Meantone family: Difference between revisions

Line 1,950:

[[Comma list]]: 81/80, 2401/2400

: mapping generators: ~2, ~9/7

: mapping generators: ~2, ~14/9

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000{{c}}, ~9/7 = ~~425~~.~~695~~{{c}}

* [[WE]]: ~2 = 1201.2488{{c}}, ~14/9 = 774.8640{{c}}

: [[error map]]: {{val| +1.249 -3.748 +1.520 +1.204 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~14/9 = 774.1560{{c}}

: error map: {{val| 0.000 -5.331 +0.183 -1.422 }}

<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~14/9 = 774.305{{c}}

: [[error map]]: {{val| 0.000 -4.734 +2.570 -0.079 }}

* [[POTE]]: ~2 = 1200.000{{c}}, ~9/7 = ~~425~~.~~942~~{{c}}

* [[POTE]]: ~2 = 1200.000{{c}}, ~14/9 = 774.058{{c}}

: error map: {{val| 0.000 -5.721 -1.378 -2.300 }}

: error map: {{val| 0.000 -5.721 -1.378 -2.300 }} -->

[[Minimax tuning]]:

Line 1,969:

Line 1,973:

[[Badness]] (~~Smith~~): 0.~~045993~~

[[Badness]] (Sintel): 1.16

Scales: [[skwares8]], [[skwares11]], [[skwares14]]

Line 1,978:

Line 1,982:

Comma list: 81/80, 99/98, 121/120

Mapping: {{mapping| 1 3 ~~8 6 7~~ | 0 -4 -16 -9 -10 }}

Mapping: {{mapping| 1 -1 -8 -3 -3 | 0 4 16 9 10 }}

Optimal tunings:

* CTE: ~2 = 1200.000{{c}}, ~9/7 = ~~425~~.~~599~~{{c}}

* WE: ~2 = 1201.6657{{c}}, ~11/7 = 775.1171{{c}}

* POTE: ~2 = 1200.000{{c}}, ~9/7 = ~~425~~.~~957~~{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 774.1754{{c}}

<!-- * CTE: ~2 = 1200.000{{c}}, ~11/7 = 774.401{{c}}

* POTE: ~2 = 1200.000{{c}}, ~11/7 = 774.043{{c}} -->

Badness (~~Smith~~): 0.~~021636~~

Badness (Sintel): 0.715

==== 13-limit ====

Line 1,993:

Line 1,999:

Comma list: 66/65, 81/80, 99/98, 121/120

Mapping: {{mapping| 1 3 ~~8 6 7~~ 3 | 0 -4 -16 -9 -10 2 }}

Mapping: {{mapping| 1 -1 -8 -3 -3 5 | 0 4 16 9 10 -2 }}

Optimal tunings:

* CTE: ~2 = 1200.000{{c}}, ~9/7 = ~~425~~.~~578~~{{c}}

* WE: ~2 = 1199.8419{{c}}, ~11/7 = 774.3484{{c}}

* POTE: ~2 = 1200.000{{c}}, ~9/7 = ~~425~~.~~550~~{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 774.4422{{c}}

<!-- * CTE: ~2 = 1200.000{{c}}, ~11/7 = 774.422{{c}}

* POTE: ~2 = 1200.000{{c}}, ~11/7 = 774.450{{c}} -->

Badness (~~Smith~~): 0.~~025514~~

Badness (Sintel): 1.05

==== Squad ====

Line 2,008:

Line 2,016:

Comma list: 78/77, 81/80, 91/90, 99/98

Mapping: {{mapping| 1 3 8 6 ~~7 9~~ | 0 -4 -16 -9 -10 -15 }}

Mapping: {{mapping| 1 -1 -8 -3 -3 -6 | 0 4 16 9 10 15 }}

Optimal tunings:

* CTE: ~2 = 1200.000{{c}}, ~9/7 = ~~425~~.~~297~~{{c}}

* WE: ~2 = 1202.0312{{c}}, ~11/7 = 775.5589{{c}}

* POTE: ~2 = 1200.000{{c}}, ~9/7 = ~~425~~.~~752~~{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 774.4140{{c}}

<!-- * CTE: ~2 = 1200.000{{c}}, ~11/7 = 774.703{{c}}

* POTE: ~2 = 1200.000{{c}}, ~11/7 = 774.248{{c}} -->

Badness (~~Smith~~): 0.~~026877~~

Badness (Sintel): 1.11

==== Agora ====

Line 2,023:

Line 2,033:

Comma list: 81/80, 99/98, 105/104, 121/120

Mapping: {{mapping| 1 3 ~~8 6 7 14~~ | 0 -4 -16 -9 -10 -29 }}

Mapping: {{mapping| 1 -1 -8 -3 -3 -15 | 0 4 16 9 10 29 }}

Optimal tunings:

* CTE: ~2 = 1200.000{{c}}, ~9/7 = ~~425~~.~~870~~{{c}}

* WE: ~2 = 1202.3228{{c}}, ~11/7 = 775.2214{{c}}

* POTE: ~2 = 1200.000{{c}}, ~9/7 = ~~426~~.~~276~~{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 773.8617{{c}}

<!-- * CTE: ~2 = 1200.000{{c}}, ~11/7 = 774.130{{c}}

* POTE: ~2 = 1200.000{{c}}, ~11/7 = 773.724{{c}} -->

Badness (~~Smith~~): 0.~~024522~~

Badness (Sintel): 1.01

===== 17-limit =====

Line 2,038:

Line 2,050:

Comma list: 81/80, 99/98, 105/104, 120/119, 121/119

Mapping: {{mapping| 1 3 ~~8 6 7 14 8~~ | 0 -4 -16 -9 -10 -29 -11 }}

Mapping: {{mapping| 1 -1 -8 -3 -3 -15 -3 | 0 4 16 9 10 29 11 }}

Optimal tunings:

* CTE: ~2 = 1200.000{{c}}, ~9/7 = ~~425~~.~~919~~{{c}}

* WE: ~2 = 1201.4340{{c}}, ~11/7 = 774.7375{{c}}

* POTE: ~2 = 1200.000{{c}}, ~9/7 = ~~426~~.~~187~~{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 773.8955{{c}}

<!-- * CTE: ~2 = 1200.000{{c}}, ~11/7 = 774.081{{c}}

* POTE: ~2 = 1200.000{{c}}, ~11/7 = 773.813{{c}} -->

Badness (~~Smith~~): 0.~~022573~~

Badness (Sintel): 1.15

===== 19-limit =====

Line 2,053:

Line 2,067:

Comma list: 77/76, 81/80, 99/98, 105/104, 120/119, 121/119

Mapping: {{mapping| 1 3 8 ~~6 7 14 8 11~~ | 0 -4 -16 -9 -10 -29 -11 -19 }}

Mapping: {{mapping| 1 -1 -8 -3 -3 -15 -3 -8 | 0 4 16 9 10 29 11 19 }}

Optimal tunings:

* CTE: ~2 = 1200.000{{c}}, ~9/7 = ~~425~~.~~984~~{{c}}

* WE: ~2 = 1201.2461{{c}}, ~11/7 = 774.5783{{c}}

* POTE: ~2 = 1200.000{{c}}, ~9/7 = ~~426~~.~~225~~{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 773.8479{{c}}

<!-- * CTE: ~2 = 1200.000{{c}}, ~11/7 = 774.016{{c}}

* POTE: ~2 = 1200.000{{c}}, ~11/7 = 773.775{{c}} -->

Badness (~~Smith~~): 0.~~018839~~

Badness (Sintel): 1.15

=== Cuboctahedra ===

Line 2,068:

Line 2,084:

Comma list: 81/80, 385/384, 1375/1372

Mapping: {{mapping| 1 3 8 6 -4 | 0 -4 -16 -9 21 }}

Mapping: {{mapping| 1 -1 -8 -3 17 | 0 4 16 9 -21 }}

Optimal tunings:

* CTE: ~2 = 1200.000{{c}}, ~9/7 = ~~425~~.~~899~~{{c}}

* WE: ~2 = 1201.4436{{c}}, ~14/9 = 774.9386{{c}}

* POTE: ~2 = 1200.000{{c}}, ~9/7 = ~~425~~.~~993~~{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 774.0243{{c}}

<!-- * CTE: ~2 = 1200.000{{c}}, ~14/9 = 774.101{{c}}

* POTE: ~2 = 1200.000{{c}}, ~14/9 = 774.007{{c}} -->

Badness (~~Smith~~): 0.~~056826~~

Badness (Sintel): 1.88

== Jerome ==

Line 2,090:

Line 2,108:

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000{{c}}, ~54/49 = 139.371{{c}}

* [[WE]]: ~2 = 1200.1640{{c}}, ~54/49 = 139.3624{{c}}

: [[error map]]: {{val| +0.164 -4.979 +0.934 +7.039 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~54/49 = 139.3528{{c}}

: error map: {{val| 0.000 -5.191 +0.741 +6.643 }}

<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~54/49 = 139.371{{c}}

: [[error map]]: {{val| 0.000 -5.098 +1.114 +6.774 }}

* [[POTE]]: ~2 = 1200.000{{c}}, ~54/49 = 139.343{{c}}

: error map: {{val| 0.000 -5.238 +0.553 +6.577 }}

: error map: {{val| 0.000 -5.238 +0.553 +6.577 }} -->

[[Badness]] (~~Smith~~): 0.~~108656~~

[[Badness]] (Sintel): 2.75

=== 11-limit ===

Line 2,107:

Line 2,129:

Optimal tunings:

* CTE: ~2 = 1200.000{{c}}, ~12/11 = 139.349{{c}}

* WE: ~2 = 1201.4436{{c}}, ~12/11 = 139.3714{{c}}

* POTE: ~2 = 1200.000{{c}}, ~12/11 = 139.428{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 139.4038{{c}}

<!-- * CTE: ~2 = 1200.000{{c}}, ~12/11 = 139.349{{c}}

* POTE: ~2 = 1200.000{{c}}, ~12/11 = 139.428{{c}} -->

Badness (~~Smith~~): 0.~~047914~~

Badness (Sintel): 1.58

=== 13-limit ===

Line 2,122:

Line 2,146:

Optimal tunings:

* CTE: ~2 = 1200.000{{c}}, ~13/12 = 139.369{{c}}

* WE: ~2 = 1199.8860{{c}}, ~13/12 = 139.3737{{c}}

* POTE: ~2 = 1200.000{{c}}, ~13/12 = 139.387{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.3817{{c}}

<!-- * CTE: ~2 = 1200.000{{c}}, ~13/12 = 139.369{{c}}

* POTE: ~2 = 1200.000{{c}}, ~13/12 = 139.387{{c}} -->

Badness (~~Smith~~): 0.~~029285~~

Badness (Sintel): 1.21

=== 17-limit ===

Line 2,137:

Line 2,163:

Optimal tunings:

* CTE: ~2 = 1200.000{{c}}, ~13/12 = 139.334{{c}}

* WE: ~2 = 1199.8346{{c}}, ~13/12 = 139.3431{{c}}

* POTE: ~2 = 1200.000{{c}}, ~13/12 = 139.362{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.3544{{c}}

<!-- * CTE: ~2 = 1200.000{{c}}, ~13/12 = 139.334{{c}}

* POTE: ~2 = 1200.000{{c}}, ~13/12 = 139.362{{c}} -->

Badness (~~Smith~~): 0.~~020878~~

Badness (Sintel): 1.06

=== 19-limit ===

Line 2,152:

Line 2,180:

Optimal tunings:

* CTE: ~2 = 1200.000{{c}}, ~13/12 = 139.296{{c}}

* WE: ~2 = 1199.8891{{c}}, ~13/12 = 139.3001{{c}}

* POTE: ~2 = 1200.000{{c}}, ~13/12 = 139.313{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.3080{{c}}

<!-- * CTE: ~2 = 1200.000{{c}}, ~13/12 = 139.296{{c}}

* POTE: ~2 = 1200.000{{c}}, ~13/12 = 139.313{{c}} -->

Badness (~~Smith~~): 0.~~018229~~

Badness (Sintel): 1.11

== Meantritone ==

Line 2,166:

Line 2,196:

[[Comma list]]: 81/80, 16875/16807

: mapping generators: ~2, ~10/7

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000{{c}}, ~7/5 = ~~580~~.~~568~~{{c}}

* [[WE]]: ~2 = 1201.3832{{c}}, ~10/7 = 619.9478{{c}}

: [[error map]]: {{val| +1.383 -3.599 +1.576 +0.499 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 619.3176{{c}}

: error map: {{val| 0.000 -5.367 +0.038 -1.791 }}

<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~10/7 = 619.432{{c}}

: [[error map]]: {{val| 0.000 -4.795 +2.325 +0.381 }}

* [[POTE]]: ~2 = 1200.000{{c}}, ~7/5 = ~~580~~.~~766~~{{c}}

* [[POTE]]: ~2 = 1200.000{{c}}, ~10/7 = 619.234{{c}}

: error map: {{val| 0.000 -5.785 -1.634 -3.380 }}

: error map: {{val| 0.000 -5.785 -1.634 -3.380 }} -->

[[Badness]] (~~Smith~~): 0.~~082239~~

[[Badness]] (Sintel): 2.08

=== 11-limit ===

Line 2,183:

Line 2,219:

Comma list: 81/80, 99/98, 2541/2500

Mapping: {{mapping| 1 ~~4 12 12 17~~ | 0 -5 -20 -19 -28 }}

Mapping: {{mapping| 1 -1 -8 -7 -11 | 0 5 20 19 28 }}

Optimal tunings:

* CTE: ~2 = 1200.000{{c}}, ~7/5 = ~~580~~.~~482~~{{c}}

* WE: ~2 = 1201.2054{{c}}, ~10/7 = 619.9752{{c}}

* POTE: ~2 = 1200.000{{c}}, ~7/5 = ~~580~~.~~647~~{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.4223{{c}}

<!-- * CTE: ~2 = 1200.000{{c}}, ~10/7 = 619.518{{c}}

* POTE: ~2 = 1200.000{{c}}, ~10/7 = 619.353{{c}} -->

Badness (~~Smith~~): 0.~~042869~~

Badness (Sintel): 1.42

== Injera ==

Line 2,207:

Line 2,245:

[[Optimal tuning]]s:

* [[CTE]]: ~7/5 = 600.000{{c}}, ~3/2 = 695.330{{c}} (~21/20 = 95.330{{c}})

* [[WE]]: ~7/5 = 600.6662{{c}}, ~3/2 = 695.1463{{c}} (~21/20 = 94.4801{{c}})

: [[error map]]: {{val| +1.332 -5.476 -5.729 +12.425 }}

* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 694.7712{{c}} (~21/20 = 94.7712{{c}})

: error map: {{val| 0.000 -7.184 -7.229 +10.259 }}

<!-- * [[CTE]]: ~7/5 = 600.000{{c}}, ~3/2 = 695.330{{c}} (~21/20 = 95.330{{c}})

: [[error map]]: {{val| 0.000 -6.625 -4.993 +12.495 }}

* [[POTE]]: ~7/5 = 600.000{{c}}, ~3/2 = 694.375{{c}} (~21/20 = 94.375{{c}})

: error map: {{val| 0.000 -7.580 -8.813 +8.675 }}

: error map: {{val| 0.000 -7.580 -8.813 +8.675 }} -->

[[Tuning ranges]]:

Line 2,219:

Line 2,261:

[[Badness]] (~~Smith~~): 0.~~031130~~

[[Badness]] (Sintel): 0.788

; Music

Line 2,232:

Line 2,274:

Optimal tunings:

* CTE: ~7/5 = 600.000{{c}}, ~3/2 = 694.098{{c}} (~21/20 = 94.098{{c}})

* WE: ~7/5 = 600.9350{{c}}, ~3/2 = 693.9198{{c}} (~21/20 = 92.9848{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 692.840{{c}} (~21/20 = 92.840{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 693.3539{{c}} (~21/20 = 93.3539{{c}})

<!-- * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 694.098{{c}} (~21/20 = 94.098{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 692.840{{c}} (~21/20 = 92.840{{c}}) -->

Tuning ranges:

Line 2,241:

Line 2,285:

Badness (~~Smith~~): 0.~~023124~~

Badness (Sintel): 0.764

==== 13-limit ====

Line 2,251:

Line 2,295:

Optimal tunings:

* CTE: ~7/5 = 600.000{{c}}, ~3/2 = 693.806{{c}} (~21/20 = 93.806{{c}})

* WE: ~7/5 = 600.9982{{c}}, ~3/2 = 693.8249{{c}} (~21/20 = 92.8267{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 692.673{{c}} (~21/20 = 92.673{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 693.0992{{c}} (~21/20 = 93.0992{{c}})

<!-- * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 693.806{{c}} (~21/20 = 93.806{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 692.673{{c}} (~21/20 = 92.673{{c}}) -->

Tuning ranges:

Line 2,260:

Line 2,306:

Badness (~~Smith~~): 0.~~021565~~

Badness (Sintel): 0.891

===== 17-limit =====

Line 2,270:

Line 2,316:

Optimal tunings:

* CTE: ~7/5 = 600.000{{c}}, ~3/2 = 693.852{{c}} (~21/20 = 93.852{{c}})

* WE: ~7/5 = 601.1757{{c}}, ~3/2 = 693.8441{{c}} (~21/20 = 92.6684{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 692.487{{c}} (~21/20 = 92.487{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 692.8879{{c}} (~21/20 = 92.8879{{c}})

<!-- * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 693.852{{c}} (~21/20 = 93.852{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 692.487{{c}} (~21/20 = 92.487{{c}}) -->

Badness (~~Smith~~): 0.~~018358~~

Badness (Sintel): 0.935

===== 19-limit =====

Line 2,285:

Line 2,333:

Optimal tunings:

* CTE: ~7/5 = 600.000{{c}}, ~3/2 = 694.031{{c}} (~21/20 = 94.031{{c}})

* WE: ~7/5 = 601.4245{{c}}, ~3/2 = 693.9426{{c}} (~21/20 = 92.5181{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 692.299{{c}} (~21/20 = 92.299{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 692.7606{{c}} (~21/20 = 92.7606{{c}})

<!-- * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 694.031{{c}} (~21/20 = 94.031{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 692.299{{c}} (~21/20 = 92.299{{c}}) -->

Badness (~~Smith~~): 0.~~015118~~

Badness (Sintel): 0.920

==== Enjera ====

Line 2,300:

Line 2,350:

Optimal tunings:

* CTE: ~7/5 = 600.000{{c}}, ~3/2 = 693.088{{c}} (~21/20 = 93.088{{c}})

* WE: ~7/5 = 599.1863{{c}}, ~3/2 = 693.1791{{c}} (~21/20 = 93.9929{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 694.121{{c}} (~21/20 = 94.121{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 693.6809{{c}} (~21/20 = 93.6809{{c}})

<!-- * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 693.088{{c}} (~21/20 = 93.088{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 694.121{{c}} (~21/20 = 94.121{{c}}) -->

Badness (~~Smith~~): 0.~~026542~~

Badness (Sintel): 1.10

=== Injerous ===

Line 2,315:

Line 2,367:

Optimal tunings:

* CTE: ~7/5 = 600.000{{c}}, ~3/2 = 694.619{{c}} (~21/20 = 94.619{{c}})

* WE: ~7/5 = 603.1682{{c}}, ~3/2 = 694.1945{{c}} (~21/20 = 91.0264{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 690.548{{c}} (~21/20 = 90.548{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 691.6107{{c}} (~21/20 = 91.6107{{c}})

<!-- * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 694.619{{c}} (~21/20 = 94.619{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 690.548{{c}} (~21/20 = 90.548{{c}}) -->

Badness (~~Smith~~): 0.~~038577~~

Badness (Sintel): 1.28

=== Lahoh ===

Line 2,330:

Line 2,384:

Optimal tunings:

* CTE: ~7/5 = 600.000{{c}}, ~3/2 = 695.330{{c}} (~21/20 = 95.330{{c}})

* WE: ~7/5 = 597.3179{{c}}, ~3/2 = 695.8759{{c}} (~21/20 = 98.5581{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 699.001{{c}} (~21/20 = 99.001{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 697.8757{{c}} (~21/20 = 97.8757{{c}})

<!-- * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 695.330{{c}} (~21/20 = 95.330{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 699.001{{c}} (~21/20 = 99.001{{c}}) -->

Badness (~~Smith~~): 0.~~043062~~

Badness (Sintel): 1.42

=== Teff ===

Line 2,351:

Line 2,407:

Optimal tunings:

* CTE: ~7/5 = 600.000{{c}}, ~11/8 = ~~552~~.~~331~~{{c}} (~33/32 = 47.669{{c}})

* WE: ~7/5 = 600.2802{{c}}, ~16/11 = 647.7720{{c}} (~33/32 = 47.4918{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~11/8 = ~~552~~.~~530~~{{c}} (~33/32 = 47.470{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~16/11 = 647.5224{{c}} (~33/32 = 47.5224{{c}})

<!-- * CTE: ~7/5 = 600.000{{c}}, ~16/11 = 647.669{{c}} (~33/32 = 47.669{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~16/11 = 647.470{{c}} (~33/32 = 47.470{{c}}) -->

Badness (~~Smith~~): 0.~~070689~~

Badness (Sintel): 2.34

==== 13-limit ====

Line 2,366:

Line 2,424:

Optimal tunings:

* CTE: ~7/5 = 600.000{{c}}, ~11/8 = ~~552~~.~~297~~{{c}} (~33/32 = 47.703{{c}})

* WE: ~7/5 = 600.3037{{c}}, ~16/11 = 647.7954{{c}} (~33/32 = 47.4917{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~11/8 = ~~552~~.~~532~~{{c}} (~33/32 = 47.468{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~16/11 = 647.5256{{c}} (~33/32 = 47.5256{{c}})

<!-- * CTE: ~7/5 = 600.000{{c}}, ~16/11 = 647.703{{c}} (~33/32 = 47.703{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~16/11 = 647.468{{c}} (~33/32 = 47.468{{c}}) -->

Badness (~~Smith~~): 0.~~040047~~

Badness (Sintel): 1.65

==== 17-limit ====

Line 2,381:

Line 2,441:

Optimal tunings:

* CTE: ~7/5 = 600.000{{c}}, ~11/8 = ~~552~~.~~249~~{{c}} (~34/33 = 47.751{{c}})

* WE: ~7/5 = 600.5123{{c}}, ~16/11 = 647.8970{{c}} (~34/33 = 47.3846{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~11/8 = ~~552~~.~~656~~{{c}} (~34/33 = 47.344{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~16/11 = 647.4314{{c}} (~34/33 = 47.4314{{c}})

<!-- * CTE: ~7/5 = 600.000{{c}}, ~16/11 = 647.751{{c}} (~34/33 = 47.751{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~16/11 = 647.344{{c}} (~34/33 = 47.344{{c}}) -->

Badness (~~Smith~~): 0.~~029499~~

Badness (Sintel): 1.50

==== 19-limit ====

Line 2,396:

Line 2,458:

Optimal tunings:

* CTE: ~7/5 = 600.000{{c}}, ~11/8 = ~~552~~.~~107~~{{c}} (~34/33 = 47.893{{c}})

* WE: ~7/5 = 600.6308{{c}}, ~16/11 = 648.0424{{c}} (~34/33 = 47.4116{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~11/8 = ~~552~~.~~638~~{{c}} (~34/33 = 47.362{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~16/11 = 647.4715{{c}} (~34/33 = 47.4715{{c}})

<!-- * CTE: ~7/5 = 600.000{{c}}, ~16/11 = 647.893{{c}} (~34/33 = 47.893{{c}})

* POTE: ~7/5 = 600.000{{c}}, ~16/11 = 647.362{{c}} (~34/33 = 47.362{{c}}) -->

Badness (~~Smith~~): 0.~~023133~~

Badness (Sintel): 1.41

== Pombe ==

Line 2,415:

Line 2,479:

[[Optimal tuning]]s:

* [[~~CTE~~]]: ~735/512 = ~~600~~.~~000~~{{c}}, ~48/35 = ~~551~~.~~845~~{{c}} (~36/35 = 48.~~155~~{{c}})

* [[WE]]: ~735/512 = 601.0652{{c}}, ~35/24 = 648.9295{{c}} (~36/35 = 47.8642{{c}})

: [[error map]]: {{val| 0.~~000~~ -5.~~645~~ -1.~~075 -9.600~~ }}

: [[error map]]: {{val| +2.130 -3.031 +0.861 -1.756 }}

* [[~~POTE~~]]: ~735/512 = 600.~~000~~{{c}}, ~48/35 = ~~552~~.~~221~~{{c}} (~36/35 = 48.~~779~~{{c}})

* [[CWE]]: ~735/512 = 600.0000{{c}}, ~35/24 = 647.8628{{c}} (~36/35 = 47.8628{{c}})

: error map: {{val| 0.000 -6.229 -3.411 -8.140 }}

<!-- * [[CTE]]: ~735/512 = 600.000{{c}}, ~35/24 = 648.155{{c}} (~36/35 = 48.155{{c}})

: error map: {{val| 0.000 -5.645 -1.075 -9.600 }}

* [[POTE]]: ~735/512 = 600.000{{c}}, ~35/24 = 648.779{{c}} (~36/35 = 48.779{{c}})

: error map: {{val| 0.000 -6.396 -4.078 -7.723 }} -->

{{Optimal ET sequence|legend=1| 24, 26, 50, 126bcd, 176bcdd, 226bbcdd }}

[[Badness]] (~~Smith~~): 0.~~116104~~

[[Badness]] (Sintel): 2.94

=== 11-limit ===

Line 2,432:

Line 2,500:

Optimal tunings:

* CTE: ~99/70 = 600.000{{c}}, ~11/8 = ~~551~~.~~843~~{{c}} (~36/35 = 48.157{{c}})

* WE: ~99/70 = 600.7890{{c}}, ~16/11 = 648.7592{{c}} (~36/35 = 47.9701{{c}})

* POTE: ~99/70 = 600.000{{c}}, ~11/8 = ~~552~~.~~093~~{{c}} (~36/35 = 47.907{{c}})

* CWE: ~99/70 = 600.0000{{c}}, ~16/11 = 647.9516{{c}} (~36/35 = 47.9516{{c}})

<!-- * CTE: ~99/70 = 600.000{{c}}, ~16/11 = 648.157{{c}} (~36/35 = 48.157{{c}})

* POTE: ~99/70 = 600.000{{c}}, ~16/11 = 647.907{{c}} (~36/35 = 47.907{{c}}) -->

Badness (~~Smith~~): 0.~~052099~~

Badness (Sintel): 1.72

=== 13-limit ===

Line 2,447:

Line 2,517:

Optimal tunings:

* CTE: ~99/70 = 600.000{{c}}, ~11/8 = ~~551~~.~~848~~{{c}} (~36/35 = 48.152{{c}})

* WE: ~99/70 = 600.6971{{c}}, ~16/11 = 648.6029{{c}} (~36/35 = 47.9058{{c}})

* POTE: ~99/70 = 600.000{{c}}, ~11/8 = ~~552~~.~~150~~{{c}} (~36/35 = 47.850{{c}})

* CWE: ~99/70 = 600.0000{{c}}, ~16/11 = 647.8990{{c}} (~36/35 = 47.8990{{c}})

<!-- * CTE: ~99/70 = 600.000{{c}}, ~16/11 = 648.152{{c}} (~36/35 = 48.152{{c}})

* POTE: ~99/70 = 600.000{{c}}, ~16/11 = 647.850{{c}} (~36/35 = 47.850{{c}}) -->

Badness (~~Smith~~): 0.~~031039~~

Badness (Sintel): 1.28

=== 17-limit ===

Line 2,462:

Line 2,534:

Optimal tunings:

* CTE: ~17/12 = 600.000{{c}}, ~11/8 = ~~551~~.~~793~~{{c}} (~36/35 = 48.207{{c}})

* WE: ~17/12 = 600.7610{{c}}, ~16/11 = 648.6638{{c}} (~36/35 = 47.9028{{c}})

* POTE: ~17/12 = 600.000{{c}}, ~11/8 = ~~552~~.~~158~~{{c}} (~36/35 = 47.842{{c}})

* CWE: ~17/12 = 600.0000{{c}}, ~16/11 = 647.8990{{c}} (~36/35 = 47.8990{{c}})

<!-- * CTE: ~17/12 = 600.000{{c}}, ~16/11 = 648.207{{c}} (~36/35 = 48.207{{c}})

* POTE: ~17/12 = 600.000{{c}}, ~16/11 = 647.842{{c}} (~36/35 = 47.842{{c}}) -->

Badness (~~Smith~~): 0.~~021260~~

Badness (Sintel): 1.08

=== 19-limit ===

Line 2,477:

Line 2,551:

Optimal tunings:

* CTE: ~17/12 = 600.000{{c}}, ~11/8 = ~~551~~.~~660~~{{c}} (~36/35 = 48.340{{c}})

* WE: ~17/12 = 600.8048{{c}}, ~16/11 = 648.7494{{c}} (~36/35 = 47.9446{{c}})

* POTE: ~17/12 = 600.000{{c}}, ~11/8 = ~~552~~.~~120~~{{c}} (~36/35 = 47.880{{c}})

* CWE: ~17/12 = 600.0000{{c}}, ~16/11 = 647.9425{{c}} (~36/35 = 47.9425{{c}})

<!-- * CTE: ~17/12 = 600.000{{c}}, ~16/11 = 648.340{{c}} (~36/35 = 48.340{{c}})

* POTE: ~17/12 = 600.000{{c}}, ~16/11 = 647.880{{c}} (~36/35 = 47.880{{c}}) -->

Badness (~~Smith~~): 0.~~016548~~

Badness (Sintel): 1.01

== Orphic ==

Line 2,494:

Line 2,570:

[[Optimal tuning]]s:

* [[CTE]]: ~2401/1728 = 600.000{{c}}, ~343/288 = 324.275{{c}} (~7/6 = 275.725{{c}})

* [[WE]]: ~2401/1728 = 600.1767{{c}}, ~343/288 = 324.3015{{c}} (~7/6 = 275.8751{{c}})

: [[error map]]: {{val| +0.353 -4.572 +1.804 +4.785 }}

* [[CWE]]: ~2401/1728 = 600.0000{{c}}, ~343/288 = 324.2285{{c}} (~7/6 = 275.7715{{c}})

: error map: {{val| 0.000 -5.041 +1.342 +3.860 }}

<!-- * [[CTE]]: ~2401/1728 = 600.000{{c}}, ~343/288 = 324.275{{c}} (~7/6 = 275.725{{c}})

: [[error map]]: {{val| 0.000 -4.854 +2.091 +4.000 }}

* [[POTE]]: ~2401/1728 = 600.000{{c}}, ~343/288 = 324.206{{c}} (~7/6 = 275.794{{c}})

: error map: {{val| 0.000 -5.131 +0.983 +3.792 }}

: error map: {{val| 0.000 -5.131 +0.983 +3.792 }} -->

[[Badness]] (~~Smith~~): 0.~~258825~~

[[Badness]] (Sintel): 6.55

=== 11-limit ===

Line 2,508:

Line 2,588:

Comma list: 81/80, 99/98, 73728/73205

Mapping: {{mapping| 2 1 -4 4 8 | 0 -4 -16 -3 2 }}

Mapping: {{mapping| 2 1 -4 4 8 | 0 4 16 3 -2 }}

Optimal tunings:

* CTE: ~363/256 = 600.000{{c}}, ~77/64 = 324.276{{c}} (~7/6 = 275.724{{c}})

* WE: ~363/256 = 600.1011{{c}}, ~77/64 = 324.2923{{c}} (~7/6 = 275.8088{{c}})

* POTE: ~363/256 = 600.000{{c}}, ~77/64 = 324.238{{c}} (~7/6 = 275.762{{c}})

* CWE: ~363/256 = 600.0000{{c}}, ~77/64 = 324.2463{{c}} (~7/6 = 275.7537{{c}})

<!-- * CTE: ~363/256 = 600.000{{c}}, ~77/64 = 324.276{{c}} (~7/6 = 275.724{{c}})

* POTE: ~363/256 = 600.000{{c}}, ~77/64 = 324.238{{c}} (~7/6 = 275.762{{c}}) -->

Badness (~~Smith~~): 0.~~101499~~

Badness (Sintel): 3.36

=== 13-limit ===

Line 2,523:

Line 2,605:

Comma list: 81/80, 99/98, 144/143, 2200/2197

Mapping: {{mapping| 2 1 -4 4 8 2 | 0 -4 -16 -3 2 -10 }}

Mapping: {{mapping| 2 1 -4 4 8 2 | 0 4 16 3 -2 10 }}

Optimal tunings:

* CTE: ~55/39 = 600.000{{c}}, ~77/64 = 324.250{{c}} (~7/6 = 275.750{{c}})

* WE: ~55/39 = 600.0540{{c}}, ~77/64 = 324.2551{{c}} (~7/6 = 275.7989{{c}})

* POTE: ~55/39 = 600.000{{c}}, ~77/64 = 324.226{{c}} (~7/6 = 275.774{{c}})

* CWE: ~55/39 = 600.0000{{c}}, ~77/64 = 324.2307{{c}} (~7/6 = 275.7693{{c}})

<!-- * CTE: ~55/39 = 600.000{{c}}, ~77/64 = 324.250{{c}} (~7/6 = 275.750{{c}})

* POTE: ~55/39 = 600.000{{c}}, ~77/64 = 324.226{{c}} (~7/6 = 275.774{{c}}) -->

Badness (~~Smith~~): 0.~~053482~~

Badness (Sintel): 2.21

== Cloudtone ==

The cloudtone temperament (5 &~~amp;~~ 50) tempers out the [[cloudy comma]], 16807/16384 and the [[81/80|syntonic comma]], 81/80 in the 7-limit. It can be extended to the 11- and 13-limit by adding 385/384 and 105/104 to the comma list in this order.

The cloudtone temperament ({{nowrap| 5 & 50 }}) tempers out the [[cloudy comma]], 16807/16384 and the [[81/80|syntonic comma]], 81/80 in the 7-limit. It can be extended to the 11- and 13-limit by adding 385/384 and 105/104 to the comma list in this order.

[[Subgroup]]: 2.3.5.7

Line 2,545:

Line 2,629:

[[Optimal tuning]]s:

* [[CTE]]: ~8/7 = 240.000{{c}}, ~3/2 = 697.214{{c}} (~49/48 = 22.786{{c}})

* [[WE]]: ~8/7 = 240.4267{{c}}, ~3/2 = 696.9566{{c}} (~49/48 = 24.3235{{c}})

: [[error map]]: {{val| 0.000 -4.741 +2.544 -8.826 }}

: [[error map]]: {{val| +2.133 -2.865 +1.513 -2.852 }}

* [[CWE]]: ~8/7 = 240.0000{{c}}, ~3/2 = 696.1637{{c}} (~49/48 = 23.8373{{c}})

: error map: {{val| 0.000 -5.791 -1.659 -8.826 }}

<!-- * [[CTE]]: ~8/7 = 240.000{{c}}, ~3/2 = 697.214{{c}} (~49/48 = 22.786{{c}})

: error map: {{val| 0.000 -4.741 +2.544 -8.826 }}

* [[POTE]]: ~8/7 = 240.000{{c}}, ~3/2 = 695.720{{c}} (~49/48 = 24.280{{c}})

: error map: {{val| 0.000 -6.235 -3.435 -8.826 }}

: error map: {{val| 0.000 -6.235 -3.435 -8.826 }} -->

[[Badness]] (~~Smith~~): 0.~~102256~~

[[Badness]] (Sintel): 2.59

=== 11-limit ===

Line 2,562:

Line 2,650:

Optimal tunings:

* CTE: ~8/7 = 240.000{{c}}, ~3/2 = 697.034{{c}} (~56/55 = 22.966{{c}})

* WE: ~8/7 = 240.2740{{c}}, ~3/2 = 697.3317{{c}} (~56/55 = 23.4904{{c}})

* POTE: ~8/7 = 240.000{{c}}, ~3/2 = 696.536{{c}} (~56/55 = 23.464{{c}})

* CWE: ~8/7 = 240.0000{{c}}, ~3/2 = 696.6269{{c}} (~56/55 = 23.3731{{c}})

<!-- * CTE: ~8/7 = 240.000{{c}}, ~3/2 = 697.034{{c}} (~56/55 = 22.966{{c}})

* POTE: ~8/7 = 240.000{{c}}, ~3/2 = 696.536{{c}} (~56/55 = 23.464{{c}}) -->

Badness (~~Smith~~): 0.~~070378~~

Badness (Sintel): 2.33

=== 13-limit ===

Line 2,577:

Line 2,667:

Optimal tunings:

* CTE: ~8/7 = 240.000{{c}}, ~3/2 = 696.749{{c}} (~91/90 = 23.251{{c}})

* WE: ~8/7 = 240.2435{{c}}, ~3/2 = 696.8686{{c}} (~91/90 = 23.8618{{c}})

* POTE: ~8/7 = 240.000{{c}}, ~3/2 = 696.162{{c}} (~91/90 = 23.838{{c}})

* CWE: ~8/7 = 240.0000{{c}}, ~3/2 = 696.2653{{c}} (~91/90 = 23.7347{{c}})

<!-- * CTE: ~8/7 = 240.000{{c}}, ~3/2 = 696.749{{c}} (~91/90 = 23.251{{c}})

* POTE: ~8/7 = 240.000{{c}}, ~3/2 = 696.162{{c}} (~91/90 = 23.838{{c}}) -->

Badness (~~Smith~~): 0.~~048829~~

Badness (Sintel): 2.02

== Subgroup extensions ==

@@ Line 1,950: / Line 1,950: @@
 [[Comma list]]: 81/80, 2401/2400
-{{Mapping|legend=1| 1 3 8 6 | 0 -4 -16 -9 }}
+{{Mapping|legend=1| 1 -1 -8 -3 | 0 4 16 9 }}
-: mapping generators: ~2, ~9/7
+: mapping generators: ~2, ~14/9
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000{{c}}, ~9/7 = 425.695{{c}}
+* [[WE]]: ~2 = 1201.2488{{c}}, ~14/9 = 774.8640{{c}}
+: [[error map]]: {{val| +1.249 -3.748 +1.520 +1.204 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~14/9 = 774.1560{{c}}
+: error map: {{val| 0.000 -5.331 +0.183 -1.422 }}
+<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~14/9 = 774.305{{c}}
 : [[error map]]: {{val| 0.000 -4.734 +2.570 -0.079 }}
-* [[POTE]]: ~2 = 1200.000{{c}}, ~9/7 = 425.942{{c}}
+* [[POTE]]: ~2 = 1200.000{{c}}, ~14/9 = 774.058{{c}}
-: error map: {{val| 0.000 -5.721 -1.378 -2.300 }}
+: error map: {{val| 0.000 -5.721 -1.378 -2.300 }} -->
 [[Minimax tuning]]:
@@ Line 1,969: / Line 1,973: @@
 {{Optimal ET sequence|legend=1| 14c, 17c, 31, 169b, 200b }}
-[[Badness]] (Smith): 0.045993
+[[Badness]] (Sintel): 1.16
 Scales: [[skwares8]], [[skwares11]], [[skwares14]]
@@ Line 1,978: / Line 1,982: @@
 Comma list: 81/80, 99/98, 121/120
-Mapping: {{mapping| 1 3 8 6 7 | 0 -4 -16 -9 -10 }}
+Mapping: {{mapping| 1 -1 -8 -3 -3 | 0 4 16 9 10 }}
 Optimal tunings:
-* CTE: ~2 = 1200.000{{c}}, ~9/7 = 425.599{{c}}
+* WE: ~2 = 1201.6657{{c}}, ~11/7 = 775.1171{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~9/7 = 425.957{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 774.1754{{c}}
+<!-- * CTE: ~2 = 1200.000{{c}}, ~11/7 = 774.401{{c}}
+* POTE: ~2 = 1200.000{{c}}, ~11/7 = 774.043{{c}} -->
 {{Optimal ET sequence|legend=0| 14c, 17c, 31, 130bee, 169beee }}
-Badness (Smith): 0.021636
+Badness (Sintel): 0.715
 ==== 13-limit ====
@@ Line 1,993: / Line 1,999: @@
 Comma list: 66/65, 81/80, 99/98, 121/120
-Mapping: {{mapping| 1 3 8 6 7 3 | 0 -4 -16 -9 -10 2 }}
+Mapping: {{mapping| 1 -1 -8 -3 -3 5 | 0 4 16 9 10 -2 }}
 Optimal tunings:
-* CTE: ~2 = 1200.000{{c}}, ~9/7 = 425.578{{c}}
+* WE: ~2 = 1199.8419{{c}}, ~11/7 = 774.3484{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~9/7 = 425.550{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 774.4422{{c}}
+<!-- * CTE: ~2 = 1200.000{{c}}, ~11/7 = 774.422{{c}}
+* POTE: ~2 = 1200.000{{c}}, ~11/7 = 774.450{{c}} -->
 {{Optimal ET sequence|legend=0| 14c, 17c, 31, 79cf }}
-Badness (Smith): 0.025514
+Badness (Sintel): 1.05
 ==== Squad ====
@@ Line 2,008: / Line 2,016: @@
 Comma list: 78/77, 81/80, 91/90, 99/98
-Mapping: {{mapping| 1 3 8 6 7 9 | 0 -4 -16 -9 -10 -15 }}
+Mapping: {{mapping| 1 -1 -8 -3 -3 -6 | 0 4 16 9 10 15 }}
 Optimal tunings:
-* CTE: ~2 = 1200.000{{c}}, ~9/7 = 425.297{{c}}
+* WE: ~2 = 1202.0312{{c}}, ~11/7 = 775.5589{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~9/7 = 425.752{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 774.4140{{c}}
+<!-- * CTE: ~2 = 1200.000{{c}}, ~11/7 = 774.703{{c}}
+* POTE: ~2 = 1200.000{{c}}, ~11/7 = 774.248{{c}} -->
 {{Optimal ET sequence|legend=0| 14cf, 17c, 31f }}
-Badness (Smith): 0.026877
+Badness (Sintel): 1.11
 ==== Agora ====
@@ Line 2,023: / Line 2,033: @@
 Comma list: 81/80, 99/98, 105/104, 121/120
-Mapping: {{mapping| 1 3 8 6 7 14 | 0 -4 -16 -9 -10 -29 }}
+Mapping: {{mapping| 1 -1 -8 -3 -3 -15 | 0 4 16 9 10 29 }}
 Optimal tunings:
-* CTE: ~2 = 1200.000{{c}}, ~9/7 = 425.870{{c}}
+* WE: ~2 = 1202.3228{{c}}, ~11/7 = 775.2214{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~9/7 = 426.276{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 773.8617{{c}}
+<!-- * CTE: ~2 = 1200.000{{c}}, ~11/7 = 774.130{{c}}
+* POTE: ~2 = 1200.000{{c}}, ~11/7 = 773.724{{c}} -->
 {{Optimal ET sequence|legend=0| 14cf, 31, 45ef, 76e }}
-Badness (Smith): 0.024522
+Badness (Sintel): 1.01
 ===== 17-limit =====
@@ Line 2,038: / Line 2,050: @@
 Comma list: 81/80, 99/98, 105/104, 120/119, 121/119
-Mapping: {{mapping| 1 3 8 6 7 14 8 | 0 -4 -16 -9 -10 -29 -11 }}
+Mapping: {{mapping| 1 -1 -8 -3 -3 -15 -3 | 0 4 16 9 10 29 11 }}
 Optimal tunings:
-* CTE: ~2 = 1200.000{{c}}, ~9/7 = 425.919{{c}}
+* WE: ~2 = 1201.4340{{c}}, ~11/7 = 774.7375{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~9/7 = 426.187{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 773.8955{{c}}
+<!-- * CTE: ~2 = 1200.000{{c}}, ~11/7 = 774.081{{c}}
+* POTE: ~2 = 1200.000{{c}}, ~11/7 = 773.813{{c}} -->
 {{Optimal ET sequence|legend=0| 14cf, 31 }}
-Badness (Smith): 0.022573
+Badness (Sintel): 1.15
 ===== 19-limit =====
@@ Line 2,053: / Line 2,067: @@
 Comma list: 77/76, 81/80, 99/98, 105/104, 120/119, 121/119
-Mapping: {{mapping| 1 3 8 6 7 14 8 11 | 0 -4 -16 -9 -10 -29 -11 -19 }}
+Mapping: {{mapping| 1 -1 -8 -3 -3 -15 -3 -8 | 0 4 16 9 10 29 11 19 }}
 Optimal tunings:
-* CTE: ~2 = 1200.000{{c}}, ~9/7 = 425.984{{c}}
+* WE: ~2 = 1201.2461{{c}}, ~11/7 = 774.5783{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~9/7 = 426.225{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 773.8479{{c}}
+<!-- * CTE: ~2 = 1200.000{{c}}, ~11/7 = 774.016{{c}}
+* POTE: ~2 = 1200.000{{c}}, ~11/7 = 773.775{{c}} -->
 {{Optimal ET sequence|legend=0| 14cf, 31 }}
-Badness (Smith): 0.018839
+Badness (Sintel): 1.15
 === Cuboctahedra ===
@@ Line 2,068: / Line 2,084: @@
 Comma list: 81/80, 385/384, 1375/1372
-Mapping: {{mapping| 1 3 8 6 -4 | 0 -4 -16 -9 21 }}
+Mapping: {{mapping| 1 -1 -8 -3 17 | 0 4 16 9 -21 }}
 Optimal tunings:
-* CTE: ~2 = 1200.000{{c}}, ~9/7 = 425.899{{c}}
+* WE: ~2 = 1201.4436{{c}}, ~14/9 = 774.9386{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~9/7 = 425.993{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 774.0243{{c}}
+<!-- * CTE: ~2 = 1200.000{{c}}, ~14/9 = 774.101{{c}}
+* POTE: ~2 = 1200.000{{c}}, ~14/9 = 774.007{{c}} -->
 {{Optimal ET sequence|legend=0| 31, 107b, 138b, 169be, 200be }}
-Badness (Smith): 0.056826
+Badness (Sintel): 1.88
 == Jerome ==
@@ Line 2,090: / Line 2,108: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000{{c}}, ~54/49 = 139.371{{c}}
+* [[WE]]: ~2 = 1200.1640{{c}}, ~54/49 = 139.3624{{c}}
+: [[error map]]: {{val| +0.164 -4.979 +0.934 +7.039 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~54/49 = 139.3528{{c}}
+: error map: {{val| 0.000 -5.191 +0.741 +6.643 }}
+<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~54/49 = 139.371{{c}}
 : [[error map]]: {{val| 0.000 -5.098 +1.114 +6.774 }}
 * [[POTE]]: ~2 = 1200.000{{c}}, ~54/49 = 139.343{{c}}
-: error map: {{val| 0.000 -5.238 +0.553 +6.577 }}
+: error map: {{val| 0.000 -5.238 +0.553 +6.577 }} -->
 {{Optimal ET sequence|legend=1| 17c, 26, 43 }}
-[[Badness]] (Smith): 0.108656
+[[Badness]] (Sintel): 2.75
 === 11-limit ===
@@ Line 2,107: / Line 2,129: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000{{c}}, ~12/11 = 139.349{{c}}
+* WE: ~2 = 1201.4436{{c}}, ~12/11 = 139.3714{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~12/11 = 139.428{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 139.4038{{c}}
+<!-- * CTE: ~2 = 1200.000{{c}}, ~12/11 = 139.349{{c}}
+* POTE: ~2 = 1200.000{{c}}, ~12/11 = 139.428{{c}} -->
 {{Optimal ET sequence|legend=0| 17c, 26, 43 }}
-Badness (Smith): 0.047914
+Badness (Sintel): 1.58
 === 13-limit ===
@@ Line 2,122: / Line 2,146: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000{{c}}, ~13/12 = 139.369{{c}}
+* WE: ~2 = 1199.8860{{c}}, ~13/12 = 139.3737{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~13/12 = 139.387{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.3817{{c}}
+<!-- * CTE: ~2 = 1200.000{{c}}, ~13/12 = 139.369{{c}}
+* POTE: ~2 = 1200.000{{c}}, ~13/12 = 139.387{{c}} -->
 {{Optimal ET sequence|legend=0| 17c, 26, 43 }}
-Badness (Smith): 0.029285
+Badness (Sintel): 1.21
 === 17-limit ===
@@ Line 2,137: / Line 2,163: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000{{c}}, ~13/12 = 139.334{{c}}
+* WE: ~2 = 1199.8346{{c}}, ~13/12 = 139.3431{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~13/12 = 139.362{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.3544{{c}}
+<!-- * CTE: ~2 = 1200.000{{c}}, ~13/12 = 139.334{{c}}
+* POTE: ~2 = 1200.000{{c}}, ~13/12 = 139.362{{c}} -->
 {{Optimal ET sequence|legend=0| 17cg, 26, 43 }}
-Badness (Smith): 0.020878
+Badness (Sintel): 1.06
 === 19-limit ===
@@ Line 2,152: / Line 2,180: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000{{c}}, ~13/12 = 139.296{{c}}
+* WE: ~2 = 1199.8891{{c}}, ~13/12 = 139.3001{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~13/12 = 139.313{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.3080{{c}}
+<!-- * CTE: ~2 = 1200.000{{c}}, ~13/12 = 139.296{{c}}
+* POTE: ~2 = 1200.000{{c}}, ~13/12 = 139.313{{c}} -->
 {{Optimal ET sequence|legend=0| 17cgh, 26, 43, 69 }}
-Badness (Smith): 0.018229
+Badness (Sintel): 1.11
 == Meantritone ==
@@ Line 2,166: / Line 2,196: @@
 [[Comma list]]: 81/80, 16875/16807
-{{Mapping|legend=1| 1 4 12 12 | 0 -5 -20 -19 }}
+{{Mapping|legend=1| 1 -1 -8 -7 | 0 5 20 19 }}
+: mapping generators: ~2, ~10/7
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000{{c}}, ~7/5 = 580.568{{c}}
+* [[WE]]: ~2 = 1201.3832{{c}}, ~10/7 = 619.9478{{c}}
+: [[error map]]: {{val| +1.383 -3.599 +1.576 +0.499 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 619.3176{{c}}
+: error map: {{val| 0.000 -5.367 +0.038 -1.791 }}
+<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~10/7 = 619.432{{c}}
 : [[error map]]: {{val| 0.000 -4.795 +2.325 +0.381 }}
-* [[POTE]]: ~2 = 1200.000{{c}}, ~7/5 = 580.766{{c}}
+* [[POTE]]: ~2 = 1200.000{{c}}, ~10/7 = 619.234{{c}}
-: error map: {{val| 0.000 -5.785 -1.634 -3.380 }}
+: error map: {{val| 0.000 -5.785 -1.634 -3.380 }} -->
 {{Optimal ET sequence|legend=1| 29cd, 31, 188bcd, 219bbcd }}
-[[Badness]] (Smith): 0.082239
+[[Badness]] (Sintel): 2.08
 === 11-limit ===
@@ Line 2,183: / Line 2,219: @@
 Comma list: 81/80, 99/98, 2541/2500
-Mapping: {{mapping| 1 4 12 12 17 | 0 -5 -20 -19 -28 }}
+Mapping: {{mapping| 1 -1 -8 -7 -11 | 0 5 20 19 28 }}
 Optimal tunings:
-* CTE: ~2 = 1200.000{{c}}, ~7/5 = 580.482{{c}}
+* WE: ~2 = 1201.2054{{c}}, ~10/7 = 619.9752{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~7/5 = 580.647{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.4223{{c}}
+<!-- * CTE: ~2 = 1200.000{{c}}, ~10/7 = 619.518{{c}}
+* POTE: ~2 = 1200.000{{c}}, ~10/7 = 619.353{{c}} -->
 {{Optimal ET sequence|legend=0| 29cde, 31 }}
-Badness (Smith): 0.042869
+Badness (Sintel): 1.42
 == Injera ==
@@ Line 2,207: / Line 2,245: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~7/5 = 600.000{{c}}, ~3/2 = 695.330{{c}} (~21/20 = 95.330{{c}})
+* [[WE]]: ~7/5 = 600.6662{{c}}, ~3/2 = 695.1463{{c}} (~21/20 = 94.4801{{c}})
+: [[error map]]: {{val| +1.332 -5.476 -5.729 +12.425 }}
+* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 694.7712{{c}} (~21/20 = 94.7712{{c}})
+: error map: {{val| 0.000 -7.184 -7.229 +10.259 }}
+<!-- * [[CTE]]: ~7/5 = 600.000{{c}}, ~3/2 = 695.330{{c}} (~21/20 = 95.330{{c}})
 : [[error map]]: {{val| 0.000 -6.625 -4.993 +12.495 }}
 * [[POTE]]: ~7/5 = 600.000{{c}}, ~3/2 = 694.375{{c}} (~21/20 = 94.375{{c}})
-: error map: {{val| 0.000 -7.580 -8.813 +8.675 }}
+: error map: {{val| 0.000 -7.580 -8.813 +8.675 }} -->
 [[Tuning ranges]]:
@@ Line 2,219: / Line 2,261: @@
 {{Optimal ET sequence|legend=1| 12, 26, 38 }}
-[[Badness]] (Smith): 0.031130
+[[Badness]] (Sintel): 0.788
 ; Music
@@ Line 2,232: / Line 2,274: @@
 Optimal tunings:
-* CTE: ~7/5 = 600.000{{c}}, ~3/2 = 694.098{{c}} (~21/20 = 94.098{{c}})
+* WE: ~7/5 = 600.9350{{c}}, ~3/2 = 693.9198{{c}} (~21/20 = 92.9848{{c}})
-* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 692.840{{c}} (~21/20 = 92.840{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 693.3539{{c}} (~21/20 = 93.3539{{c}})
+<!-- * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 694.098{{c}} (~21/20 = 94.098{{c}})
+* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 692.840{{c}} (~21/20 = 92.840{{c}}) -->
 Tuning ranges:
@@ Line 2,241: / Line 2,285: @@
 {{Optimal ET sequence|legend=0| 12, 26 }}
-Badness (Smith): 0.023124
+Badness (Sintel): 0.764
 ==== 13-limit ====
@@ Line 2,251: / Line 2,295: @@
 Optimal tunings:
-* CTE: ~7/5 = 600.000{{c}}, ~3/2 = 693.806{{c}} (~21/20 = 93.806{{c}})
+* WE: ~7/5 = 600.9982{{c}}, ~3/2 = 693.8249{{c}} (~21/20 = 92.8267{{c}})
-* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 692.673{{c}} (~21/20 = 92.673{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 693.0992{{c}} (~21/20 = 93.0992{{c}})
+<!-- * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 693.806{{c}} (~21/20 = 93.806{{c}})
+* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 692.673{{c}} (~21/20 = 92.673{{c}}) -->
 Tuning ranges:
@@ Line 2,260: / Line 2,306: @@
 {{Optimal ET sequence|legend=0| 12f, 14cf, 26 }}
-Badness (Smith): 0.021565
+Badness (Sintel): 0.891
 ===== 17-limit =====
@@ Line 2,270: / Line 2,316: @@
 Optimal tunings:
-* CTE: ~7/5 = 600.000{{c}}, ~3/2 = 693.852{{c}} (~21/20 = 93.852{{c}})
+* WE: ~7/5 = 601.1757{{c}}, ~3/2 = 693.8441{{c}} (~21/20 = 92.6684{{c}})
-* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 692.487{{c}} (~21/20 = 92.487{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 692.8879{{c}} (~21/20 = 92.8879{{c}})
+<!-- * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 693.852{{c}} (~21/20 = 93.852{{c}})
+* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 692.487{{c}} (~21/20 = 92.487{{c}}) -->
 {{Optimal ET sequence|legend=0| 12f, 14cf, 26 }}
-Badness (Smith): 0.018358
+Badness (Sintel): 0.935
 ===== 19-limit =====
@@ Line 2,285: / Line 2,333: @@
 Optimal tunings:
-* CTE: ~7/5 = 600.000{{c}}, ~3/2 = 694.031{{c}} (~21/20 = 94.031{{c}})
+* WE: ~7/5 = 601.4245{{c}}, ~3/2 = 693.9426{{c}} (~21/20 = 92.5181{{c}})
-* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 692.299{{c}} (~21/20 = 92.299{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 692.7606{{c}} (~21/20 = 92.7606{{c}})
+<!-- * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 694.031{{c}} (~21/20 = 94.031{{c}})
+* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 692.299{{c}} (~21/20 = 92.299{{c}}) -->
 {{Optimal ET sequence|legend=0| 12f, 14cf, 26 }}
-Badness (Smith): 0.015118
+Badness (Sintel): 0.920
 ==== Enjera ====
@@ Line 2,300: / Line 2,350: @@
 Optimal tunings:
-* CTE: ~7/5 = 600.000{{c}}, ~3/2 = 693.088{{c}} (~21/20 = 93.088{{c}})
+* WE: ~7/5 = 599.1863{{c}}, ~3/2 = 693.1791{{c}} (~21/20 = 93.9929{{c}})
-* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 694.121{{c}} (~21/20 = 94.121{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 693.6809{{c}} (~21/20 = 93.6809{{c}})
+<!-- * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 693.088{{c}} (~21/20 = 93.088{{c}})
+* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 694.121{{c}} (~21/20 = 94.121{{c}}) -->
 {{Optimal ET sequence|legend=0| 10cdeef, 12f }}
-Badness (Smith): 0.026542
+Badness (Sintel): 1.10
 === Injerous ===
@@ Line 2,315: / Line 2,367: @@
 Optimal tunings:
-* CTE: ~7/5 = 600.000{{c}}, ~3/2 = 694.619{{c}} (~21/20 = 94.619{{c}})
+* WE: ~7/5 = 603.1682{{c}}, ~3/2 = 694.1945{{c}} (~21/20 = 91.0264{{c}})
-* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 690.548{{c}} (~21/20 = 90.548{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 691.6107{{c}} (~21/20 = 91.6107{{c}})
+<!-- * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 694.619{{c}} (~21/20 = 94.619{{c}})
+* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 690.548{{c}} (~21/20 = 90.548{{c}}) -->
 {{Optimal ET sequence|legend=0| 12e, 14c, 26e, 40cee }}
-Badness (Smith): 0.038577
+Badness (Sintel): 1.28
 === Lahoh ===
@@ Line 2,330: / Line 2,384: @@
 Optimal tunings:
-* CTE: ~7/5 = 600.000{{c}}, ~3/2 = 695.330{{c}} (~21/20 = 95.330{{c}})
+* WE: ~7/5 = 597.3179{{c}}, ~3/2 = 695.8759{{c}} (~21/20 = 98.5581{{c}})
-* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 699.001{{c}} (~21/20 = 99.001{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 697.8757{{c}} (~21/20 = 97.8757{{c}})
+<!-- * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 695.330{{c}} (~21/20 = 95.330{{c}})
+* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 699.001{{c}} (~21/20 = 99.001{{c}}) -->
 {{Optimal ET sequence|legend=0| 10cd, 12 }}
-Badness (Smith): 0.043062
+Badness (Sintel): 1.42
 === Teff ===
@@ Line 2,351: / Line 2,407: @@
 Optimal tunings:
-* CTE: ~7/5 = 600.000{{c}}, ~11/8 = 552.331{{c}} (~33/32 = 47.669{{c}})
+* WE: ~7/5 = 600.2802{{c}}, ~16/11 = 647.7720{{c}} (~33/32 = 47.4918{{c}})
-* POTE: ~7/5 = 600.000{{c}}, ~11/8 = 552.530{{c}} (~33/32 = 47.470{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~16/11 = 647.5224{{c}} (~33/32 = 47.5224{{c}})
+<!-- * CTE: ~7/5 = 600.000{{c}}, ~16/11 = 647.669{{c}} (~33/32 = 47.669{{c}})
+* POTE: ~7/5 = 600.000{{c}}, ~16/11 = 647.470{{c}} (~33/32 = 47.470{{c}}) -->
 {{Optimal ET sequence|legend=0| 24d, 26, 50d }}
-Badness (Smith): 0.070689
+Badness (Sintel): 2.34
 ==== 13-limit ====
@@ Line 2,366: / Line 2,424: @@
 Optimal tunings:
-* CTE: ~7/5 = 600.000{{c}}, ~11/8 = 552.297{{c}} (~33/32 = 47.703{{c}})
+* WE: ~7/5 = 600.3037{{c}}, ~16/11 = 647.7954{{c}} (~33/32 = 47.4917{{c}})
-* POTE: ~7/5 = 600.000{{c}}, ~11/8 = 552.532{{c}} (~33/32 = 47.468{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~16/11 = 647.5256{{c}} (~33/32 = 47.5256{{c}})
+<!-- * CTE: ~7/5 = 600.000{{c}}, ~16/11 = 647.703{{c}} (~33/32 = 47.703{{c}})
+* POTE: ~7/5 = 600.000{{c}}, ~16/11 = 647.468{{c}} (~33/32 = 47.468{{c}}) -->
 {{Optimal ET sequence|legend=0| 24d, 26, 50d }}
-Badness (Smith): 0.040047
+Badness (Sintel): 1.65
 ==== 17-limit ====
@@ Line 2,381: / Line 2,441: @@
 Optimal tunings:
-* CTE: ~7/5 = 600.000{{c}}, ~11/8 = 552.249{{c}} (~34/33 = 47.751{{c}})
+* WE: ~7/5 = 600.5123{{c}}, ~16/11 = 647.8970{{c}} (~34/33 = 47.3846{{c}})
-* POTE: ~7/5 = 600.000{{c}}, ~11/8 = 552.656{{c}} (~34/33 = 47.344{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~16/11 = 647.4314{{c}} (~34/33 = 47.4314{{c}})
+<!-- * CTE: ~7/5 = 600.000{{c}}, ~16/11 = 647.751{{c}} (~34/33 = 47.751{{c}})
+* POTE: ~7/5 = 600.000{{c}}, ~16/11 = 647.344{{c}} (~34/33 = 47.344{{c}}) -->
 {{Optimal ET sequence|legend=0| 24d, 26 }}
-Badness (Smith): 0.029499
+Badness (Sintel): 1.50
 ==== 19-limit ====
@@ Line 2,396: / Line 2,458: @@
 Optimal tunings:
-* CTE: ~7/5 = 600.000{{c}}, ~11/8 = 552.107{{c}} (~34/33 = 47.893{{c}})
+* WE: ~7/5 = 600.6308{{c}}, ~16/11 = 648.0424{{c}} (~34/33 = 47.4116{{c}})
-* POTE: ~7/5 = 600.000{{c}}, ~11/8 = 552.638{{c}} (~34/33 = 47.362{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~16/11 = 647.4715{{c}} (~34/33 = 47.4715{{c}})
+<!-- * CTE: ~7/5 = 600.000{{c}}, ~16/11 = 647.893{{c}} (~34/33 = 47.893{{c}})
+* POTE: ~7/5 = 600.000{{c}}, ~16/11 = 647.362{{c}} (~34/33 = 47.362{{c}}) -->
 {{Optimal ET sequence|legend=0| 24d, 26 }}
-Badness (Smith): 0.023133
+Badness (Sintel): 1.41
 == Pombe ==
@@ Line 2,415: / Line 2,479: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~735/512 = 600.000{{c}}, ~48/35 = 551.845{{c}} (~36/35 = 48.155{{c}})
+* [[WE]]: ~735/512 = 601.0652{{c}}, ~35/24 = 648.9295{{c}} (~36/35 = 47.8642{{c}})
-: [[error map]]: {{val| 0.000 -5.645 -1.075 -9.600 }}
+: [[error map]]: {{val| +2.130 -3.031 +0.861 -1.756 }}
-* [[POTE]]: ~735/512 = 600.000{{c}}, ~48/35 = 552.221{{c}} (~36/35 = 48.779{{c}})
+* [[CWE]]: ~735/512 = 600.0000{{c}}, ~35/24 = 647.8628{{c}} (~36/35 = 47.8628{{c}})
 : error map: {{val| 0.000 -6.229 -3.411 -8.140 }}
+<!-- * [[CTE]]: ~735/512 = 600.000{{c}}, ~35/24 = 648.155{{c}} (~36/35 = 48.155{{c}})
+: error map: {{val| 0.000 -5.645 -1.075 -9.600 }}
+* [[POTE]]: ~735/512 = 600.000{{c}}, ~35/24 = 648.779{{c}} (~36/35 = 48.779{{c}})
+: error map: {{val| 0.000 -6.396 -4.078 -7.723 }} -->
 {{Optimal ET sequence|legend=1| 24, 26, 50, 126bcd, 176bcdd, 226bbcdd }}
-[[Badness]] (Smith): 0.116104
+[[Badness]] (Sintel): 2.94
 === 11-limit ===
@@ Line 2,432: / Line 2,500: @@
 Optimal tunings:
-* CTE: ~99/70 = 600.000{{c}}, ~11/8 = 551.843{{c}} (~36/35 = 48.157{{c}})
+* WE: ~99/70 = 600.7890{{c}}, ~16/11 = 648.7592{{c}} (~36/35 = 47.9701{{c}})
-* POTE: ~99/70 = 600.000{{c}}, ~11/8 = 552.093{{c}} (~36/35 = 47.907{{c}})
+* CWE: ~99/70 = 600.0000{{c}}, ~16/11 = 647.9516{{c}} (~36/35 = 47.9516{{c}})
+<!-- * CTE: ~99/70 = 600.000{{c}}, ~16/11 = 648.157{{c}} (~36/35 = 48.157{{c}})
+* POTE: ~99/70 = 600.000{{c}}, ~16/11 = 647.907{{c}} (~36/35 = 47.907{{c}}) -->
 {{Optimal ET sequence|legend=0| 24, 26, 50 }}
-Badness (Smith): 0.052099
+Badness (Sintel): 1.72
 === 13-limit ===
@@ Line 2,447: / Line 2,517: @@
 Optimal tunings:
-* CTE: ~99/70 = 600.000{{c}}, ~11/8 = 551.848{{c}} (~36/35 = 48.152{{c}})
+* WE: ~99/70 = 600.6971{{c}}, ~16/11 = 648.6029{{c}} (~36/35 = 47.9058{{c}})
-* POTE: ~99/70 = 600.000{{c}}, ~11/8 = 552.150{{c}} (~36/35 = 47.850{{c}})
+* CWE: ~99/70 = 600.0000{{c}}, ~16/11 = 647.8990{{c}} (~36/35 = 47.8990{{c}})
+<!-- * CTE: ~99/70 = 600.000{{c}}, ~16/11 = 648.152{{c}} (~36/35 = 48.152{{c}})
+* POTE: ~99/70 = 600.000{{c}}, ~16/11 = 647.850{{c}} (~36/35 = 47.850{{c}}) -->
 {{Optimal ET sequence|legend=0| 24, 26, 50 }}
-Badness (Smith): 0.031039
+Badness (Sintel): 1.28
 === 17-limit ===
@@ Line 2,462: / Line 2,534: @@
 Optimal tunings:
-* CTE: ~17/12 = 600.000{{c}}, ~11/8 = 551.793{{c}} (~36/35 = 48.207{{c}})
+* WE: ~17/12 = 600.7610{{c}}, ~16/11 = 648.6638{{c}} (~36/35 = 47.9028{{c}})
-* POTE: ~17/12 = 600.000{{c}}, ~11/8 = 552.158{{c}} (~36/35 = 47.842{{c}})
+* CWE: ~17/12 = 600.0000{{c}}, ~16/11 = 647.8990{{c}} (~36/35 = 47.8990{{c}})
+<!-- * CTE: ~17/12 = 600.000{{c}}, ~16/11 = 648.207{{c}} (~36/35 = 48.207{{c}})
+* POTE: ~17/12 = 600.000{{c}}, ~16/11 = 647.842{{c}} (~36/35 = 47.842{{c}}) -->
 {{Optimal ET sequence|legend=0| 24, 26, 50 }}
-Badness (Smith): 0.021260
+Badness (Sintel): 1.08
 === 19-limit ===
@@ Line 2,477: / Line 2,551: @@
 Optimal tunings:
-* CTE: ~17/12 = 600.000{{c}}, ~11/8 = 551.660{{c}} (~36/35 = 48.340{{c}})
+* WE: ~17/12 = 600.8048{{c}}, ~16/11 = 648.7494{{c}} (~36/35 = 47.9446{{c}})
-* POTE: ~17/12 = 600.000{{c}}, ~11/8 = 552.120{{c}} (~36/35 = 47.880{{c}})
+* CWE: ~17/12 = 600.0000{{c}}, ~16/11 = 647.9425{{c}} (~36/35 = 47.9425{{c}})
+<!-- * CTE: ~17/12 = 600.000{{c}}, ~16/11 = 648.340{{c}} (~36/35 = 48.340{{c}})
+* POTE: ~17/12 = 600.000{{c}}, ~16/11 = 647.880{{c}} (~36/35 = 47.880{{c}}) -->
 {{Optimal ET sequence|legend=0| 24, 26, 50 }}
-Badness (Smith): 0.016548
+Badness (Sintel): 1.01
 == Orphic ==
@@ Line 2,494: / Line 2,570: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2401/1728 = 600.000{{c}}, ~343/288 = 324.275{{c}} (~7/6 = 275.725{{c}})
+* [[WE]]: ~2401/1728 = 600.1767{{c}}, ~343/288 = 324.3015{{c}} (~7/6 = 275.8751{{c}})
+: [[error map]]: {{val| +0.353 -4.572 +1.804 +4.785 }}
+* [[CWE]]: ~2401/1728 = 600.0000{{c}}, ~343/288 = 324.2285{{c}} (~7/6 = 275.7715{{c}})
+: error map: {{val| 0.000 -5.041 +1.342 +3.860 }}
+<!-- * [[CTE]]: ~2401/1728 = 600.000{{c}}, ~343/288 = 324.275{{c}} (~7/6 = 275.725{{c}})
 : [[error map]]: {{val| 0.000 -4.854 +2.091 +4.000 }}
 * [[POTE]]: ~2401/1728 = 600.000{{c}}, ~343/288 = 324.206{{c}} (~7/6 = 275.794{{c}})
-: error map: {{val| 0.000 -5.131 +0.983 +3.792 }}
+: error map: {{val| 0.000 -5.131 +0.983 +3.792 }} -->
 {{Optimal ET sequence|legend=1| 26, 48c, 74 }}
-[[Badness]] (Smith): 0.258825
+[[Badness]] (Sintel): 6.55
 === 11-limit ===
@@ Line 2,508: / Line 2,588: @@
 Comma list: 81/80, 99/98, 73728/73205
-Mapping: {{mapping| 2 1 -4 4 8 | 0 -4 -16 -3 2 }}
+Mapping: {{mapping| 2 1 -4 4 8 | 0 4 16 3 -2 }}
 Optimal tunings:
-* CTE: ~363/256 = 600.000{{c}}, ~77/64 = 324.276{{c}} (~7/6 = 275.724{{c}})
+* WE: ~363/256 = 600.1011{{c}}, ~77/64 = 324.2923{{c}} (~7/6 = 275.8088{{c}})
-* POTE: ~363/256 = 600.000{{c}}, ~77/64 = 324.238{{c}} (~7/6 = 275.762{{c}})
+* CWE: ~363/256 = 600.0000{{c}}, ~77/64 = 324.2463{{c}} (~7/6 = 275.7537{{c}})
+<!-- * CTE: ~363/256 = 600.000{{c}}, ~77/64 = 324.276{{c}} (~7/6 = 275.724{{c}})
+* POTE: ~363/256 = 600.000{{c}}, ~77/64 = 324.238{{c}} (~7/6 = 275.762{{c}}) -->
 {{Optimal ET sequence|legend=0| 26, 48c, 74 }}
-Badness (Smith): 0.101499
+Badness (Sintel): 3.36
 === 13-limit ===
@@ Line 2,523: / Line 2,605: @@
 Comma list: 81/80, 99/98, 144/143, 2200/2197
-Mapping: {{mapping| 2 1 -4 4 8 2 | 0 -4 -16 -3 2 -10 }}
+Mapping: {{mapping| 2 1 -4 4 8 2 | 0 4 16 3 -2 10 }}
 Optimal tunings:
-* CTE: ~55/39 = 600.000{{c}}, ~77/64 = 324.250{{c}} (~7/6 = 275.750{{c}})
+* WE: ~55/39 = 600.0540{{c}}, ~77/64 = 324.2551{{c}} (~7/6 = 275.7989{{c}})
-* POTE: ~55/39 = 600.000{{c}}, ~77/64 = 324.226{{c}} (~7/6 = 275.774{{c}})
+* CWE: ~55/39 = 600.0000{{c}}, ~77/64 = 324.2307{{c}} (~7/6 = 275.7693{{c}})
+<!-- * CTE: ~55/39 = 600.000{{c}}, ~77/64 = 324.250{{c}} (~7/6 = 275.750{{c}})
+* POTE: ~55/39 = 600.000{{c}}, ~77/64 = 324.226{{c}} (~7/6 = 275.774{{c}}) -->
 {{Optimal ET sequence|legend=0| 26, 48c, 74 }}
-Badness (Smith): 0.053482
+Badness (Sintel): 2.21
 == Cloudtone ==
-The cloudtone temperament (5 &amp; 50) tempers out the [[cloudy comma]], 16807/16384 and the [[81/80|syntonic comma]], 81/80 in the 7-limit. It can be extended to the 11- and 13-limit by adding 385/384 and 105/104 to the comma list in this order.
+The cloudtone temperament ({{nowrap| 5 & 50 }}) tempers out the [[cloudy comma]], 16807/16384 and the [[81/80|syntonic comma]], 81/80 in the 7-limit. It can be extended to the 11- and 13-limit by adding 385/384 and 105/104 to the comma list in this order.
 [[Subgroup]]: 2.3.5.7
@@ Line 2,545: / Line 2,629: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~8/7 = 240.000{{c}}, ~3/2 = 697.214{{c}} (~49/48 = 22.786{{c}})
+* [[WE]]: ~8/7 = 240.4267{{c}}, ~3/2 = 696.9566{{c}} (~49/48 = 24.3235{{c}})
-: [[error map]]: {{val| 0.000 -4.741 +2.544 -8.826 }}
+: [[error map]]: {{val| +2.133 -2.865 +1.513 -2.852 }}
+* [[CWE]]: ~8/7 = 240.0000{{c}}, ~3/2 = 696.1637{{c}} (~49/48 = 23.8373{{c}})
+: error map: {{val| 0.000 -5.791 -1.659 -8.826 }}
+<!-- * [[CTE]]: ~8/7 = 240.000{{c}}, ~3/2 = 697.214{{c}} (~49/48 = 22.786{{c}})
+: error map: {{val| 0.000 -4.741 +2.544 -8.826 }}
 * [[POTE]]: ~8/7 = 240.000{{c}}, ~3/2 = 695.720{{c}} (~49/48 = 24.280{{c}})
-: error map: {{val| 0.000 -6.235 -3.435 -8.826 }}
+: error map: {{val| 0.000 -6.235 -3.435 -8.826 }} -->
 {{Optimal ET sequence|legend=1| 5, 40c, 45, 50 }}
-[[Badness]] (Smith): 0.102256
+[[Badness]] (Sintel): 2.59
 === 11-limit ===
@@ Line 2,562: / Line 2,650: @@
 Optimal tunings:
-* CTE: ~8/7 = 240.000{{c}}, ~3/2 = 697.034{{c}} (~56/55 = 22.966{{c}})
+* WE: ~8/7 = 240.2740{{c}}, ~3/2 = 697.3317{{c}} (~56/55 = 23.4904{{c}})
-* POTE: ~8/7 = 240.000{{c}}, ~3/2 = 696.536{{c}} (~56/55 = 23.464{{c}})
+* CWE: ~8/7 = 240.0000{{c}}, ~3/2 = 696.6269{{c}} (~56/55 = 23.3731{{c}})
+<!-- * CTE: ~8/7 = 240.000{{c}}, ~3/2 = 697.034{{c}} (~56/55 = 22.966{{c}})
+* POTE: ~8/7 = 240.000{{c}}, ~3/2 = 696.536{{c}} (~56/55 = 23.464{{c}}) -->
 {{Optimal ET sequence|legend=0| 5, 45, 50 }}
-Badness (Smith): 0.070378
+Badness (Sintel): 2.33
 === 13-limit ===
@@ Line 2,577: / Line 2,667: @@
 Optimal tunings:
-* CTE: ~8/7 = 240.000{{c}}, ~3/2 = 696.749{{c}} (~91/90 = 23.251{{c}})
+* WE: ~8/7 = 240.2435{{c}}, ~3/2 = 696.8686{{c}} (~91/90 = 23.8618{{c}})
-* POTE: ~8/7 = 240.000{{c}}, ~3/2 = 696.162{{c}} (~91/90 = 23.838{{c}})
+* CWE: ~8/7 = 240.0000{{c}}, ~3/2 = 696.2653{{c}} (~91/90 = 23.7347{{c}})
+<!-- * CTE: ~8/7 = 240.000{{c}}, ~3/2 = 696.749{{c}} (~91/90 = 23.251{{c}})
+* POTE: ~8/7 = 240.000{{c}}, ~3/2 = 696.162{{c}} (~91/90 = 23.838{{c}}) -->
 {{Optimal ET sequence|legend=0| 5, 45f, 50 }}
-Badness (Smith): 0.048829
+Badness (Sintel): 2.02
 == Subgroup extensions ==