Breed family: Difference between revisions

Line 1:

The '''breed family''' of [[temperament]]~~s are~~ [[~~Rank-3~~ temperament|~~rank-3~~]] [[microtemperament]]s which [[~~Tempering~~ out|temper out]] [[2401/2400]]~~. While it is so accurate it hardly matters what is used to temper it, or whether it is tempered at all, the [[optimal patent val]] 2749et will certainly do the trick~~.

The '''breed family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperament]]s are [[microtemperament]]s which [[tempering out|temper out]] [[2401/2400]].

== Breed ==

Breed has the same lattice structure as 2.5.7 JI. In terms of extension from the 5-limit, it splits 25/6 into four equal parts representing 10/7.

Breed has the same lattice structure as the [[2.5.7 subgroup]] of JI. In terms of extension from the 5-limit, it splits 25/6 into four equal parts representing 10/7. While it is so accurate it hardly matters what is used to temper it, or whether it is tempered at all, the [[optimal patent val]] [[2749edo|2749et]] will certainly do the trick.

[[Subgroup]]: 2.3.5.7

Line 10:

: Mapping generators: ~2, ~49/40, ~10/7

Line 20:

Line 19:

[[Minimax tuning]]:

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

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

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.~~021¢~~, ~49/40 = 350.~~972¢~~, ~10/7 = 617.~~683¢~~

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

* [[CWE]]: ~2 = 1200.~~000¢~~, ~49/40 = 350.~~974¢~~, ~10/7 = 617.~~681¢~~

* [[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 }}

Line 30:

Line 29:

[[Badness]] (Sintel): 0.067

[[Projection pair]]: ~3 ~~= ~~~2401/800 to 2.5.7

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

Scales: [[breed11]]

Line 52:

Line 51:

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.~~098¢~~, ~11/9 = 350.~~532¢~~, ~10/7 = 617.~~878¢~~

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

* [[CWE]]: ~2 = 1200.~~000¢~~, ~11/9 = 350.~~537¢~~, ~10/7 = 617.~~871¢~~

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

Line 59:

Line 58:

[[Badness]] (Sintel): 0.290

Projection ~~pairs~~: ~3 ~~= ~~~242/81, ~5 ~~= ~~~2200/441, ~7 ~~= ~~~440/63, ~11 ~~= ~~~644204/59049 to 2.7/5.11/9

[[Projection pair]]s: <code>3 242/81, 5 2200/441, 7 440/63, 11 644204/59049</code> to 2.7/5.11/9

=== Jovial ===

Line 73:

Line 72:

Optimal tunings:

* WE: ~2 = 1199.~~977¢~~, ~11/9 = 350.~~711¢~~, ~10/7 = 617.~~817¢~~

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

* CWE: ~2 = 1200.~~000¢~~, ~11/9 = 350.~~713¢~~, ~10/7 = 617.~~818¢~~

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

~~Optimal ET sequence:~~ {{Optimal ET sequence| 27eff, 31f, 41, 58, 72, 130, 243, 301e, 373e }}

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

Badness (Sintel): 0.583

Line 91:

Line 90:

Optimal tunings:

* WE: ~2 = 1200.~~088¢~~, ~11/9 = 350.~~720¢~~, ~10/7 = 617.~~577¢~~

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

* CWE: ~2 = 1200.~~000¢~~, ~11/9 = 350.~~714¢~~, ~10/7 = 617.~~561¢~~

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

~~Optimal ET sequence:~~ {{Optimal ET sequence| 27effg, 31fg, 41, 58, 72, 130, 171, 243 }}

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

Badness (Sintel): 0.704

Line 108:

Line 107:

Optimal tunings:

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

* WE: ~2 = 1199.559{{c}}, ~119/108 = 175.353{{c}}, ~27/17 = 793.685{{c}}

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

* CWE: ~2 = 1200.000{{c}}, ~119/108 = 175.371{{c}}, ~27/17 = 793.756{{c}}

~~Optimal ET sequence:~~ {{Optimal ET sequence| 14cf, 27effg, 41, 89, 130g }}

Badness (Sintel): 2.843

Line 123:

Line 122:

Optimal tunings:

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

* WE: ~2 = 1199.733{{c}}, ~21/19 = 175.347{{c}}, ~19/12 = 793.779{{c}}

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

* CWE: ~2 = 1200.000{{c}}, ~21/19 = 175.358{{c}}, ~19/12 = 793.819{{c}}

~~Optimal ET sequence:~~ {{Optimal ET sequence| 14cf, 27effg, 41, 89, 130g }}

Badness (Sintel): 2.294

Line 138:

Line 137:

Optimal tunings:

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

* WE: ~2 = 1198.953{{c}}, ~11/9 = 351.141{{c}}, ~10/7 = 618.349{{c}}

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

* CWE: ~2 = 1200.000{{c}}, ~11/9 = 351.254{{c}}, ~10/7 = 618.593{{c}}

~~Optimal ET sequence:~~ {{Optimal ET sequence| 27e, 31, 41, 58, 99ef, 157eff }}

Badness (Sintel): 0.701

Line 153:

Line 152:

Optimal tunings:

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

* WE: ~2 = 1200.144{{c}}, ~11/9 = 350.435{{c}}, ~10/7 = 618.177{{c}}

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

* CWE: ~2 = 1200.000{{c}}, ~11/9 = 350.440{{c}}, ~10/7 = 618.176{{c}}

~~Optimal ET sequence:~~ {{Optimal ET sequence| 27e, 31, 45ef, 58, 72, 103, 130, 233, 363 }}

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

Badness (Sintel): 0.507

Line 179:

Line 178:

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.~~417¢~~, ~49/40 = 350.~~836¢~~, ~10/7 = 617.~~219¢~~

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

* [[CWE]]: ~2 = 1200.~~000¢~~, ~49/40 = 350.~~837¢~~, ~10/7 = 616.~~991¢~~

* [[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 194:

Line 193:

Optimal tunings:

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

* WE: ~2 = 1200.441{{c}}, ~49/40 = 350.809{{c}}, ~10/7 = 617.372{{c}}

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

* CWE: ~2 = 1200.000{{c}}, ~49/40 = 350.805{{c}}, ~10/7 = 617.157{{c}}

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

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

Badness (Sintel): 0.863

Line 210:

Line 209:

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

[[Badness]]: 0.640 × 10-3

[[Badness]] (Smith): 0.640 × 10-3

=== 13-limit ===

Line 219:

Line 218:

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

{{Optimal ET sequence|legend=1| 31, 78f, 99e, 109, 130, 239, 270, 571, 701, 841, 971, 1241 }}

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

Badness: 0.830 × 10-3

Badness (Smith): 0.830 × 10-3

== Lif ==

Line 230:

Line 229:

[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~49/40 = 351.0959, ~10/7 = 617.6652

[[Optimal tuning]] ([[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]]: 0.793 × 10-3

[[Badness]] (Smith): 0.793 × 10-3

=== 13-limit ===

Line 243:

Line 242:

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

Optimal tuning (CTE): ~2 = ~~1\1~~, ~49/40 = 351.0960, ~10/7 = 617.6533

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

{{Optimal ET sequence|legend=1| 41, 89, 99, 130, 270, 581, 711, 981, 1292, 1562 }}

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

Badness: 0.579 × 10-3

Badness (Smith): 0.579 × 10-3

=== 2.3.5.7.11.13.19 subgroup ===

Line 256:

Line 255:

Sval 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 = ~~1\1~~, ~49/40 = 351.1007, ~10/7 = 617.6501

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

{{Optimal ET sequence|legend=1| 41, 89, 130, 229, 270, 581, 851, 1562, 1832, 2413 }}

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

Badness: 0.499 × 10-3

Badness (Smith): 0.499 × 10-3

== Baldur ==

Line 268:

Line 267:

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

Line 277:

Line 275:

[[Optimal tuning]]s:

* [[WE]]: ~99/70 = 600.~~015¢~~, ~343/198 = 950.~~972¢~~, ~10/7 = 617.~~701¢~~

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

* [[CWE]]: ~99/70 = 600.~~000¢~~, ~343/198 = 950.~~956¢~~, ~10/7 = 617.~~702¢~~

* [[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 294:

Line 292:

Optimal tunings:

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

* WE: ~99/70 = 599.987{{c}}, ~26/15 = 951.054{{c}}, ~10/7 = 617.806{{c}}

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

* CWE: ~99/70 = 600.000{{c}}, ~26/15 = 951.069{{c}}, ~10/7 = 617.807{{c}}

{{Optimal ET sequence|legend=1| 58, 72, 130, 198, 270, 940, 1210f }}

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

Badness (Sintel): 0.415

Line 303:

Line 301:

Complexity spectrum: 15/13, 7/5, 8/7, 7/6, 4/3, 15/14, 5/4, 18/13, 13/12, 14/13, 13/10, 6/5, 16/15, 11/10, 9/7, 9/8, 16/13, 10/9, 14/11, 11/8, 15/11, 12/11, 13/11, 11/9

Projection pairs: ~2 ~~= ~~~19600/9801, ~3 ~~= ~~~676/225, ~5 ~~= ~~~10400/2079, ~7 ~~= ~~~20384000/2910897, ~11 ~~= ~~~19208000000000000/1750211597736459, ~13 ~~= ~~~5026736/385875 to 10/7.200/99.26/15

Projection pairs: <code>2 19600/9801, 3 676/225, 5 10400/2079, 7 20384000/2910897, 11 19208000000000000/1750211597736459, 13 5026736/385875</code> to 10/7.200/99.26/15

==== Midnatssol ====

Line 313:

Line 311:

Optimal tunings:

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

* WE: ~17/12 = 600.112{{c}}, ~26/15 = 951.191{{c}}, ~10/7 = 617.610{{c}}

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

* CWE: ~17/12 = 600.000{{c}}, ~26/15 = 951.063{{c}}, ~10/7 = 617.584{{c}}

Badness (Sintel): 0.720

Line 326:

Line 324:

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

Line 334:

Line 331:

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

[[Badness]]: 0.170 × 10-3

[[Badness]] (Smith): 0.170 × 10-3

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

Line 345:

Line 342:

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

{{Optimal ET sequence|legend=1| 31, 41, 72f, 198f, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615 }}

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

Badness: 0.855 × 10-3

Badness (Smith): 0.855 × 10-3

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

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

=== Eir ===

Line 360:

Line 357:

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

{{Optimal ET sequence|legend=1| 13cdf, 31f, 41, 72, 157, 185cf, 198, 270, 581, 851, 1504, 1774f, 2085, 2355f }}

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

Badness: 0.581 × 10-3

Badness (Smith): 0.581 × 10-3

==== 17-limit ====

Line 371:

Line 368:

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

{{Optimal ET sequence|legend=1| 41g, 72, 198g, 239f, 270, 311, 509, 581, 1234, 1815 }}

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

Badness: 0.700 × 10-3

Badness (Smith): 0.700 × 10-3

==== 19-limit ====

Line 381:

Line 378:

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

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

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

~~{{Optimal ET sequence|legend=1| 41g, 72, 198g, 239f, 270, 311, 581, 1234, 1815 }}~~

Badness (Smith): 0.692 × 10-3

Badness: 0.692 × 10-3

=== Heimlaug ===

Line 397:

Line 393:

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

{{Optimal ET sequence|legend=1| 8bcef, 15bbccdeeff, 23bcf, 31, 72, 103, 167, 198, 270, 571, 643, 913f }}

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

Badness: 0.601 × 10-3

Badness (Smith): 0.601 × 10-3

==== 17-limit ====

Line 409:

Line 405:

Mapping: {{mapping| 1 1 3 3 2 7 7 | 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=1| 8bcefg, 15bbccdeeffggg, 23bcfg, 31, 64be, 72, 103, 167, 198g, 239, 270 }}

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

Badness: 0.829 × 10-3

Badness (Smith): 0.829 × 10-3

== Vili ==

Line 425:

Line 420:

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

[[Badness]]: 1.26 × 10-3

[[Badness]] (Smith): 1.26 × 10-3

=== 13-limit ===

Line 434:

Line 429:

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

{{Optimal ET sequence|legend=1| 27e, 37, 64be, 76e, 93, 103, 130, 233, 243e, 270, 643, 913f }}

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

Badness: 0.738 × 10-3

Badness (Smith): 0.738 × 10-3

== Frigg ==

Line 447:

Line 442:

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

[[Badness]]: 1.79 × 10-3

[[Badness]] (Smith): 1.79 × 10-3

=== 13-limit ===

Line 456:

Line 451:

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

{{Optimal ET sequence|legend=1| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} <nowiki>*</nowiki>

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

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

Badness: 0.934 × 10-3

Badness (Smith): 0.934 × 10-3

== Ennealimmic ==

[[Subgroup]]: 2.3.5.7.11

Line 469:

Line 464:

: 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 }}

[[Badness]]: 0.275 × 10-3

[[Badness]] (Smith): 0.275 × 10-3

=== 13-limit ===

Line 483:

Line 477:

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

{{Optimal ET sequence|legend=1| 27, 45f, 54cff, 72, 171, 198, 270, 639, 711, 981, 1692e }}

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

Badness: 0.755 × 10-3

Badness (Smith): 0.755 × 10-3

[[Category:Temperament families]]

@@ Line 1: / Line 1: @@
 {{Technical data page}}
-The '''breed family''' of [[temperament]]s are [[Rank-3 temperament|rank-3]] [[microtemperament]]s which [[Tempering out|temper out]] [[2401/2400]]. While it is so accurate it hardly matters what is used to temper it, or whether it is tempered at all, the [[optimal patent val]] 2749et will certainly do the trick.
+The '''breed family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperament]]s are [[microtemperament]]s which [[tempering out|temper out]] [[2401/2400]].
 == Breed ==
-Breed has the same lattice structure as 2.5.7 JI. In terms of extension from the 5-limit, it splits 25/6 into four equal parts representing 10/7.
+Breed has the same lattice structure as the [[2.5.7 subgroup]] of JI. In terms of extension from the 5-limit, it splits 25/6 into four equal parts representing 10/7. While it is so accurate it hardly matters what is used to temper it, or whether it is tempered at all, the [[optimal patent val]] [[2749edo|2749et]] will certainly do the trick.
 [[Subgroup]]: 2.3.5.7
@@ Line 10: / Line 10: @@
 {{Mapping|legend=1| 1 1 1 2 | 0 2 1 1 | 0 0 2 1 }}
 : Mapping generators: ~2, ~49/40, ~10/7
@@ Line 20: / Line 19: @@
 [[Minimax tuning]]:
-* [[7-odd-limit|7-]] and [[9-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.5
+* [[7-odd-limit|7-]] and [[9-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.5
 [[Optimal tuning]]s:
-* [[WE]]: ~2 = 1200.021¢, ~49/40 = 350.972¢, ~10/7 = 617.683¢
+* [[WE]]: ~2 = 1200.021{{c}}, ~49/40 = 350.972{{c}}, ~10/7 = 617.683{{c}}
-* [[CWE]]: ~2 = 1200.000¢, ~49/40 = 350.974¢, ~10/7 = 617.681¢
+* [[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 }}
@@ Line 30: / Line 29: @@
 [[Badness]] (Sintel): 0.067
-[[Projection pair]]: ~3 = ~2401/800 to 2.5.7
+[[Projection pair]]: <code>3 2401/800</code> to 2.5.7
 Scales: [[breed11]]
@@ Line 52: / Line 51: @@
 [[Optimal tuning]]s:
-* [[WE]]: ~2 = 1200.098¢, ~11/9 = 350.532¢, ~10/7 = 617.878¢
+* [[WE]]: ~2 = 1200.098{{c}}, ~11/9 = 350.532{{c}}, ~10/7 = 617.878{{c}}
-* [[CWE]]: ~2 = 1200.000¢, ~11/9 = 350.537¢, ~10/7 = 617.871¢
+* [[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 59: / Line 58: @@
 [[Badness]] (Sintel): 0.290
-Projection pairs: ~3 = ~242/81, ~5 = ~2200/441, ~7 = ~440/63, ~11 = ~644204/59049 to 2.7/5.11/9
+[[Projection pair]]s: <code>3 242/81, 5 2200/441, 7 440/63, 11 644204/59049</code> to 2.7/5.11/9
 === Jovial ===
@@ Line 73: / Line 72: @@
 Optimal tunings:
-* WE: ~2 = 1199.977¢, ~11/9 = 350.711¢, ~10/7 = 617.817¢
+* WE: ~2 = 1199.977{{c}}, ~11/9 = 350.711{{c}}, ~10/7 = 617.817{{c}}
-* CWE: ~2 = 1200.000¢, ~11/9 = 350.713¢, ~10/7 = 617.818¢
+* CWE: ~2 = 1200.000{{c}}, ~11/9 = 350.713{{c}}, ~10/7 = 617.818{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 27eff, 31f, 41, 58, 72, 130, 243, 301e, 373e }}
+{{Optimal ET sequence|legend=0| 27eff, 31f, 41, 58, 72, 130, 243, 301e, 373e }}
 Badness (Sintel): 0.583
@@ Line 91: / Line 90: @@
 Optimal tunings:
-* WE: ~2 = 1200.088¢, ~11/9 = 350.720¢, ~10/7 = 617.577¢
+* WE: ~2 = 1200.088{{c}}, ~11/9 = 350.720{{c}}, ~10/7 = 617.577{{c}}
-* CWE: ~2 = 1200.000¢, ~11/9 = 350.714¢, ~10/7 = 617.561¢
+* CWE: ~2 = 1200.000{{c}}, ~11/9 = 350.714{{c}}, ~10/7 = 617.561{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 27effg, 31fg, 41, 58, 72, 130, 171, 243 }}
+{{Optimal ET sequence|legend=0| 27effg, 31fg, 41, 58, 72, 130, 171, 243 }}
 Badness (Sintel): 0.704
@@ Line 108: / Line 107: @@
 Optimal tunings:
-* WE: ~2 = 1199.559¢, ~119/108 = 175.353¢, ~27/17 = 793.685¢
+* WE: ~2 = 1199.559{{c}}, ~119/108 = 175.353{{c}}, ~27/17 = 793.685{{c}}
-* CWE: ~2 = 1200.000¢, ~119/108 = 175.371¢, ~27/17 = 793.756¢
+* CWE: ~2 = 1200.000{{c}}, ~119/108 = 175.371{{c}}, ~27/17 = 793.756{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 14cf, 27effg, 41, 89, 130g }}
+{{Optimal ET sequence|legend=0| 14cf, 27effg, 41, 89, 130g }}
 Badness (Sintel): 2.843
@@ Line 123: / Line 122: @@
 Optimal tunings:
-* WE: ~2 = 1199.733¢, ~21/19 = 175.347¢, ~19/12 = 793.779¢
+* WE: ~2 = 1199.733{{c}}, ~21/19 = 175.347{{c}}, ~19/12 = 793.779{{c}}
-* CWE: ~2 = 1200.000¢, ~21/19 = 175.358¢, ~19/12 = 793.819¢
+* CWE: ~2 = 1200.000{{c}}, ~21/19 = 175.358{{c}}, ~19/12 = 793.819{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 14cf, 27effg, 41, 89, 130g }}
+{{Optimal ET sequence|legend=0| 14cf, 27effg, 41, 89, 130g }}
 Badness (Sintel): 2.294
@@ Line 138: / Line 137: @@
 Optimal tunings:
-* WE: ~2 = 1198.953¢, ~11/9 = 351.141¢, ~10/7 = 618.349¢
+* WE: ~2 = 1198.953{{c}}, ~11/9 = 351.141{{c}}, ~10/7 = 618.349{{c}}
-* CWE: ~2 = 1200.000¢, ~11/9 = 351.254¢, ~10/7 = 618.593¢
+* CWE: ~2 = 1200.000{{c}}, ~11/9 = 351.254{{c}}, ~10/7 = 618.593{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 27e, 31, 41, 58, 99ef, 157eff }}
+{{Optimal ET sequence|legend=0| 27e, 31, 41, 58, 99ef, 157eff }}
 Badness (Sintel): 0.701
@@ Line 153: / Line 152: @@
 Optimal tunings:
-* WE: ~2 = 1200.144¢, ~11/9 = 350.435¢, ~10/7 = 618.177¢
+* WE: ~2 = 1200.144{{c}}, ~11/9 = 350.435{{c}}, ~10/7 = 618.177{{c}}
-* CWE: ~2 = 1200.000¢, ~11/9 = 350.440¢, ~10/7 = 618.176¢
+* CWE: ~2 = 1200.000{{c}}, ~11/9 = 350.440{{c}}, ~10/7 = 618.176{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 27e, 31, 45ef, 58, 72, 103, 130, 233, 363 }}
+{{Optimal ET sequence|legend=0| 27e, 31, 45ef, 58, 72, 103, 130, 233, 363 }}
 Badness (Sintel): 0.507
@@ Line 179: / Line 178: @@
 [[Optimal tuning]]s:
-* [[WE]]: ~2 = 1200.417¢, ~49/40 = 350.836¢, ~10/7 = 617.219¢
+* [[WE]]: ~2 = 1200.417{{c}}, ~49/40 = 350.836{{c}}, ~10/7 = 617.219{{c}}
-* [[CWE]]: ~2 = 1200.000¢, ~49/40 = 350.837¢, ~10/7 = 616.991¢
+* [[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 194: / Line 193: @@
 Optimal tunings:
-* WE: ~2 = 1200.441¢, ~49/40 = 350.809¢, ~10/7 = 617.372¢
+* WE: ~2 = 1200.441{{c}}, ~49/40 = 350.809{{c}}, ~10/7 = 617.372{{c}}
-* CWE: ~2 = 1200.000¢, ~49/40 = 350.805¢, ~10/7 = 617.157¢
+* CWE: ~2 = 1200.000{{c}}, ~49/40 = 350.805{{c}}, ~10/7 = 617.157{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 31, 68, 72, 103, 140, 212, 243e, 315ef, 455eef, 770cdeeeff }}
+{{Optimal ET sequence|legend=0| 31, 68, 72, 103, 140, 212, 243e, 315ef, 455eef, 770cdeeeff }}
 Badness (Sintel): 0.863
@@ Line 210: / Line 209: @@
 {{Optimal ET sequence|legend=1| 31, 68e, 99e, 130, 239, 270, 670, 940, 1210, 2150c }}
-[[Badness]]: 0.640 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.640 × 10<sup>-3</sup>
 === 13-limit ===
@@ Line 219: / Line 218: @@
 Mapping: {{mapping| 1 1 1 2 -3 7 | 0 2 1 1 8 -6 | 0 0 2 1 8 -3 }}
-{{Optimal ET sequence|legend=1| 31, 78f, 99e, 109, 130, 239, 270, 571, 701, 841, 971, 1241 }}
+{{Optimal ET sequence|legend=0| 31, 78f, 99e, 109, 130, 239, 270, 571, 701, 841, 971, 1241 }}
-Badness: 0.830 × 10<sup>-3</sup>
+Badness (Smith): 0.830 × 10<sup>-3</sup>
 == Lif ==
@@ Line 230: / Line 229: @@
 {{Mapping|legend=1| 1 1 1 2 8 | 0 2 1 1 -12 | 0 0 2 1 -2 }}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~49/40 = 351.0959, ~10/7 = 617.6652
+[[Optimal tuning]] ([[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]]: 0.793 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.793 × 10<sup>-3</sup>
 === 13-limit ===
@@ Line 243: / Line 242: @@
 Mapping: {{mapping| 1 1 1 2 8 7 | 0 2 1 1 -12 -6 | 0 0 2 1 -2 -3 }}
-Optimal tuning (CTE): ~2 = 1\1, ~49/40 = 351.0960, ~10/7 = 617.6533
+Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~49/40 = 351.0960{{c}}, ~10/7 = 617.6533{{c}}
-{{Optimal ET sequence|legend=1| 41, 89, 99, 130, 270, 581, 711, 981, 1292, 1562 }}
+{{Optimal ET sequence|legend=0| 41, 89, 99, 130, 270, 581, 711, 981, 1292, 1562 }}
-Badness: 0.579 × 10<sup>-3</sup>
+Badness (Smith): 0.579 × 10<sup>-3</sup>
 === 2.3.5.7.11.13.19 subgroup ===
@@ Line 256: / Line 255: @@
 Sval 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 = 1\1, ~49/40 = 351.1007, ~10/7 = 617.6501
+Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~49/40 = 351.1007{{c}}, ~10/7 = 617.6501{{c}}
-{{Optimal ET sequence|legend=1| 41, 89, 130, 229, 270, 581, 851, 1562, 1832, 2413 }}
+{{Optimal ET sequence|legend=0| 41, 89, 130, 229, 270, 581, 851, 1562, 1832, 2413 }}
-Badness: 0.499 × 10<sup>-3</sup>
+Badness (Smith): 0.499 × 10<sup>-3</sup>
 == Baldur ==
@@ Line 268: / Line 267: @@
 {{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
@@ Line 277: / Line 275: @@
 [[Optimal tuning]]s:
-* [[WE]]: ~99/70 = 600.015¢, ~343/198 = 950.972¢, ~10/7 = 617.701¢
+* [[WE]]: ~99/70 = 600.015{{c}}, ~343/198 = 950.972{{c}}, ~10/7 = 617.701{{c}}
-* [[CWE]]: ~99/70 = 600.000¢, ~343/198 = 950.956¢, ~10/7 = 617.702¢
+* [[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 294: / Line 292: @@
 Optimal tunings:
-* WE: ~99/70 = 599.987¢, ~26/15 = 951.054¢, ~10/7 = 617.806¢
+* WE: ~99/70 = 599.987{{c}}, ~26/15 = 951.054{{c}}, ~10/7 = 617.806{{c}}
-* CWE: ~99/70 = 600.000¢, ~26/15 = 951.069¢, ~10/7 = 617.807¢
+* CWE: ~99/70 = 600.000{{c}}, ~26/15 = 951.069{{c}}, ~10/7 = 617.807{{c}}
-{{Optimal ET sequence|legend=1| 58, 72, 130, 198, 270, 940, 1210f }}
+{{Optimal ET sequence|legend=0| 58, 72, 130, 198, 270, 940, 1210f }}
 Badness (Sintel): 0.415
@@ Line 303: / Line 301: @@
 Complexity spectrum: 15/13, 7/5, 8/7, 7/6, 4/3, 15/14, 5/4, 18/13, 13/12, 14/13, 13/10, 6/5, 16/15, 11/10, 9/7, 9/8, 16/13, 10/9, 14/11, 11/8, 15/11, 12/11, 13/11, 11/9
-Projection pairs: ~2 = ~19600/9801, ~3 = ~676/225, ~5 = ~10400/2079, ~7 = ~20384000/2910897, ~11 = ~19208000000000000/1750211597736459, ~13 = ~5026736/385875 to 10/7.200/99.26/15
+Projection pairs: <code>2 19600/9801, 3 676/225, 5 10400/2079, 7 20384000/2910897, 11 19208000000000000/1750211597736459, 13 5026736/385875</code> to 10/7.200/99.26/15
 ==== Midnatssol ====
@@ Line 313: / Line 311: @@
 Optimal tunings:
-* WE: ~17/12 = 600.112¢, ~26/15 = 951.191¢, ~10/7 = 617.610¢
+* WE: ~17/12 = 600.112{{c}}, ~26/15 = 951.191{{c}}, ~10/7 = 617.610{{c}}
-* CWE: ~17/12 = 600.000¢, ~26/15 = 951.063¢, ~10/7 = 617.584¢
+* CWE: ~17/12 = 600.000{{c}}, ~26/15 = 951.063{{c}}, ~10/7 = 617.584{{c}}
-{{Optimal ET sequence|legend=1| 58, 72, 130, 140, 198, 270g }}
+{{Optimal ET sequence|legend=0| 58, 72, 130, 140, 198, 270g }}
 Badness (Sintel): 0.720
@@ Line 326: / Line 324: @@
 {{Mapping|legend=1| 1 1 3 3 2 | 0 2 3 2 1 | 0 0 -4 -2 3 }}
 : Mapping generators: ~2, ~49/40, ~55/42
@@ Line 334: / Line 331: @@
 {{Optimal ET sequence|legend=1| 31, 41, 72, 167, 188, 198, 239, 270, 342, 612, 954, 1566, 3101de, 3443de, 4055de, 4397cdee, 4667dee, 5009cddee }}
-[[Badness]]: 0.170 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.170 × 10<sup>-3</sup>
 [[Projection pair]]s: ~3 = ~2401/800, ~5 = ~22880495169/4575312500, ~7 = ~1058841/151250, ~11 = ~33275/3024 to 2.49/5.77/3
@@ Line 345: / Line 342: @@
 Mapping: {{mapping| 1 1 3 3 2 4 | 0 2 3 2 1 -9 | 0 0 -4 -2 3 6 }}
-{{Optimal ET sequence|legend=1| 31, 41, 72f, 198f, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615 }}
+{{Optimal ET sequence|legend=0| 31, 41, 72f, 198f, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615 }}
-Badness: 0.855 × 10<sup>-3</sup>
+Badness (Smith): 0.855 × 10<sup>-3</sup>
-Projection pairs: ~3 = ~2401/800, ~5 = ~22880495169/4575312500, ~7 = ~1058841/151250, ~11 = ~33275/3024, ~13 = ~1814078464000000000000000/139662717676432916098329 to 2.49/5.77/3
+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
 === Eir ===
@@ Line 360: / Line 357: @@
 Mapping: {{mapping| 1 1 3 3 2 0 | 0 2 3 2 1 6 | 0 0 -4 -2 3 5 }}
-{{Optimal ET sequence|legend=1| 13cdf, 31f, 41, 72, 157, 185cf, 198, 270, 581, 851, 1504, 1774f, 2085, 2355f }}
+{{Optimal ET sequence|legend=0| 13cdf, 31f, 41, 72, 157, 185cf, 198, 270, 581, 851, 1504, 1774f, 2085, 2355f }}
-Badness: 0.581 × 10<sup>-3</sup>
+Badness (Smith): 0.581 × 10<sup>-3</sup>
 ==== 17-limit ====
@@ Line 371: / Line 368: @@
 Mapping: {{mapping| 1 1 3 3 2 0 7 | 0 2 3 2 1 6 6 | 0 0 -4 -2 3 5 -12 }}
-{{Optimal ET sequence|legend=1| 41g, 72, 198g, 239f, 270, 311, 509, 581, 1234, 1815 }}
+{{Optimal ET sequence|legend=0| 41g, 72, 198g, 239f, 270, 311, 509, 581, 1234, 1815 }}
-Badness: 0.700 × 10<sup>-3</sup>
+Badness (Smith): 0.700 × 10<sup>-3</sup>
 ==== 19-limit ====
@@ Line 381: / Line 378: @@
 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 generators: ~2, ~49/40, ~55/42
-Mapping generators: ~2, ~49/40, ~55/42
+{{Optimal ET sequence|legend=0| 41g, 72, 198g, 239f, 270, 311, 581, 1234, 1815 }}
-{{Optimal ET sequence|legend=1| 41g, 72, 198g, 239f, 270, 311, 581, 1234, 1815 }}
+Badness (Smith): 0.692 × 10<sup>-3</sup>
-Badness: 0.692 × 10<sup>-3</sup>
 === Heimlaug ===
@@ Line 397: / Line 393: @@
 Mapping: {{mapping| 1 1 3 3 2 7 | 0 2 3 2 1 6 | 0 0 -4 -2 3 -13 }}
-{{Optimal ET sequence|legend=1| 8bcef, 15bbccdeeff, 23bcf, 31, 72, 103, 167, 198, 270, 571, 643, 913f }}
+{{Optimal ET sequence|legend=0| 8bcef, 15bbccdeeff, 23bcf, 31, 72, 103, 167, 198, 270, 571, 643, 913f }}
-Badness: 0.601 × 10<sup>-3</sup>
+Badness (Smith): 0.601 × 10<sup>-3</sup>
 ==== 17-limit ====
@@ Line 409: / Line 405: @@
 Mapping: {{mapping| 1 1 3 3 2 7 7 | 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=1| 8bcefg, 15bbccdeeffggg, 23bcfg, 31, 64be, 72, 103, 167, 198g, 239, 270 }}
+{{Optimal ET sequence|legend=0| 8bcefg, 15bbccdeeffggg, 23bcfg, 31, 64be, 72, 103, 167, 198g, 239, 270 }}
-Badness: 0.829 × 10<sup>-3</sup>
+Badness (Smith): 0.829 × 10<sup>-3</sup>
 == Vili ==
@@ Line 425: / Line 420: @@
 {{Optimal ET sequence|legend=1| 27e, 64be, 76e, 93, 103, 130, 233, 243e, 270, 643, 670, 913, 1043, 1313, 1583 }}
-[[Badness]]: 1.26 × 10<sup>-3</sup>
+[[Badness]] (Smith): 1.26 × 10<sup>-3</sup>
 === 13-limit ===
@@ Line 434: / Line 429: @@
 Mapping: {{mapping| 1 1 5 4 10 4 | 0 2 3 2 6 1 | 0 0 -6 -3 -14 -1 }}
-{{Optimal ET sequence|legend=1| 27e, 37, 64be, 76e, 93, 103, 130, 233, 243e, 270, 643, 913f }}
+{{Optimal ET sequence|legend=0| 27e, 37, 64be, 76e, 93, 103, 130, 233, 243e, 270, 643, 913f }}
-Badness: 0.738 × 10<sup>-3</sup>
+Badness (Smith): 0.738 × 10<sup>-3</sup>
 == Frigg ==
@@ Line 447: / Line 442: @@
 {{Optimal ET sequence|legend=1| 45e, 58, 103, 161, 212, 270, 643, 913, 1183e }}
-[[Badness]]: 1.79 × 10<sup>-3</sup>
+[[Badness]] (Smith): 1.79 × 10<sup>-3</sup>
 === 13-limit ===
@@ Line 456: / Line 451: @@
 Mapping: {{mapping| 1 1 3 3 4 5 | 0 2 3 2 4 3 | 0 0 -10 -5 -11 -14 }}
-{{Optimal ET sequence|legend=1| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} <nowiki>*</nowiki>
+{{Optimal ET sequence|legend=0| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} <nowiki>*</nowiki>
 <nowiki>*</nowiki> [[optimal patent val]]: [[1241edo|1241]]
-Badness: 0.934 × 10<sup>-3</sup>
+Badness (Smith): 0.934 × 10<sup>-3</sup>
 == Ennealimmic ==
 {{Distinguish|Ennealimnic}}
 [[Subgroup]]: 2.3.5.7.11
@@ Line 469: / Line 464: @@
 {{Mapping|legend=1| 9 1 1 12 0 | 0 2 3 2 0 | 0 0 0 0 1 }}
 : 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 }}
-[[Badness]]: 0.275 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.275 × 10<sup>-3</sup>
 === 13-limit ===
@@ Line 483: / Line 477: @@
 Mapping: {{mapping| 9 1 1 12 0 -31 | 0 2 3 2 0 5 | 0 0 0 0 1 1 }}
-{{Optimal ET sequence|legend=1| 27, 45f, 54cff, 72, 171, 198, 270, 639, 711, 981, 1692e }}
+{{Optimal ET sequence|legend=0| 27, 45f, 54cff, 72, 171, 198, 270, 639, 711, 981, 1692e }}
-Badness: 0.755 × 10<sup>-3</sup>
+Badness (Smith): 0.755 × 10<sup>-3</sup>
 [[Category:Temperament families]]