Breedsmic temperaments: Difference between revisions

Revision as of 20:02, 26 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 the breedsma (monzo: [-5 -1 -2 4⟩, ratio: 2401/2400). This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12edo, for example) which does not possess a neutral third cannot be tempering out the breedsma.

The breedsma is also the amount by which four stacked 10/7 intervals exceed 25/6: 10000/2401 × 2401/2400 = 10000/2400 = 25/6, which is two octaves above the classic chromatic semitone, 25/24. We might note also that (49/40)(10/7) = 7/4 and (49/40)(10/7)² = 5/2, relationships which will be significant in any breedsmic temperament. As a consequence of these facts, the 49/40~60/49 neutral third and the 7/5 and 10/7 intervals tend to have relatively low complexity in a breedsmic system.

Temperaments discussed elsewhere include:

Decimal (+25/24, 49/48 or 50/49) → Dicot family
Beatles (+64/63 or 686/675) → Archytas clan
Squares (+81/80) → Meantone family
Myna (+126/125) → Starling temperaments
Miracle (+225/224) → Gamelismic clan
Octacot (+245/243) → Tetracot family
Greenwood (+405/392 or 1323/1280) → Greenwoodmic temperaments
Quasitemp (+875/864) → Keemic temperaments
Quadrasruta (+2048/2025) → Diaschismic family
Quadrimage (+3125/3072) → Magic family
Hemiwürschmidt (+3136/3125 or 6144/6125) → Hemimean clan
Ennealimmal (+4375/4374) → Ragismic microtemperaments
Quadritikleismic (+15625/15552) → Kleismic family
Harry (+19683/19600) → Gravity family
Sesquiquartififths (+32805/32768) → Schismatic family
Amicable (+1600000/1594323) → Amity family
Neptune (+48828125/48771072) → Gammic family
Decoid (+67108864/66976875) → Quintosec family
Tertiseptisix (+390625000/387420489) → Quartonic family
Eagle (+10485760000/10460353203) → Vulture family

Hemififths

Main article: Hemififths

Hemififths may be described as the 41 & 58 temperament, tempering out 5120/5103, the hemifamity comma, and 10976/10935, hemimage. It has a neutral third as a generator; its ploidacot is dicot. 99edo and 140edo provides good tunings, and 239edo an even better one; and other possible tunings are 160^(1/25), giving just 5's, the 7- and 9-odd-limit minimax tuning, or 14^(1/13), giving just 7's. It requires 25 generator steps to get to the class for the harmonic 5, whereas the 7 is half as complex, and hence hemififths makes for a good no-fives temperament, to which the 17- and 24-note mos are suited. The full force of this highly accurate temperament can be found using the 41-note mos or even the 34-note 2mos^{[clarification needed]}.

By adding 243/242 (which also means 441/440, 540/539 and 896/891) to the commas, hemififths extends to a less accurate 11-limit version, but one where 11/4 is only five generator steps. 99edo is an excellent tuning; one which loses little of the accuracy of the 7-limit but improves the 11-limit a bit. Now adding 144/143 brings in the 13-limit with less accuracy yet, but with very low complexity, as the generator can be taken to be 16/13. 99 remains a good tuning choice.

Subgroup: 2.3.5.7

Comma list: 2401/2400, 5120/5103

Mapping: [⟨1 1 -5 -1], ⟨0 2 25 13]]

mapping generators: ~2, ~49/40

Optimal tunings:

WE: ~2 = 1199.7412 ¢, ~49/40 = 351.4016 ¢

error map: ⟨-0.259 +0.590 +0.021 -0.346]

CWE: ~2 = 1200.0000 ¢, ~49/40 = 351.4671 ¢

error map: ⟨0.000 +0.979 +0.364 +0.246]

Minimax tuning:

7- and 9-odd-limit minimax: ~49/40 = [1/5 0 1/25⟩

[[1 0 0 0⟩, [7/5 0 2/25 0⟩, [0 0 1 0⟩, [8/5 0 13/25 0⟩]

unchanged-interval (eigenmonzo) basis: 2.5

Algebraic generator: (2 + sqrt(2))/2

Optimal ET sequence: 17c, 41, 58, 99, 239, 338

Badness (Sintel): 0.563

11-limit

Subgroup: 2.3.5.7.11

Comma list: 243/242, 441/440, 896/891

Mapping: [⟨1 1 -5 -1 2], ⟨0 2 25 13 5]]

Optimal tunings:

WE: ~2 = 1199.2845 ¢, ~11/9 = 351.3110 ¢
CWE: ~2 = 1200.0000 ¢, ~11/9 = 351.4956 ¢

Optimal ET sequence: 17c, 41, 58, 99e

Badness (Sintel): 0.777

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 196/195, 243/242, 364/363

Mapping: [⟨1 1 -5 -1 2 4], ⟨0 2 25 13 5 -1]]

Optimal tunings:

WE: ~2 = 1198.8875 ¢, ~11/9 = 351.2475 ¢
CWE: ~2 = 1200.0000 ¢, ~11/9 = 351.5438 ¢

Optimal ET sequence: 17c, 41, 58, 99ef, 157eff

Badness (Sintel): 0.789

Semihemi

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 3388/3375, 5120/5103

Mapping: [⟨2 0 -35 -15 -47], ⟨0 2 25 13 34]]

mapping generators: ~99/70, ~400/231

Optimal tunings:

WE: ~99/70 = 599.8556 ¢, ~400/231 = 951.2757 ¢
CWE: ~99/70 = 600.0000 ¢, ~400/231 = 951.4939 ¢

Optimal ET sequence: 58, 140, 198

Badness (Sintel): 1.40

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 676/675, 847/845, 1716/1715

Mapping: [⟨2 0 -35 -15 -47 -37], ⟨0 2 25 13 34 28]]

Optimal tunings:

WE: ~99/70 = 599.8513 ¢, ~26/15 = 951.2662 ¢
CWE: ~99/70 = 600.0000 ¢, ~26/15 = 951.4905 ¢

Optimal ET sequence: 58, 140, 198, 536f

Badness (Sintel): 0.876

Quadrafifths

This has been logged as semihemififths in Graham Breed's temperament finder, but quadrafifths arguably makes more sense because it straight-up splits the fifth in four.

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 3025/3024, 5120/5103

Mapping: [⟨1 1 -5 -1 8], ⟨0 4 50 26 -31]]

mapping generators: ~2, ~243/220

Optimal tunings:

WE: ~2 = 1199.7520 ¢, ~243/220 = 175.7015 ¢
CWE: ~2 = 1200.0000 ¢, ~243/220 = 175.7360 ¢

Optimal ET sequence: 41, 157, 198, 239, 676b, 915be

Badness (Sintel): 1.33

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 847/845, 2401/2400, 3025/3024

Mapping: [⟨1 1 -5 -1 8 10], ⟨0 4 50 26 -31 -43]]

Optimal tunings:

WE: ~2 = 1199.6502 ¢, ~72/65 = 175.6957 ¢
CWE: ~2 = 1200.0000 ¢, ~72/65 = 175.7461 ¢

Optimal ET sequence: 41, 157, 198, 437f, 635bcff

Badness (Sintel): 1.29

Tertiaseptal

Main article: Tertiaseptal

Aside from the breedsma, tertiaseptal tempers out 65625/65536, the horwell comma, 703125/702464, the meter, and 2100875/2097152, the rainy comma. It can be described as the 31 & 171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. 171edo makes for an excellent tuning, although 171edo - 31edo = 140edo also makes sense, and in very high limits 140edo + 171edo = 311edo is especially notable. The 15- or 16-note mos can be used to explore no-threes harmony, and the 31-note mos gives plenty of room for those as well.

Subgroup: 2.3.5.7

Comma list: 2401/2400, 65625/65536

Mapping: [⟨1 -19 7 0], ⟨0 22 -5 3]]

mapping generators: ~2, ~245/128

Optimal tunings:

WE: ~2 = 1200.1004 ¢, ~245/128 = 1122.9024 ¢ (~256/245 = 77.1979)

error map: ⟨+0.100 -0.008 -0.123 -0.119]

CWE: ~2 = 1200.0000 ¢, ~245/128 = 1122.8101 ¢ (~256/245 = 77.1899)

error map: ⟨0.000 -0.133 -0.364 -0.396]

Optimal ET sequence: 31, 109, 140, 171

Badness (Sintel): 0.329

11-limit

Subgroup: 2.3.5.7.11

Comma list: 243/242, 441/440, 65625/65536

Mapping: [⟨1 -19 7 0 -48], ⟨0 22 -5 3 55]]

Optimal tunings:

WE: ~2 = 1200.1034 ¢, ~245/128 = 1122.8694 ¢ (~256/245 = 77.2340 ¢)
CWE: ~2 = 1200.0000 ¢, ~245/128 = 1122.7743 ¢ (~256/245 = 77.2257 ¢)

Optimal ET sequence: 31, 109e, 140e, 171, 202

Badness (Sintel): 1.18

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 441/440, 625/624, 3584/3575

Mapping: [⟨1 -19 7 0 -48 43], ⟨0 22 -5 3 55 -42]]

Optimal tunings:

WE: ~2 = 1199.8783 ¢, ~224/117 = 1122.6835 ¢ (~117/112 = 77.1948 ¢)
CWE: ~2 = 1200.0000 ¢, ~224/117 = 1122.7968 ¢ (~117/112 = 77.2032 ¢)

Optimal ET sequence: 31, 140e, 171, 373ef

Badness (Sintel): 1.52

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 243/242, 375/374, 441/440, 625/624, 3584/3575

Mapping: [⟨1 -19 7 0 -48 43 49], ⟨0 22 -5 3 55 -42 -48]]

Optimal tunings:

WE: ~2 = 1199.8677 ¢, ~65/34 = 1122.6748 ¢ (~68/65 = 77.1929 ¢)
CWE: ~2 = 1200.0000 ¢, ~65/34 = 1122.7985 ¢ (~68/65 = 77.2015 ¢)

Optimal ET sequence: 31, 140e, 171

Badness (Sintel): 1.40

Tertia

Subgroup:2.3.5.7.11

Comma list: 385/384, 1331/1323, 1375/1372

Mapping: [⟨1 -19 7 0 -19], ⟨0 22 -5 3 24]]

Optimal tunings:

WE: ~2 = 1200.2336 ¢, ~21/11 = 1123.0454 ¢ (~22/21 = 77.1882 ¢)
CWE: ~2 = 1200.0000 ¢, ~21/11 = 1122.8311 ¢ (~22/21 = 77.1689 ¢)

Optimal ET sequence: 31, 109, 140, 171e, 311e

Badness (Sintel): 0.997

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 385/384, 625/624, 1331/1323

Mapping: [⟨1 -19 7 0 -19 43], ⟨0 22 -5 3 24 -42]]

Optimal tunings:

WE: ~2 = 1200.1395 ¢, ~21/11 = 1122.9727 ¢ (~22/21 = 77.1669 ¢)
CWE: ~2 = 1200.0000 ¢, ~21/11 = 1122.8426 ¢ (~22/21 = 77.1574 ¢)

Optimal ET sequence: 31, 78f, 109, 140

Badness (Sintel): 1.17

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 352/351, 385/384, 561/560, 625/624, 715/714

Mapping: [⟨1 -19 7 0 -19 43 49], ⟨0 22 -5 3 24 -42 -48]]

Optimal tunings:

WE: ~2 = 1200.1655 ¢, ~21/11 = 1122.9926 ¢ (~22/21 = 77.1729 ¢)
CWE: ~2 = 1200.0000 ¢, ~21/11 = 1122.8376 ¢ (~22/21 = 77.1624 ¢)

Optimal ET sequence: 31, 78fg, 109g, 140

Badness (Sintel): 1.14

Tertiaseptia

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 6250/6237, 65625/65536

Mapping: [⟨1 -19 7 0 112], ⟨0 22 -5 3 -116]]

Optimal tunings:

WE: ~2 = 1200.0053 ¢, ~245/128 = 1122.8357 ¢ (~256/245 = 77.1696 ¢)
CWE: ~2 = 1200.0000 ¢, ~245/128 = 1122.8308 ¢ (~256/245 = 77.1692 ¢)

Optimal ET sequence: 31e, 140, 171, 311

Badness (Sintel): 1.88

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 625/624, 2080/2079, 2200/2197, 2401/2400

Mapping: [⟨1 -19 7 0 112 43], ⟨0 22 -5 3 -116 -42]]

Optimal tunings:

WE: ~2 = 1199.9823 ¢, ~224/117 = 1122.8150 ¢ (~117/112 = 77.1673 ¢)
CWE: ~2 = 1200.0000 ¢, ~224/117 = 1122.8316 ¢ (~117/112 = 77.1684 ¢)

Optimal ET sequence: 31e, 140, 171, 311, 1073

Badness (Sintel): 1.14

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 595/594, 625/624, 833/832, 1156/1155, 2200/2197

Mapping: [⟨1 -19 7 0 112 43 49], ⟨0 22 -5 3 -116 -42 -48]]

Optimal tunings:

WE: ~2 = 1200.0092 ¢, ~65/34 = 1122.8392 ¢ (~68/65 = 77.1700 ¢)
CWE: ~2 = 1200.0000 ¢, ~65/34 = 1122.8305 ¢ (~68/65 = 77.1695 ¢)

Optimal ET sequence: 31e, 140, 171, 311

Badness (Sintel): 0.956

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 595/594, 625/624, 833/832, 1156/1155, 1216/1215, 2200/2197

Mapping: [⟨1 -19 7 0 112 43 49 -94], ⟨0 22 -5 3 -116 -42 -48 105]]

Optimal tunings:

WE: ~2 = 1200.0187 ¢, ~65/34 = 1122.8489 ¢ (~68/65 = 77.1698 ¢)
CWE: ~2 = 1200.0000 ¢, ~65/34 = 1122.8313 ¢ (~68/65 = 77.1687 ¢)

Optimal ET sequence: 140, 171, 311

Badness (Sintel): 1.07

23-limit

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 595/594, 625/624, 833/832, 875/874, 1105/1104, 1156/1155, 1216/1215

Mapping: [⟨1 -19 7 0 112 43 49 -94 114], ⟨0 22 -5 3 -116 -42 -48 105 -117]]

Optimal tunings:

WE: ~2 = 1200.0101 ¢, ~44/23 = 1122.8418 ¢ (~23/22 = 77.1683 ¢)
CWE: ~2 = 1200.0000 ¢, ~44/23 = 1122.8323 ¢ (~23/22 = 77.1677 ¢)

Optimal ET sequence: 140, 311, 762g

Badness (Sintel): 1.08

29-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29

Comma list: 595/594, 625/624, 784/783, 833/832, 875/874, 1015/1014, 1105/1104, 1156/1155

Mapping: [⟨1 -19 7 0 112 43 49 -94 114 61], ⟨0 22 -5 3 -116 -42 -48 105 -117 -60]]

Optimal tunings:

WE: ~2 = 1200.0007 ¢, ~44/23 = 1122.8332 ¢ (~23/22 = 77.1675 ¢)
CWE: ~2 = 1200.0000 ¢, ~44/23 = 1122.8326 ¢ (~23/22 = 77.1674 ¢)

Optimal ET sequence: 140, 311, 762g

Badness (Sintel): 1.02

31-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29.31

Comma list: 595/594, 625/624, 714/713, 784/783, 833/832, 875/874, 900/899, 931/930, 1015/1014

Mapping: [⟨1 -19 7 0 112 43 49 -94 114 61 -83], ⟨0 22 -5 3 -116 -42 -48 105 -117 -60 94]]

Optimal tunings:

WE: ~2 = 1199.9721 ¢, ~44/23 = 1122.8047 ¢ (~23/22 = 77.1673 ¢)
CWE: ~2 = 1200.0000 ¢, ~44/23 = 1122.8309 ¢ (~23/22 = 77.1691 ¢)

Optimal ET sequence: 140, 171, 311

Badness (Sintel): 1.18

37-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37

Comma list: 595/594, 625/624, 703/702, 714/713, 784/783, 833/832, 875/874, 900/899, 931/930, 1015/1014

Mapping: [⟨1 -19 7 0 112 43 49 -94 114 61 -83 81], ⟨0 22 -5 3 -116 -42 -48 105 -117 -60 94 -81]]

Optimal tunings:

WE: ~2 = 1199.9824 ¢, ~44/23 = 1122.8139 ¢ (~23/22 = 77.1685 ¢)
CWE: ~2 = 1200.0000 ¢, ~44/23 = 1122.8304 ¢ (~23/22 = 77.1696 ¢)

Optimal ET sequence: 140, 171, 311

Badness (Sintel): 1.19

41-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41

Comma list: 595/594, 625/624, 697/696, 703/702, 714/713, 784/783, 820/819, 833/832, 875/874, 900/899, 931/930

Mapping: [⟨1 -19 7 0 112 43 49 -94 114 61 -83 81 -4], ⟨0 22 -5 3 -116 -42 -48 105 -117 -60 94 -81 10]]

Optimal tunings:

WE: ~2 = 1199.9957 ¢, ~44/23 = 1122.8266 ¢ (~23/22 = 77.1691 ¢)
CWE: ~2 = 1200.0000 ¢, ~44/23 = 1122.8306 ¢ (~23/22 = 77.1694 ¢)

Optimal ET sequence: 140, 171, 311

Badness (Sintel): 1.20

Hemitert

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 3025/3024, 65625/65536

Mapping: [⟨1 -41 12 -3 -73], ⟨0 44 -10 6 79]]

mapping generators: ~2, ~88/45

Optimal tunings:

WE: ~2 = 1200.1008 ¢, ~88/45 = 1161.5020 ¢ (~45/44 = 38.5988 ¢)
CWE: ~2 = 1200.0000 ¢, ~88/45 = 1161.4053 ¢ (~45/44 = 38.5947 ¢)

Optimal ET sequence: 31, …, 280, 311, 342, 2021cde, 2363cde, …, 3389ccddee, 3731ccddee

Badness (Sintel): 0.517

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 625/624, 1575/1573, 2401/2400, 4096/4095

Mapping: [⟨1 -41 12 -3 -73 85], ⟨0 44 -10 6 79 -84]]

Optimal tunings:

WE: ~2 = 1199.9822 ¢, ~88/45 = 1161.3952 ¢ (~45/44 = 38.5871 ¢)
CWE: ~2 = 1200.0000 ¢, ~88/45 = 1161.4123 ¢ (~45/44 = 38.5877 ¢)

Optimal ET sequence: 31, 280, 311

Badness (Sintel): 1.39

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 625/624, 833/832, 1225/1224, 1575/1573, 4096/4095

Mapping: [⟨1 -41 12 -3 -73 85 97], ⟨0 44 -10 6 79 -84 -96]]

Optimal tunings:

WE: ~2 = 1200.0042 ¢, ~88/45 = 1161.4149 ¢ (~45/44 = 38.5893 ¢)
CWE: ~2 = 1200.0000 ¢, ~88/45 = 1161.4109 ¢ (~45/44 = 38.5891 ¢)

Optimal ET sequence: 31, 280, 311, 653f

Badness (Sintel): 1.29

Semitert

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 9801/9800, 65625/65536

Mapping: [⟨2 -16 9 3 47], ⟨0 22 -5 3 -46]]

mapping generators: ~99/70, ~693/512

Optimal tunings:

WE: ~99/70 = 600.0548 ¢, ~693/512 = 522.8547 ¢ (~256/245 = 77.2002 ¢)
CWE: ~99/70 = 600.0000 ¢, ~693/512 = 522.8069 ¢ (~256/245 = 77.1931 ¢)

Optimal ET sequence: 62e, 140, 202, 342

Badness (Sintel): 0.853

Quasiorwell

In addition to 2401/2400, quasiorwell tempers out the quasiorwellisma, 29360128/29296875 ([22 -1 -10 1⟩). It has a generator 1024/875, which is 6144/6125 more than 7/6. It may be described as the 31 & 270 temperament, and as one might expect, 61\270 makes for an excellent tuning choice. Other possibilities are (7/2)^1/8, giving just 7's, or 384^1/38, giving pure fifths.

Adding 3025/3024 extends to the 11-limit and as expected, 270 remains an excellent tuning.

Subgroup: 2.3.5.7

Comma list: 2401/2400, 29360128/29296875

Mapping: [⟨1 -7 3 1], ⟨0 38 -3 8]]

mapping generators: ~2, ~1024/875

Optimal tunings:

WE: ~2 = 1199.9403 ¢, ~1024/875 = 271.0935 ¢

error map: ⟨-0.060 +0.018 +0.226 -0.137]

CWE: ~2 = 1200.0000 ¢, ~1024/875 = 271.1064 ¢

error map: ⟨0.000 +0.087 +0.367 +0.025]

Optimal ET sequence: 31, …, 177, 208, 239, 270, 571, 841, 1111

Badness (Sintel): 0.907

11-limit

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 3025/3024, 5632/5625

Mapping: [⟨1 -7 3 1 -11], ⟨0 38 -3 8 64]]

Optimal tunings:

WE: ~2 = 1199.9484 ¢, ~90/77 = 271.0989 ¢
CWE: ~2 = 1200.0000 ¢, ~90/77 = 271.1099 ¢

Optimal ET sequence: 31, …, 177e, 208, 239, 270

Badness (Sintel): 0.580

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1001/1000, 1716/1715, 3025/3024, 4096/4095

Mapping: [⟨1 -7 3 1 -11 22], ⟨0 38 -3 8 64 -81]]

Optimal tunings:

WE: ~2 = 1199.9916 ¢, ~90/77 = 271.1051 ¢
CWE: ~2 = 1200.0000 ¢, ~90/77 = 271.1070 ¢

Optimal ET sequence: 31, 239, 270, 571, 841, 1111

Badness (Sintel): 0.741

Neominor

The generator for neominor temperament is tridecimal minor third 13/11, also known as Neo-gothic minor third.

Subgroup: 2.3.5.7

Comma list: 2401/2400, 177147/175616

Mapping: [⟨1 -3 -29 -14], ⟨0 6 41 22]]

mapping generators: ~2, ~320/189

Optimal tunings:

WE: ~2 = 1200.4276 ¢, ~320/189 = 917.0471 ¢

error map: ⟨+0.428 -0.955 +0.216 +0.224]

CWE: ~2 = 1200.0000 ¢, ~320/189 = 916.7320 ¢

error map: ⟨0.000 -1.563 -0.301 -0.722]

Optimal ET sequence: 17c, 55c, 72, 161, 233, 305

Badness (Sintel): 2.23

11-limit

Subgroup: 2.3.5.7.11

Comma list: 243/242, 441/440, 35937/35840

Mapping: [⟨1 -3 -29 -14 -8], ⟨0 6 41 22 15]]

Optimal tunings:

WE: ~2 = 1200.3466 ¢, ~56/33 = 916.9889 ¢
CWE: ~2 = 1200.0000 ¢, ~56/33 = 916.7330 ¢

Optimal ET sequence: 17c, 55c, 72, 161, 233, 305

Badness (Sintel): 0.924

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 243/242, 364/363, 441/440

Mapping: [⟨1 -3 -29 -14 -8 -7], ⟨0 6 41 22 15 14]]

Optimal tunings:

WE: ~2 = 1200.6874 ¢, ~22/13 = 917.2313 ¢
CWE: ~2 = 1200.0000 ¢, ~22/13 = 916.7228 ¢

Optimal ET sequence: 17c, 55cf, 72

Badness (Sintel): 1.11

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 169/168, 221/220, 243/242, 273/272, 364/363

Mapping: [⟨1 -3 -29 -14 -8 -7 -28], ⟨0 6 41 22 15 14 42]]

Optimal tunings:

WE: ~2 = 1200.6905 ¢, ~17/10 = 917.2356 ¢
CWE: ~2 = 1200.0000 ¢, ~17/10 = 916.7252 ¢

Optimal ET sequence: 17cg, 55cfg, 72

Badness (Sintel): 0.918

Emmthird

The generator for emmthird is the hemimage third, sharper than 5/4 by the hemimage comma, 10976/10935.

Subgroup: 2.3.5.7

Comma list: 2401/2400, 14348907/14336000

Mapping: [⟨1 -3 -17 -8], ⟨0 14 59 33]]

mapping generators: ~2, ~2744/2187

Optimal tunings:

WE: ~2 = 1200.0435 ¢, ~2744/2187 = 393.0021 ¢

error map: ⟨+0.043 -0.057 +0.069 -0.106]

CWE: ~2 = 1200.0000 ¢, ~2744/2187 = 392.9887 ¢

error map: ⟨0.000 -0.113 +0.022 -0.197]

Optimal ET sequence: 58, 113, 171, 742, 913, 1084, 1255, 2681d, 3936d

Badness (Sintel): 0.424

11-limit

Subgroup: 2.3.5.7.11

Comma list: 243/242, 441/440, 1792000/1771561

Mapping: [⟨1 -3 -17 -8 -8], ⟨0 14 59 33 35]]

Optimal tunings:

WE: ~2 = 1199.8090 ¢, ~1372/1089 = 392.9286 ¢
CWE: ~2 = 1200.0000 ¢, ~1372/1089 = 392.9870 ¢

Optimal ET sequence: 58, 113, 171

Badness (Sintel): 1.73

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 364/363, 441/440, 2200/2197

Mapping: [⟨1 -3 -17 -8 -8 -13], ⟨0 14 59 33 35 51]]

Optimal tunings:

WE: ~2 = 1199.7756 ¢, ~180/143 = 392.9154 ¢
CWE: ~2 = 1200.0000 ¢, ~180/143 = 392.9840 ¢

Optimal ET sequence: 58, 113, 171

Badness (Sintel): 1.11

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 243/242, 364/363, 441/440, 595/594, 2200/2197

Mapping: [⟨1 -3 -17 -8 -8 -13 9], ⟨0 14 59 33 35 51 -15]]

Optimal tunings:

WE: ~2 = 1199.8396 ¢, ~64/51 = 392.9322 ¢
CWE: ~2 = 1200.0000 ¢, ~64/51 = 392.9826 ¢

Optimal ET sequence: 58, 113, 171

Badness (Sintel): 1.18

Quinmite

The generator for quinmite is quasi-tempered minor third 25/21, flatter than 6/5 by the starling comma, 126/125. It is also generated by 1/5 of minor tenth 12/5, and its name is a play on the words "quintans" (Latin for "one fifth") and "minor tenth", given by Petr Pařízek in 2011^[1]^[2].

Subgroup: 2.3.5.7

Comma list: 2401/2400, 1959552/1953125

Mapping: [⟨1 -7 -5 -3], ⟨0 34 29 23]]

mapping generators: ~2, ~25/21

Optimal tunings:

WE: ~2 = 1199.9361 ¢, ~25/21 = 302.9808 ¢

error map: ⟨-0.064 -0.162 +0.448 -0.077]

CWE: ~2 = 1200.0000 ¢, ~25/21 = 302.9953 ¢

error map: ⟨0.000 -0.116 +0.549 +0.065]

Optimal ET sequence: 99, 202, 301, 400, 701, 1101c, 1802c

Badness (Sintel): 0.945

Unthirds

Despite the complexity of its mapping, unthirds is an important temperament to the structure of the 11-limit; this is hinted at by unthirds' representation as the 72 & 311 temperament, the join of two tuning systems well-known for their high accuracy in the 11-limit and 41-limit respectively. It is generated by the interval of 14/11 (undecimal major third, hence the name) tuned less than a cent flat, and the 23-note MOS this interval generates serves as a well temperament of, of all things, 23edo. The 49-note MOS is needed to access the 3rd, 5th, 7th, and 11th harmonics, however.

The commas it tempers out include the breedsma (2401/2400), the lehmerisma (3025/3024), the pine comma (4000/3993), the unisquary comma (12005/11979), the argyria (41503/41472), and 42875/42768, all of which appear individually in various 11-limit systems. It is also notable that there is a restriction of the temperament to the 2.5/3.7/3.11/3 fractional subgroup that tempers out 3025/3024 and 12005/11979, which is of considerably less complexity, and which is shared with sqrtphi (whose generator is tuned flat of 72edo's).

Subgroup: 2.3.5.7

Comma list: 2401/2400, 68359375/68024448

Mapping: [⟨1 -13 -14 -9], ⟨0 42 47 34]]

mapping generators: ~2, ~3969/3125

Optimal tunings:

WE: ~2 = 1200.0859 ¢, ~3969/3125 = 416.7465 ¢

error map: ⟨+0.086 +0.281 -0.431 -0.218]

CWE: ~2 = 1200.0000 ¢, ~3969/3125 = 416.7184 ¢

error map: ⟨0.000 +0.220 -0.547 -0.399]

Optimal ET sequence: 72, 167, 239, 311, 694, 1005c

Badness (Sintel): 1.90

11-limit

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 3025/3024, 4000/3993

Mapping: [⟨1 -13 -14 -9 -8], ⟨0 42 47 34 33]]

Optimal tunings:

WE: ~2 = 1200.0246 ¢, ~14/11 = 416.7270 ¢
CWE: ~2 = 1200.0000 ¢, ~14/11 = 416.7190 ¢

Optimal ET sequence: 72, 167, 239, 311

Badness (Sintel): 0.758

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 625/624, 1575/1573, 2080/2079, 2401/2400

Mapping: [⟨1 -13 -14 -9 -8 -47], ⟨0 42 47 34 33 146]]

Optimal tunings:

WE: ~2 = 1200.0536 ¢, ~14/11 = 416.7343 ¢
CWE: ~2 = 1200.0000 ¢, ~14/11 = 416.7164 ¢

Optimal ET sequence: 72, 239f, 311, 694, 1005c

Badness (Sintel): 0.863

Newt

Newt has a generator of a neutral third (0.2 cents flat of 49/40) and tempers out the garischisma. It can be described as the 41 & 270 temperament, and extends naturally to the no-17 19-limit, a.k.a. neonewt. 270edo and 311edo are obvious tuning choices, but 581edo and especially 851edo work much better.

Subgroup: 2.3.5.7

Comma list: 2401/2400, 33554432/33480783

Mapping: [⟨1 1 19 11], ⟨0 2 -57 -28]]

mapping generators: ~2, ~49/40

Optimal tunings:

WE: ~2 = 1199.9315 ¢, ~49/40 = 351.0932 ¢

error map: ⟨-0.068 +0.163 +0.075 -0.188]

CWE: ~2 = 1200.0000 ¢, ~49/40 = 351.1141 ¢

error map: ⟨0.000 +0.273 +0.180 -0.022]

Optimal ET sequence: 41, 147c, 188, 229, 270, 1121, 1391, 1661, 1931, 2201

Badness (Sintel): 1.06

11-limit

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 3025/3024, 19712/19683

Mapping: [⟨1 1 19 11 -10], ⟨0 2 -57 -28 46]]

Optimal tunings:

WE: ~2 = 1199.9603 ¢, ~49/40 = 351.1038 ¢
CWE: ~2 = 1200.0000 ¢, ~49/40 = 351.1155 ¢

Optimal ET sequence: 41, 188, 229, 270, 581, 851, 1121, 1972

Badness (Sintel): 0.643

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 2401/2400, 3025/3024, 4096/4095

Mapping: [⟨1 1 19 11 -10 -20], ⟨0 2 -57 -28 46 81]]

Optimal tunings:

WE: ~2 = 1199.9747 ¢, ~49/40 = 351.1094 ¢
CWE: ~2 = 1200.0000 ¢, ~49/40 = 351.1168 ¢

Optimal ET sequence: 41, 229, 270, 581, 851, 2283b

Badness (Sintel): 0.571

2.3.5.7.11.13.19 subgroup (neonewt)

Subgroup: 2.3.5.7.11.13.19

Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079, 2401/2400

Mapping: [⟨1 1 19 11 -10 -20 18], ⟨0 2 -57 -28 46 81 -47]]

Optimal tunings:

WE: ~2 = 1199.9782 ¢, ~49/40 = 351.1102 ¢
CWE: ~2 = 1200.0000 ¢, ~49/40 = 351.1166 ¢

Optimal ET sequence: 41, 229, 270, 581, 851

Badness (Sintel): 0.438

Septidiasemi

Main article: Septidiasemi

Aside from 2401/2400, septidiasemi tempers out 2152828125/2147483648 in the 7-limit. It is so named because the generator is a "septimal diatonic semitone" (0.15 cents flat of 15/14). It is an excellent tuning for 2.3.5.7.13 and 2.3.5.7.13.17 subgroups rather than full 13- and 17-limit.

Subgroup: 2.3.5.7

Comma list: 2401/2400, 2152828125/2147483648

Mapping: [⟨1 -1 6 4], ⟨0 26 -37 -12]]

mpping generators: ~2, ~15/14

Optimal tunings:

WE: ~2 = 1200.1043 ¢, ~15/14 = 119.3076 ¢

error map: ⟨+0.104 -0.061 -0.070 -0.100]

CWE: ~2 = 1200.0000 ¢, ~15/14 = 119.2971 ¢

error map: ⟨0.000 -0.230 -0.307 -0.391]

Optimal ET sequence: 10, 151, 161, 171, 3581bcdd, 3752bcdd, …, 5633bbccddd, 5804bbccddd

Badness (Sintel): 1.12

Sedia

The sedia temperament (10 & 161) is an 11-limit extension of the septidiasemi, which tempers out 243/242 and 441/440.

Subgroup: 2.3.5.7.11

Comma list: 243/242, 441/440, 939524096/935859375

Mapping: [⟨1 -1 6 4 -3], ⟨0 26 -37 -12 65]]

Optimal tunings:

WE: ~2 = 1199.9635 ¢, ~15/14 = 119.2755 ¢
CWE: ~2 = 1200.0000 ¢, ~15/14 = 119.2791 ¢

Optimal ET sequence: 10, 151, 161, 171, 332

Badness (Sintel): 3.00

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 441/440, 2200/2197, 3584/3575

Mapping: [⟨1 -1 6 4 -3 4], ⟨0 26 -37 -12 65 -3]]

Optimal tunings:

WE: ~2 = 1199.8922 ¢, ~15/14 = 119.2700 ¢
CWE: ~2 = 1200.0000 ¢, ~15/14 = 119.2804 ¢

Optimal ET sequence: 10, 151, 161, 171, 332

Badness (Sintel): 1.89

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 243/242, 441/440, 833/832, 2200/2197, 3584/3575

Mapping: [⟨1 -1 6 4 -3 4 2], ⟨0 26 -37 -12 65 -3 21]]

Optimal tunings:

WE: ~2 = 1199.9088 ¢, ~15/14 = 119.2719 ¢
CWE: ~2 = 1200.0000 ¢, ~15/14 = 119.2808 ¢

Optimal ET sequence: 10, 151, 161, 171, 332, 503ef

Badness (Sintel): 1.39

Maviloid

See also: Ragismic microtemperaments § Parakleismic

Subgroup: 2.3.5.7

Comma list: 2401/2400, 1224440064/1220703125

Mapping: [⟨1 -21 -22 -15], ⟨0 52 56 41]]

mapping generators: ~2, ~875/648

Optimal tunings:

WE: ~2 = 1199.9863 ¢, ~875/648 = 521.1837 ¢

error map: ⟨-0.014 -0.115 +0.274 -0.089]

CWE: ~2 = 1200.0000 ¢, ~875/648 = 521.1894 ¢

error map: ⟨0.000 -0.106 +0.293 -0.060]

Optimal ET sequence: 76, 99, 274, 373, 472, 571, 1043, 1614

Badness (Sintel): 1.46

Subneutral

See also: Luna family

Subgroup: 2.3.5.7

Comma list: 2401/2400, 274877906944/274658203125

Mapping: [⟨1 -41 8 -5], ⟨0 60 -8 11]]

mapping generators: ~2, ~46875/28672

Optimal tunings:

WE: ~2 = 1199.9998 ¢, ~46875/28672 = 851.6994 (~57344/46875 = 348.3005 ¢)

error map: ⟨-0.000 +0.013 +0.090 -0.132]

CWE: ~2 = 1200.0000 ¢, ~46875/28672 = 851.6995 ¢ (~57344/46875 = 348.3005 ¢)

error map: ⟨0.000 +0.014 +0.090 -0.132]

Optimal ET sequence: 31, …, 348, 379, 410, 441, 1354, 1795, 2236

Badness (Sintel): 1.16

Osiris

See also: Metric microtemperaments § Geb

Subgroup: 2.3.5.7

Comma list: 2401/2400, 31381059609/31360000000

Mapping: [⟨1 13 33 21], ⟨0 32 86 51]]

mapping generators: ~2, ~2187/1400

Optimal tunings:

WE: ~2 = 1200.0285 ¢, ~2187/1400 = 771.9522 ¢

error map: ⟨+0.028 -0.025 +0.068 -0.117]

CWE: ~2 = 1200.0000 ¢, ~2187/1400 = 771.9343 ¢

error map: ⟨0.000 -0.056 +0.039 -0.175]

Optimal ET sequence: 157, 171, 1012, 1183, 1354, 1525, 1696

Badness (Sintel): 0.716

Gorgik

Subgroup: 2.3.5.7

Comma list: 2401/2400, 28672/28125

Mapping: [⟨1 -13 8 2], ⟨0 18 -7 1]]

mapping generators: ~2, ~7/4

Optimal tunings:

WE: ~2 = 1198.5503 ¢, ~7/4 = 971.3132 ¢ (~8/7 = 227.2371 ¢)

error map: ⟨-1.450 +0.528 +2.896 -0.412]

CWE: ~2 = 1200.0000 ¢, ~7/4 = 972.4675 ¢ (~8/7 = 227.5325 ¢)

error map: ⟨0.000 +2.460 +6.414 +3.642]

Optimal ET sequence: 21, 37, 58, 153bc, 211bccd, 269bccd

Badness (Sintel): 4.01

11-limit

Subgroup: 2.3.5.7.11

Comma list: 176/175, 2401/2400, 2560/2541

Mapping: [⟨1 -13 8 2 14], ⟨0 18 -7 1 -13]]

Optimal tunings:

WE: ~2 = 1198.4615 ¢, ~7/4 = 971.2535 ¢ (~8/7 = 227.2079 ¢)
CWE: ~2 = 1200.0000 ¢, ~7/4 = 972.4918 ¢ (~8/7 = 227.5082 ¢)

Optimal ET sequence: 21, 37, 58, 153bce, 211bccdee, 269bccdee

Badness (Sintel): 1.96

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 176/175, 196/195, 364/363, 512/507

Mapping: [⟨1 -13 8 2 14 11], ⟨0 18 -7 1 -13 -9]]

Optimal tunings:

WE: ~2 = 1198.4012 ¢, ~7/4 = 971.2110 ¢ (~8/7 = 227.1903 ¢)
CWE: ~2 = 1200.0000 ¢, ~7/4 = 972.5030 ¢ (~8/7 = 227.4970 ¢)

Optimal ET sequence: 21, 37, 58, 153bcef, 211bccdeeff

Badness (Sintel): 1.33

Fibo

Subgroup: 2.3.5.7

Comma list: 2401/2400, 341796875/339738624

Mapping: [⟨1 -27 -7 -9], ⟨0 46 15 19]]

mapping generators: ~2, ~192/125

Optimal tunings:

WE: ~2 = 1200.2050 ¢, ~192/125 = 745.8170 ¢

error map: ⟨+0.205 +0.094 -0.493 -0.147]

CWE: ~2 = 1200.0000 ¢, ~192/125 = 745.6927 ¢

error map: ⟨0.000 -0.092 -0.924 -0.665]

Optimal ET sequence: 37, 66b, 103, 140, 243, 383, 1009cd, 1392ccd

Badness (Sintel): 2.54

11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 1375/1372, 43923/43750

Mapping: [⟨1 -27 -7 -9 -4], ⟨0 46 15 19 12]]

Optimal tunings:

WE: ~2 = 1200.4064 ¢, ~77/50 = 745.9349 ¢
CWE: ~2 = 1200.0000 ¢, ~77/50 = 745.6876 ¢

Optimal ET sequence: 37, 66b, 103, 140, 243e

Badness (Sintel): 1.87

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 385/384, 625/624, 847/845, 1375/1372

Mapping: [⟨1 -27 -7 -9 -4 -5], ⟨0 46 15 19 12 14]]

Optimal tunings:

WE: ~2 = 1200.3728 ¢, ~20/13 = 745.9152 ¢
CWE: ~2 = 1200.0000 ¢, ~20/13 = 745.6879 ¢

Optimal ET sequence: 37, 66b, 103, 140, 243e

Badness (Sintel): 1.13

Mintone

In addition to 2401/2400, mintone tempers out 177147/175000 ([-3 11 -5 -1⟩) in the 7-limit; 243/242, 441/440, and 43923/43750 in the 11-limit. It has a generator tuned around 49/44. It may be described as the 58 & 103 temperament, and as one might expect, 25\161 makes for an excellent tuning choice.

Subgroup: 2.3.5.7

Comma list: 2401/2400, 177147/175000

Mapping: [⟨1 -17 -34 -20], ⟨0 22 43 27]]

mapping generators: ~2, ~9/5

Optimal tunings:

WE: ~2 = 1200.1458 ¢, ~9/5 = 1013.7798 ¢

error map: ⟨+0.146 -1.277 +1.263 +0.314]

CWE: ~2 = 1200.0000 ¢, ~9/5 = 1013.6611 ¢

error map: ⟨0.000 -1.410 +1.116 +0.025]

Optimal ET sequence: 45, 58, 103, 161

Badness (Sintel): 3.18

11-limit

Subgroup: 2.3.5.7.11

Comma list: 243/242, 441/440, 43923/43750

Mapping: [⟨1 -17 -34 -20 -43], ⟨0 22 43 27 55]]

Optimal tunings:

WE: ~2 = 1200.1491 ¢, ~9/5 = 1013.7809 ¢
CWE: ~2 = 1200.0000 ¢, ~9/5 = 1013.6593 ¢

Optimal ET sequence: 45e, 58, 103, 161, 425b

Badness (Sintel): 1.32

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 351/350, 441/440, 847/845

Mapping: [⟨1 -17 -34 -20 -43 -36], ⟨0 22 43 27 55 47]]

Optimal tunings:

WE: ~2 = 1200.0928 ¢, ~9/5 = 1013.7311 ¢
CWE: ~2 = 1200.0000 ¢, ~9/5 = 1013.6556 ¢

Optimal ET sequence: 45ef, 58, 103, 161

Badness (Sintel): 0.903

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 243/242, 351/350, 441/440, 561/560, 847/845

Mapping: [⟨1 -17 -34 -20 -43 -36 10], ⟨0 22 43 27 55 47 -7]]

Optimal tunings:

WE: ~2 = 1200.1085 ¢, ~9/5 = 1013.7433 ¢
CWE: ~2 = 1200.0000 ¢, ~9/5 = 1013.6537 ¢

Optimal ET sequence: 45ef, 58, 103, 161

Badness (Sintel): 1.03

Catafourth

See also: Sensipent family

Subgroup: 2.3.5.7

Comma list: 2401/2400, 78732/78125

Mapping: [⟨1 -15 -19 -12], ⟨0 28 36 25]]

mapping generators: ~2, ~189/125

Optimal tunings:

WE: ~2 = 1199.9278 ¢, ~189/125 = 710.7220 ¢

error map: ⟨-0.072 -0.656 +1.050 +0.091]

CWE: ~2 = 1200.0000 ¢, ~189/125 = 710.7626 ¢

error map: ⟨0.000 -0.603 +1.139 +0.238]

Optimal ET sequence: 27, 76, 103, 130

Badness (Sintel): 2.01

11-limit

Subgroup: 2.3.5.7.11

Comma list: 243/242, 441/440, 78408/78125

Mapping: [⟨1 -15 -19 -12 -38], ⟨0 28 36 25 70]]

Optimal tunings:

WE: ~2 = 1200.0219 ¢, ~189/125 = 710.7610 ¢
CWE: ~2 = 1200.0000 ¢, ~189/125 = 710.7487 ¢

Optimal ET sequence: 27e, 76e, 103, 130, 233, 363, 493e

Badness (Sintel): 1.22

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 351/350, 441/440, 10985/10976

Mapping: [⟨1 -15 -19 -12 -38 -4], ⟨0 28 36 25 70 13]]

Optimal tunings:

WE: ~2 = 1200.1023 ¢, ~98/65 = 710.8043 ¢
CWE: ~2 = 1200.0000 ¢, ~98/65 = 710.7459 ¢

Optimal ET sequence: 27e, 76e, 103, 130, 233, 363

Badness (Sintel): 0.896

Cotritone

Subgroup: 2.3.5.7

Comma list: 2401/2400, 390625/387072

Mapping: [⟨1 -13 -4 -4], ⟨0 30 13 14]]

mappping generators: ~2, ~7/5

Optimal tunings:

WE: ~2 = 1199.9278 ¢, ~7/5 = 583.5994 ¢

error map: ⟨+0.441 +0.289 -1.287 -0.200]

CWE: ~2 = 1200.0000 ¢, ~7/5 = 583.3956 ¢

error map: ⟨0.000 -0.086 -2.170 -1.287]

Optimal ET sequence: 35, 37, 72, 181, 253, 325c

Badness (Sintel): 2.49

11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 1375/1372, 4000/3993

Mapping: [⟨1 -13 -4 -4 2], ⟨0 30 13 14 3]]

Optimal tunings:

WE: ~2 = 1200.4058 ¢, ~7/5 = 583.5845 ¢
CWE: ~2 = 1200.0000 ¢, ~7/5 = 583.3950 ¢

Optimal ET sequence: 35, 37, 72, 181, 253, 325c

Badness (Sintel): 1.07

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 364/363, 385/384, 625/624

Mapping: [⟨1 -13 -4 -4 2 -7], ⟨0 30 13 14 3 22]]

Optimal tunings:

WE: ~2 = 1200.6111 ¢, ~7/5 = 583.6837 ¢
CWE: ~2 = 1200.0000 ¢, ~7/5 = 583.3987 ¢

Optimal ET sequence: 35f, 37, 72, 181f, 253ff

Badness (Sintel): 1.19

Quasimoha

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

Subgroup: 2.3.5.7

Comma list: 2401/2400, 3645/3584

Mapping: [⟨1 1 9 6], ⟨0 2 -23 -11]]

mapping generators: ~2, ~49/40

Optimal tunings:

WE: ~2 = 1201.5059 ¢, ~49/40 = 348.0409 ¢

error map: ⟨+1.506 -2.367 -0.702 +0.759]

CWE: ~2 = 1200.0000 ¢, ~49/40 = 348.5582 ¢

error map: ⟨0.000 -4.839 -3.152 -2.966]

Optimal ET sequence: 24c, 31, 117c, 148bc, 179bcd

Badness (Sintel): 2.80

11-limit

Subgroup: 2.3.5.7.11

Comma list: 243/242, 441/440, 1815/1792

Mapping: [⟨1 1 9 6 2], ⟨0 2 -23 -11 5]]

Optimal tunings:

WE: ~2 = 1201.7630 ¢, ~11/9 = 349.1510 ¢
CWE: ~2 = 1200.0000 ¢, ~11/9 = 348.6050 ¢

Optimal ET sequence: 24c, 31, 86ce, 117ce, 148bce

Badness (Sintel): 1.53

Lockerbie

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

Lockerbie can be described as the 103 & 270 temperament. Its generator is 120/77 or 77/60. An obvious tuning is given by 270edo, but 373edo and especially 643edo work as well.

The temperament derives its name from the Scottish town, where a flight numbered 103 crashed with 270 casualties, and the temperament is defined as 103 & 270, hence the name. The name is proposed by Eliora, who favours it due to simplicity, ease of pronunciation and relation to numbers 103 and 270.

Lockerbie also has a unique extension that adds the 41st harmonic such that the generator below 600 cents is also on the same step in 103 or 270 as 41/32, which means that 616/615 is tempered out.

Subgroup: 2.3.5.7

Comma list: 2401/2400, [24 13 -18 -1⟩

Mapping: [⟨1 -25 -16 -13], ⟨0 74 51 44]]

mapping generators: ~2, ~3828125/2985984

Optimal tunings:

WE: ~2 = 1199.9950 ¢, ~3828125/2985984 = 431.1055 ¢

error map: ⟨-0.005 -0.024 +0.146 -0.120]

CWE: ~2 = 1200.0000 ¢, ~3828125/2985984 = 431.1072 ¢

error map: ⟨0.0000 -0.020 +0.155 -0.108]

Optimal ET sequence: 103, 167, 270, 643, 913, 1183

Badness (Sintel): 1.51

11-limit

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 3025/3024, 766656/765625

Mapping: [⟨1 -25 -16 -13 -26], ⟨0 74 51 44 82]]

Optimal tunings:

WE: ~2 = 1200.0199 ¢, ~77/60 = 431.1147 ¢
CWE: ~2 = 1200.0000 ¢, ~77/60 = 431.1078 ¢

Optimal ET sequence: 103, 167, 270, 643, 913, 1183e

Badness (Sintel): 0.865

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1001/1000, 1716/1715, 3025/3024, 4225/4224

Mapping: [⟨1 -25 -16 -13 -26 -6], ⟨0 74 51 44 82 27]]

Optimal tunings:

WE: ~2 = 1200.0707 ¢, ~77/60 = 431.1316 ¢
CWE: ~2 = 1200.0000 ¢, ~77/60 = 431.1069 ¢

Optimal ET sequence: 103, 167, 270, 643, 913f

Badness (Sintel): 0.662

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 715/714, 936/935, 1001/1000, 1225/1224, 4225/4224

Mapping: [⟨1 -25 -16 -13 -26 -6 -11], ⟨0 74 51 44 82 27 42]]

Optimal tunings:

WE: ~2 = 1199.9639 ¢, ~77/60 = 431.0957 ¢
CWE: ~2 = 1200.0000 ¢, ~77/60 = 431.1083 ¢

Optimal ET sequence: 103, 167, 270

Badness (Sintel): 1.07

2.3.5.7.11.13.17.41 subgroup

Subgroup: 2.3.5.7.11.13.17.41

Comma list: 616/615, 715/714, 936/935, 1001/1000, 1225/1224, 4225/4224

Mapping: [⟨1 -25 -16 -13 -26 -6 -11 5], ⟨0 74 51 44 82 27 42 1]]

Optimal tunings:

WE: ~2 = 1199.8693 ¢, ~41/32 = 431.0650 ¢
CWE: ~2 = 1200.000 ¢, ~41/32 = 431.1109 ¢

Optimal ET sequence: 103, 167, 270

Badness (Sintel): 1.25

Hemigoldis

For the 5-limit version, see Diaschismic–gothmic equivalence continuum #Goldis.

Though fairly complex in the 7-limit, hemigoldis does a lot better in badness metrics than pure 5-limit goldis, and yet again has many possible extensions to other primes. For example, two periods minus six generators yields a "tetracot second" which can be interpreted as ~21/19 to add prime 19 or perhaps more accurately ~31/28 to add prime 7, or even simply as ~32/29 to add prime 29, though the other two have the benefit of clearly connecting to the 7-limit representation. Note that again 89edo is a possible tuning for combining it with flat nestoria and not appearing in the optimal ET sequence.

Subgroup: 2.3.5.7

Comma list: 2401/2400, 549755813888/533935546875

Mapping: [⟨1 21 -9 2], ⟨0 24 -14 -1]]

mapping generators: ~2, ~8/7

Optimal tunings:

WE: ~2 = 1199.2264 ¢, ~8/7 = 229.1679 ¢

error map: ⟨-0.774 +0.394 +1.468 -0.314]

CWE: ~2 = 1200.0000 ¢, ~8/7 = 229.3103 ¢

error map: ⟨0.000 +1.491 +3.343 +1.864]

Optimal ET sequence: 21, 47b, 68, 157, 382bccd, 529bccd

Badness (Sintel): 4.40

Surmarvelpyth

Surmarvelpyth is named for the generator fifth, 675/448 being 225/224 (marvel comma) sharp of 3/2. It can be described as the 311 & 431 temperament, starting with the 7-limit to the 19-limit.

Subgroup: 2.3.5.7

Comma list: 2401/2400, [93 -32 -17 -1⟩

Mapping: [⟨1 -27 55 22], ⟨0 70 -129 -47]]

mapping generators: ~2, ~896/675

Optimal tunings:

WE: ~2 = 1200.0051 ¢, ~896/675 = 490.0303 ¢

error map: ⟨+0.005 +0.025 +0.063 -0.136]

CWE: ~2 = 1200.0000 ¢, ~896/675 = 490.0282 ¢

error map: ⟨0.000 +0.017 +0.052 -0.150]

Optimal ET sequence: 120, 191, 311, 742, 1053, 2848, 3901

Badness (Sintel): 5.12

11-limit

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 820125/819896, 2097152/2096325

Mapping: [⟨1 -27 55 22 -19], ⟨0 70 -129 -47 55]]

Optimal tunings:

WE: ~2 = 1199.9901 ¢, ~896/675 = 490.0239 ¢
CWE: ~2 = 1200.000 ¢, ~896/675 = 490.0279 ¢

Optimal ET sequence: 120, 191, 311, 742, 1053, 1795

Badness (Sintel): 1.73

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2401/2400, 4096/4095, 6656/6655, 24192/24167

Mapping: [⟨1 -27 55 22 -19 -11], ⟨0 70 -129 -47 55 36]]

Optimal tunings:

WE: ~2 = 1199.9701 ¢, ~65/49 = 490.0155 ¢
CWE: ~2 = 1200.0000 ¢, ~65/49 = 490.0277 ¢

Optimal ET sequence: 120, 191, 311, 742, 1053, 1795f

Badness (Sintel): 1.34

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 2401/2400, 2601/2600, 4096/4095, 6656/6655, 8624/8619

Mapping: [⟨1 -27 55 22 -19 -11 78], ⟨0 70 -129 -47 55 36 -181]]

Optimal tunings:

WE: ~2 = 1199.9726 ¢, ~65/49 = 490.0164 ¢
CWE: ~2 = 1200.0000 ¢, ~65/49 = 490.0276 ¢

Optimal ET sequence: 120g, 191g, 311, 431, 742, 1795f

Badness (Sintel): 1.07

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 2401/2400, 2601/2600, 2926/2925, 3136/3135, 3213/3211, 5985/5984

Mapping: [⟨1 -27 55 22 -19 -11 78 41], ⟨0 70 -129 -47 55 36 -181 -90]]

Optimal tunings:

WE: ~2 = 1199.9756 ¢, ~65/49 = 490.0176 ¢
CWE: ~2 = 1200.0000 ¢, ~65/49 = 490.0276 ¢

Optimal ET sequence: 120g, 191g, 311, 431, 742, 1795f

Badness (Sintel): 0.838

References

[1] Yahoo! Tuning Group | Suggested names for the unclasified temperaments

[2] Yahoo! Tuning Group | 2D temperament names, part I -- reclassified temperaments from message #101780

[1]

[2]

@@ Line 41: / Line 41: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.4464{{c}}
+* [[WE]]: ~2 = 1199.7412{{c}}, ~49/40 = 351.4016{{c}}
+: [[error map]]: {{val| -0.259 +0.590 +0.021 -0.346 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.4671{{c}}
+: error map: {{val| 0.000 +0.979 +0.364 +0.246 }}
+<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.4464{{c}}
 : [[error map]]: {{val| 0.0000 +0.9379 -0.1531 -0.0224 }}
 * [[POTE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.4774{{c}}
-: error map: {{val| 0.0000 +0.9999 +0.6221 +0.0307 }}
+: error map: {{val| 0.0000 +0.9999 +0.6221 +0.0307 }} -->
 [[Minimax tuning]]:
@@ Line 53: / Line 57: @@
 [[Algebraic generator]]: (2 + sqrt(2))/2
-{{Optimal ET sequence|legend=1| 41, 58, 99, 239, 338 }}
+{{Optimal ET sequence|legend=1| 17c, 41, 58, 99, 239, 338 }}
-[[Badness]] (Smith): 0.022243
+[[Badness]] (Sintel): 0.563
 === 11-limit ===
@@ Line 65: / Line 69: @@
 Optimal tunings:
-* CTE: ~2 = 1200.0000{{c}}, ~11/9 = 351.4289{{c}}
+* WE: ~2 = 1199.2845{{c}}, ~11/9 = 351.3110{{c}}
-* POTE: ~2 = 1200.0000{{c}}, ~11/9 = 351.5206{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.4956{{c}}
+<!-- * CTE: ~2 = 1200.0000{{c}}, ~11/9 = 351.4289{{c}}
+* POTE: ~2 = 1200.0000{{c}}, ~11/9 = 351.5206{{c}} -->
 {{Optimal ET sequence|legend=0| 17c, 41, 58, 99e }}
-Badness (Smith): 0.023498
+Badness (Sintel): 0.777
 ==== 13-limit ====
@@ Line 80: / Line 86: @@
 Optimal tunings:
-* CTE: ~2 = 1200.0000{{c}}, ~11/9 = 351.4331{{c}}
+* WE: ~2 = 1198.8875{{c}}, ~11/9 = 351.2475{{c}}
-* POTE: ~2 = 1200.0000{{c}}, ~11/9 = 351.5734{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.5438{{c}}
+<!-- * CTE: ~2 = 1200.0000{{c}}, ~11/9 = 351.4331{{c}}
+* POTE: ~2 = 1200.0000{{c}}, ~11/9 = 351.5734{{c}} -->
 {{Optimal ET sequence|legend=0| 17c, 41, 58, 99ef, 157eff }}
-Badness (Smith): 0.019090
+Badness (Sintel): 0.789
 === Semihemi ===
@@ Line 96: / Line 104: @@
 Optimal tunings:
-* CTE: ~99/70 = 600.0000{{c}}, ~49/40 = 351.4722{{c}}
+* WE: ~99/70 = 599.8556{{c}}, ~400/231 = 951.2757{{c}}
-* POTE: ~99/70 = 600.0000{{c}}, ~49/40 = 351.5047{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~400/231 = 951.4939{{c}}
+<!-- * CTE: ~99/70 = 600.0000{{c}}, ~400/231 = 951.4722{{c}}
+* POTE: ~99/70 = 600.0000{{c}}, ~400/231 = 951.5047{{c}} -->
 {{Optimal ET sequence|legend=0| 58, 140, 198 }}
-Badness (Smith): 0.042487
+Badness (Sintel): 1.40
 ==== 13-limit ====
@@ Line 111: / Line 121: @@
 Optimal tunings:
-* CTE: ~99/70 = 600.0000{{c}}, ~49/40 = 351.4674{{c}}
+* WE: ~99/70 = 599.8513{{c}}, ~26/15 = 951.2662{{c}}
-* POTE: ~99/70 = 600.0000{{c}}, ~49/40 = 351.5019{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~26/15 = 951.4905{{c}}
+<!-- * CTE: ~99/70 = 600.0000{{c}}, ~26/15 = 951.4674{{c}}
+* POTE: ~99/70 = 600.0000{{c}}, ~26/15 = 951.5019{{c}} -->
 {{Optimal ET sequence|legend=0| 58, 140, 198, 536f }}
-Badness (Smith): 0.021188
+Badness (Sintel): 0.876
 === Quadrafifths ===
@@ Line 126: / Line 138: @@
 Mapping: {{mapping| 1 1 -5 -1 8 | 0 4 50 26 -31 }}
-: Mapping generators: ~2, ~243/220
+: mapping generators: ~2, ~243/220
 Optimal tunings:
-* CTE: ~2 = 1200.0000{{c}}, ~243/220 = 175.7284{{c}}
+* WE: ~2 = 1199.7520{{c}}, ~243/220 = 175.7015{{c}}
-* POTE: ~2 = 1200.0000{{c}}, ~243/220 = 175.7378{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~243/220 = 175.7360{{c}}
+<!-- * CTE: ~2 = 1200.0000{{c}}, ~243/220 = 175.7284{{c}}
+* POTE: ~2 = 1200.0000{{c}}, ~243/220 = 175.7378{{c}} -->
 {{Optimal ET sequence|legend=0| 41, 157, 198, 239, 676b, 915be }}
-Badness (Smith): 0.040170
+Badness (Sintel): 1.33
 ==== 13-limit ====
@@ Line 144: / Line 158: @@
 Optimal tunings:
-* CTE: ~2 = 1200.0000{{c}}, ~72/65 = 175.7412{{c}}
+* WE: ~2 = 1199.6502{{c}}, ~72/65 = 175.6957{{c}}
-* POTE: ~2 = 1200.0000{{c}}, ~72/65 = 175.7470{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~72/65 = 175.7461{{c}}
+<!-- * CTE: ~2 = 1200.0000{{c}}, ~72/65 = 175.7412{{c}}
+* POTE: ~2 = 1200.0000{{c}}, ~72/65 = 175.7470{{c}} -->
 {{Optimal ET sequence|legend=0| 41, 157, 198, 437f, 635bcff }}
-Badness (Smith): 0.031144
+Badness (Sintel): 1.29
 == Tertiaseptal ==
@@ Line 160: / Line 176: @@
 [[Comma list]]: 2401/2400, 65625/65536
-{{Mapping|legend=1| 1 3 2 3 | 0 -22 5 -3 }}
+{{Mapping|legend=1| 1 -19 7 0 | 0 22 -5 3 }}
-: mapping generators: ~2, ~256/245
+: mapping generators: ~2, ~245/128
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~256/245 = 77.191{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.1004{{c}}, ~245/128 = 1122.9024{{c}} (~256/245 = 77.1979)
+: [[error map]]: {{val| +0.100 -0.008 -0.123 -0.119 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~245/128 = 1122.8101{{c}} (~256/245 = 77.1899)
+: error map: {{val| 0.000 -0.133 -0.364 -0.396 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~256/245 = 77.191{{c}} -->
 {{Optimal ET sequence|legend=1| 31, 109, 140, 171 }}
-[[Badness]] (Smith): 0.012995
+[[Badness]] (Sintel): 0.329
 === 11-limit ===
@@ Line 174: / Line 195: @@
 Comma list: 243/242, 441/440, 65625/65536
-Mapping: {{mapping| 1 3 2 3 7 | 0 -22 5 -3 -55 }}
+Mapping: {{mapping| 1 -19 7 0 -48 | 0 22 -5 3 55 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~256/245 = 77.227{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.1034{{c}}, ~245/128 = 1122.8694{{c}} (~256/245 = 77.2340{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~245/128 = 1122.7743{{c}} (~256/245 = 77.2257{{c}})
+<!-- * POTE: ~2 = 1200.000{{c}}, ~256/245 = 77.227{{c}} -->
 {{Optimal ET sequence|legend=0| 31, 109e, 140e, 171, 202 }}
-Badness (Smith): 0.035576
+Badness (Sintel): 1.18
 ==== 13-limit ====
@@ Line 187: / Line 211: @@
 Comma list: 243/242, 441/440, 625/624, 3584/3575
-Mapping: {{mapping| 1 3 2 3 7 1 | 0 -22 5 -3 -55 42 }}
+Mapping: {{mapping| 1 -19 7 0 -48 43 | 0 22 -5 3 55 -42 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~117/112 = 77.203{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.8783{{c}}, ~224/117 = 1122.6835{{c}} (~117/112 = 77.1948{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~224/117 = 1122.7968{{c}} (~117/112 = 77.2032{{c}})
+<!-- * POTE: ~2 = 1200.000{{c}}, ~117/112 = 77.203{{c}} -->
-{{Optimal ET sequence|legend=0| 31, 109e, 140e, 171 }}
+{{Optimal ET sequence|legend=0| 31, 140e, 171, 373ef }}
-Badness (Smith): 0.036876
+Badness (Sintel): 1.52
 ==== 17-limit ====
@@ Line 200: / Line 227: @@
 Comma list: 243/242, 375/374, 441/440, 625/624, 3584/3575
-Mapping: {{mapping| 1 3 2 3 7 1 1 | 0 -22 5 -3 -55 42 48 }}
+Mapping: {{mapping| 1 -19 7 0 -48 43 49 | 0 22 -5 3 55 -42 -48 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~68/65 = 77.201{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.8677{{c}}, ~65/34 = 1122.6748{{c}} (~68/65 = 77.1929{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~65/34 = 1122.7985{{c}} (~68/65 = 77.2015{{c}})
+<!-- * POTE: ~2 = 1200.000{{c}}, ~68/65 = 77.201{{c}} -->
-{{Optimal ET sequence|legend=0| 31, 109eg, 140e, 171 }}
+{{Optimal ET sequence|legend=0| 31, 140e, 171 }}
-Badness (Smith): 0.027398
+Badness (Sintel): 1.40
 === Tertia ===
@@ Line 213: / Line 243: @@
 Comma list: 385/384, 1331/1323, 1375/1372
-Mapping: {{mapping| 1 3 2 3 5 | 0 -22 5 -3 -24 }}
+Mapping: {{mapping| 1 -19 7 0 -19 | 0 22 -5 3 24 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~22/21 = 77.173{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.2336{{c}}, ~21/11 = 1123.0454{{c}} (~22/21 = 77.1882{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~21/11 = 1122.8311{{c}} (~22/21 = 77.1689{{c}})
+<!-- * POTE: ~2 = 1200.000{{c}}, ~22/21 = 77.173{{c}} -->
 {{Optimal ET sequence|legend=0| 31, 109, 140, 171e, 311e }}
-Badness (Smith): 0.030171
+Badness (Sintel): 0.997
 ==== 13-limit ====
@@ Line 226: / Line 259: @@
 Comma list: 352/351, 385/384, 625/624, 1331/1323
-Mapping: {{mapping| 1 3 2 3 5 1 | 0 -22 5 -3 -24 42 }}
+Mapping: {{mapping| 1 -19 7 0 -19 43 | 0 22 -5 3 24 -42 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~22/21 = 77.158{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.1395{{c}}, ~21/11 = 1122.9727{{c}} (~22/21 = 77.1669{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~21/11 = 1122.8426{{c}} (~22/21 = 77.1574{{c}})
+<!-- * POTE: ~2 = 1200.000{{c}}, ~22/21 = 77.158{{c}} -->
-{{Optimal ET sequence|legend=0| 31, 109, 140, 311e, 451ee }}
+{{Optimal ET sequence|legend=0| 31, 78f, 109, 140 }}
-Badness (Smith): 0.028384
+Badness (Sintel): 1.17
 ==== 17-limit ====
@@ Line 239: / Line 275: @@
 Comma list: 352/351, 385/384, 561/560, 625/624, 715/714
-Mapping: {{mapping| 1 3 2 3 5 1 1 | 0 -22 5 -3 -24 42 48 }}
+Mapping: {{mapping| 1 -19 7 0 -19 43 49 | 0 22 -5 3 24 -42 -48 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~22/21 = 77.162{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.1655{{c}}, ~21/11 = 1122.9926{{c}} (~22/21 = 77.1729{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~21/11 = 1122.8376{{c}} (~22/21 = 77.1624{{c}})
+<!-- * POTE: ~2 = 1200.000{{c}}, ~22/21 = 77.162{{c}} -->
-{{Optimal ET sequence|legend=0| 31, 109g, 140, 311e, 451ee }}
+{{Optimal ET sequence|legend=0| 31, 78fg, 109g, 140 }}
-Badness (Smith): 0.022416
+Badness (Sintel): 1.14
 === Tertiaseptia ===
@@ Line 252: / Line 291: @@
 Comma list: 2401/2400, 6250/6237, 65625/65536
-Mapping: {{mapping| 1 3 2 3 -4 | 0 -22 5 -3 116 }}
+Mapping: {{mapping| 1 -19 7 0 112 | 0 22 -5 3 -116 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~256/245 = 77.169{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.0053{{c}}, ~245/128 = 1122.8357{{c}} (~256/245 = 77.1696{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~245/128 = 1122.8308{{c}} (~256/245 = 77.1692{{c}})
+<!-- * POTE: ~2 = 1200.000{{c}}, ~256/245 = 77.169{{c}} -->
-{{Optimal ET sequence|legend=0| 140, 171, 311, 1695c, 2006bcd, 2317bcd, 2628bccde, 2939bccde, 3250bccde }}
+{{Optimal ET sequence|legend=0| 31e, 140, 171, 311 }}
-Badness (Smith): 0.056926
+Badness (Sintel): 1.88
 ==== 13-limit ====
@@ Line 265: / Line 307: @@
 Comma list: 625/624, 2080/2079, 2200/2197, 2401/2400
-Mapping: {{mapping| 1 3 2 3 -4 1 | 0 -22 5 -3 116 42 }}
+Mapping: {{mapping| 1 -19 7 0 112 43 | 0 22 -5 3 -116 -42 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~117/112 = 77.168{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9823{{c}}, ~224/117 = 1122.8150{{c}} (~117/112 = 77.1673{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~224/117 = 1122.8316{{c}} (~117/112 = 77.1684{{c}})
+<!-- * POTE: ~2 = 1200.000{{c}}, ~117/112 = 77.168{{c}} -->
-{{Optimal ET sequence|legend=0| 140, 171, 311, 1073, 1384cf, 1695cf, 2006bcdf }}
+{{Optimal ET sequence|legend=0| 31e, 140, 171, 311, 1073 }}
-Badness (Smith): 0.027474
+Badness (Sintel): 1.14
 ==== 17-limit ====
@@ Line 278: / Line 323: @@
 Comma list: 595/594, 625/624, 833/832, 1156/1155, 2200/2197
-Mapping: {{mapping| 1 3 2 3 -4 1 1 | 0 -22 5 -3 116 42 48 }}
+Mapping: {{mapping| 1 -19 7 0 112 43 49 | 0 22 -5 3 -116 -42 -48 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~68/65 = 77.169{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.0092{{c}}, ~65/34 = 1122.8392{{c}} (~68/65 = 77.1700{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~65/34 = 1122.8305{{c}} (~68/65 = 77.1695{{c}})
+<!-- * POTE: ~2 = 1200.000{{c}}, ~68/65 = 77.169{{c}} -->
-{{Optimal ET sequence|legend=0| 140, 171, 311 }}
+{{Optimal ET sequence|legend=0| 31e, 140, 171, 311 }}
-Badness (Smith): 0.018773
+Badness (Sintel): 0.956
 ==== 19-limit ====
@@ Line 291: / Line 339: @@
 Comma list: 595/594, 625/624, 833/832, 1156/1155, 1216/1215, 2200/2197
-Mapping: {{mapping| 1 3 2 3 -4 1 1 11 | 0 -22 5 -3 116 42 48 -105 }}
+Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 | 0 22 -5 3 -116 -42 -48 105 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~68/65 = 77.169{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.0187{{c}}, ~65/34 = 1122.8489{{c}} (~68/65 = 77.1698{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~65/34 = 1122.8313{{c}} (~68/65 = 77.1687{{c}})
+<!-- * POTE: ~2 = 1200.000{{c}}, ~68/65 = 77.169{{c}} -->
-{{Optimal ET sequence|legend=0| 140, 171, 311, 1384cfgg, 1695cfgg, 2006bcdfgg }}
+{{Optimal ET sequence|legend=0| 140, 171, 311 }}
-Badness (Smith): 0.017653
+Badness (Sintel): 1.07
 ==== 23-limit ====
@@ Line 304: / Line 355: @@
 Comma list: 595/594, 625/624, 833/832, 875/874, 1105/1104, 1156/1155, 1216/1215
-Mapping: {{mapping| 1 3 2 3 -4 1 1 11 -3 | 0 -22 5 -3 116 42 48 -105 117 }}
+Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 114 | 0 22 -5 3 -116 -42 -48 105 -117 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~23/22 = 77.168{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.0101{{c}}, ~44/23 = 1122.8418{{c}} (~23/22 = 77.1683{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122.8323{{c}} (~23/22 = 77.1677{{c}})
+<!-- * POTE: ~2 = 1200.000{{c}}, ~23/22 = 77.168{{c}} -->
-{{Optimal ET sequence|legend=0| 140, 311, 762g, 1073g, 1384cfgg }}
+{{Optimal ET sequence|legend=0| 140, 311, 762g }}
-Badness (Smith): 0.015123
+Badness (Sintel): 1.08
 ==== 29-limit ====
@@ Line 317: / Line 371: @@
 Comma list: 595/594, 625/624, 784/783, 833/832, 875/874, 1015/1014, 1105/1104, 1156/1155
-Mapping: {{mapping| 1 3 2 3 -4 1 1 11 -3 1 | 0 -22 5 -3 116 42 48 -105 117 60 }}
+Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 114 61 | 0 22 -5 3 -116 -42 -48 105 -117 -60 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~23/22 = 77.167{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.0007{{c}}, ~44/23 = 1122.8332{{c}} (~23/22 = 77.1675{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122.8326{{c}} (~23/22 = 77.1674{{c}})
+<!-- * POTE: ~2 = 1200.000{{c}}, ~23/22 = 77.167{{c}} -->
-{{Optimal ET sequence|legend=0| 140, 311, 762g, 1073g, 1384cfggj }}
+{{Optimal ET sequence|legend=0| 140, 311, 762g }}
-Badness (Smith): 0.012181
+Badness (Sintel): 1.02
 ==== 31-limit ====
@@ Line 330: / Line 387: @@
 Comma list: 595/594, 625/624, 714/713, 784/783, 833/832, 875/874, 900/899, 931/930, 1015/1014
-Mapping: {{mapping| 1 3 2 3 -4 1 1 11 -3 1 11 | 0 -22 5 -3 116 42 48 -105 117 60 -94 }}
+Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 114 61 -83 | 0 22 -5 3 -116 -42 -48 105 -117 -60 94 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~23/22 = 77.169{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9721{{c}}, ~44/23 = 1122.8047{{c}} (~23/22 = 77.1673{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122.8309{{c}} (~23/22 = 77.1691{{c}})
+<!-- * POTE: ~2 = 1200.000{{c}}, ~23/22 = 77.169{{c}} -->
 {{Optimal ET sequence|legend=0| 140, 171, 311 }}
-Badness (Smith): 0.012311
+Badness (Sintel): 1.18
 ==== 37-limit ====
@@ Line 343: / Line 403: @@
 Comma list: 595/594, 625/624, 703/702, 714/713, 784/783, 833/832, 875/874, 900/899, 931/930, 1015/1014
-Mapping: {{mapping| 1 3 2 3 -4 1 1 11 -3 1 11 0 | 0 -22 5 -3 116 42 48 -105 117 60 -94 81 }}
+Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 114 61 -83 81 | 0 22 -5 3 -116 -42 -48 105 -117 -60 94 -81 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~23/22 = 77.170{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9824{{c}}, ~44/23 = 1122.8139{{c}} (~23/22 = 77.1685{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122.8304{{c}} (~23/22 = 77.1696{{c}})
+<!-- * POTE: ~2 = 1200.000{{c}}, ~23/22 = 77.170{{c}} -->
 {{Optimal ET sequence|legend=0| 140, 171, 311 }}
-Badness (Smith): 0.010949
+Badness (Sintel): 1.19
 ==== 41-limit ====
@@ Line 356: / Line 419: @@
 Comma list: 595/594, 625/624, 697/696, 703/702, 714/713, 784/783, 820/819, 833/832, 875/874, 900/899, 931/930
-Mapping: {{mapping| 1 3 2 3 -4 1 1 11 -3 1 11 0 6 | 0 -22 5 -3 116 42 48 -105 117 60 -94 81 -10 }}
+Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 114 61 -83 81 -4 | 0 22 -5 3 -116 -42 -48 105 -117 -60 94 -81 10 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~23/22 = 77.169{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9957{{c}}, ~44/23 = 1122.8266{{c}} (~23/22 = 77.1691{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122.8306{{c}} (~23/22 = 77.1694{{c}})
+<!-- * POTE: ~2 = 1200.000{{c}}, ~23/22 = 77.169{{c}} -->
 {{Optimal ET sequence|legend=0| 140, 171, 311 }}
-Badness (Smith): 0.009825
+Badness (Sintel): 1.20
 === Hemitert ===
@@ Line 369: / Line 435: @@
 Comma list: 2401/2400, 3025/3024, 65625/65536
-Mapping: {{mapping| 1 3 2 3 6 | 0 -44 10 -6 -79 }}
+Mapping: {{mapping| 1 -41 12 -3 -73 | 0 44 -10 6 79 }}
-: mapping generators: ~2, ~45/44
+: mapping generators: ~2, ~88/45
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~45/44 = 38.596{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.1008{{c}}, ~88/45 = 1161.5020{{c}} (~45/44 = 38.5988{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~88/45 = 1161.4053{{c}} (~45/44 = 38.5947{{c}})
+<!-- * POTE: ~2 = 1200.000{{c}}, ~45/44 = 38.596{{c}} -->
-{{Optimal ET sequence|legend=0| 31, 280, 311, 342 }}
+{{Optimal ET sequence|legend=0| 31, …, 280, 311, 342, 2021cde, 2363cde, …, 3389ccddee, 3731ccddee }}
-Badness (Smith): 0.015633
+Badness (Sintel): 0.517
 ==== 13-limit ====
@@ Line 383: / Line 452: @@
 Comma list: 625/624, 1575/1573, 2401/2400, 4096/4095
-Mapping: {{mapping| 1 3 2 3 6 1 | 0 -44 10 -6 -79 84 }}
+Mapping: {{mapping| 1 -41 12 -3 -73 85 | 0 44 -10 6 79 -84 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~45/44 = 38.588{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9822{{c}}, ~88/45 = 1161.3952{{c}} (~45/44 = 38.5871{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~88/45 = 1161.4123{{c}} (~45/44 = 38.5877{{c}})
+<!-- * POTE: ~2 = 1200.000{{c}}, ~45/44 = 38.588{{c}} -->
-{{Optimal ET sequence|legend=0| 31, 280, 311, 964f, 1275f, 1586cff }}
+{{Optimal ET sequence|legend=0| 31, 280, 311 }}
-Badness (Smith): 0.033573
+Badness (Sintel): 1.39
 ==== 17-limit ====
@@ Line 396: / Line 468: @@
 Comma list: 625/624, 833/832, 1225/1224, 1575/1573, 4096/4095
-Mapping: {{mapping| 1 3 2 3 6 1 1 | 0 -44 10 -6 -79 84 96 }}
+Mapping: {{mapping| 1 -41 12 -3 -73 85 97| 0 44 -10 6 79 -84 -96 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~45/44 = 38.589{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.0042{{c}}, ~88/45 = 1161.4149{{c}} (~45/44 = 38.5893{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~88/45 = 1161.4109{{c}} (~45/44 = 38.5891{{c}})
+<!-- * POTE: ~2 = 1200.000{{c}}, ~45/44 = 38.589{{c}} -->
-{{Optimal ET sequence|legend=0| 31, 280, 311, 653f, 964f }}
+{{Optimal ET sequence|legend=0| 31, 280, 311, 653f }}
-Badness (Smith): 0.025298
+Badness (Sintel): 1.29
 === Semitert ===
@@ Line 409: / Line 484: @@
 Comma list: 2401/2400, 9801/9800, 65625/65536
-Mapping: {{mapping| 2 6 4 6 1 | 0 -22 5 -3 46 }}
+Mapping: {{mapping| 2 -16 9 3 47 | 0 22 -5 3 -46 }}
-: mapping generators: ~99/70, ~256/245
+: mapping generators: ~99/70, ~693/512
-Optimal tuning (POTE): ~99/70 = 1200.000{{c}}, ~256/245 = 77.193{{c}}
+Optimal tunings:
+* WE: ~99/70 = 600.0548{{c}}, ~693/512 = 522.8547{{c}} (~256/245 = 77.2002{{c}})
+* CWE: ~99/70 = 600.0000{{c}}, ~693/512 = 522.8069{{c}} (~256/245 = 77.1931{{c}})
+<!-- * POTE: ~99/70 = 600.000{{c}}, ~256/245 = 77.193{{c}} -->
 {{Optimal ET sequence|legend=0| 62e, 140, 202, 342 }}
-Badness (Smith): 0.025790
+Badness (Sintel): 0.853
 == Quasiorwell ==
@@ Line 427: / Line 505: @@
 [[Comma list]]: 2401/2400, 29360128/29296875
-{{Mapping|legend=1| 1 31 0 9 | 0 -38 3 -8 }}
+{{Mapping|legend=1| 1 -7 3 1 | 0 38 -3 8 }}
-: mapping generators: ~2, ~875/512
+: mapping generators: ~2, ~1024/875
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~1024/875 = 271.107{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9403{{c}}, ~1024/875 = 271.0935{{c}}
+: [[error map]]: {{val| -0.060 +0.018 +0.226 -0.137 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~1024/875 = 271.1064{{c}}
+: error map: {{val| 0.000 +0.087 +0.367 +0.025 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~1024/875 = 271.107{{c}} -->
-{{Optimal ET sequence|legend=1| 31, 177, 208, 239, 270, 571, 841, 1111 }}
+{{Optimal ET sequence|legend=1| 31, …, 177, 208, 239, 270, 571, 841, 1111 }}
-[[Badness]] (Smith): 0.035832
+[[Badness]] (Sintel): 0.907
 === 11-limit ===
@@ Line 441: / Line 524: @@
 Comma list: 2401/2400, 3025/3024, 5632/5625
-Mapping: {{mapping| 1 31 0 9 53 | 0 -38 3 -8 -64 }}
+Mapping: {{mapping| 1 -7 3 1 -11 | 0 38 -3 8 64 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~90/77 = 271.111{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9484{{c}}, ~90/77 = 271.0989{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~90/77 = 271.1099{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~90/77 = 271.111{{c}} -->
-{{Optimal ET sequence|legend=0| 31, 208, 239, 270 }}
+{{Optimal ET sequence|legend=0| 31, …, 177e, 208, 239, 270 }}
-Badness (Smith): 0.017540
+Badness (Sintel): 0.580
 === 13-limit ===
@@ Line 454: / Line 540: @@
 Comma list: 1001/1000, 1716/1715, 3025/3024, 4096/4095
-Mapping: {{mapping| 1 31 0 9 53 -59 | 0 -38 3 -8 -64 81 }}
+Mapping: {{mapping| 1 -7 3 1 -11 22 | 0 38 -3 8 64 -81 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~90/77 = 271.107{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9916{{c}}, ~90/77 = 271.1051{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~90/77 = 271.1070{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~90/77 = 271.107{{c}} -->
 {{Optimal ET sequence|legend=0| 31, 239, 270, 571, 841, 1111 }}
-Badness (Smith): 0.017921
+Badness (Sintel): 0.741
 == Neominor ==
@@ Line 469: / Line 558: @@
 [[Comma list]]: 2401/2400, 177147/175616
-{{Mapping|legend=1| 1 3 12 8 | 0 -6 -41 -22 }}
+{{Mapping|legend=1| 1 -3 -29 -14 | 0 6 41 22 }}
-: mapping generators: ~2, ~189/160
+: mapping generators: ~2, ~320/189
 [[Optimal tuning]]s:
-* [[TE]]: ~2 = 1200.428{{c}}, ~189/160 = 283.381{{c}}
+* [[WE]]: ~2 = 1200.4276{{c}}, ~320/189 = 917.0471{{c}}
-* [[CTE]]: ~2 = 1200.000{{c}}, ~189/160 = 283.247{{c}}
+: [[error map]]: {{val| +0.428 -0.955 +0.216 +0.224 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~320/189 = 916.7320{{c}}
+: error map: {{val| 0.000 -1.563 -0.301 -0.722 }}
+<!-- * [[TE]]: ~2 = 1200.428{{c}}, ~320/189 = 916.619{{c}}
+* [[CTE]]: ~2 = 1200.000{{c}}, ~320/189 = 916.753{{c}} -->
-{{Optimal ET sequence|legend=1| 72, 161, 233, 305 }}
+{{Optimal ET sequence|legend=1| 17c, 55c, 72, 161, 233, 305 }}
-[[Badness]] (Sintel): 2.233
+[[Badness]] (Sintel): 2.23
 === 11-limit ===
@@ Line 485: / Line 578: @@
 Comma list: 243/242, 441/440, 35937/35840
-Mapping: {{mapping| 1 3 12 8 7 | 0 -6 -41 -22 -15 }}
+Mapping: {{mapping| 1 -3 -29 -14 -8 | 0 6 41 22 15 }}
 Optimal tunings:
-* TE: ~2 = 1200.347{{c}}, ~33/28 = 283.358{{c}}
+* WE: ~2 = 1200.3466{{c}}, ~56/33 = 916.9889{{c}}
-* CTE: ~2 = 1200.000{{c}}, ~33/28 = 283.247{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~56/33 = 916.7330{{c}}
+<!-- * TE: ~2 = 1200.347{{c}}, ~56/33 = 916.642{{c}}
+* CTE: ~2 = 1200.000{{c}}, ~56/33 = 916.753{{c}} -->
-{{Optimal ET sequence|legend=0| 72, 161, 233, 305 }}
+{{Optimal ET sequence|legend=0| 17c, 55c, 72, 161, 233, 305 }}
 Badness (Sintel): 0.924
@@ Line 500: / Line 595: @@
 Comma list: 169/168, 243/242, 364/363, 441/440
-Mapping: {{mapping| 1 3 12 8 7 7 | 0 -6 -41 -22 -15 -14 }}
+Mapping: {{mapping| 1 -3 -29 -14 -8 -7 | 0 6 41 22 15 14 }}
 Optimal tunings:
-* TE: ~2 = 1200.689{{c}}, ~13/11 = 283.457{{c}}
+* WE: ~2 = 1200.6874{{c}}, ~22/13 = 917.2313{{c}}
-* CTE: ~2 = 1200.000{{c}}, ~13/11 = 283.233{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~22/13 = 916.7228{{c}}
+<!-- * TE: ~2 = 1200.689{{c}}, ~22/13 = 916.543{{c}}
+* CTE: ~2 = 1200.000{{c}}, ~22/13 = 916.767{{c}} -->
-{{Optimal ET sequence|legend=0| 72, 161f, 233ff }}
+{{Optimal ET sequence|legend=0| 17c, 55cf, 72 }}
-Badness (Sintel): 1.113
+Badness (Sintel): 1.11
 === 17-limit ===
@@ Line 515: / Line 612: @@
 Comma list: 169/168, 221/220, 243/242, 273/272, 364/363
-Mapping: {{mapping| 1 3 12 8 7 7 14 | 0 -6 -41 -22 -15 -14 -42 }}
+Mapping: {{mapping| 1 -3 -29 -14 -8 -7 -28 | 0 6 41 22 15 14 42 }}
 Optimal tunings:
-* TE: ~2 = 1200.692{{c}}, ~13/11 = 283.455{{c}}
+* WE: ~2 = 1200.6905{{c}}, ~17/10 = 917.2356{{c}}
-* CTE: ~2 = 1200.000{{c}}, ~13/11 = 283.229{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~17/10 = 916.7252{{c}}
+<!-- * TE: ~2 = 1200.692{{c}}, ~17/10 = 916.545{{c}}
+* CTE: ~2 = 1200.000{{c}}, ~17/10 = 916.771{{c}} -->
-{{Optimal ET sequence|legend=0| 72, 161f, 233ff }}
+{{Optimal ET sequence|legend=0| 17cg, 55cfg, 72 }}
 Badness (Sintel): 0.918
@@ Line 532: / Line 631: @@
 [[Comma list]]: 2401/2400, 14348907/14336000
-{{Mapping|legend=1| 1 11 42 25 | 0 -14 -59 -33 }}
+{{Mapping|legend=1| 1 -3 -17 -8 | 0 14 59 33 }}
-: mapping generators: ~2, ~2187/1372
+: mapping generators: ~2, ~2744/2187
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~2744/2187 = 392.988{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0435{{c}}, ~2744/2187 = 393.0021{{c}}
+: [[error map]]: {{val| +0.043 -0.057 +0.069 -0.106 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~2744/2187 = 392.9887{{c}}
+: error map: {{val| 0.000 -0.113 +0.022 -0.197 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~2744/2187 = 392.988{{c}} -->
 {{Optimal ET sequence|legend=1| 58, 113, 171, 742, 913, 1084, 1255, 2681d, 3936d }}
-[[Badness]] (Smith): 0.016736
+[[Badness]] (Sintel): 0.424
 === 11-limit ===
@@ Line 546: / Line 650: @@
 Comma list: 243/242, 441/440, 1792000/1771561
-Mapping: {{mapping| 1 11 42 25 27 | 0 -14 -59 -33 -35 }}
+Mapping: {{mapping| 1 -3 -17 -8 -8 | 0 14 59 33 35 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~1372/1089 = 392.991{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.8090{{c}}, ~1372/1089 = 392.9286{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~1372/1089 = 392.9870{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~1372/1089 = 392.991{{c}} -->
 {{Optimal ET sequence|legend=0| 58, 113, 171 }}
-Badness (Smith): 0.052358
+Badness (Sintel): 1.73
 === 13-limit ===
@@ Line 559: / Line 666: @@
 Comma list: 243/242, 364/363, 441/440, 2200/2197
-Mapping: {{mapping| 1 11 42 25 27 38 | 0 -14 -59 -33 -35 -51 }}
+Mapping: {{mapping| 1 -3 -17 -8 -8 -13 | 0 14 59 33 35 51 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~180/143 = 392.989{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.7756{{c}}, ~180/143 = 392.9154{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~180/143 = 392.9840{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~180/143 = 392.989{{c}} -->
 {{Optimal ET sequence|legend=0| 58, 113, 171 }}
-Badness (Smith): 0.026974
+Badness (Sintel): 1.11
 === 17-limit ===
@@ Line 574: / Line 684: @@
 Mapping: {{mapping| 1 -3 -17 -8 -8 -13 9 | 0 14 59 33 35 51 -15 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~64/51 = 392.985{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.8396{{c}}, ~64/51 = 392.9322{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~64/51 = 392.9826{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~64/51 = 392.985{{c}} -->
 {{Optimal ET sequence|legend=0| 58, 113, 171 }}
-Badness (Smith): 0.023205
+Badness (Sintel): 1.18
 == Quinmite ==
@@ Line 587: / Line 700: @@
 [[Comma list]]: 2401/2400, 1959552/1953125
-{{Mapping|legend=1| 1 27 24 20 | 0 -34 -29 -23 }}
+{{Mapping|legend=1| 1 -7 -5 -3 | 0 34 29 23 }}
-: mapping generators: ~2, ~42/25
+: mapping generators: ~2, ~25/21
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~25/21 = 302.997{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9361{{c}}, ~25/21 = 302.9808{{c}}
+: [[error map]]: {{val| -0.064 -0.162 +0.448 -0.077 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~25/21 = 302.9953{{c}}
+: error map: {{val| 0.000 -0.116 +0.549 +0.065 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~25/21 = 302.997{{c}} -->
-{{Optimal ET sequence|legend=1| 99, 202, 301, 400, 701, 1101c, 1802c, 2903cc }}
+{{Optimal ET sequence|legend=1| 99, 202, 301, 400, 701, 1101c, 1802c }}
-[[Badness]] (Smith): 0.037322
+[[Badness]] (Sintel): 0.945
 == Unthirds ==
@@ Line 605: / Line 723: @@
 [[Comma list]]: 2401/2400, 68359375/68024448
-{{Mapping|legend=1| 1 29 33 25 | 0 -42 -47 -34 }}
+{{Mapping|legend=1| 1 -13 -14 -9 | 0 42 47 34 }}
-: mapping generators: ~2, ~6125/3888
+: mapping generators: ~2, ~3969/3125
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3969/3125 = 416.717{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0859{{c}}, ~3969/3125 = 416.7465{{c}}
+: [[error map]]: {{val| +0.086 +0.281 -0.431 -0.218 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3969/3125 = 416.7184{{c}}
+: error map: {{val| 0.000 +0.220 -0.547 -0.399 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~3969/3125 = 416.717{{c}} -->
 {{Optimal ET sequence|legend=1| 72, 167, 239, 311, 694, 1005c }}
-[[Badness]] (Smith): 0.075253
+[[Badness]] (Sintel): 1.90
 === 11-limit ===
@@ Line 619: / Line 742: @@
 Comma list: 2401/2400, 3025/3024, 4000/3993
-Mapping: {{mapping| 1 29 33 25 25 | 0 -42 -47 -34 -33 }}
+Mapping: {{mapping| 1 -13 -14 -9 -8 | 0 42 47 34 33 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~14/11 = 416.718{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.0246{{c}}, ~14/11 = 416.7270{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~14/11 = 416.7190{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~14/11 = 416.718{{c}} -->
 {{Optimal ET sequence|legend=0| 72, 167, 239, 311 }}
-Badness (Smith): 0.022926
+Badness (Sintel): 0.758
 === 13-limit ===
@@ Line 632: / Line 758: @@
 Comma list: 625/624, 1575/1573, 2080/2079, 2401/2400
-Mapping: {{mapping| 1 29 33 25 25 99 | 0 -42 -47 -34 -33 -146 }}
+Mapping: {{mapping| 1 -13 -14 -9 -8 -47 | 0 42 47 34 33 146 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~14/11 = 416.716{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.0536{{c}}, ~14/11 = 416.7343{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~14/11 = 416.7164{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~14/11 = 416.716{{c}} -->
 {{Optimal ET sequence|legend=0| 72, 239f, 311, 694, 1005c }}
-Badness (Smith): 0.020888
+Badness (Sintel): 0.863
 == Newt ==
@@ Line 650: / Line 779: @@
 : mapping generators: ~2, ~49/40
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~49/40 = 351.113{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9315{{c}}, ~49/40 = 351.0932{{c}}
+: [[error map]]: {{val| -0.068 +0.163 +0.075 -0.188 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.1141{{c}}
+: error map: {{val| 0.000 +0.273 +0.180 -0.022 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~49/40 = 351.113{{c}} -->
 {{Optimal ET sequence|legend=1| 41, 147c, 188, 229, 270, 1121, 1391, 1661, 1931, 2201 }}
-[[Badness]] (Smith): 0.041878
+[[Badness]] (Sintel): 1.06
 === 11-limit ===
@@ Line 663: / Line 797: @@
 Mapping: {{mapping| 1 1 19 11 -10 | 0 2 -57 -28 46 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~49/40 = 351.115{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9603{{c}}, ~49/40 = 351.1038{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1155{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~49/40 = 351.115{{c}} -->
-{{Optimal ET sequence|legend=0| 41, 147ce, 188, 229, 270, 581, 851, 1121, 1972 }}
+{{Optimal ET sequence|legend=0| 41, 188, 229, 270, 581, 851, 1121, 1972 }}
-Badness (Smith): 0.019461
+Badness (Sintel): 0.643
 === 13-limit ===
@@ Line 676: / Line 813: @@
 Mapping: {{mapping| 1 1 19 11 -10 -20 | 0 2 -57 -28 46 81 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~49/40 = 351.117{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9747{{c}}, ~49/40 = 351.1094{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1168{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~49/40 = 351.117{{c}} -->
-{{Optimal ET sequence|legend=0| 41, 147cef, 188f, 229, 270, 581, 851, 2283b, 3134b }}
+{{Optimal ET sequence|legend=0| 41, 229, 270, 581, 851, 2283b }}
-Badness (Smith): 0.013830
+Badness (Sintel): 0.571
 === 2.3.5.7.11.13.19 subgroup (neonewt) ===
@@ Line 689: / Line 829: @@
 Mapping: {{mapping| 1 1 19 11 -10 -20 18 | 0 2 -57 -28 46 81 -47 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~49/40 = 351.117{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9782{{c}}, ~49/40 = 351.1102{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1166{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~49/40 = 351.117{{c}} -->
+{{Optimal ET sequence|legend=0| 41, 229, 270, 581, 851 }}
-{{Optimal ET sequence|legend=0| 41, 147cefh, 188f, 229, 270, 581, 851, 3134b, 3985b, 4836bb }}
+Badness (Sintel): 0.438
 == Septidiasemi ==
@@ Line 702: / Line 847: @@
 [[Comma list]]: 2401/2400, 2152828125/2147483648
-{{Mapping|legend=1| 1 25 -31 -8 | 0 -26 37 12 }}
+{{Mapping|legend=1| 1 -1 6 4 | 0 26 -37 -12 }}
-: mpping generators: ~2, ~28/15
+: mpping generators: ~2, ~15/14
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~15/14 = 119.297{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.1043{{c}}, ~15/14 = 119.3076{{c}}
+: [[error map]]: {{val| +0.104 -0.061 -0.070 -0.100 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~15/14 = 119.2971{{c}}
+: error map: {{val| 0.000 -0.230 -0.307 -0.391 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~15/14 = 119.297{{c}} -->
-{{Optimal ET sequence|legend=1| 10, 151, 161, 171, 3581bcdd, 3752bcdd, 3923bcdd, 4094bcdd, 4265bccdd, 4436bccdd, 4607bccdd }}
+{{Optimal ET sequence|legend=1| 10, 151, 161, 171, 3581bcdd, 3752bcdd, …, 5633bbccddd, 5804bbccddd }}
-[[Badness]] (Smith): 0.044115
+[[Badness]] (Sintel): 1.12
 === Sedia ===
@@ Line 718: / Line 868: @@
 Comma list: 243/242, 441/440, 939524096/935859375
-Mapping: {{mapping| 1 25 -31 -8 62 | 0 -26 37 12 -65 }}
+Mapping: {{mapping| 1 -1 6 4 -3 | 0 26 -37 -12 65 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/14 = 119.279{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9635{{c}}, ~15/14 = 119.2755{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 119.2791{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~15/14 = 119.279{{c}} -->
 {{Optimal ET sequence|legend=0| 10, 151, 161, 171, 332 }}
-Badness (Smith): 0.090687
+Badness (Sintel): 3.00
 ==== 13-limit ====
@@ Line 731: / Line 884: @@
 Comma list: 243/242, 441/440, 2200/2197, 3584/3575
-Mapping: {{mapping| 1 25 -31 -8 62 1 | 0 -26 37 12 -65 3 }}
+Mapping: {{mapping| 1 -1 6 4 -3 4 | 0 26 -37 -12 65 -3 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/14 = 119.281{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.8922{{c}}, ~15/14 = 119.2700{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 119.2804{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~15/14 = 119.281{{c}} -->
-{{Optimal ET sequence|legend=0| 10, 151, 161, 171, 332, 835eeff }}
+{{Optimal ET sequence|legend=0| 10, 151, 161, 171, 332 }}
-Badness (Smith): 0.045773
+Badness (Sintel): 1.89
 ==== 17-limit ====
@@ Line 744: / Line 900: @@
 Comma list: 243/242, 441/440, 833/832, 2200/2197, 3584/3575
-Mapping: {{mapping| 1 25 -31 -8 62 1 23 | 0 -26 37 12 -65 3 -21 }}
+Mapping: {{mapping| 1 -1 6 4 -3 4 2 | 0 26 -37 -12 65 -3 21 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/14 = 119.281{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9088{{c}}, ~15/14 = 119.2719{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 119.2808{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~15/14 = 119.281{{c}} -->
-{{Optimal ET sequence|legend=0| 10, 151, 161, 171, 332, 503ef, 835eeff }}
+{{Optimal ET sequence|legend=0| 10, 151, 161, 171, 332, 503ef }}
-Badness (Smith): 0.027322
+Badness (Sintel): 1.39
 == Maviloid ==
@@ Line 759: / Line 918: @@
 [[Comma list]]: 2401/2400, 1224440064/1220703125
-{{Mapping|legend=1| 1 31 34 26 | 0 -52 -56 -41 }}
+{{Mapping|legend=1| 1 -21 -22 -15 | 0 52 56 41 }}
-: mapping generators: ~2, ~1296/875
+: mapping generators: ~2, ~875/648
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~1296/875 = 678.810{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9863{{c}}, ~875/648 = 521.1837{{c}}
+: [[error map]]: {{val| -0.014 -0.115 +0.274 -0.089 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~875/648 = 521.1894{{c}}
+: error map: {{val| 0.000 -0.106 +0.293 -0.060 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~875/648 = 521.190{{c}} -->
 {{Optimal ET sequence|legend=1| 76, 99, 274, 373, 472, 571, 1043, 1614 }}
-[[Badness]] (Smith): 0.057632
+[[Badness]] (Sintel): 1.46
 == Subneutral ==
@@ Line 775: / Line 939: @@
 [[Comma list]]: 2401/2400, 274877906944/274658203125
-{{Mapping|legend=1| 1 19 0 6 | 0 -60 8 -11 }}
+{{Mapping|legend=1| 1 -41 8 -5 | 0 60 -8 11 }}
-: mapping generators: ~2, ~57344/46875
+: mapping generators: ~2, ~46875/28672
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~57344/46875 = 348.301{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9998{{c}}, ~46875/28672 = 851.6994 (~57344/46875 = 348.3005{{c}})
+: [[error map]]: {{val| -0.000 +0.013 +0.090 -0.132 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~46875/28672 = 851.6995{{c}} (~57344/46875 = 348.3005{{c}})
+: error map: {{val| 0.000 +0.014 +0.090 -0.132 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~57344/46875 = 348.301{{c}} -->
 {{Optimal ET sequence|legend=1| 31, …, 348, 379, 410, 441, 1354, 1795, 2236 }}
-[[Badness]] (Smith): 0.045792
+[[Badness]] (Sintel): 1.16
 == Osiris ==
@@ Line 791: / Line 960: @@
 [[Comma list]]: 2401/2400, 31381059609/31360000000
-{{Mapping|legend=1| 1 13 33 21 | 0 -32 -86 -51 }}
+{{Mapping|legend=1| 1 13 33 21 | 0 32 86 51 }}
-: mapping generators: ~2, ~2800/2187
+: mapping generators: ~2, ~2187/1400
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~2800/2187 = 428.066{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0285{{c}}, ~2187/1400 = 771.9522{{c}}
+: [[error map]]: {{val| +0.028 -0.025 +0.068 -0.117 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~2187/1400 = 771.9343{{c}}
+: error map: {{val| 0.000 -0.056 +0.039 -0.175 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~2187/1400 = 771.934{{c}} -->
 {{Optimal ET sequence|legend=1| 157, 171, 1012, 1183, 1354, 1525, 1696 }}
-[[Badness]] (Smith): 0.028307
+[[Badness]] (Sintel): 0.716
 == Gorgik ==
@@ Line 805: / Line 979: @@
 [[Comma list]]: 2401/2400, 28672/28125
-{{Mapping|legend=1| 1 5 1 3 | 0 -18 7 -1 }}
+{{Mapping|legend=1| 1 -13 8 2 | 0 18 -7 1 }}
-: mapping generators: ~2, ~8/7
+: mapping generators: ~2, ~7/4
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~8/7 = 227.512{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1198.5503{{c}}, ~7/4 = 971.3132{{c}} (~8/7 = 227.2371{{c}})
+: [[error map]]: {{val| -1.450 +0.528 +2.896 -0.412 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 972.4675{{c}} (~8/7 = 227.5325{{c}})
+: error map: {{val| 0.000 +2.460 +6.414 +3.642 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~8/7 = 227.512{{c}} -->
 {{Optimal ET sequence|legend=1| 21, 37, 58, 153bc, 211bccd, 269bccd }}
-[[Badness]] (Smith): 0.158384
+[[Badness]] (Sintel): 4.01
 === 11-limit ===
@@ Line 819: / Line 998: @@
 Comma list: 176/175, 2401/2400, 2560/2541
-Mapping: {{mapping| 1 5 1 3 1 | 0 -18 7 -1 13 }}
+Mapping: {{mapping| 1 -13 8 2 14 | 0 18 -7 1 -13 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~8/7 = 227.500{{c}}
+Optimal tunings:
+* WE: ~2 = 1198.4615{{c}}, ~7/4 = 971.2535{{c}} (~8/7 = 227.2079{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 972.4918{{c}} (~8/7 = 227.5082{{c}})
+<!-- * POTE: ~2 = 1200.000{{c}}, ~8/7 = 227.500{{c}} -->
 {{Optimal ET sequence|legend=0| 21, 37, 58, 153bce, 211bccdee, 269bccdee }}
-Badness (Smith): 0.059260
+Badness (Sintel): 1.96
 === 13-limit ===
@@ Line 832: / Line 1,014: @@
 Comma list: 176/175, 196/195, 364/363, 512/507
-Mapping: {{mapping| 1 5 1 3 1 2 | 0 -18 7 -1 13 9 }}
+Mapping: {{mapping| 1 -13 8 2 14 11 | 0 18 -7 1 -13 -9 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~8/7 = 227.493{{c}}
+Optimal tunings:
+* WE: ~2 = 1198.4012{{c}}, ~7/4 = 971.2110{{c}} (~8/7 = 227.1903{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 972.5030{{c}} (~8/7 = 227.4970{{c}})
+<!-- * POTE: ~2 = 1200.000{{c}}, ~8/7 = 227.493{{c}} -->
 {{Optimal ET sequence|legend=0| 21, 37, 58, 153bcef, 211bccdeeff }}
-Badness (Smith): 0.032205
+Badness (Sintel): 1.33
 == Fibo ==
@@ Line 845: / Line 1,030: @@
 [[Comma list]]: 2401/2400, 341796875/339738624
-{{Mapping|legend=1| 1 19 8 10 | 0 -46 -15 -19 }}
+{{Mapping|legend=1| 1 -27 -7 -9 | 0 46 15 19 }}
-: mapping generators: ~2, ~125/96
+: mapping generators: ~2, ~192/125
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~125/96 = 454.310{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.2050{{c}}, ~192/125 = 745.8170{{c}}
+: [[error map]]: {{val| +0.205 +0.094 -0.493 -0.147 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~192/125 = 745.6927{{c}}
+: error map: {{val| 0.000 -0.092 -0.924 -0.665 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~192/125 = 745.690{{c}} -->
 {{Optimal ET sequence|legend=1| 37, 66b, 103, 140, 243, 383, 1009cd, 1392ccd }}
-Badness (Smith): 0.100511
+Badness (Sintel): 2.54
 === 11-limit ===
@@ Line 859: / Line 1,049: @@
 Comma list: 385/384, 1375/1372, 43923/43750
-Mapping: {{mapping| 1 19 8 10 8 | 0 -46 -15 -19 -12 }}
+Mapping: {{mapping| 1 -27 -7 -9 -4 | 0 46 15 19 12 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~100/77 = 454.318{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.4064{{c}}, ~77/50 = 745.9349{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~77/50 = 745.6876{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~77/50 = 745.682{{c}} -->
 {{Optimal ET sequence|legend=0| 37, 66b, 103, 140, 243e }}
-Badness (Smith): 0.056514
+Badness (Sintel): 1.87
 === 13-limit ===
@@ Line 872: / Line 1,065: @@
 Comma list: 385/384, 625/624, 847/845, 1375/1372
-Mapping: {{mapping| 1 19 8 10 8 9 | 0 -46 -15 -19 -12 -14 }}
+Mapping: {{mapping| 1 -27 -7 -9 -4 -5 | 0 46 15 19 12 14 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~13/10 = 454.316{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.3728{{c}}, ~20/13 = 745.9152{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 745.6879{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~20/13 = 745.684{{c}} -->
 {{Optimal ET sequence|legend=0| 37, 66b, 103, 140, 243e }}
-Badness (Smith): 0.027429
+Badness (Sintel): 1.13
 == Mintone ==
@@ Line 887: / Line 1,083: @@
 [[Comma list]]: 2401/2400, 177147/175000
-{{Mapping|legend=1| 1 5 9 7 | 0 -22 -43 -27 }}
+{{Mapping|legend=1| 1 -17 -34 -20 | 0 22 43 27 }}
-: mapping generators: ~2, ~10/9
+: mapping generators: ~2, ~9/5
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~10/9 = 186.343{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.1458{{c}}, ~9/5 = 1013.7798{{c}}
+: [[error map]]: {{val| +0.146 -1.277 +1.263 +0.314 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~9/5 = 1013.6611{{c}}
+: error map: {{val| 0.000 -1.410 +1.116 +0.025 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~9/5 = 1013.657{{c}} -->
-{{Optimal ET sequence|legend=1| 45, 58, 103, 161, 586b, 747bc, 908bbc }}
+{{Optimal ET sequence|legend=1| 45, 58, 103, 161 }}
-[[Badness]] (Smith): 0.125672
+[[Badness]] (Sintel): 3.18
 === 11-limit ===
@@ Line 901: / Line 1,102: @@
 Comma list: 243/242, 441/440, 43923/43750
-Mapping: {{mapping| 1 5 9 7 12 | 0 -22 -43 -27 -55 }}
+Mapping: {{mapping| 1 -17 -34 -20 -43 | 0 22 43 27 55 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 186.345{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.1491{{c}}, ~9/5 = 1013.7809{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~9/5 = 1013.6593{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~9/5 = 1013.655{{c}} -->
-{{Optimal ET sequence|legend=0| 58, 103, 161, 425b, 586b, 747bc }}
+{{Optimal ET sequence|legend=0| 45e, 58, 103, 161, 425b }}
-Badness (Smith): 0.039962
+Badness (Sintel): 1.32
 === 13-limit ===
@@ Line 914: / Line 1,118: @@
 Comma list: 243/242, 351/350, 441/440, 847/845
-Mapping: {{mapping| 1 5 9 7 12 11 | 0 -22 -43 -27 -55 -47 }}
+Mapping: {{mapping| 1 -17 -34 -20 -43 -36 | 0 22 43 27 55 47 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 186.347{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.0928{{c}}, ~9/5 = 1013.7311{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~9/5 = 1013.6556{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~9/5 = 1013.653{{c}} -->
-{{Optimal ET sequence|legend=0| 58, 103, 161, 425b, 586bf }}
+{{Optimal ET sequence|legend=0| 45ef, 58, 103, 161 }}
-Badness (Smith): 0.021849
+Badness (Sintel): 0.903
 === 17-limit ===
@@ Line 927: / Line 1,134: @@
 Comma list: 243/242, 351/350, 441/440, 561/560, 847/845
-Mapping: {{mapping| 1 5 9 7 12 11 3 | 0 -22 -43 -27 -55 -47 7 }}
+Mapping: {{mapping| 1 -17 -34 -20 -43 -36 10 | 0 22 43 27 55 47 -7 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 186.348{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.1085{{c}}, ~9/5 = 1013.7433{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~9/5 = 1013.6537{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~9/5 = 1013.652{{c}} -->
-{{Optimal ET sequence|legend=0| 58, 103, 161, 425b, 586bf }}
+{{Optimal ET sequence|legend=0| 45ef, 58, 103, 161 }}
-Badness (Smith): 0.020295
+Badness (Sintel): 1.03
 == Catafourth ==
@@ Line 942: / Line 1,152: @@
 [[Comma list]]: 2401/2400, 78732/78125
-{{Mapping|legend=1| 1 13 17 13 | 0 -28 -36 -25 }}
+{{Mapping|legend=1| 1 -15 -19 -12 | 0 28 36 25 }}
-: mapping generators: ~2, ~250/189
+: mapping generators: ~2, ~189/125
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~250/189 = 489.235{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9278{{c}}, ~189/125 = 710.7220{{c}}
+: [[error map]]: {{val| -0.072 -0.656 +1.050 +0.091 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~189/125 = 710.7626{{c}}
+: error map: {{val| 0.000 -0.603 +1.139 +0.238 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~189/125 = 710.765{{c}} -->
 {{Optimal ET sequence|legend=1| 27, 76, 103, 130 }}
-Badness (Smith): 0.079579
+[[Badness]] (Sintel): 2.01
 === 11-limit ===
@@ Line 956: / Line 1,171: @@
 Comma list: 243/242, 441/440, 78408/78125
-Mapping: {{mapping| 1 13 17 13 32 | 0 -28 -36 -25 -70 }}
+Mapping: {{mapping| 1 -15 -19 -12 -38 | 0 28 36 25 70 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~250/189 = 489.252{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.0219{{c}}, ~189/125 = 710.7610{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~189/125 = 710.7487{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~189/125 = 710.748{{c}} -->
-{{Optimal ET sequence|legend=0| 103, 130, 233, 363, 493e, 856be }}
+{{Optimal ET sequence|legend=0| 27e, 76e, 103, 130, 233, 363, 493e }}
-Badness (Smith): 0.036785
+Badness (Sintel): 1.22
 === 13-limit ===
@@ Line 969: / Line 1,187: @@
 Comma list: 243/242, 351/350, 441/440, 10985/10976
-Mapping: {{mapping| 1 13 17 13 32 9 | 0 -28 -36 -25 -70 -13 }}
+Mapping: {{mapping| 1 -15 -19 -12 -38 -4 | 0 28 36 25 70 13 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~65/49 = 489.256{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.1023{{c}}, ~98/65 = 710.8043{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~98/65 = 710.7459{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~98/65 = 710.744{{c}} -->
-{{Optimal ET sequence|legend=0| 103, 130, 233, 363 }}
+{{Optimal ET sequence|legend=0| 27e, 76e, 103, 130, 233, 363 }}
-Badness (Smith): 0.021694
+Badness (Sintel): 0.896
 == Cotritone ==
@@ Line 982: / Line 1,203: @@
 [[Comma list]]: 2401/2400, 390625/387072
-{{Mapping|legend=1| 1 17 9 10 | 0 -30 -13 -14 }}
+{{Mapping|legend=1| 1 -13 -4 -4 | 0 30 13 14 }}
-: mappping generators: ~2, ~10/7
+: mappping generators: ~2, ~7/5
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~7/5 = 583.385{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9278{{c}}, ~7/5 = 583.5994{{c}}
+: [[error map]]: {{val| +0.441 +0.289 -1.287 -0.200 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/5 = 583.3956{{c}}
+: error map: {{val| 0.000 -0.086 -2.170 -1.287 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~7/5 = 583.385{{c}} -->
-{{Optimal ET sequence|legend=1| 35, 37, 72, 109, 181, 253 }}
+{{Optimal ET sequence|legend=1| 35, 37, 72, 181, 253, 325c }}
-[[Badness]] (Smith): 0.098322
+[[Badness]] (Sintel): 2.49
 === 11-limit ===
@@ Line 996: / Line 1,222: @@
 Comma list: 385/384, 1375/1372, 4000/3993
-Mapping: {{mapping| 1 17 9 10 5 | 0 -30 -13 -14 -3 }}
+Mapping: {{mapping| 1 -13 -4 -4 2 | 0 30 13 14 3 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 583.387{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.4058{{c}}, ~7/5 = 583.5845{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~7/5 = 583.3950{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~7/5 = 583.387{{c}} -->
-{{Optimal ET sequence|legend=0| 35, 37, 72, 109, 181, 253 }}
+{{Optimal ET sequence|legend=0| 35, 37, 72, 181, 253, 325c }}
-Badness (Smith): 0.032225
+Badness (Sintel): 1.07
 === 13-limit ===
@@ Line 1,009: / Line 1,238: @@
 Comma list: 169/168, 364/363, 385/384, 625/624
-Mapping: {{mapping| 1 17 9 10 5 15 | 0 -30 -13 -14 -3 -22 }}
+Mapping: {{mapping| 1 -13 -4 -4 2 -7 | 0 30 13 14 3 22 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 583.387{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.6111{{c}}, ~7/5 = 583.6837{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~7/5 = 583.3987{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~7/5 = 583.387{{c}} -->
-{{Optimal ET sequence|legend=0| 37, 72, 109, 181f }}
+{{Optimal ET sequence|legend=0| 35f, 37, 72, 181f, 253ff }}
-Badness (Smith): 0.028683
+Badness (Sintel): 1.19
 == Quasimoha ==
@@ Line 1,027: / Line 1,259: @@
 : mapping generators: ~2, ~49/40
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~49/40 = 348.603{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1201.5059{{c}}, ~49/40 = 348.0409{{c}}
+: [[error map]]: {{val| +1.506 -2.367 -0.702 +0.759 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 348.5582{{c}}
+: error map: {{val| 0.000 -4.839 -3.152 -2.966 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~49/40 = 348.603{{c}} -->
-{{Optimal ET sequence|legend=1| 31, 117c, 148bc, 179bc }}
+{{Optimal ET sequence|legend=1| 24c, 31, 117c, 148bc, 179bcd }}
-[[Badness]] (Smith): 0.110820
+[[Badness]] (Sintel): 2.80
 === 11-limit ===
@@ Line 1,040: / Line 1,277: @@
 Mapping: {{mapping| 1 1 9 6 2 | 0 2 -23 -11 5 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/9 = 348.639{{c}}
+Optimal tunings:
+* WE: ~2 = 1201.7630{{c}}, ~11/9 = 349.1510{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 348.6050{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~11/9 = 348.639{{c}} -->
-{{Optimal ET sequence|legend=0| 31, 86ce, 117ce, 148bce }}
+{{Optimal ET sequence|legend=0| 24c, 31, 86ce, 117ce, 148bce }}
-Badness (Smith): 0.046181
+Badness (Sintel): 1.53
 == Lockerbie ==
@@ Line 1,063: / Line 1,303: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.0000{{c}}, ~3828125/2985984 = 431.1071{{c}}
+* [[WE]]: ~2 = 1199.9950{{c}}, ~3828125/2985984 = 431.1055{{c}}
-: [[error map]]: {{val| 0.0000 -0.0270 +0.1502 -0.1120 }}
+: [[error map]]: {{val| -0.005 -0.024 +0.146 -0.120 }}
 * [[CWE]]: ~2 = 1200.0000{{c}}, ~3828125/2985984 = 431.1072{{c}}
-: error map: {{val| 0.0000 -0.0205 +0.1547 -0.1081 }}
+: error map: {{val| 0.0000 -0.020 +0.155 -0.108 }}
+<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~3828125/2985984 = 431.1071{{c}}
+: [[error map]]: {{val| 0.000 -0.027 +0.150 -0.112 }} -->
-{{Optimal ET sequence|legend=1| 103, 167, 270, 643, 913 }}
+{{Optimal ET sequence|legend=1| 103, 167, 270, 643, 913, 1183 }}
-[[Badness]] (Smith): 0.0597
+[[Badness]] (Sintel): 1.51
 === 11-limit ===
@@ Line 1,080: / Line 1,322: @@
 Optimal tunings:
-* CTE: ~2 = 1200.0000{{c}}, ~77/60 = 431.1082{{c}}
+* WE: ~2 = 1200.0199{{c}}, ~77/60 = 431.1147{{c}}
 * CWE: ~2 = 1200.0000{{c}}, ~77/60 = 431.1078{{c}}
+<!-- * CTE: ~2 = 1200.0000{{c}}, ~77/60 = 431.1082{{c}} -->
 {{Optimal ET sequence|legend=0| 103, 167, 270, 643, 913, 1183e }}
-Badness (Smith): 0.0262
+Badness (Sintel): 0.865
 === 13-limit ===
@@ Line 1,095: / Line 1,338: @@
 Optimal tunings:
-* CTE: ~2 = 1200.0000{{c}}, ~77/60 = 431.1085{{c}}
+* WE: ~2 = 1200.0707{{c}}, ~77/60 = 431.1316{{c}}
 * CWE: ~2 = 1200.0000{{c}}, ~77/60 = 431.1069{{c}}
+<!-- * CTE: ~2 = 1200.0000{{c}}, ~77/60 = 431.1085{{c}} -->
 {{Optimal ET sequence|legend=0| 103, 167, 270, 643, 913f }}
-Badness (Smith): 0.0160
+Badness (Sintel): 0.662
 === 17-limit ===
@@ Line 1,110: / Line 1,354: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000{{c}}, ~77/60 = 431.107{{c}}
+* WE: ~2 = 1199.9639{{c}}, ~77/60 = 431.0957{{c}}
-* CWE: ~2 = 1200.000{{c}}, ~77/60 = 431.108{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~77/60 = 431.1083{{c}}
+<!-- * CTE: ~2 = 1200.000{{c}}, ~77/60 = 431.107{{c}} -->
 {{Optimal ET sequence|legend=0| 103, 167, 270 }}
-Badness (Smith): 0.0210
+Badness (Sintel): 1.07
 === 2.3.5.7.11.13.17.41 subgroup ===
@@ Line 1,125: / Line 1,370: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000{{c}}, ~41/32 = 431.107{{c}}
+* WE: ~2 = 1199.8693{{c}}, ~41/32 = 431.0650{{c}}
-* CWE: ~2 = 1200.000{{c}}, ~41/32 = 431.111{{c}}
+* CWE: ~2 = 1200.000{{c}}, ~41/32 = 431.1109{{c}}
+<!-- * CTE: ~2 = 1200.000{{c}}, ~41/32 = 431.107{{c}} -->
 {{Optimal ET sequence|legend=0| 103, 167, 270 }}
+Badness (Sintel): 1.25
 == Hemigoldis ==
@@ Line 1,139: / Line 1,387: @@
 [[Comma list]]: 2401/2400, 549755813888/533935546875
-{{Mapping|legend=1| 1 21 -9 2 | 0 -24 14 1 }}
+{{Mapping|legend=1| 1 21 -9 2 | 0 24 -14 -1 }}
-: mapping generators: ~2, ~7/4
+: mapping generators: ~2, ~8/7
-[[Optimal tuning]] ([[CWE]]): ~2 = 1200.000{{c}}, ~7/4 = 970.690{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.2264{{c}}, ~8/7 = 229.1679{{c}}
+: [[error map]]: {{val| -0.774 +0.394 +1.468 -0.314 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 229.3103{{c}}
+: error map: {{val| 0.000 +1.491 +3.343 +1.864 }}
 {{Optimal ET sequence|legend=1| 21, 47b, 68, 157, 382bccd, 529bccd }}
@@ Line 1,155: / Line 1,407: @@
 [[Comma list]]: 2401/2400, {{monzo| 93 -32 -17 -1 }}
-{{Mapping|legend=1| 1 43 -74 -25 | 0 -70 129 47 }}
+{{Mapping|legend=1| 1 -27 55 22 | 0 70 -129 -47 }}
-: mapping generators: ~2, ~675/448
+: mapping generators: ~2, ~896/675
-[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~675/448 = 709.9719{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0051{{c}}, ~896/675 = 490.0303{{c}}
+: [[error map]]: {{val| +0.005 +0.025 +0.063 -0.136 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~896/675 = 490.0282{{c}}
+: error map: {{val| 0.000 +0.017 +0.052 -0.150 }}
+<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~896/675 = 490.0281{{c}} -->
 {{Optimal ET sequence|legend=1| 120, 191, 311, 742, 1053, 2848, 3901 }}
-[[Badness]] (Smith): 0.202249
+[[Badness]] (Sintel): 5.12
 === 11-limit ===
@@ Line 1,169: / Line 1,426: @@
 Comma list: 2401/2400, 820125/819896, 2097152/2096325
-Mapping: {{mapping| 1 43 -74 -25 36 | 0 -70 129 47 -55 }}
+Mapping: {{mapping| 1 -27 55 22 -19 | 0 70 -129 -47 55 }}
-Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~675/448 = 709.9720{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9901{{c}}, ~896/675 = 490.0239{{c}}
+* CWE: ~2 = 1200.000{{c}}, ~896/675 = 490.0279{{c}}
+<!-- * CTE: ~2 = 1200.0000{{c}}, ~896/675 = 490.0280{{c}} -->
 {{Optimal ET sequence|legend=0| 120, 191, 311, 742, 1053, 1795 }}
-Badness (Smith): 0.052308
+Badness (Sintel): 1.73
 === 13-limit ===
@@ Line 1,182: / Line 1,442: @@
 Comma list: 2401/2400, 4096/4095, 6656/6655, 24192/24167
-Mapping: {{mapping| 1 43 -74 -25 36 25 | 0 -70 129 47 -55 -36 }}
+Mapping: {{mapping| 1 -27 55 22 -19 -11 | 0 70 -129 -47 55 36 }}
-Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~98/65 = 709.9723{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9701{{c}}, ~65/49 = 490.0155{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~65/49 = 490.0277{{c}}
+<!-- * CTE: ~2 = 1200.0000{{c}}, ~65/49 = 490.0277{{c}} -->
 {{Optimal ET sequence|legend=0| 120, 191, 311, 742, 1053, 1795f }}
-Badness (Smith): 0.032503
+Badness (Sintel): 1.34
 === 17-limit ===
@@ Line 1,195: / Line 1,458: @@
 Comma list: 2401/2400, 2601/2600, 4096/4095, 6656/6655, 8624/8619
-Mapping: {{mapping| 1 43 -74 -25 36 25 -103 | 0 -70 129 47 -55 -36 181 }}
+Mapping: {{mapping| 1 -27 55 22 -19 -11 78 | 0 70 -129 -47 55 36 -181 }}
-Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~98/65 = 709.9722{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9726{{c}}, ~65/49 = 490.0164{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~65/49 = 490.0276{{c}}
+<!-- * CTE: ~2 = 1200.0000{{c}}, ~65/49 = 490.0278{{c}} -->
 {{Optimal ET sequence|legend=0| 120g, 191g, 311, 431, 742, 1795f }}
-Badness (Smith): 0.020995
+Badness (Sintel): 1.07
 === 19-limit ===
@@ Line 1,208: / Line 1,474: @@
 Comma list: 2401/2400, 2601/2600, 2926/2925, 3136/3135, 3213/3211, 5985/5984
-Mapping: {{mapping| 1 43 -74 -25 36 25 -103 -49 | 0 -70 129 47 -55 -36 181 90 }}
+Mapping: {{mapping| 1 -27 55 22 -19 -11 78 41 | 0 70 -129 -47 55 36 -181 -90 }}
-Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~98/65 = 709.9722{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9756{{c}}, ~65/49 = 490.0176{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~65/49 = 490.0276{{c}}
+<!-- * CTE:~2 = 1200.0000{{c}}, ~98/65 = 709.9722{{c}} -->
 {{Optimal ET sequence|legend=0| 120g, 191g, 311, 431, 742, 1795f }}
-Badness (Smith): 0.013771
+Badness (Sintel): 0.838
 == References ==