {{val| +3.383 -3.214 +3.587 -8.457 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 630.9827{{c}}
+: error map: {{val| 0.000 -9.007 -3.192 -16.687 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~10/7 = 631.135{{c}} -->
 {{Optimal ET sequence|legend=1| 2, 17d, 19, 78bd, 97bd }}
-[[Badness]] (Smith): 0.059245
+[[Badness]] (Sintel): 1.50
 === 11-limit ===
@@ Line 422: / Line 508: @@
 Mapping: {{mapping| 1 0 6 7 4 | 0 3 -7 -8 -1 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 569.144{{c}}
+Optimal tunings:
+* WE: ~2 = 1201.3875{{c}}, ~10/7 = 631.5852{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 630.8007{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~7/5 = 569.144{{c}} -->
-{{Optimal ET sequence|legend=0| 2, 17d, 19, 59bde, 78bde, 97bde }}
+{{Optimal ET sequence|legend=0| 2, 17d, 19 }}
-Badness (Smith): 0.045675
+Badness (Sintel): 1.51
 == Marvolo ==
@@ Line 434: / Line 523: @@
 {{Mapping|legend=1| 1 2 1 1 | 0 -6 19 26 }}
+: mapping generators: ~2, ~21/20
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~21/20 = 83.348{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.7714{{c}}, ~21/20 = 83.4014{{c}}
+: [[error map]]: {{val| +0.772 -0.820 -0.916 +0.381 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 83.3640{{c}}
+: error map: {{val| 0.000 -2.139 -2.398 -1.362 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~21/20 = 83.348{{c}} -->
-{{Optimal ET sequence|legend=1| 29, 43, 72, 619bcd, 691bcd }}
+{{Optimal ET sequence|legend=1| 29, 43, 72, 619bbccd, 691bbccd }}
-[[Badness]] (Smith): 0.083338
+[[Badness]] (Sintel): 2.11
 === 11-limit ===
@@ Line 448: / Line 543: @@
 Mapping: {{mapping| 1 2 1 1 2 | 0 -6 19 26 21 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/20 = 83.340{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.7075{{c}}, ~21/20 = 83.3888{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3564{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~21/20 = 83.340{{c}} -->
 {{Optimal ET sequence|legend=0| 29, 43, 72 }}
-Badness (Smith): 0.028965
+Badness (Sintel): 0.958
 === 13-limit ===
@@ Line 461: / Line 559: @@
 Mapping: {{mapping| 1 2 1 1 2 3 | 0 -6 19 26 21 10 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/20 = 83.330{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.9467{{c}}, ~21/20 = 83.3956{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3516{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~21/20 = 83.330{{c}} -->
-{{Optimal ET sequence|legend=0| 29, 43, 72, 115f }}
+{{Optimal ET sequence|legend=0| 29, 43, 72 }}
-Badness (Smith): 0.021470
+Badness (Sintel): 0.887
 === 17-limit ===
@@ Line 474: / Line 575: @@
 Mapping: {{mapping| 1 2 1 1 2 3 2 | 0 -6 19 26 21 10 30 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/20 = 83.330{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.9606{{c}}, ~21/20 = 83.4030{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3594{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~21/20 = 83.330{{c}} -->
 {{Optimal ET sequence|legend=0| 29g, 43, 72 }}
-Badness (Smith): 0.014924
+Badness (Sintel): 0.760
 === 19-limit ===
@@ Line 487: / Line 591: @@
 Mapping: {{mapping| 1 2 1 1 2 3 2 3 | 0 -6 19 26 21 10 30 18 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/20 = 83.330{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.7625{{c}}, ~21/20 = 83.3895{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3551{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~21/20 = 83.330{{c}} -->
 {{Optimal ET sequence|legend=0| 29g, 43, 72 }}
-Badness (Smith): 0.014722
+Badness (Sintel): 0.895
 == Enneaportent ==
@@ Line 499: / Line 606: @@
 {{Mapping|legend=1| 9 0 28 11 | 0 2 -1 2 }}
-: Mapping generators: ~2592/2401, ~12005/6912
+: mapping generators: ~2592/2401, ~12005/6912
-[[Optimal tuning]] ([[POTE]]): ~2592/2401 = 133.3333{{c}}, ~12005/6912 = 950.1680{{c}} (~1728/1715 = 16.8347{{c}})
+[[Optimal tuning]]s:
+* [[WE]]: ~2592/2401 = 133.4174{{c}}, ~12005/6912 = 950.7667{{c}} (~1728/1715 = 16.8452{{c}})
+: [[error map]]: {{val| +0.756 -0.422 -1.395 +0.298 }}
+* [[CWE]]: ~2592/2401 = 133.3333{{c}}, ~12005/6912 = 950.2969{{c}} (~1728/1715 = 16.9636{{c}})
+: error map: {{val| 0.000 -1.361 -3.277 -1.565 }}
+<!-- * [[POTE]]: ~2592/2401 = 133.3333{{c}}, ~12005/6912 = 950.1680{{c}} (~1728/1715 = 16.8347{{c}}) -->
-{{Optimal ET sequence|legend=1| 9, 63, 72, 495bcd }}
+{{Optimal ET sequence|legend=1| 9, 54, 63, 72, 495bccd, 567bcccd }}
-[[Badness]] (Smith): 0.093679
+[[Badness]] (Sintel): 2.37
 === 11-limit ===
@@ Line 514: / Line 626: @@
 Mapping: {{mapping| 9 0 28 11 24 | 0 2 -1 2 1 }}
-Optimal tuning (POTE): ~121/112 = 133.3333{{c}}, ~210/121 = 950.1873{{c}} (~99/98 = 16.8540{{c}})
+Optimal tunings:
+* WE: ~121/112 = 133.4071{{c}}, ~210/121 = 950.7131{{c}} (~99/98 = 16.8633{{c}})
+* CWE: ~121/112 = 133.3333{{c}}, ~210/121 = 950.2994{{c}} (~99/98 = 16.9661{{c}})
+<!-- POTE: ~121/112 = 133.3333{{c}}, ~210/121 = 950.1873{{c}} (~99/98 = 16.8540{{c}}) -->
-{{Optimal ET sequence|legend=0| 9, 63, 72, 423cd, 495bcd }}
+{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}
-Badness (Smith): 0.030426
+Badness (Sintel): 1.01
 === 13-limit ===
@@ Line 527: / Line 642: @@
 Mapping: {{mapping| 9 0 28 11 24 19 | 0 2 -1 2 1 2 }}
-Optimal tuning (POTE): ~14/13 = 133.3333{{c}}, ~26/15 = 950.2867{{c}} (~105/104 = 16.9534{{c}})
+Optimal tunings:
+* WE: ~14/13 = 133.4245{{c}}, ~26/15 = 950.9362{{c}} (~105/104 = 16.9650{{c}})
+* CWE: ~14/13 = 133.3333{{c}}, ~26/15 = 950.4364{{c}} (~99/98 = 17.1031{{c}})
+<!-- POTE: ~14/13 = 133.3333{{c}}, ~26/15 = 950.2867{{c}} (~105/104 = 16.9534{{c}}) -->
-{{Optimal ET sequence|legend=0| 9, 63, 72, 279cf }}
+{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}
-Badness (Smith): 0.022322
+Badness (Sintel): 0.922
 == Gracecordial ==
@@ Line 541: / Line 659: @@
 {{Mapping|legend=1| 1 0 34 63 | 0 1 -20 -38 }}
+: mapping generators: ~2, ~3
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 700.824{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.4904{{c}}, ~3/2 = 701.1103{{c}}
+: [[error map]]: {{val| +0.490 -0.354 -1.655 +1.241 }}
+* [[CWE]]: ~2 = 1200.3333{{c}}, ~3/2 = 700.8112{{c}}
+: error map: {{val| 0.000 -1.144 -2.537 +0.349 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 700.824{{c}} -->
-{{Optimal ET sequence|legend=1| 12, 113, 125, 238c, 363c }}
+{{Optimal ET sequence|legend=1| 12, …, 113, 125, 238c, 363c }}
-[[Badness]] (Smith): 0.096279
+[[Badness]] (Sintel): 2.44
 === 11-limit ===
@@ Line 555: / Line 679: @@
 Mapping: {{mapping| 1 0 34 63 -90 | 0 1 -20 -38 59 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.834{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.5571{{c}}, ~3/2 = 701.1589{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8328{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.834{{c}} -->
-{{Optimal ET sequence|legend=0| 12e, 101cde, 113, 125, 238c }}
+{{Optimal ET sequence|legend=0| 12e, 113, 125, 238c }}
-Badness (Smith): 0.089588
+Badness (Sintel): 2.96
 ==== 13-limit ====
@@ Line 568: / Line 695: @@
 Mapping: {{mapping| 1 0 34 63 -90 -66 | 0 1 -20 -38 59 44 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.841{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.6282{{c}}, ~3/2 = 701.2080{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8421{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.841{{c}} -->
-{{Optimal ET sequence|legend=0| 12e, 101cde, 113, 125f, 238cf }}
+{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}
-Badness (Smith): 0.052235
+Badness (Sintel): 2.16
 ==== 17-limit ====
@@ Line 581: / Line 711: @@
 Mapping: {{mapping| 1 0 34 63 -90 -66 -7 | 0 1 -20 -38 59 44 7 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.841{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.5058{{c}}, ~3/2 = 701.1360{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8414{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.841{{c}} -->
-{{Optimal ET sequence|legend=0| 12e, 101cde, 113, 125f, 238cf }}
+{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}
-Badness (Smith): 0.038565
+Badness (Sintel): 1.96
 ==== 19-limit ====
@@ Line 594: / Line 727: @@
 Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 | 0 1 -20 -38 59 44 7 -3 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.842{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.4418{{c}}, ~3/2 = 701.0999{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8425{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.842{{c}} -->
-{{Optimal ET sequence|legend=0| 12e, 101cde, 113, 125f, 238cf }}
+{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}
-Badness (Smith): 0.028165
+Badness (Sintel): 1.71
 ==== 23-limit ====
@@ Line 607: / Line 743: @@
 Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 | 0 1 -20 -38 59 44 7 -3 30 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.843{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.4641{{c}}, ~3/2 = 701.1145{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8444{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.843{{c}} -->
-{{Optimal ET sequence|legend=0| 12e, 101cde, 113, 238cfi }}
+{{Optimal ET sequence|legend=0| 12e, 113, 238cfi }}
-Badness (Smith): 0.021879
+Badness (Sintel): 1.57
 ==== 29-limit ====
@@ Line 620: / Line 759: @@
 Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 | 0 1 -20 -38 59 44 7 -3 30 34 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.842{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.4400{{c}}, ~3/2 = 701.0986{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8428{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.842{{c}} -->
-{{Optimal ET sequence|legend=0| 12e, 101cde, 113, 125f, 238cfi }}
+{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cfi }}
-Badness (Smith): 0.018011
+Badness (Sintel): 1.50
 ==== 31-limit ====
@@ Line 633: / Line 775: @@
 Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 -79 | 0 1 -20 -38 59 44 7 -3 30 34 53 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.838{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.4178{{c}}, ~3/2 = 701.0822{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8396{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.838{{c}} -->
-{{Optimal ET sequence|legend=0| 12e, 101cdek, 113, 125f, 238cfi }}
+{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cfi }}
-Badness (Smith): 0.016007
+Badness (Sintel): 1.53
 === Gracecord ===
@@ Line 646: / Line 791: @@
 Mapping: {{mapping| 1 0 34 63 89 | 0 1 -20 -38 -54 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.885{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.6064{{c}}, ~3/2 = 701.2398{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8718{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.885{{c}} -->
-{{Optimal ET sequence|legend=0| 12, 101cd, 113 }}
+{{Optimal ET sequence|legend=0| 12, …, 101cd, 113 }}
-Badness (Smith): 0.066964
+Badness (Sintel): 2.21
 ==== 13-limit ====
@@ Line 659: / Line 807: @@
 Mapping: {{mapping| 1 0 34 63 89 113 | 0 1 -20 -38 -54 -69 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.890{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.6225{{c}}, ~3/2 = 701.2539{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8781{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.890{{c}} -->
-{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}
+{{Optimal ET sequence|legend=0| 12f, …, 101cdf, 113 }}
-Badness (Smith): 0.044196
+Badness (Sintel): 1.83
 ==== 17-limit ====
@@ Line 672: / Line 823: @@
 Mapping: {{mapping| 1 0 34 63 89 113 -7 | 0 1 -20 -38 -54 -69 7 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.870{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.3308{{c}}, ~3/2 = 701.0632{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8654{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.870{{c}} -->
 {{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}
-Badness (Smith): 0.036637
+Badness (Sintel): 1.87
 ==== 19-limit ====
@@ Line 685: / Line 839: @@
 Mapping: {{mapping| 1 0 34 63 89 113 -7 9 | 0 1 -20 -38 -54 -69 7 -3 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 700.866{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.2658{{c}}, ~3/2 = 701.0213{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8629{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~3/2 = 700.866{{c}} -->
 {{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}
-Badness (Smith): 0.027559
+Badness (Sintel): 1.68
 == Alphorn ==
@@ Line 696: / Line 853: @@
 [[Comma list]]: 225/224, 5764801/5668704
-{{Mapping|legend=1| 1 9 0 13 | 0 -16 5 -22 }}
+{{Mapping|legend=1| 1 -7 5 -9 | 0 16 -5 22 }}
+: mapping generators: ~2, ~35/24
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~48/35 = 556.221{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1201.3004{{c}}, ~35/24 = 644.4767{{c}}
+: [[error map]]: {{val| +1.300 +0.569 -2.195 -2.043 }}
+* [[CWE]]: ~2 = 1200.3333{{c}}, ~35/24 = 643.8137{{c}}
+: error map: {{val| 0.000 -0.936 -5.382 -4.924 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~35/24 = 643.779{{c}} -->
-{{Optimal ET sequence|legend=1| 28d, 41, 151cd, 192cd, 233cd }}
+{{Optimal ET sequence|legend=1| 13d, 28d, 41, 151cd, 192cdd, 233ccdd }}
-[[Badness]] (Smith): 0.129258
+[[Badness]] (Sintel): 3.27
 === 11-limit ===
@@ Line 709: / Line 872: @@
 Comma list: 225/224, 385/384, 12250/11979
-Mapping: {{mapping| 1 9 0 13 3 | 0 -16 5 -22 1 }}
+Mapping: {{mapping| 1 -7 5 -9 4 | 0 16 -5 22 -1 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/8 = 556.144{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.5123{{c}}, ~16/11 = 644.1307{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~16/11 = 643.8662{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~11/8 = 556.144{{c}} -->
-{{Optimal ET sequence|legend=0| 28d, 41, 315cde }}
+{{Optimal ET sequence|legend=0| 13d, 28d, 41 }}
-Badness (Smith): 0.073459
+Badness (Sintel): 2.43
 == Misneb ==
@@ Line 724: / Line 890: @@
 [[Comma list]]: 225/224, 4194304/4117715
-{{Mapping|legend=1| 1 3 1 3 | 0 -15 14 -2 }}
+{{Mapping|legend=1| 1 -12 15 1 | 0 15 -14 2 }}
+: mapping generators: ~2, ~15/8
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~16/15 = 113.235{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.7642{{c}}, ~15/8 = 1086.5513{{c}}
+: [[error map]]: {{val| -0.236 -0.856 -1.569 +4.041 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~15/8 = 1086.7633{{c}}
+: error map: {{val| 0.000 -0.506 -0.999 +4.701 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~15/8 = 1086.765{{c}} -->
 {{Optimal ET sequence|legend=1| 21, 32, 53 }}
-[[Badness]] (Smith): 0.140970
+[[Badness]] (Sintel): 3.57
 === 11-limit ===
@@ Line 737: / Line 909: @@
 Comma list: 99/98, 176/175, 1310720/1294139
-Mapping: {{mapping| 1 3 1 3 1 | 0 -15 14 -2 26 }}
+Mapping: {{mapping| 1 -12 15 1 27 | 0 15 -14 2 -26 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~16/15 = 113.323{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.1654{{c}}, ~15/8 = 1086.8269{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.6766{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~15/8 = 1086.677{{c}} -->
-{{Optimal ET sequence|legend=0| 21, 32e, 53, 127, 180de }}
+{{Optimal ET sequence|legend=0| 21, 32e, 53, 127 }}
-Badness (Smith): 0.085390
+Badness (Sintel): 2.82
 ==== 13-limit ====
@@ Line 750: / Line 925: @@
 Comma list: 99/98, 176/175, 640/637, 847/845
-Mapping: {{mapping| 1 3 1 3 1 2 | 0 -15 14 -2 26 18 }}
+Mapping: {{mapping| 1 -12 15 1 27 20 | 0 15 -14 2 -26 -18 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~16/15 = 113.323{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.1687{{c}}, ~15/8 = 1086.8295{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.6757{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~16/15 = 113.323{{c}} -->
-{{Optimal ET sequence|legend=0| 21, 32e, 53, 127, 180de }}
+{{Optimal ET sequence|legend=0| 21, 32e, 53, 127 }}
-Badness (Smith): 0.045569
+Badness (Sintel): 1.88
 === Musneb ===
@@ Line 765: / Line 943: @@
 Mapping: {{mapping| 1 3 1 3 6 | 0 -15 14 -2 -27 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~16/15 = 113.142{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.0839{{c}}, ~15/8 = 1086.9343{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.8593{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~15/8 = 1086.858{{c}} -->
-{{Optimal ET sequence|legend=0| 32, 53, 191de, 244cddee, 297cddee }}
+{{Optimal ET sequence|legend=0| 21e, 32, 53 }}
-Badness (Smith): 0.087333
+Badness (Sintel): 2.89
 == Untriton ==
@@ Line 778: / Line 959: @@
 [[Comma list]]: 225/224, 125000000/121060821
-{{Mapping|legend=1| 1 6 -7 -7 | 0 -9 19 20 }}
+{{Mapping|legend=1| 1 -3 12 13 | 0 9 -19 -20 }}
+: mapping generators: ~2, ~10/7
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~7/5 = 588.641{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.8275{{c}}, ~10/7 = 611.2710{{c}}
+: [[error map]]: {{val| -0.172 +0.002 -2.533 +3.511 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 611.3614{{c}}
+: error map: {{val| 0.000 +0.298 -2.181 +3.946 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~10/7 = 611.359{{c}} -->
-{{Optimal ET sequence|legend=1| 51, 53, 316cd, 369cdd, 422cdd }}
+{{Optimal ET sequence|legend=1| 51, 53 }}
-[[Badness]] (Smith): 0.143976
+[[Badness]] (Sintel): 3.64
 === 11-limit ===
@@ Line 791: / Line 978: @@
 Comma list: 121/120, 225/224, 22000/21609
-Mapping: {{mapping| 1 6 -7 -7 1 | 0 -9 19 20 5 }}
+Mapping: {{mapping| 1 -3 12 13 6 | 0 9 -19 -20 -5 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 588.626{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.3591{{c}}, ~10/7 = 611.5569{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 611.3690{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~10/7 = 611.374{{c}} -->
 {{Optimal ET sequence|legend=0| 51, 53 }}
-Badness (Smith): 0.074295
+Badness (Sintel): 2.46
 === 13-limit ===
@@ Line 804: / Line 994: @@
 Comma list: 121/120, 225/224, 275/273, 1040/1029
-Mapping: {{mapping| 1 6 -7 -7 1 -12 | 0 -9 19 20 5 32 }}
+Mapping: {{mapping| 1 -3 12 13 6 20 | 0 9 -19 -20 -5 -32 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 588.654{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.4078{{c}}, ~10/7 = 611.5536{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 611.3392{{c}}
+<!-- POTE: ~2 = 1200.000{{c}}, ~10/7 = 588.654{{c}} -->
 {{Optimal ET sequence|legend=0| 51f, 53 }}
-Badness (Smith): 0.047441
+Badness (Sintel): 1.96
 == Naiadical ==
@@ Line 817: / Line 1,010: @@
 [[Comma list]]: 225/224, 823543/800000
-{{Mapping|legend=1| 1 5 -3 -1 | 0 -9 14 10 }}
+{{Mapping|legend=1| 1 -4 11 9 | 0 9 -14 -10 }}
+: mapping generators: ~2, ~32/21
 [[Optimal tuning]]s:
-* [[WE]]: ~2 = 1202.120{{c}}, ~21/16 = 456.652{{c}}
+* [[WE]]: ~2 = 1202.1198{{c}}, ~32/21 = 745.4675{{c}}
-* [[CWE]]: ~2 = 1200.000{{c}}, ~21/16 = 455.868{{c}}
+: [[error map]]: {{val| +2.120 -1.227 +0.459 -4.423 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~32/21 = 744.1318{{c}}
+: error map: {{val| 0.000 -4.769 -4.159 -10.144 }}
-{{Optimal ET sequence|legend=1| 21, 29, 50, 79d }}
+{{Optimal ET sequence|legend=1| 21, 29, 50, 79d, 129cdd, 179bcddd }}
-[[Badness]] (Sintel): 3.667
+[[Badness]] (Sintel): 3.67
 === 11-limit ===
@@ Line 832: / Line 1,028: @@
 Comma list: 225/224, 245/242, 1617/1600
-Mapping: {{Mapping| 1 5 -3 -1 -3 | 0 -9 14 10 17 }}
+Mapping: {{Mapping| 1 -4 11 9 14 | 0 9 -14 -10 -17 }}
 Optimal tunings:
-* WE: ~2 = 1201.901, ~21/16{{c}} = 456.514{{c}}
+* WE: ~2 = 1201.9008{{c}}, ~21/16 = 745.3867{{c}}
-* CWE: ~2 = 1200.000, ~21/16{{c}} = 455.822{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~32/21 = 744.1777{{c}}
 {{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}
-Badness (Sintel): 1.998
+Badness (Sintel): 2.00
 === 13-limit ===
@@ Line 847: / Line 1,043: @@
 Comma list: 105/104, 196/195, 245/242, 1001/1000
-Mapping: {{Mapping| 1 5 -3 -1 -3 -2 | 0 -9 14 10 17 15 }}
+Mapping: {{Mapping| 1 -4 11 9 14 13 | 0 9 -14 -10 -17 -15 }}
 Optimal tunings:
-* WE: ~2 = 1201.786{{c}}, ~13/10 = 456.452{{c}}
+* WE: ~2 = 1201.7863{{c}}, ~20/13 = 745.3344{{c}}
-* CWE: ~2 = 1200.000{{c}}, ~13/10 = 455.807{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.1931{{c}}
 {{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}
-Badness (Sintel): 1.430
+Badness (Sintel): 1.43
 === 17-limit ===
@@ Line 862: / Line 1,058: @@
 Comma list: 105/104, 170/169, 196/195, 221/220, 245/242
-Mapping: {{Mapping| 1 5 -3 -1 -3 -2 -2 | 0 -9 14 10 17 15 16 }}
+Mapping: {{Mapping| 1 -4 11 9 14 13 14 | 0 9 -14 -10 -17 -15 -16 }}
 Optimal tunings:
-* WE: ~2 = 1201.921{{c}}, ~13/10 = 456.523{{c}}
+* WE: ~2 = 1201.9208{{c}}, ~20/13 = 745.3976{{c}}
-* CWE: ~2 = 1200.000{{c}}, ~13/10 = 455.833{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.1669{{c}}
 {{Optimal ET sequence|legend=0| 21, 29g, 50, 79dg }}
-Badness (Sintel): 1.260
+Badness (Sintel): 1.26
 == Quintannic ==
@@ Line 878: / Line 1,074: @@
 {{Mapping|legend=1| 1 1 5 7 | 0 5 -23 -36 }}
+: mapping generators: ~2, ~10000/9261
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~10000/9261 = 139.838{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.9803{{c}}, ~10000/9261 = 139.9522{{c}}
+: [[error map]]: {{val| +0.980 -1.214 -0.313 -0.243 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~10000/9261 = 139.8184{{c}}
+: error map: {{val| 0.000 -2.863 -2.136 -2.287 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~10000/9261 = 139.838{{c}} -->
 {{Optimal ET sequence|legend=1| 43, 60, 103, 266bcd, 369bcd }}
-[[Badness]] (Smith): 0.150565
+[[Badness]] (Sintel): 3.81
 === 11-limit ===
@@ Line 892: / Line 1,094: @@
 Mapping: {{mapping| 1 1 5 7 8 | 0 5 -23 -36 -39 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~320/297 = 139.827{{c}}
+Optimal tunings:
+* WE: ~2 = 1201.0031{{c}}, ~320/297 = 139.9435{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~320/297 = 139.8053{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~320/297 = 139.827{{c}} -->
-{{Optimal ET sequence|legend=0| 43, 60e, 103 }}
+{{Optimal ET sequence|legend=0| 43, 60e, 103, 369bcdeee, 472bbcddeee }}
-Badness (Smith): 0.052590
+Badness (Sintel): 1.74
 === 13-limit ===
@@ Line 905: / Line 1,110: @@
 Mapping: {{mapping| 1 1 5 7 8 3 | 0 5 -23 -36 -39 6 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~13/12 = 139.812{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.8354{{c}}, ~13/12 = 139.9095{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.7997{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~13/12 = 139.812{{c}} -->
 {{Optimal ET sequence|legend=0| 43, 60e, 103 }}
-Badness (Smith): 0.032730
+Badness (Sintel): 1.35
 === 17-limit ===
@@ Line 918: / Line 1,126: @@
 Mapping: {{mapping| 1 1 5 7 8 3 7 | 0 5 -23 -36 -39 6 -25 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~13/12 = 139.815{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.7402{{c}}, ~13/12 = 139.9015{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.8038{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~13/12 = 139.815{{c}} -->
 {{Optimal ET sequence|legend=0| 43, 60e, 103 }}
-Badness (Smith): 0.023038
+Badness (Sintel): 1.17
 == Gwazy ==
@@ Line 932: / Line 1,143: @@
 {{Mapping|legend=1| 2 1 6 4 | 0 8 -5 6 }}
+: mapping generators: ~2401/1728, ~35/32
-[[Optimal tuning]] ([[POTE]]): ~2401/1728 = 600.000{{c}}, ~35/32 = 162.658{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2401/1728 = 599.7132{{c}}, ~35/32 = 162.5806{{c}}
+: [[error map]]: {{val| -0.574 -1.597 -0.937 +5.510 }}
+* [[CWE]]: ~2401/1728 = 600.0000{{c}}, ~35/32 = 162.6388{{c}}
+: error map: {{val| 0.000 -0.844 +0.492 +7.007 }}
+<!-- * [[POTE]]: ~2401/1728 = 600.000{{c}}, ~35/32 = 162.658{{c}} -->
 {{Optimal ET sequence|legend=1| 22, 74, 96, 118d }}
-[[Badness]] (Smith): 0.178826
+[[Badness]] (Sintel): 4.53
 === 11-limit ===
@@ Line 946: / Line 1,163: @@
 Mapping: {{mapping| 2 1 6 4 8 | 0 8 -5 6 -4 }}
-Optimal tuning (POTE): ~363/256 = 600.000{{c}}, ~11/10 = 162.592{{c}}
+Optimal tunings:
+* WE: ~363/256 = 599.8517{{c}}, ~11/10 = 162.5518{{c}}
+* CWE: ~363/256 = 600.0000{{c}}, ~11/10 = 162.5863{{c}}
+<!-- * POTE: ~363/256 = 600.000{{c}}, ~11/10 = 162.592{{c}} -->
-{{Optimal ET sequence|legend=0| 22, 74, 96, 118d }}
+{{Optimal ET sequence|legend=0| 22, 74, 96 }}
-Badness (Smith): 0.068410
+Badness (Sintel): 2.26
 == Tertiosec ==
@@ Line 959: / Line 1,179: @@
 [[Comma list]]: 225/224, 14495514624/13841287201
-{{Mapping|legend=1| 3 7 5 9 | 0 -8 7 -2 }}
+{{Mapping|legend=1| 3 -1 12 7 | 0 8 -7 2 }}
+: mapping generators: ~3072/2401, ~2048/1715
-[[Optimal tuning]] ([[POTE]]): ~3072/2401 = 400.000{{c}}, ~15/14 = 112.283{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~3072/2401 = 399.8257{{c}}, ~2048/1715 = 287.5920{{c}}
+: [[error map]]: {{val| -0.523 -1.044 -1.549 +5.138 }}
+* [[CWE]]: ~3072/2401 = 400.0000{{c}}, ~2048/1715 = 287.7088{{c}}
+: error map: {{val| 0.000 -0.284 -0.276 +6.592 }}
+<!-- * [[POTE]]: ~3072/2401 = 400.000{{c}}, ~2048/1715 = 287.717{{c}} -->
 {{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171d }}
-[[Badness]] (Smith): 0.431636
+[[Badness]] (Sintel): 10.9
 === 11-limit ===
@@ Line 972: / Line 1,198: @@
 Comma list: 225/224, 3840/3773, 12005/11979
-Mapping: {{mapping| 3 7 5 9 9 | 0 -8 7 -2 5 }}
+Mapping: {{mapping| 3 -1 12 7 14 | 0 8 -7 2 -5 }}
-Optimal tuning (POTE): ~44/35 = 400.000{{c}}, ~15/14 = 112.171{{c}}
+Optimal tunings:
+* WE: ~44/35 = 399.6550{{c}}, ~33/28 = 287.5803{{c}}
+* CWE: ~44/35 = 400.0000{{c}}, ~33/28 = 287.8224{{c}}
+<!-- * POTE: ~44/35 = 400.000{{c}}, ~33/28 = 287.829{{c}} -->
 {{Optimal ET sequence|legend=0| 21, 54, 75e }}
-Badness (Smith): 0.173485
+Badness (Sintel): 5.74
 [[Category:Temperament collections]]
 [[Category:Marvel temperaments| ]] <!-- main article -->
 [[Category:Rank 2]]

Marvel temperaments: Difference between revisions

Revision as of 13:45, 22 February 2026

Wizard

11-limit

Lizard

17-limit

19-limit

Gizzard

17-limit

19-limit

Mage

Tritonic

11-limit

13-limit

17-limit

19-limit

23-limit

Tritoni

Septimin

11-limit

13-limit

Merman

11-limit

13-limit

Slender

11-limit

13-limit

Triton

11-limit

Marvolo

11-limit

13-limit

17-limit

19-limit

Enneaportent

11-limit

13-limit

Gracecordial

11-limit

13-limit

17-limit

19-limit

23-limit

29-limit

31-limit

Gracecord

13-limit

17-limit

19-limit

Alphorn

11-limit

Misneb

11-limit

13-limit

Musneb

Untriton

11-limit

13-limit

Naiadical

11-limit

13-limit

17-limit

Quintannic

11-limit

13-limit

17-limit

Gwazy

11-limit

Tertiosec

11-limit

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