Breed family: Difference between revisions

Line 17:

: 49/40 length = 0.7858, 8/7 length = 1.1241

: Angle (49/40, 8/7) = 107.367°

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.0206{{c}}, ~49/40 = 350.9724{{c}}, ~10/7 = 617.6826{{c}}

: [[error map]]: {{val| +0.021 +0.010 +0.044 -0.130 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 350.9743{{c}}, ~10/7 = 617.6807{{c}}

: error map: {{val| 0.000 -0.006 +0.022 -0.171 }}

[[Minimax tuning]]:

* [[7-odd-limit|7-]] and [[9-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.5

~~[[Optimal tuning]]s:~~

* [[WE]]: ~2 = 1200.021{{c}}, ~49/40 = 350.972{{c}}, ~10/7 = 617.683{{c}}

* [[CWE]]: ~2 = 1200.000{{c}}, ~49/40 = 350.974{{c}}, ~10/7 = 617.681{{c}}

{{Optimal ET sequence|legend=1| 27, 31, 41, 58, 68, 72, 99, 171, 441, 612, 1966, 2308, 2578, 2749, 3361d }}

[[Badness]] (Sintel): 0.~~067~~

[[Badness]] (Sintel): 0.0674

[[Projection pair]]: <code>3 2401/800</code> to 2.5.7

Line 46:

Line 48:

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.0985{{c}}, ~11/9 = 350.5322{{c}}, ~10/7 = 617.8782{{c}}

: [[error map]]: {{val| +0.098 -0.792 +0.073 -0.218 +1.540 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/9 = 350.5374{{c}}, ~10/7 = 617.8712{{c}}

: error map: {{val| 0.000 -0.880 -0.034 -0.417 +1.369 }}

[[Minimax tuning]]:

* [[11-odd-limit]] [[~~Eigenmonzo~~ basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11

* [[11-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11

~~[[Optimal tuning]]s:~~

* [[WE]]: ~2 = 1200.098{{c}}, ~11/9 = 350.532{{c}}, ~10/7 = 617.878{{c}}

* [[CWE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.537{{c}}, ~10/7 = 617.871{{c}}

Line 66:

Line 70:

Mapping: {{mapping| 1 1 1 2 2 1 | 0 2 1 1 5 11 | 0 0 2 1 0 -1 }}

Optimal tunings:

* WE: ~2 = 1199.9775{{c}}, ~11/9 = 350.7113{{c}}, ~10/7 = 617.8170{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 350.7130{{c}}, ~10/7 = 617.8178{{c}}

Minimax tuning:

* 13-odd-limit unchanged-interval (eigenmonzo) basis: 2.9/5.13/9

* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7/5.15/13

~~Optimal tunings:~~

* WE: ~2 = 1199.977{{c}}, ~11/9 = 350.711{{c}}, ~10/7 = 617.817{{c}}

* CWE: ~2 = 1200.000{{c}}, ~11/9 = 350.713{{c}}, ~10/7 = 617.818{{c}}

{{Optimal ET sequence|legend=0| 27eff, 31f, 41, 58, 72, 130, 243, 301e, 373e }}

Line 85:

Line 89:

Mapping: {{mapping| 1 1 1 2 2 1 3 | 0 2 1 1 5 11 9 | 0 0 2 1 0 -1 -3 }}

Optimal tunings:

* WE: ~2 = 1200.0876{{c}}, ~11/9 = 350.7203{{c}}, ~10/7 = 617.5766{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 350.7138{{c}}, ~10/7 = 617.5610{{c}}

Minimax tuning:

* 17-odd-limit unchanged-interval (eigenmonzo) basis: 2.5/3.17/9

~~Optimal tunings:~~

* WE: ~2 = 1200.088{{c}}, ~11/9 = 350.720{{c}}, ~10/7 = 617.577{{c}}

* CWE: ~2 = 1200.000{{c}}, ~11/9 = 350.714{{c}}, ~10/7 = 617.561{{c}}

{{Optimal ET sequence|legend=0| 27effg, 31fg, 41, 58, 72, 130, 171, 243 }}

Line 103:

Line 107:

Mapping: {{mapping| 1 1 1 2 2 1 3 | 0 4 0 1 10 23 12 | 0 0 2 1 0 -1 -1 }}

: Mapping generators: ~2, ~119/108, ~27/17

Optimal tunings:

* WE: ~2 = 1199.~~559~~{{c}}, ~119/108 = 175.~~353~~{{c}}, ~27/17 = 793.~~685~~{{c}}

* WE: ~2 = 1199.5594{{c}}, ~119/108 = 175.3533{{c}}, ~27/17 = 793.6847{{c}}

* CWE: ~2 = 1200.~~000~~{{c}}, ~119/108 = 175.~~371~~{{c}}, ~27/17 = 793.~~756~~{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~119/108 = 175.3707{{c}}, ~27/17 = 793.7559{{c}}

{{Optimal ET sequence|legend=0| 14cf, 27effg, 41, 75ce, 89, 116cefg, 130g }}

Badness (Sintel): 2.~~843~~

Badness (Sintel): 2.84

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

Line 122:

Line 125:

Optimal tunings:

* WE: ~2 = 1199.~~733~~{{c}}, ~21/19 = 175.~~347~~{{c}}, ~19/12 = 793.~~779~~{{c}}

* WE: ~2 = 1199.7333{{c}}, ~21/19 = 175.3472{{c}}, ~19/12 = 793.7794{{c}}

* CWE: ~2 = 1200.~~000~~{{c}}, ~21/19 = 175.~~358~~{{c}}, ~19/12 = 793.~~819~~{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~21/19 = 175.3584{{c}}, ~19/12 = 793.8194{{c}}

{{Optimal ET sequence|legend=0| 14cf, 27effg, 41, 75ce, 89, 116cefg, 130g }}

Badness (Sintel): 2.~~294~~

Badness (Sintel): 2.29

=== Jofur ===

Line 137:

Line 140:

Optimal tunings:

* WE: ~2 = 1198.~~953~~{{c}}, ~11/9 = 351.~~141~~{{c}}, ~10/7 = 618.~~349~~{{c}}

* WE: ~2 = 1198.9534{{c}}, ~11/9 = 351.1412{{c}}, ~10/7 = 618.3494{{c}}

* CWE: ~2 = 1200.~~000~~{{c}}, ~11/9 = 351.~~254~~{{c}}, ~10/7 = 618.~~593~~{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.2536{{c}}, ~10/7 = 618.5932{{c}}

Line 152:

Line 155:

Optimal tunings:

* WE: ~2 = 1200.~~144~~{{c}}, ~11/9 = 350.~~435~~{{c}}, ~10/7 = 618.~~177~~{{c}}

* WE: ~2 = 1200.1435{{c}}, ~11/9 = 350.4354{{c}}, ~10/7 = 618.1775{{c}}

* CWE: ~2 = 1200.~~000~~{{c}}, ~11/9 = 350.~~440~~{{c}}, ~10/7 = 618.~~176~~{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 350.4402{{c}}, ~10/7 = 618.1759{{c}}

{{Optimal ET sequence|legend=0| 27e, 31, 45ef, 58, 72, 103, 130, 233, 363 }}

Line 171:

Line 174:

: 49/40 length = 0.756, 10/7 length = 0.819

: Angle (49/40, 10/7) = 106.460 degrees

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.4168{{c}}, ~49/40 = 350.8363{{c}}, ~10/7 = 617.2187{{c}}

: [[error map]]: {{val| +0.417 +0.134 -0.623 +0.063 -0.890 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 350.8369{{c}}, ~10/7 = 616.9907{{c}}

: error map: {{val| 0.000 -0.281 -1.495 -0.998 -2.290 }}

[[Minimax tuning]]:

* [[11-odd-limit]]

: [{{monzo| 1 0 0 0 0 }}, {{monzo| 0 1 0 0 0 }}, {{monzo| 23/10 3/10 2/5 0 -2/5 }}, {{monzo| 12/5 2/5 1/5 0 -1/5 }}, {{monzo| 23/10 3/10 -3/5 0 3/5 }}]

: [[~~Eigenmonzo~~ basis|unchanged-interval (eigenmonzo) basis]]: 2.3.11/5

: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.11/5

~~[[Optimal tuning]]s:~~

* [[WE]]: ~2 = 1200.417{{c}}, ~49/40 = 350.836{{c}}, ~10/7 = 617.219{{c}}

* [[CWE]]: ~2 = 1200.000{{c}}, ~49/40 = 350.837{{c}}, ~10/7 = 616.991{{c}}

{{Optimal ET sequence|legend=1| 27, 31, 41, 68, 72, 140, 171e, 212, 284, 496ce, 527cee, 739cdeee, 811ccdeee, 1023ccdeee }}

Line 193:

Line 198:

Optimal tunings:

* WE: ~2 = 1200.~~441~~{{c}}, ~49/40 = 350.~~809~~{{c}}, ~10/7 = 617.~~372~~{{c}}

* WE: ~2 = 1200.4413{{c}}, ~49/40 = 350.8092{{c}}, ~10/7 = 617.3718{{c}}

* CWE: ~2 = 1200.~~000~~{{c}}, ~49/40 = 350.~~805~~{{c}}, ~10/7 = 617.~~157~~{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 350.8046{{c}}, ~10/7 = 617.1572{{c}}

{{Optimal ET sequence|legend=0| 31, 68, 72, 103, 140, 212, 243e, 315ef, 455eef, 770cdeeeff }}

Line 206:

Line 211:

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9178{{c}}, ~49/40 = 350.0519{{c}}, ~10/7 = 617.8150{{c}}

: [[error map]]: {{val| -0.082 +0.067 +0.286 -0.123 -0.135 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 350.0615{{c}}, ~10/7 = 617.8571{{c}}

: error map: {{val| 0.000 +0.168 +0.462 +0.093 +0.032 }}

{{Optimal ET sequence|legend=1| 31, 68e, 99e, 130, 239, 270, 670, 940, 1210, 2150c }}

[[Badness]] (~~Smith~~): 0.~~640 × 10-3~~

[[Badness]] (Sintel): 0.769

=== 13-limit ===

Line 217:

Line 228:

Mapping: {{mapping| 1 1 1 2 -3 7 | 0 2 1 1 8 -6 | 0 0 2 1 8 -3 }}

Optimal tunings:

* WE: ~2 = 1199.9787{{c}}, ~49/40 = 350.9976{{c}}, ~10/7 = 617.8701{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0039{{c}}, ~10/7 = 617.8795{{c}}

{{Optimal ET sequence|legend=0| 31, 78f, 99e, 109, 130, 239, 270, 571, 701, 841, 971, 1241 }}

Badness (~~Smith~~): 0.~~830 × 10-3~~

Badness (Sintel): 0.776

== Lif ==

Line 229:

Line 244:

[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~49/40 = 351.0959{{c}}, ~10/7 = 617.6652{{c}}

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9386{{c}}, ~49/40 = 350.0586{{c}}, ~10/7 = 617.7065{{c}}

: [[error map]]: {{val| -0.061 +0.101 +0.096 -0.184 +0.075 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.0806{{c}}, ~10/7 = 617.7228{{c}}

: error map: {{val| 0.000 +0.206 +0.213 -0.022 +0.269 }}

{{Optimal ET sequence|legend=1| 41, 89, 130, 229, 270, 581, 670, 711, 981, 1251, 2232e }}

[[Badness]] (~~Smith~~): 0.~~793 × 10-3~~

[[Badness]] (Sintel): 0.953

=== 13-limit ===

Line 242:

Line 262:

Mapping: {{mapping| 1 1 1 2 8 7 | 0 2 1 1 -12 -6 | 0 0 2 1 -2 -3 }}

Optimal ~~tuning (~~CTE): ~2 = 1200.0000{{c}}, ~49/40 = 351.0960{{c}}, ~10/7 = 617.6533{{c}}

Optimal tunings:

* WE: ~2 = 1199.9597{{c}}, ~49/40 = 351.0718{{c}}, ~10/7 = 617.6543{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0856{{c}}, ~10/7 = 617.6715{{c}}

{{Optimal ET sequence|legend=0| 41, 89, 99, 130, 270, 581, 711, 981, 1292, 1562 }}

Badness (~~Smith~~): 0.~~579 × 10-3~~

Badness (Sintel): 0.542

=== 2.3.5.7.11.13.19 subgroup ===

Line 253:

Line 276:

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

~~Sval~~ mapping: {{mapping| 1 1 1 2 8 7 0 | 0 2 1 1 -12 -6 11 | 0 0 2 1 -2 -3 2 }}

Subgroup-val mapping: {{mapping| 1 1 1 2 8 7 0 | 0 2 1 1 -12 -6 11 | 0 0 2 1 -2 -3 2 }}

Optimal ~~tuning (~~CTE): ~2 = 1200.0000{{c}}, ~49/40 = 351.1007{{c}}, ~10/7 = 617.6501{{c}}

Optimal tunings:

* WE: ~2 = 1199.9752{{c}}, ~49/40 = 351.0908{{c}}, ~10/7 = 617.6473{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0984{{c}}, ~10/7 = 617.6588{{c}}

{{Optimal ET sequence|legend=0| 41, 89, 130, 229, 270, 581, 851, 1562, 1832, 2413 }}

Badness (~~Smith~~): 0.~~499 × 10-3~~

Badness (Sintel): 0.488

== Baldur ==

Line 268:

Line 294:

: Mapping generators: ~99/70, ~343/198, ~10/7

[[Optimal tuning]]s:

* [[WE]]: ~99/70 = 600.0149{{c}}, ~343/198 = 950.9717{{c}}, ~10/7 = 617.7007{{c}}

: [[error map]]: {{val| +0.030 -0.012 +0.074 -0.109 -0.055 }}

* [[CWE]]: ~99/70 = 600.0000{{c}}, ~343/198 = 950.9565{{c}}, ~10/7 = 617.7017{{c}}

: error map: {{val| 0.000 -0.042 +0.046 -0.168 -0.126 }}

[[Minimax tuning]]:

* [[11-odd-limit]]

: [{{monzo| 1 0 0 0 0 }}, {{monzo| 3/4 0 1/2 1/2 -1/2 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 23/16 0 5/8 1/8 -1/8 }}, {{monzo| 23/16 0 5/8 -7/8 7/8 }}]

: [[~~Eigenmonzo~~ basis|unchanged-interval (eigenmonzo) basis]]: 2.5.11/7

: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.11/7

~~[[Optimal tuning]]s:~~

* [[WE]]: ~99/70 = 600.015{{c}}, ~343/198 = 950.972{{c}}, ~10/7 = 617.701{{c}}

* [[CWE]]: ~99/70 = 600.000{{c}}, ~343/198 = 950.956{{c}}, ~10/7 = 617.702{{c}}

{{Optimal ET sequence|legend=1| 58, 72, 130, 198, 212, 270, 342, 612, 954, 1084, 1354, 1696, 4004de, 5700de }}

Line 282:

Line 310:

[[Badness]] (Sintel): 0.200

[[Projection pair]]s: ~2 ~~= ~~~9801/4900, ~3 ~~= ~~~117649/39204, ~7 ~~= ~~~9801/1400, ~11 ~~= ~~~913517247483640899/83082326424002500 to 5.7/2.99/4

[[Projection pair]]s: <code>2 9801/4900, 3 117649/39204, 7 9801/1400, 11 913517247483640899/83082326424002500</code> to 5.7/2.99/4

=== Greenland ===

Line 292:

Line 320:

Optimal tunings:

* WE: ~99/70 = 599.~~987~~{{c}}, ~26/15 = 951.~~054~~{{c}}, ~10/7 = 617.~~806~~{{c}}

* WE: ~99/70 = 599.9868{{c}}, ~26/15 = 951.0538{{c}}, ~10/7 = 617.8062{{c}}

* CWE: ~99/70 = 600.~~000~~{{c}}, ~26/15 = 951.~~069~~{{c}}, ~10/7 = 617.~~807~~{{c}}

* CWE: ~99/70 = 600.0000{{c}}, ~26/15 = 951.0689{{c}}, ~10/7 = 617.8067{{c}}

{{Optimal ET sequence|legend=0| 58, 72, 130, 198, 270, 940, 1210f }}

Line 311:

Line 339:

Optimal tunings:

* WE: ~17/12 = 600.~~112~~{{c}}, ~26/15 = 951.~~191~~{{c}}, ~10/7 = 617.~~610~~{{c}}

* WE: ~17/12 = 600.1118{{c}}, ~26/15 = 951.1907{{c}}, ~10/7 = 617.6100{{c}}

* CWE: ~17/12 = 600.~~000~~{{c}}, ~26/15 = 951.~~063~~{{c}}, ~10/7 = 617.~~584~~{{c}}

* CWE: ~17/12 = 600.0000{{c}}, ~26/15 = 951.0626{{c}}, ~10/7 = 617.5842{{c}}

{{Optimal ET sequence|legend=0| 58, 72, 130, 140, 198, 212g, 270g, 342fg, 482fgg }}

Badness (Sintel): 0.720

Line 323:

Line 351:

[[Comma list]]: 2401/2400, 3025/3024

: Mapping generators: ~2, ~49/40, ~55/42

: Mapping generators: ~2, ~49/40, ~84/55

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.0491{{c}}, ~49/40 = 350.9820{{c}}, ~84/55 = 733.3514{{c}}

: [[error map]]: {{val| +0.030 -0.012 +0.074 -0.109 -0.055 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 350.9890{{c}}, ~84/55 = 733.3160{{c}}

: error map: {{val| 0.000 -0.042 +0.046 -0.168 -0.126 }}

[[Minimax tuning]]:

* [[11-odd-limit]] ~~eigenmonzos~~ (unchanged-~~intervals~~): 2~~, 14/~~11~~, 4~~/3

* [[11-odd-limit]] [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3.11/7

{{Optimal ET sequence|legend=1| 31, 41, 72, 167, 188, 198, 239, 270, 342, 612, 954, 1566, 3101de, 3443de, 4055de, 4397cdee, 4667dee, 5009cddee }}

[[Badness]] (~~Smith~~): 0.~~170 × 10-3~~

[[Badness]] (Sintel): 0.204

[[Projection pair]]s: ~3 = ~2401/800, ~5 = ~22880495169/4575312500, ~7 = ~1058841/151250, ~11 = ~33275/3024 to 2.49/5.77/3

Line 340:

Line 374:

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

Mapping: {{mapping| 1 1 ~~3 3 2 4~~ | 0 2 3 2 1 -9 | 0 0 -4 -2 3 6 }}

Mapping: {{mapping| 1 1 -1 1 5 10 | 0 2 3 2 1 -9 | 0 0 4 2 -3 -6 }}

Optimal tunings:

* WE: ~2 = 1199.9870{{c}}, ~49/40 = 351.0502{{c}}, ~84/55 = 733.2969{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0534{{c}}, ~84/55 = 733.3055{{c}}

{{Optimal ET sequence|legend=0| 31, 41, 72f, 198f, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615 }}

Badness (~~Smith~~): 0.~~855 × 10-3~~

Badness (Sintel): 0.800

Projection pairs: <code>3 2401/800, 5 22880495169/4575312500, 7 1058841/151250, 11 33275/3024, 13 1814078464000000000000000/139662717676432916098329</code> to 2.49/5.77/3

Line 355:

Line 393:

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

Mapping: {{mapping| 1 1 ~~3 3 2 0~~ | 0 2 3 2 1 6 | 0 0 -4 -2 3 5 }}

Mapping: {{mapping| 1 1 -1 1 5 5 | 0 2 3 2 1 6 | 0 0 4 2 -3 -5 }}

Optimal tunings:

* WE: ~2 = 1199.9994{{c}}, ~49/40 = 351.0880{{c}}, ~84/55 = 733.2478{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0880{{c}}, ~84/55 = 733.2482{{c}}

{{Optimal ET sequence|legend=0| 13cdf, 31f, 41, 72, 157, 185cf, 198, 270, 581, 851, 1504, 1774f, 2085, 2355f }}

Badness (~~Smith~~): 0.~~581 × 10-3~~

Badness (Sintel): 0.543

==== 17-limit ====

Line 366:

Line 408:

Comma list: 1225/1224, 2058/2057, 2080/2079, 2401/2400

Mapping: {{mapping| 1 1 ~~3 3 2 0 7~~ | 0 2 3 2 1 6 6 | 0 0 -4 -2 3 5 -12 }}

Mapping: {{mapping| 1 1 -1 1 5 5 -5 | 0 2 3 2 1 6 6 | 0 0 4 2 -3 -5 12 }}

Optimal tunings:

* WE: ~2 = 1200.0038{{c}}, ~49/40 = 351.0756{{c}}, ~84/55 = 733.2270{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0755{{c}}, ~84/55 = 733.2246{{c}}

{{Optimal ET sequence|legend=0| 41g, 72, 198g, 239f, 270, 311, 509, 581, 1234, 1815 }}

Badness (~~Smith~~): 0.~~700 × 10-3~~

Badness (Sintel): 0.665

==== 19-limit ====

Line 377:

Line 423:

Comma list: 1225/1224, 1540/1539, 2080/2079, 3136/3135, 4200/4199

Mapping: {{mapping| 1 1 3 ~~3 2 0 7 6~~ | 0 2 3 2 1 6 6 -2 | 0 0 -4 -2 3 5 -12 -3 }}

Mapping: {{mapping| 1 1 -1 1 5 5 -5 3 | 0 2 3 2 1 6 6 -2 | 0 0 4 2 -3 -5 12 3 }}

: ~~Mapping generators~~: ~2, ~49/40, ~55/42

Optimal tunings:

* WE: ~2 = 1200.0015{{c}}, ~49/40 = 351.0770{{c}}, ~84/55 = 733.2252{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0768{{c}}, ~84/55 = 733.2243{{c}}

{{Optimal ET sequence|legend=0| 41g, 72, 198g, 239f, 270, 311, 581, 1234, 1815 }}

Badness (~~Smith~~): 0.~~692 × 10-3~~

Badness (Sintel): 0.712

=== Heimlaug ===

Line 391:

Line 440:

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

Mapping: {{mapping| 1 1 ~~3 3 2 7~~ | 0 2 3 2 1 6 | 0 0 -4 -2 3 -13 }}

Mapping: {{mapping| 1 1 -1 1 5 -6 | 0 2 3 2 1 6 | 0 0 4 2 -3 13 }}

{{~~Optimal ET sequence|legend~~=~~0| 8bcef~~, ~~15bbccdeeff~~, ~~23bcf~~, ~~31, 72, 103, 167, 198, 270, 571, 643, 913f~~ }}

Optimal tunings:

* WE: ~2 = 1200.0601{{c}}, ~49/40 = 350.9562{{c}}, ~84/55 = 733.4471{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 350.9646{{c}}, ~84/55 = 733.4049{{c}}

Badness (~~Smith~~): 0.~~601 × 10-3~~

{{Optimal ET sequence|legend=0| 31, 72, 103, 167, 198, 270, 571, 643, 913f }}

Badness (Sintel): 0.562

==== 17-limit ====

Line 404:

Line 457:

Comma list: 715/714, 936/935, 1001/1000, 1225/1224, 1716/1715

Mapping: {{mapping| 1 1 ~~3 3 2 7 7~~ | 0 2 3 2 1 6 6 | 0 0 -4 -2 3 -13 -12 }}

Mapping: {{mapping| 1 1 -1 1 5 -6 -5 | 0 2 3 2 1 6 6 | 0 0 4 2 -3 13 12 }}

~~: Mapping generators: ~2, ~49/40, ~17/13~~

{{~~Optimal ET sequence|legend~~=~~0| 8bcefg~~, ~~15bbccdeeffggg~~, ~~23bcfg~~, ~~31, 64be, 72, 103, 167, 198g, 239, 270~~ }}

Optimal tunings:

* WE: ~2 = 1200.0446{{c}}, ~49/40 = 350.9662{{c}}, ~26/17 = 733.3826{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 350.9724{{c}}, ~26/17 = 733.3515{{c}}

Badness (~~Smith~~): 0.~~829 × 10-3~~

{{Optimal ET sequence|legend=0| 31, 64be, 72, 103, 167, 198g, 239, 270 }}

Badness (Sintel): 0.789

== Vili ==

Line 416:

Line 472:

[[Comma list]]: 2401/2400, 391314/390625

: Mapping generators: ~2, ~49/40, ~175/132

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9872{{c}}, ~49/40 = 350.9740{{c}}, ~175/132 = 488.9418{{c}}

: [[error map]]: {{val| -0.013 -0.020 +0.272 -0.065 -0.238 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 350.9728{{c}}, ~175/132 = 488.9475{{c}}

: error map: {{val| 0.000 -0.009 +0.290 -0.038 -0.216 }}

{{Optimal ET sequence|legend=1| 27e, 64be, 76e, 93, 103, 130, 233, 243e, 270, 643, 670, 913, 1043, 1313, 1583 }}

[[Badness]] (~~Smith~~): 1.~~26 × 10-3~~

[[Badness]] (Sintel): 1.51

=== 13-limit ===

Line 427:

Line 490:

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

Mapping: {{mapping| 1 1 ~~5 4 10~~ 4 | 0 2 3 2 6 1 | 0 0 -6 -3 -14 -1 }}

Mapping: {{mapping| 1 1 -1 1 -4 3 | 0 2 3 2 6 1 | 0 0 6 3 14 1 }}

Optimal tunings:

* WE: ~2 = 1200.0597{{c}}, ~49/40 = 350.9419{{c}}, ~65/49 = 488.9741{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 350.9441{{c}}, ~65/49 = 488.9475{{c}}

{{Optimal ET sequence|legend=0| 27e, 37, 64be, 76e, 93, 103, 130, 233, 243e, 270, 643, 913f }}

Badness (~~Smith~~): 0.~~738 × 10-3~~

Badness (Sintel): 0.690

== Frigg ==

Line 438:

Line 505:

[[Comma list]]: 2401/2400, 644204/643125

: Mapping generators: ~2, ~49/40, ~88/49

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.0183{{c}}, ~49/40 = 350.9854{{c}}, ~88/49 = 1013.3709{{c}}

: [[error map]]: {{val| +0.018 +0.034 +0.223 -0.037 -0.425 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 350.9871{{c}}, ~88/49 = 1013.3556{{c}}

: error map: {{val| 0.000 +0.019 +0.203 -0.074 -0.458 }}

{{Optimal ET sequence|legend=1| 45e, 58, 103, 161, 212, 270, 643, 913, 1183e }}

[[Badness]] (~~Smith~~): 1.~~79 × 10-3~~

[[Badness]] (Sintel): 2.15

=== 13-limit ===

Line 449:

Line 523:

Comma list: 1001/1000, 1716/1715, 10648/10647

Mapping: {{mapping| 1 1 ~~3 3 4 5~~ | 0 2 3 2 4 3 | 0 0 -10 -5 -11 -14 }}

Mapping: {{mapping| 1 1 -7 -2 -7 -9 | 0 2 3 2 4 3 | 0 0 10 5 11 14 }}

Optimal tunings:

* WE: ~2 = 1200.0387{{c}}, ~49/40 = 350.9502{{c}}, ~70/39 = 1013.4065{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 350.9526{{c}}, ~70/39 = 1013.3747{{c}}

{{Optimal ET sequence|legend=0| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} <nowiki>*</nowiki>

<nowiki>*</nowiki> [[optimal patent val]]: [[1241edo|1241]]

Badness (~~Smith~~): 0.~~934 × 10-3~~

Badness (Sintel): 0.873

== Ennealimmic ==

Line 466:

Line 544:

: Mapping generators: ~27/25, ~5/3, ~11

{{Optimal ET sequence|legend=1| ~~27, 45~~, 72, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd }}

[[Optimal tuning]]s:

* [[WE]]: ~27/25 = 133.3357{{c}}, ~5/3 = 884.3288{{c}}, ~11/8 = 551.2529{{c}}

: [[error map]]: {{val| +0.021 +0.038 +0.009 -0.139 -0.000 }}

* [[CWE]]: ~27/25 = 133.3333{{c}}, ~5/3 = 884.3215{{c}}, ~11/8 = 551.2775{{c}}

: error map: {{val| 0.000 +0.021 -0.016 -0.183 -0.040 }}

{{Optimal ET sequence|legend=1| 72, …, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd, 6903dd }}

[[Badness]] (~~Smith~~): 0.~~275 × 10-3~~

[[Badness]] (Sintel): 0.330

=== 13-limit ===

Line 477:

Line 561:

Mapping: {{mapping| 9 1 1 12 0 -31 | 0 2 3 2 0 5 | 0 0 0 0 1 1 }}

{{Optimal ET sequence|legend=0| 27, ~~45f, 54cff, 72~~, 171, 198, 270, 639, 711, 981, 1692e }}

Optimal tunings:

* WE: ~27/25 = 133.3276{{c}}, ~5/3 = 884.3660{{c}}, ~11/8 = 551.7221{{c}}

* CWE: ~27/25 = 133.3333{{c}}, ~5/3 = 884.3905{{c}}, ~11/8 = 551.7085{{c}}

{{Optimal ET sequence|legend=0| 72, …, 171, 198, 270, 639, 711, 981, 1692e }}

Badness (~~Smith~~): 0.~~755 × 10-3~~

Badness (Sintel): 0.706

[[Category:Temperament families]]

@@ Line 17: / Line 17: @@
 : 49/40 length = 0.7858, 8/7 length = 1.1241
 : Angle (49/40, 8/7) = 107.367°
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0206{{c}}, ~49/40 = 350.9724{{c}}, ~10/7 = 617.6826{{c}}
+: [[error map]]: {{val| +0.021 +0.010 +0.044 -0.130 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 350.9743{{c}}, ~10/7 = 617.6807{{c}}
+: error map: {{val| 0.000 -0.006 +0.022 -0.171 }}
 [[Minimax tuning]]:
 * [[7-odd-limit|7-]] and [[9-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.5
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1200.021{{c}}, ~49/40 = 350.972{{c}}, ~10/7 = 617.683{{c}}
-* [[CWE]]: ~2 = 1200.000{{c}}, ~49/40 = 350.974{{c}}, ~10/7 = 617.681{{c}}
 {{Optimal ET sequence|legend=1| 27, 31, 41, 58, 68, 72, 99, 171, 441, 612, 1966, 2308, 2578, 2749, 3361d }}
-[[Badness]] (Sintel): 0.067
+[[Badness]] (Sintel): 0.0674
 [[Projection pair]]: <code>3 2401/800</code> to 2.5.7
@@ Line 46: / Line 48: @@
 {{Mapping|legend=1| 1 1 1 2 2 | 0 2 1 1 5 | 0 0 2 1 0 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0985{{c}}, ~11/9 = 350.5322{{c}}, ~10/7 = 617.8782{{c}}
+: [[error map]]: {{val| +0.098 -0.792 +0.073 -0.218 +1.540 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/9 = 350.5374{{c}}, ~10/7 = 617.8712{{c}}
+: error map: {{val| 0.000 -0.880 -0.034 -0.417 +1.369 }}
 [[Minimax tuning]]:
-* [[11-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11
+* [[11-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1200.098{{c}}, ~11/9 = 350.532{{c}}, ~10/7 = 617.878{{c}}
-* [[CWE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.537{{c}}, ~10/7 = 617.871{{c}}
 {{Optimal ET sequence|legend=1| 27e, 31, 41, 58, 72, 130, 202 }}
@@ Line 66: / Line 70: @@
 Mapping: {{mapping| 1 1 1 2 2 1 | 0 2 1 1 5 11 | 0 0 2 1 0 -1 }}
+Optimal tunings:
+* WE: ~2 = 1199.9775{{c}}, ~11/9 = 350.7113{{c}}, ~10/7 = 617.8170{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 350.7130{{c}}, ~10/7 = 617.8178{{c}}
 Minimax tuning:
 * 13-odd-limit unchanged-interval (eigenmonzo) basis: 2.9/5.13/9
 * 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7/5.15/13
-Optimal tunings:
-* WE: ~2 = 1199.977{{c}}, ~11/9 = 350.711{{c}}, ~10/7 = 617.817{{c}}
-* CWE: ~2 = 1200.000{{c}}, ~11/9 = 350.713{{c}}, ~10/7 = 617.818{{c}}
 {{Optimal ET sequence|legend=0| 27eff, 31f, 41, 58, 72, 130, 243, 301e, 373e }}
@@ Line 85: / Line 89: @@
 Mapping: {{mapping| 1 1 1 2 2 1 3 | 0 2 1 1 5 11 9 | 0 0 2 1 0 -1 -3 }}
+Optimal tunings:
+* WE: ~2 = 1200.0876{{c}}, ~11/9 = 350.7203{{c}}, ~10/7 = 617.5766{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 350.7138{{c}}, ~10/7 = 617.5610{{c}}
 Minimax tuning:
 * 17-odd-limit unchanged-interval (eigenmonzo) basis: 2.5/3.17/9
-Optimal tunings:
-* WE: ~2 = 1200.088{{c}}, ~11/9 = 350.720{{c}}, ~10/7 = 617.577{{c}}
-* CWE: ~2 = 1200.000{{c}}, ~11/9 = 350.714{{c}}, ~10/7 = 617.561{{c}}
 {{Optimal ET sequence|legend=0| 27effg, 31fg, 41, 58, 72, 130, 171, 243 }}
@@ Line 103: / Line 107: @@
 Mapping: {{mapping| 1 1 1 2 2 1 3 | 0 4 0 1 10 23 12 | 0 0 2 1 0 -1 -1 }}
 : Mapping generators: ~2, ~119/108, ~27/17
 Optimal tunings:
-* WE: ~2 = 1199.559{{c}}, ~119/108 = 175.353{{c}}, ~27/17 = 793.685{{c}}
+* WE: ~2 = 1199.5594{{c}}, ~119/108 = 175.3533{{c}}, ~27/17 = 793.6847{{c}}
-* CWE: ~2 = 1200.000{{c}}, ~119/108 = 175.371{{c}}, ~27/17 = 793.756{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~119/108 = 175.3707{{c}}, ~27/17 = 793.7559{{c}}
-{{Optimal ET sequence|legend=0| 14cf, 27effg, 41, 89, 130g }}
+{{Optimal ET sequence|legend=0| 14cf, 27effg, 41, 75ce, 89, 116cefg, 130g }}
-Badness (Sintel): 2.843
+Badness (Sintel): 2.84
 ===== 19-limit =====
@@ Line 122: / Line 125: @@
 Optimal tunings:
-* WE: ~2 = 1199.733{{c}}, ~21/19 = 175.347{{c}}, ~19/12 = 793.779{{c}}
+* WE: ~2 = 1199.7333{{c}}, ~21/19 = 175.3472{{c}}, ~19/12 = 793.7794{{c}}
-* CWE: ~2 = 1200.000{{c}}, ~21/19 = 175.358{{c}}, ~19/12 = 793.819{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~21/19 = 175.3584{{c}}, ~19/12 = 793.8194{{c}}
-{{Optimal ET sequence|legend=0| 14cf, 27effg, 41, 89, 130g }}
+{{Optimal ET sequence|legend=0| 14cf, 27effg, 41, 75ce, 89, 116cefg, 130g }}
-Badness (Sintel): 2.294
+Badness (Sintel): 2.29
 === Jofur ===
@@ Line 137: / Line 140: @@
 Optimal tunings:
-* WE: ~2 = 1198.953{{c}}, ~11/9 = 351.141{{c}}, ~10/7 = 618.349{{c}}
+* WE: ~2 = 1198.9534{{c}}, ~11/9 = 351.1412{{c}}, ~10/7 = 618.3494{{c}}
-* CWE: ~2 = 1200.000{{c}}, ~11/9 = 351.254{{c}}, ~10/7 = 618.593{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.2536{{c}}, ~10/7 = 618.5932{{c}}
 {{Optimal ET sequence|legend=0| 27e, 31, 41, 58, 99ef, 157eff }}
@@ Line 152: / Line 155: @@
 Optimal tunings:
-* WE: ~2 = 1200.144{{c}}, ~11/9 = 350.435{{c}}, ~10/7 = 618.177{{c}}
+* WE: ~2 = 1200.1435{{c}}, ~11/9 = 350.4354{{c}}, ~10/7 = 618.1775{{c}}
-* CWE: ~2 = 1200.000{{c}}, ~11/9 = 350.440{{c}}, ~10/7 = 618.176{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 350.4402{{c}}, ~10/7 = 618.1759{{c}}
 {{Optimal ET sequence|legend=0| 27e, 31, 45ef, 58, 72, 103, 130, 233, 363 }}
@@ Line 171: / Line 174: @@
 : 49/40 length = 0.756, 10/7 length = 0.819
 : Angle (49/40, 10/7) = 106.460 degrees
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.4168{{c}}, ~49/40 = 350.8363{{c}}, ~10/7 = 617.2187{{c}}
+: [[error map]]: {{val| +0.417 +0.134 -0.623 +0.063 -0.890 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 350.8369{{c}}, ~10/7 = 616.9907{{c}}
+: error map: {{val| 0.000 -0.281 -1.495 -0.998 -2.290 }}
 [[Minimax tuning]]:
 * [[11-odd-limit]]
 : [{{monzo| 1 0 0 0 0 }}, {{monzo| 0 1 0 0 0 }}, {{monzo| 23/10 3/10 2/5 0 -2/5 }}, {{monzo| 12/5 2/5 1/5 0 -1/5 }}, {{monzo| 23/10 3/10 -3/5 0 3/5 }}]
-: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.11/5
+: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.11/5
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1200.417{{c}}, ~49/40 = 350.836{{c}}, ~10/7 = 617.219{{c}}
-* [[CWE]]: ~2 = 1200.000{{c}}, ~49/40 = 350.837{{c}}, ~10/7 = 616.991{{c}}
 {{Optimal ET sequence|legend=1| 27, 31, 41, 68, 72, 140, 171e, 212, 284, 496ce, 527cee, 739cdeee, 811ccdeee, 1023ccdeee }}
@@ Line 193: / Line 198: @@
 Optimal tunings:
-* WE: ~2 = 1200.441{{c}}, ~49/40 = 350.809{{c}}, ~10/7 = 617.372{{c}}
+* WE: ~2 = 1200.4413{{c}}, ~49/40 = 350.8092{{c}}, ~10/7 = 617.3718{{c}}
-* CWE: ~2 = 1200.000{{c}}, ~49/40 = 350.805{{c}}, ~10/7 = 617.157{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 350.8046{{c}}, ~10/7 = 617.1572{{c}}
 {{Optimal ET sequence|legend=0| 31, 68, 72, 103, 140, 212, 243e, 315ef, 455eef, 770cdeeeff }}
@@ Line 206: / Line 211: @@
 {{Mapping|legend=1| 1 1 1 2 -3 | 0 2 1 1 8 | 0 0 2 1 8 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9178{{c}}, ~49/40 = 350.0519{{c}}, ~10/7 = 617.8150{{c}}
+: [[error map]]: {{val| -0.082 +0.067 +0.286 -0.123 -0.135 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 350.0615{{c}}, ~10/7 = 617.8571{{c}}
+: error map: {{val| 0.000 +0.168 +0.462 +0.093 +0.032 }}
 {{Optimal ET sequence|legend=1| 31, 68e, 99e, 130, 239, 270, 670, 940, 1210, 2150c }}
-[[Badness]] (Smith): 0.640 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.769
 === 13-limit ===
@@ Line 217: / Line 228: @@
 Mapping: {{mapping| 1 1 1 2 -3 7 | 0 2 1 1 8 -6 | 0 0 2 1 8 -3 }}
+Optimal tunings:
+* WE: ~2 = 1199.9787{{c}}, ~49/40 = 350.9976{{c}}, ~10/7 = 617.8701{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0039{{c}}, ~10/7 = 617.8795{{c}}
 {{Optimal ET sequence|legend=0| 31, 78f, 99e, 109, 130, 239, 270, 571, 701, 841, 971, 1241 }}
-Badness (Smith): 0.830 × 10<sup>-3</sup>
+Badness (Sintel): 0.776
 == Lif ==
@@ Line 229: / Line 244: @@
 {{Mapping|legend=1| 1 1 1 2 8 | 0 2 1 1 -12 | 0 0 2 1 -2 }}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~49/40 = 351.0959{{c}}, ~10/7 = 617.6652{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9386{{c}}, ~49/40 = 350.0586{{c}}, ~10/7 = 617.7065{{c}}
+: [[error map]]: {{val| -0.061 +0.101 +0.096 -0.184 +0.075 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.0806{{c}}, ~10/7 = 617.7228{{c}}
+: error map: {{val| 0.000 +0.206 +0.213 -0.022 +0.269 }}
+<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.0959{{c}}, ~10/7 = 617.6652{{c}} -->
 {{Optimal ET sequence|legend=1| 41, 89, 130, 229, 270, 581, 670, 711, 981, 1251, 2232e }}
-[[Badness]] (Smith): 0.793 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.953
 === 13-limit ===
@@ Line 242: / Line 262: @@
 Mapping: {{mapping| 1 1 1 2 8 7 | 0 2 1 1 -12 -6 | 0 0 2 1 -2 -3 }}
-Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~49/40 = 351.0960{{c}}, ~10/7 = 617.6533{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9597{{c}}, ~49/40 = 351.0718{{c}}, ~10/7 = 617.6543{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0856{{c}}, ~10/7 = 617.6715{{c}}
+<!-- * CTE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0960{{c}}, ~10/7 = 617.6533{{c}} -->
 {{Optimal ET sequence|legend=0| 41, 89, 99, 130, 270, 581, 711, 981, 1292, 1562 }}
-Badness (Smith): 0.579 × 10<sup>-3</sup>
+Badness (Sintel): 0.542
 === 2.3.5.7.11.13.19 subgroup ===
@@ Line 253: / Line 276: @@
 Comma list: 1216/1215, 1729/1728, 2080/2079, 2401/2400
-Sval mapping: {{mapping| 1 1 1 2 8 7 0 | 0 2 1 1 -12 -6 11 | 0 0 2 1 -2 -3 2 }}
+Subgroup-val mapping: {{mapping| 1 1 1 2 8 7 0 | 0 2 1 1 -12 -6 11 | 0 0 2 1 -2 -3 2 }}
-Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~49/40 = 351.1007{{c}}, ~10/7 = 617.6501{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9752{{c}}, ~49/40 = 351.0908{{c}}, ~10/7 = 617.6473{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0984{{c}}, ~10/7 = 617.6588{{c}}
+<!-- * CTE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1007{{c}}, ~10/7 = 617.6501{{c}} -->
 {{Optimal ET sequence|legend=0| 41, 89, 130, 229, 270, 581, 851, 1562, 1832, 2413 }}
-Badness (Smith): 0.499 × 10<sup>-3</sup>
+Badness (Sintel): 0.488
 == Baldur ==
@@ Line 268: / Line 294: @@
 {{Mapping|legend=1| 2 0 1 3 7 | 0 2 1 1 -2 | 0 0 2 1 3 }}
 : Mapping generators: ~99/70, ~343/198, ~10/7
+[[Optimal tuning]]s:
+* [[WE]]: ~99/70 = 600.0149{{c}}, ~343/198 = 950.9717{{c}}, ~10/7 = 617.7007{{c}}
+: [[error map]]: {{val| +0.030 -0.012 +0.074 -0.109 -0.055 }}
+* [[CWE]]: ~99/70 = 600.0000{{c}}, ~343/198 = 950.9565{{c}}, ~10/7 = 617.7017{{c}}
+: error map: {{val| 0.000 -0.042 +0.046 -0.168 -0.126 }}
 [[Minimax tuning]]:
 * [[11-odd-limit]]
 : [{{monzo| 1 0 0 0 0 }}, {{monzo| 3/4 0 1/2 1/2 -1/2 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 23/16 0 5/8 1/8 -1/8 }}, {{monzo| 23/16 0 5/8 -7/8 7/8 }}]
-: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.11/7
+: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.11/7
-[[Optimal tuning]]s:
-* [[WE]]: ~99/70 = 600.015{{c}}, ~343/198 = 950.972{{c}}, ~10/7 = 617.701{{c}}
-* [[CWE]]: ~99/70 = 600.000{{c}}, ~343/198 = 950.956{{c}}, ~10/7 = 617.702{{c}}
 {{Optimal ET sequence|legend=1| 58, 72, 130, 198, 212, 270, 342, 612, 954, 1084, 1354, 1696, 4004de, 5700de }}
@@ Line 282: / Line 310: @@
 [[Badness]] (Sintel): 0.200
-[[Projection pair]]s: ~2 = ~9801/4900, ~3 = ~117649/39204, ~7 = ~9801/1400, ~11 =  ~913517247483640899/83082326424002500 to 5.7/2.99/4
+[[Projection pair]]s: <code>2 9801/4900, 3 117649/39204, 7 9801/1400, 11 913517247483640899/83082326424002500</code> to 5.7/2.99/4
 === Greenland ===
@@ Line 292: / Line 320: @@
 Optimal tunings:
-* WE: ~99/70 = 599.987{{c}}, ~26/15 = 951.054{{c}}, ~10/7 = 617.806{{c}}
+* WE: ~99/70 = 599.9868{{c}}, ~26/15 = 951.0538{{c}}, ~10/7 = 617.8062{{c}}
-* CWE: ~99/70 = 600.000{{c}}, ~26/15 = 951.069{{c}}, ~10/7 = 617.807{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~26/15 = 951.0689{{c}}, ~10/7 = 617.8067{{c}}
 {{Optimal ET sequence|legend=0| 58, 72, 130, 198, 270, 940, 1210f }}
@@ Line 311: / Line 339: @@
 Optimal tunings:
-* WE: ~17/12 = 600.112{{c}}, ~26/15 = 951.191{{c}}, ~10/7 = 617.610{{c}}
+* WE: ~17/12 = 600.1118{{c}}, ~26/15 = 951.1907{{c}}, ~10/7 = 617.6100{{c}}
-* CWE: ~17/12 = 600.000{{c}}, ~26/15 = 951.063{{c}}, ~10/7 = 617.584{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~26/15 = 951.0626{{c}}, ~10/7 = 617.5842{{c}}
-{{Optimal ET sequence|legend=0| 58, 72, 130, 140, 198, 270g }}
+{{Optimal ET sequence|legend=0| 58, 72, 130, 140, 198, 212g, 270g, 342fg, 482fgg }}
 Badness (Sintel): 0.720
@@ Line 323: / Line 351: @@
 [[Comma list]]: 2401/2400, 3025/3024
-{{Mapping|legend=1| 1 1 3 3 2 | 0 2 3 2 1 | 0 0 -4 -2 3 }}
+{{Mapping|legend=1| 1 1 -1 1 5 | 0 2 3 2 1 | 0 0 4 2 -3 }}
-: Mapping generators: ~2, ~49/40, ~55/42
+: Mapping generators: ~2, ~49/40, ~84/55
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0491{{c}}, ~49/40 = 350.9820{{c}}, ~84/55 = 733.3514{{c}}
+: [[error map]]: {{val| +0.030 -0.012 +0.074 -0.109 -0.055 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 350.9890{{c}}, ~84/55 = 733.3160{{c}}
+: error map: {{val| 0.000 -0.042 +0.046 -0.168 -0.126 }}
 [[Minimax tuning]]:
-* [[11-odd-limit]] eigenmonzos (unchanged-intervals): 2, 14/11, 4/3
+* [[11-odd-limit]] [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3.11/7
 {{Optimal ET sequence|legend=1| 31, 41, 72, 167, 188, 198, 239, 270, 342, 612, 954, 1566, 3101de, 3443de, 4055de, 4397cdee, 4667dee, 5009cddee }}
-[[Badness]] (Smith): 0.170 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.204
 [[Projection pair]]s: ~3 = ~2401/800, ~5 = ~22880495169/4575312500, ~7 = ~1058841/151250, ~11 = ~33275/3024 to 2.49/5.77/3
@@ Line 340: / Line 374: @@
 Comma list: 2401/2400, 3025/3024, 4096/4095
-Mapping: {{mapping| 1 1 3 3 2 4 | 0 2 3 2 1 -9 | 0 0 -4 -2 3 6 }}
+Mapping: {{mapping| 1 1 -1 1 5 10 | 0 2 3 2 1 -9 | 0 0 4 2 -3 -6 }}
+Optimal tunings:
+* WE: ~2 = 1199.9870{{c}}, ~49/40 = 351.0502{{c}}, ~84/55 = 733.2969{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0534{{c}}, ~84/55 = 733.3055{{c}}
 {{Optimal ET sequence|legend=0| 31, 41, 72f, 198f, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615 }}
-Badness (Smith): 0.855 × 10<sup>-3</sup>
+Badness (Sintel): 0.800
 Projection pairs: <code>3 2401/800, 5 22880495169/4575312500, 7 1058841/151250, 11 33275/3024, 13 1814078464000000000000000/139662717676432916098329</code> to 2.49/5.77/3
@@ Line 355: / Line 393: @@
 Comma list: 2080/2079, 2401/2400, 3025/3024
-Mapping: {{mapping| 1 1 3 3 2 0 | 0 2 3 2 1 6 | 0 0 -4 -2 3 5 }}
+Mapping: {{mapping| 1 1 -1 1 5 5 | 0 2 3 2 1 6 | 0 0 4 2 -3 -5 }}
+Optimal tunings:
+* WE: ~2 = 1199.9994{{c}}, ~49/40 = 351.0880{{c}}, ~84/55 = 733.2478{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0880{{c}}, ~84/55 = 733.2482{{c}}
 {{Optimal ET sequence|legend=0| 13cdf, 31f, 41, 72, 157, 185cf, 198, 270, 581, 851, 1504, 1774f, 2085, 2355f }}
-Badness (Smith): 0.581 × 10<sup>-3</sup>
+Badness (Sintel): 0.543
 ==== 17-limit ====
@@ Line 366: / Line 408: @@
 Comma list: 1225/1224, 2058/2057, 2080/2079, 2401/2400
-Mapping: {{mapping| 1 1 3 3 2 0 7 | 0 2 3 2 1 6 6 | 0 0 -4 -2 3 5 -12 }}
+Mapping: {{mapping| 1 1 -1 1 5 5 -5 | 0 2 3 2 1 6 6 | 0 0 4 2 -3 -5 12 }}
+Optimal tunings:
+* WE: ~2 = 1200.0038{{c}}, ~49/40 = 351.0756{{c}}, ~84/55 = 733.2270{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0755{{c}}, ~84/55 = 733.2246{{c}}
 {{Optimal ET sequence|legend=0| 41g, 72, 198g, 239f, 270, 311, 509, 581, 1234, 1815 }}
-Badness (Smith): 0.700 × 10<sup>-3</sup>
+Badness (Sintel): 0.665
 ==== 19-limit ====
@@ Line 377: / Line 423: @@
 Comma list: 1225/1224, 1540/1539, 2080/2079, 3136/3135, 4200/4199
-Mapping: {{mapping| 1 1 3 3 2 0 7 6 | 0 2 3 2 1 6 6 -2 | 0 0 -4 -2 3 5 -12 -3 }}
+Mapping: {{mapping| 1 1 -1 1 5 5 -5 3 | 0 2 3 2 1 6 6 -2 | 0 0 4 2 -3 -5 12 3 }}
-: Mapping generators: ~2, ~49/40, ~55/42
+Optimal tunings:
+* WE: ~2 = 1200.0015{{c}}, ~49/40 = 351.0770{{c}}, ~84/55 = 733.2252{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0768{{c}}, ~84/55 = 733.2243{{c}}
 {{Optimal ET sequence|legend=0| 41g, 72, 198g, 239f, 270, 311, 581, 1234, 1815 }}
-Badness (Smith): 0.692 × 10<sup>-3</sup>
+Badness (Sintel): 0.712
 === Heimlaug ===
@@ Line 391: / Line 440: @@
 Comma list: 1001/1000, 1716/1715, 3025/3024
-Mapping: {{mapping| 1 1 3 3 2 7 | 0 2 3 2 1 6 | 0 0 -4 -2 3 -13 }}
+Mapping: {{mapping| 1 1 -1 1 5 -6 | 0 2 3 2 1 6 | 0 0 4 2 -3 13 }}
-{{Optimal ET sequence|legend=0| 8bcef, 15bbccdeeff, 23bcf, 31, 72, 103, 167, 198, 270, 571, 643, 913f }}
+Optimal tunings:
+* WE: ~2 = 1200.0601{{c}}, ~49/40 = 350.9562{{c}}, ~84/55 = 733.4471{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 350.9646{{c}}, ~84/55 = 733.4049{{c}}
-Badness (Smith): 0.601 × 10<sup>-3</sup>
+{{Optimal ET sequence|legend=0| 31, 72, 103, 167, 198, 270, 571, 643, 913f }}
+Badness (Sintel): 0.562
 ==== 17-limit ====
@@ Line 404: / Line 457: @@
 Comma list: 715/714, 936/935, 1001/1000, 1225/1224, 1716/1715
-Mapping: {{mapping| 1 1 3 3 2 7 7 | 0 2 3 2 1 6 6 | 0 0 -4 -2 3 -13 -12 }}
+Mapping: {{mapping| 1 1 -1 1 5 -6 -5 | 0 2 3 2 1 6 6 | 0 0 4 2 -3 13 12 }}
-: Mapping generators: ~2, ~49/40, ~17/13
-{{Optimal ET sequence|legend=0| 8bcefg, 15bbccdeeffggg, 23bcfg, 31, 64be, 72, 103, 167, 198g, 239, 270 }}
+Optimal tunings:
+* WE: ~2 = 1200.0446{{c}}, ~49/40 = 350.9662{{c}}, ~26/17 = 733.3826{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 350.9724{{c}}, ~26/17 = 733.3515{{c}}
-Badness (Smith): 0.829 × 10<sup>-3</sup>
+{{Optimal ET sequence|legend=0| 31, 64be, 72, 103, 167, 198g, 239, 270 }}
+Badness (Sintel): 0.789
 == Vili ==
@@ Line 416: / Line 472: @@
 [[Comma list]]: 2401/2400, 391314/390625
-{{Mapping|legend=1| 1 1 5 4 10 | 0 2 3 2 6 | 0 0 -6 -3 -14 }}
+{{Mapping|legend=1| 1 1 -1 1 -4 | 0 2 3 2 6 | 0 0 6 3 14 }}
+: Mapping generators: ~2, ~49/40, ~175/132
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9872{{c}}, ~49/40 = 350.9740{{c}}, ~175/132 = 488.9418{{c}}
+: [[error map]]: {{val| -0.013 -0.020 +0.272 -0.065 -0.238 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 350.9728{{c}}, ~175/132 = 488.9475{{c}}
+: error map: {{val| 0.000 -0.009 +0.290 -0.038 -0.216 }}
 {{Optimal ET sequence|legend=1| 27e, 64be, 76e, 93, 103, 130, 233, 243e, 270, 643, 670, 913, 1043, 1313, 1583 }}
-[[Badness]] (Smith): 1.26 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 1.51
 === 13-limit ===
@@ Line 427: / Line 490: @@
 Comma list: 1001/1000, 1716/1715, 4225/4224
-Mapping: {{mapping| 1 1 5 4 10 4 | 0 2 3 2 6 1 | 0 0 -6 -3 -14 -1 }}
+Mapping: {{mapping| 1 1 -1 1 -4 3 | 0 2 3 2 6 1 | 0 0 6 3 14 1 }}
+Optimal tunings:
+* WE: ~2 = 1200.0597{{c}}, ~49/40 = 350.9419{{c}}, ~65/49 = 488.9741{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 350.9441{{c}}, ~65/49 = 488.9475{{c}}
 {{Optimal ET sequence|legend=0| 27e, 37, 64be, 76e, 93, 103, 130, 233, 243e, 270, 643, 913f }}
-Badness (Smith): 0.738 × 10<sup>-3</sup>
+Badness (Sintel): 0.690
 == Frigg ==
@@ Line 438: / Line 505: @@
 [[Comma list]]: 2401/2400, 644204/643125
-{{Mapping|legend=1| 1 1 3 3 4 | 0 2 3 2 4 | 0 0 -10 -5 -11 }}
+{{Mapping|legend=1| 1 1 -7 -2 -7 | 0 2 3 2 4 | 0 0 10 5 11 }}
+: Mapping generators: ~2, ~49/40, ~88/49
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0183{{c}}, ~49/40 = 350.9854{{c}}, ~88/49 = 1013.3709{{c}}
+: [[error map]]: {{val| +0.018 +0.034 +0.223 -0.037 -0.425 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 350.9871{{c}}, ~88/49 = 1013.3556{{c}}
+: error map: {{val| 0.000 +0.019 +0.203 -0.074 -0.458 }}
 {{Optimal ET sequence|legend=1| 45e, 58, 103, 161, 212, 270, 643, 913, 1183e }}
-[[Badness]] (Smith): 1.79 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 2.15
 === 13-limit ===
@@ Line 449: / Line 523: @@
 Comma list: 1001/1000, 1716/1715, 10648/10647
-Mapping: {{mapping| 1 1 3 3 4 5 | 0 2 3 2 4 3 | 0 0 -10 -5 -11 -14 }}
+Mapping: {{mapping| 1 1 -7 -2 -7 -9 | 0 2 3 2 4 3 | 0 0 10 5 11 14 }}
+Optimal tunings:
+* WE: ~2 = 1200.0387{{c}}, ~49/40 = 350.9502{{c}}, ~70/39 = 1013.4065{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 350.9526{{c}}, ~70/39 = 1013.3747{{c}}
 {{Optimal ET sequence|legend=0| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} <nowiki>*</nowiki>
 <nowiki>*</nowiki> [[optimal patent val]]: [[1241edo|1241]]
-Badness (Smith): 0.934 × 10<sup>-3</sup>
+Badness (Sintel): 0.873
 == Ennealimmic ==
@@ Line 466: / Line 544: @@
 : Mapping generators: ~27/25, ~5/3, ~11
-{{Optimal ET sequence|legend=1| 27, 45, 72, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd }}
+[[Optimal tuning]]s:
+* [[WE]]: ~27/25 = 133.3357{{c}}, ~5/3 = 884.3288{{c}}, ~11/8 = 551.2529{{c}}
+: [[error map]]: {{val| +0.021 +0.038 +0.009 -0.139 -0.000 }}
+* [[CWE]]: ~27/25 = 133.3333{{c}}, ~5/3 = 884.3215{{c}}, ~11/8 = 551.2775{{c}}
+: error map: {{val| 0.000 +0.021 -0.016 -0.183 -0.040 }}
+{{Optimal ET sequence|legend=1| 72, …, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd, 6903dd }}
-[[Badness]] (Smith): 0.275 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.330
 === 13-limit ===
@@ Line 477: / Line 561: @@
 Mapping: {{mapping| 9 1 1 12 0 -31 | 0 2 3 2 0 5 | 0 0 0 0 1 1 }}
-{{Optimal ET sequence|legend=0| 27, 45f, 54cff, 72, 171, 198, 270, 639, 711, 981, 1692e }}
+Optimal tunings:
+* WE: ~27/25 = 133.3276{{c}}, ~5/3 = 884.3660{{c}}, ~11/8 = 551.7221{{c}}
+* CWE: ~27/25 = 133.3333{{c}}, ~5/3 = 884.3905{{c}}, ~11/8 = 551.7085{{c}}
+{{Optimal ET sequence|legend=0| 72, …, 171, 198, 270, 639, 711, 981, 1692e }}
-Badness (Smith): 0.755 × 10<sup>-3</sup>
+Badness (Sintel): 0.706
 [[Category:Temperament families]]