Marvel temperaments: Difference between revisions

Revision as of 13:49, 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 59: / Line 59: @@
 * [[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 }} -->
 {{Optimal ET sequence|legend=1| 22, 50, 72, 238c, 310c, 382c, 454bccd }}
@@ Line 78: / Line 74: @@
 * WE: ~99/70 = 600.3051{{c}}, ~25/22 = 216.8782{{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 }}
@@ Line 95: / Line 89: @@
 * WE: ~55/39 = 600.4824{{c}}, ~25/22 = 216.7852{{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 }}
@@ Line 112: / Line 104: @@
 * WE: ~17/12 = 600.5032{{c}}, ~17/15 = 216.8002{{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 }}
@@ Line 129: / Line 119: @@
 * WE: ~17/12 = 600.4698{{c}}, ~17/15 = 216.6925{{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 }}
@@ Line 146: / Line 134: @@
 * WE: ~99/70 = 600.2896{{c}}, ~25/22 = 216.9343{{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 }}
@@ Line 163: / Line 149: @@
 * WE: ~17/12 = 600.3227{{c}}, ~17/15 = 216.9414{{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 }}
@@ Line 180: / Line 164: @@
 * WE: ~17/12 = 600.2637{{c}}, ~17/15 = 216.9570{{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 }}
@@ Line 197: / Line 179: @@
 * WE: ~77/54 = 600.6486{{c}}, ~55/48 = 217.1099{{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 }}
@@ Line 219: / Line 199: @@
 * [[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 }}
@@ Line 235: / Line 214: @@
 * 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, 91e, 213bcdeee }}
@@ Line 251: / Line 229: @@
 * 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 }}
@@ Line 267: / Line 244: @@
 * 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 }}
@@ Line 283: / Line 259: @@
 * 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 }}
@@ Line 299: / Line 274: @@
 * 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 }}
@@ Line 315: / Line 289: @@
 * 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 }}
@@ Line 336: / Line 309: @@
 * [[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 }}
@@ Line 352: / Line 324: @@
 * 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 }}
@@ Line 368: / Line 339: @@
 * 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 }}
@@ Line 389: / Line 359: @@
 * [[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 }}
@@ Line 405: / Line 374: @@
 * 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 }}
@@ Line 421: / Line 389: @@
 * 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 }}
@@ Line 442: / Line 409: @@
 * [[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, 406c }}
@@ Line 458: / Line 424: @@
 * 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 }}
@@ Line 474: / Line 439: @@
 * 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 }}
@@ Line 495: / Line 459: @@
 * [[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 }}
@@ Line 511: / Line 474: @@
 * 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 }}
@@ Line 530: / Line 492: @@
 * [[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, 619bbccd, 691bbccd }}
@@ Line 546: / Line 507: @@
 * 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 }}
@@ Line 562: / Line 522: @@
 * 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 }}
@@ Line 578: / Line 537: @@
 * 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 }}
@@ Line 594: / Line 552: @@
 * 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 }}
@@ Line 613: / Line 570: @@
 * [[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, 54, 63, 72, 495bccd, 567bcccd }}
@@ Line 629: / Line 585: @@
 * 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, 54, 63, 72 }}
@@ Line 645: / Line 600: @@
 * 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, 54, 63, 72 }}
@@ Line 666: / Line 620: @@
 * [[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 }}
@@ Line 682: / Line 635: @@
 * 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, 113, 125, 238c }}
@@ Line 698: / Line 650: @@
 * 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, 113, 125f, 238cf }}
@@ Line 714: / Line 665: @@
 * 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, 113, 125f, 238cf }}
@@ Line 730: / Line 680: @@
 * 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, 113, 125f, 238cf }}
@@ Line 746: / Line 695: @@
 * 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, 113, 238cfi }}
@@ Line 762: / Line 710: @@
 * 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, 113, 125f, 238cfi }}
@@ Line 778: / Line 725: @@
 * 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, 113, 125f, 238cfi }}
@@ Line 794: / Line 740: @@
 * 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 }}
@@ Line 810: / Line 755: @@
 * 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 }}
@@ Line 826: / Line 770: @@
 * 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 }}
@@ Line 842: / Line 785: @@
 * 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 }}
@@ Line 861: / Line 803: @@
 * [[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| 13d, 28d, 41, 151cd, 192cdd, 233ccdd }}
@@ Line 877: / Line 818: @@
 * 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| 13d, 28d, 41 }}
@@ Line 898: / Line 838: @@
 * [[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 }}
@@ Line 914: / Line 853: @@
 * 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 }}
@@ Line 930: / Line 868: @@
 * 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 }}
@@ Line 946: / Line 883: @@
 * 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| 21e, 32, 53 }}
@@ Line 967: / Line 903: @@
 * [[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 }}
@@ Line 983: / Line 918: @@
 * 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 }}
@@ Line 999: / Line 933: @@
 * 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 }}
@@ Line 1,081: / Line 1,014: @@
 * [[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 }}
@@ Line 1,097: / Line 1,029: @@
 * 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, 369bcdeee, 472bbcddeee }}
@@ Line 1,113: / Line 1,044: @@
 * 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 }}
@@ Line 1,129: / Line 1,059: @@
 * 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 }}
@@ Line 1,150: / Line 1,079: @@
 * [[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 }}
@@ Line 1,166: / Line 1,094: @@
 * 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 }}
@@ Line 1,187: / Line 1,114: @@
 * [[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 }}
@@ Line 1,203: / Line 1,129: @@
 * 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 }}

Marvel temperaments: Difference between revisions

Revision as of 13:49, 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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