Breed family: Difference between revisions

(14 intermediate revisions by 3 users not shown)

Line 1:

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

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

== Breed ==

Line 41:

Jove (formerly known as wonder) tempers out [[243/242]], [[441/440]], and [[540/539]]. Jove converts breed into an 11-limit temperament via 441/440, which equates [[49/40]] with [[11/9]], and 243/242, which tells us 11/9 can serve as a neutral third. While jove is no longer a super-accurate microtemperament like breed, it has the advantage of adjusting its tuning to deal with the 11-limit. [[72edo|72]], [[130edo|130]], [[171edo|171]] and [[202edo|202]] are good edo tunings for jove.

Jove (formerly known as wonder) tempers out [[243/242]], [[441/440]], and [[540/539]]. Jove converts breed into an 11-limit temperament via 441/440, which equates [[49/40]] with [[11/9]], and 243/242, which tells us 11/9 can serve as a neutral third (as in exactly half of [[~]][[3/2]]). While jove is no longer a super-accurate microtemperament like breed, it has the advantage of adjusting its tuning to deal with the 11-limit. [[72edo|72]], [[130edo|130]], [[171edo|171]] and [[202edo|202]] are good edo tunings for jove.

[[Subgroup]]: 2.3.5.7.11

Line 69:

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

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

Optimal tunings:

Line 88:

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

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

{{Mapping|legend=0| 1 1 1 2 2 1 3 | 0 2 1 1 5 11 9 | 0 0 2 1 0 -1 -3 }}

Optimal tunings:

Line 106:

Comma list: 243/242, 364/363, 441/440, 1452/1445

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

{{Mapping|legend=0| 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

Line 122:

Comma list: 171/170, 243/242, 324/323, 364/363, 441/440

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

{{Mapping|legend=0| 1 1 1 2 2 1 3 3 | 0 4 0 1 10 23 12 4 | 0 0 2 1 0 -1 -1 1 }}

Optimal tunings:

Line 137:

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

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

Optimal tunings:

Line 152:

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

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

Optimal tunings:

Line 161:

Badness (Sintel): 0.701

=== Semijove ===

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 441/440, 676/675

: mapping generators: ~55/39, ~26/15, ~10/7

Optimal tunings:

* WE: ~55/39 = 599.9886{{c}}, ~26/15 = 950.6645{{c}}, ~10/7 = 618.1458{{c}}

* CWE: ~55/39 = 600.0000{{c}}, ~26/15 = 950.6755{{c}}, ~10/7 = 618.1489{{c}}

Badness (Sintel): 0.948

== Agni ==

Agni tempers out [[385/384]] and [[1375/1372]], so that a stack of three 10/7 generators is identified with [[16/11]] plus an octave. [[140edo]], [[212edo]] and [[284edo]] show how it can be tuned distinctly from [[#Jove|jove]].

This temperament suggests at least two extensions to the 13-limit: pavaka (31 & 68 & 72), named after an alias of Agni, tempers out [[625/624]]; and svaha (41 & 68 & 72), named after Agni's wife, tempers out [[325/324]]. The edos above can be used to tune both, which reduce them to [[quadritikleismic]] without much additional damage, but note pavaka is a detemperament of [[benediction]] whereas svaha is a detemperament of [[manna]].

[[Subgroup]]: 2.3.5.7.11

Line 186:

Line 206:

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

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

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

[[Badness]] (Sintel): 0.593

=== ~~13-limit~~ ===

=== Pavaka ===

Subgroup: 2.3.5.7.11.13

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

~~Mapping:~~ {{~~mapping~~| 1 1 1 2 5 -1 | 0 2 1 1 0 2 | 0 0 2 1 -3 8 }}

Optimal tunings:

Line 204:

Line 224:

Badness (Sintel): 0.863

=== Svaha ===

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 385/384, 1375/1372

Optimal tunings:

* WE: ~2 = 1200.3582{{c}}, ~49/40 = 351.0784{{c}}, ~10/7 = 617.0054{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0491{{c}}, ~10/7 = 616.8317{{c}}

{{Optimal ET sequence|legend=0| 41, 68, 72, 140, 212, 393ce, 465cef, 677cdeeff }}

Badness (Sintel): 0.997

== Zisa ==

Line 227:

Line 262:

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

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

{{Mapping|legend=0| 1 1 1 2 -3 7 | 0 2 1 1 8 -6 | 0 0 2 1 8 -3 }}

Optimal tunings:

Line 238:

Line 273:

== Lif ==

Lif tempers out the [[olympia]] and the [[lifthrasirsma]], so that the [[rastma]] is split in halves with each part standing in not only for [[441/440]][[~]][[540/539]], but the [[32805/32768|schisma]]. Lif readily extends to the [[13-limit]] and the no-17 [[19-limit]], where the ~~undevicesimal schisma of~~ [[513/512]] is also equated with the schisma.

Lif tempers out the [[olympia]] and the [[lifthrasirsma]], so that the [[rastma]] is split in halves with each part standing in not only for [[441/440]][[~]][[540/539]], but the [[32805/32768|schisma]]. Lif readily extends to the [[13-limit]] and the no-17 [[19-limit]], where the [[513/512|undevicesimal schisma]] is also equated with the schisma.

This temperament was named by [[Flora Canou]] in 2023 along with the [[weak restriction]], [[lifthrasir]], and the corresponding comma, lifthrasirsma, after the human survivors of Ragnarök.

Line 249:

Line 284:

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9386{{c}}, ~49/40 = ~~350~~.0586{{c}}, ~10/7 = 617.7065{{c}}

* [[WE]]: ~2 = 1199.9386{{c}}, ~49/40 = 351.0586{{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}}

Line 263:

Line 298:

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

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

{{Mapping|legend=0| 1 1 1 2 8 7 | 0 2 1 1 -12 -6 | 0 0 2 1 -2 -3 }}

Optimal tunings:

Line 278:

Line 313:

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

~~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 }}

{{Mapping|legend=2| 1 1 1 2 8 7 0 | 0 2 1 1 -12 -6 11 | 0 0 2 1 -2 -3 2 }}

Optimal tunings:

Line 287:

Line 322:

Badness (Sintel): 0.488

== Freyr ==

Freyr tempers out the [[symbiotic comma]], so that the [[rastma]] is split in halves with each part standing in not only for [[441/440]][[~]][[540/539]], but the [[5120/5103|aberschisma]]. Freyr easily extends to the [[13-limit]], equating the [[352/351|major minthma]] with the aberschisma, and the no-17 [[19-limit]], equating the [[513/512|undevicesimal schisma]] with it too.

It can be notated with [[neutral chain-of-fifths notation]] with two additional sets of accidentals, one for the generic comma step, and the other for the generic aberschisma step.

This temperament was named by [[Flora Canou]] in 2026, under the impression that it functions as a counterpart of [[#Freya|freya]].

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 2401/2400, 19712/19683

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9474{{c}}, ~49/40 = 351.1064{{c}}, ~10/7 = 617.6483{{c}}

: [[error map]]: {{val| -0.053 +0.205 +0.037 -0.176 -0.104 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.1156{{c}}, ~10/7 = 617.6499{{c}}

: error map: {{val| 0.000 +0.276 +0.102 -0.060 -0.003 }}

{{Optimal ET sequence|legend=1| 41, 58, 99e, 171e, 212, 270, 581, 851, 1121, 1972, 2881bc }}

[[Badness]] (Sintel): 1.23

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 2401/2400, 10648/10647

{{Mapping|legend=0| 1 1 1 2 -1 -2 | 0 2 1 1 17 23 | 0 0 2 1 -1 -2 }}

Optimal tunings:

* WE: ~2 = 1199.9432{{c}}, ~49/40 = 351.1128{{c}}, ~10/7 = 617.6419{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1232{{c}}, ~10/7 = 617.6431{{c}}

{{Optimal ET sequence|legend=0| 41, 58, 99ef, 154cef, 171ef, 212, 270, 581, 851, 1490, 1760, 2071be, 2341b }}

Badness (Sintel): 0.760

=== 2.3.5.7.11.13.19 subgroup ===

Subgroup: 2.3.5.7.11.13.19

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

{{Mapping|legend=0| 1 1 1 2 -1 -2 0 | 0 2 1 1 17 23 11 | 0 0 2 1 -1 -2 2 }}

Optimal tunings:

* WE: ~2 = 1199.9435{{c}}, ~49/40 = 351.1127{{c}}, ~10/7 = 617.6404{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1236{{c}}, ~10/7 = 617.6459{{c}}

{{Optimal ET sequence|legend=0| 41, 58h, 99ef, 171ef, 212h, 270, 581, 851, 1490h, 1760h, 2071beh, 2341bh }}

Badness (Sintel): 0.523

== Baldur ==

Line 318:

Line 406:

Comma list: 676/675, 1001/1000, 1716/1715

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

Optimal tunings:

Line 327:

Line 415:

Badness (Sintel): 0.415

~~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: <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

Line 337:

Line 423:

Comma list: 289/288, 442/441, 561/560, 676/675

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

{{Mapping|legend=0| 2 0 1 3 7 -1 5 | 0 2 1 1 -2 4 2 | 0 0 2 1 3 2 0 }}

Optimal tunings:

Line 348:

Line 434:

== Freya ==

Freya tempers out [[3025/3024]] and [[41503/41472]], so it splits breed's [[28/27]] into two [[55/54]]~[[56/55]]'s and [[8/7]] into two [[77/72]]'s. It also takes the [[225/224]][[~]][[1029/1024]] [[kleisma (interval region)|kleisma]] to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament.

Freya tempers out [[3025/3024]] and [[41503/41472]], so it splits breed's [[28/27]] into two [[55/54]]~[[56/55]]'s and [[8/7]] into two [[77/72]]'s. It also takes the [[225/224]][[~]][[1029/1024]] [[kleisma #As an interval region|kleisma]] to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament.

[[Subgroup]]: 2.3.5.7.11

Line 370:

Line 456:

[[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

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

=== 13-limit ===

~~Freya's canonical 13-limit extension~~ maps [[352/351]] to the half-kleisma. It has [[miraculous]] as a sub-temperament.

Tridecimal freya maps [[352/351]] to the half-kleisma. It has [[miraculous]] as a sub-temperament.

Subgroup: 2.3.5.7.11.13

Line 379:

Line 465:

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

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

{{Mapping|legend=0| 1 1 -1 1 5 10 | 0 2 3 2 1 -9 | 0 0 4 2 -3 -6 }}

Optimal tunings:

Line 392:

Line 478:

=== Eir ===

~~[[User:VIxen|VIxen]] named this extension after a healer goddess or valkyrie from the Norse mythology, as it is an extension of freya with the [[ibnsinma]] that evokes associations with medicine. It~~ maps [[325/324]], [[364/363]], and [[729/728]] to the half-kleisma and has [[manna]] as a sub-temperament.

Eir maps [[325/324]], [[364/363]], and [[729/728]] to the half-kleisma and has [[manna]] as a sub-temperament. {{U|VIxen}} named this extension after a healer goddess or valkyrie from the Norse mythology, as it extends freya via the [[ibnsinma]], which evokes associations with medicine.

Subgroup: 2.3.5.7.11.13

Line 398:

Line 484:

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

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

{{Mapping|legend=0| 1 1 -1 1 5 5 | 0 2 3 2 1 6 | 0 0 4 2 -3 -5 }}

Optimal tunings:

Line 404:

Line 490:

* 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 }}

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

Badness (Sintel): 0.543

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

==== 2.3.5.7.11.13.19 subgroup ====

~~Subgroup:~~ 2.3.5.7.11.13.17

Subgroup: 2.3.5.7.11.13.19

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

~~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 }}~~

Comma list: 1540/1539, 2080/2079, 2401/2400, 3025/3024

~~Badness (Sintel): 0.665~~

{{Mapping|legend=2| 1 1 -1 1 5 5 3 | 0 2 3 2 1 6 -2 | 0 0 4 2 -3 -5 3 }}

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

~~Subgroup:~~ 2~~.3.5.7.11.13.17.19~~

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

~~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 }}

Optimal tunings:

* WE: ~2 = ~~1200~~.~~0015~~{{c}}, ~49/40 = 351.~~0770~~{{c}}, ~84/55 = 733.~~2252~~{{c}}

* WE: ~2 = 1199.9951{{c}}, ~49/40 = 351.0906{{c}}, ~84/55 = 733.2475{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.~~0768~~{{c}}, ~84/55 = 733.~~2243~~{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0913{{c}}, ~84/55 = 733.2473{{c}}

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

{{Optimal ET sequence|legend=0| 41, 72, 113, 157, 198, 270, 581, 851, 2085, 2355f }}

Badness (Sintel): 0.~~712~~

Badness (Sintel): 0.500

=== Heimlaug ===

VIxen named this extension after a völva (seeress) from the Gull-Þóris saga of Icelanders~~. It is an extension of~~ freya ~~with~~ the [[1001/1000|fairytale comma~~]] and the [[936/935|ainisma~~]], ~~both~~ adding to the mystical theme~~. The one of prophecy is bolstered by that this extension has [[benediction]] as a subtemperament. It maps [[351/350]] and [[625/624]] to the half-kleisma~~.

Heimlaug maps [[351/350]] and [[625/624]] to the half-kleisma and has [[benediction]] as a subtemperament. VIxen named this extension after a völva (seeress) from the Gull-Þóris saga of Icelanders, as it extends freya via the [[1001/1000|fairytale comma]], adding to the mystical theme.

Subgroup: 2.3.5.7.11.13

Line 445:

Line 516:

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

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

{{Mapping|legend=0| 1 1 -1 1 5 -6 | 0 2 3 2 1 6 | 0 0 4 2 -3 13 }}

Optimal tunings:

Line 454:

Line 525:

Badness (Sintel): 0.562

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

~~Subgroup: 2.3.5.7.11.13.17~~

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

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

~~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}}

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

~~Badness (Sintel): 0.789~~

== Vili ==

Line 493:

Line 549:

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

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

{{Mapping|legend=0| 1 1 -1 1 -4 3 | 0 2 3 2 6 1 | 0 0 6 3 14 1 }}

Optimal tunings:

Line 526:

Line 582:

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

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

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

Optimal tunings:

Line 532:

Line 588:

* 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>~~

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

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

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

Badness (Sintel): 0.873

Line 562:

Line 619:

Comma list: 2080/2079, 2401/2400, 4375/4374

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

{{Mapping|legend=0| 9 1 1 12 0 -31 | 0 2 3 2 0 5 | 0 0 0 0 1 1 }}

Optimal tunings:

Line 572:

Line 629:

Badness (Sintel): 0.706

[[Category:Breed family| ]]

[[Category:Breed| ]]

[[Category:Temperament families]]

[[Category:~~Breed family| ]] <!~~-~~- main article -->~~

[[Category:Catalogs of rank-3 temperaments]]

~~[[Category:Rank~~ 3]]

@@ Line 1: / Line 1: @@
 {{Technical data page}}
-The '''breed family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperament]]s are [[microtemperament]]s which [[tempering out|temper out]] [[2401/2400]].
+The '''breed family''' of [[rank-3 temperament]]s are [[microtemperament]]s which [[tempering out|temper out]] [[2401/2400]].
 == Breed ==
@@ Line 41: / Line 41: @@
 {{Main| Jove }}
-Jove (formerly known as wonder) tempers out [[243/242]], [[441/440]], and [[540/539]]. Jove converts breed into an 11-limit temperament via 441/440, which equates [[49/40]] with [[11/9]], and 243/242, which tells us 11/9 can serve as a neutral third. While jove is no longer a super-accurate microtemperament like breed, it has the advantage of adjusting its tuning to deal with the 11-limit. [[72edo|72]], [[130edo|130]], [[171edo|171]] and [[202edo|202]] are good edo tunings for jove.
+Jove (formerly known as wonder) tempers out [[243/242]], [[441/440]], and [[540/539]]. Jove converts breed into an 11-limit temperament via 441/440, which equates [[49/40]] with [[11/9]], and 243/242, which tells us 11/9 can serve as a neutral third (as in exactly half of [[~]][[3/2]]). While jove is no longer a super-accurate microtemperament like breed, it has the advantage of adjusting its tuning to deal with the 11-limit. [[72edo|72]], [[130edo|130]], [[171edo|171]] and [[202edo|202]] are good edo tunings for jove.
 [[Subgroup]]: 2.3.5.7.11
@@ Line 69: / Line 69: @@
 Comma list: 243/242, 364/363, 441/440
-Mapping: {{mapping| 1 1 1 2 2 1 | 0 2 1 1 5 11 | 0 0 2 1 0 -1 }}
+{{Mapping|legend=0| 1 1 1 2 2 1 | 0 2 1 1 5 11 | 0 0 2 1 0 -1 }}
 Optimal tunings:
@@ Line 88: / Line 88: @@
 Comma list: 243/242, 364/363, 441/440, 595/594
-Mapping: {{mapping| 1 1 1 2 2 1 3 | 0 2 1 1 5 11 9 | 0 0 2 1 0 -1 -3 }}
+{{Mapping|legend=0| 1 1 1 2 2 1 3 | 0 2 1 1 5 11 9 | 0 0 2 1 0 -1 -3 }}
 Optimal tunings:
@@ Line 106: / Line 106: @@
 Comma list: 243/242, 364/363, 441/440, 1452/1445
-Mapping: {{mapping| 1 1 1 2 2 1 3 | 0 4 0 1 10 23 12 | 0 0 2 1 0 -1 -1 }}
+{{Mapping|legend=0| 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
@@ Line 122: / Line 122: @@
 Comma list: 171/170, 243/242, 324/323, 364/363, 441/440
-Mapping: {{mapping| 1 1 1 2 2 1 3 3 | 0 4 0 1 10 23 12 4 | 0 0 2 1 0 -1 -1 1 }}
+{{Mapping|legend=0| 1 1 1 2 2 1 3 3 | 0 4 0 1 10 23 12 4 | 0 0 2 1 0 -1 -1 1 }}
 Optimal tunings:
@@ Line 137: / Line 137: @@
 Comma list: 243/242, 351/350, 441/440
-Mapping: {{mapping| 1 1 1 2 2 2 | 0 2 1 1 5 -3 | 0 0 2 1 0 5 }}
+{{Mapping|legend=0| 1 1 1 2 2 2 | 0 2 1 1 5 -3 | 0 0 2 1 0 5 }}
 Optimal tunings:
@@ Line 152: / Line 152: @@
 Comma list: 144/143, 196/195, 243/242
-Mapping: {{mapping| 1 1 1 2 2 4 | 0 2 1 1 5 -1 | 0 0 2 1 0 0 }}
+{{Mapping|legend=0| 1 1 1 2 2 4 | 0 2 1 1 5 -1 | 0 0 2 1 0 0 }}
 Optimal tunings:
@@ Line 161: / Line 161: @@
 Badness (Sintel): 0.701
+=== Semijove ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 243/242, 441/440, 676/675
+{{Mapping|legend=0| 2 0 1 3 -1 -1 | 0 2 1 1 5 4 | 0 0 2 1 0 2 }}
+: mapping generators: ~55/39, ~26/15, ~10/7
+Optimal tunings:
+* WE: ~55/39 = 599.9886{{c}}, ~26/15 = 950.6645{{c}}, ~10/7 = 618.1458{{c}}
+* CWE: ~55/39 = 600.0000{{c}}, ~26/15 = 950.6755{{c}}, ~10/7 = 618.1489{{c}}
+{{Optimal ET sequence|legend=0| 48c, 58, 72, 130 }}
+Badness (Sintel): 0.948
 == Agni ==
+Agni tempers out [[385/384]] and [[1375/1372]], so that a stack of three 10/7 generators is identified with [[16/11]] plus an octave. [[140edo]], [[212edo]] and [[284edo]] show how it can be tuned distinctly from [[#Jove|jove]].
+This temperament suggests at least two extensions to the 13-limit: pavaka (31 & 68 & 72), named after an alias of Agni, tempers out [[625/624]]; and svaha (41 & 68 & 72), named after Agni's wife, tempers out [[325/324]]. The edos above can be used to tune both, which reduce them to [[quadritikleismic]] without much additional damage, but note pavaka is a detemperament of [[benediction]] whereas svaha is a detemperament of [[manna]].
 [[Subgroup]]: 2.3.5.7.11
@@ Line 186: / Line 206: @@
 : [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.11/5
-{{Optimal ET sequence|legend=1| 27, 31, 41, 68, 72, 140, 171e, 212, 284, 496ce, 527cee, 739cdeee, 811ccdeee, 1023ccdeee }}
+{{Optimal ET sequence|legend=1| 31, 41, 68, 72, 140, 171e, 212, 284, 496ce, 527cee, 739cdeee, 811ccdeee, 1023ccdeee }}
 [[Badness]] (Sintel): 0.593
-=== 13-limit ===
+=== Pavaka ===
 Subgroup: 2.3.5.7.11.13
 Comma list: 385/384, 625/624, 1375/1372
-Mapping: {{mapping| 1 1 1 2 5 -1 | 0 2 1 1 0 2 | 0 0 2 1 -3 8 }}
+{{Mapping|legend=0| 1 1 1 2 5 -1 | 0 2 1 1 0 2 | 0 0 2 1 -3 8 }}
 Optimal tunings:
@@ Line 204: / Line 224: @@
 Badness (Sintel): 0.863
+=== Svaha ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 325/324, 385/384, 1375/1372
+{{Mapping|legend=0| 1 1 1 2 5 4 | 0 2 1 1 0 6 | 0 0 2 1 -3 -4 }}
+Optimal tunings:
+* WE: ~2 = 1200.3582{{c}}, ~49/40 = 351.0784{{c}}, ~10/7 = 617.0054{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0491{{c}}, ~10/7 = 616.8317{{c}}
+{{Optimal ET sequence|legend=0| 41, 68, 72, 140, 212, 393ce, 465cef, 677cdeeff }}
+Badness (Sintel): 0.997
 == Zisa ==
@@ Line 227: / Line 262: @@
 Comma list: 1001/1000, 1716/1715, 4096/4095
-Mapping: {{mapping| 1 1 1 2 -3 7 | 0 2 1 1 8 -6 | 0 0 2 1 8 -3 }}
+{{Mapping|legend=0| 1 1 1 2 -3 7 | 0 2 1 1 8 -6 | 0 0 2 1 8 -3 }}
 Optimal tunings:
@@ Line 238: / Line 273: @@
 == Lif ==
-Lif tempers out the [[olympia]] and the [[lifthrasirsma]], so that the [[rastma]] is split in halves with each part standing in not only for [[441/440]][[~]][[540/539]], but the [[32805/32768|schisma]]. Lif readily extends to the [[13-limit]] and the no-17 [[19-limit]], where the undevicesimal schisma of [[513/512]] is also equated with the schisma.
+Lif tempers out the [[olympia]] and the [[lifthrasirsma]], so that the [[rastma]] is split in halves with each part standing in not only for [[441/440]][[~]][[540/539]], but the [[32805/32768|schisma]]. Lif readily extends to the [[13-limit]] and the no-17 [[19-limit]], where the [[513/512|undevicesimal schisma]] is also equated with the schisma.
 This temperament was named by [[Flora Canou]] in 2023 along with the [[weak restriction]], [[lifthrasir]], and the corresponding comma, lifthrasirsma, after the human survivors of Ragnarök.
@@ Line 249: / Line 284: @@
 [[Optimal tuning]]s:
-* [[WE]]: ~2 = 1199.9386{{c}}, ~49/40 = 350.0586{{c}}, ~10/7 = 617.7065{{c}}
+* [[WE]]: ~2 = 1199.9386{{c}}, ~49/40 = 351.0586{{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}}
@@ Line 263: / Line 298: @@
 Comma list: 2080/2079, 2401/2400, 4096/4095
-Mapping: {{mapping| 1 1 1 2 8 7 | 0 2 1 1 -12 -6 | 0 0 2 1 -2 -3 }}
+{{Mapping|legend=0| 1 1 1 2 8 7 | 0 2 1 1 -12 -6 | 0 0 2 1 -2 -3 }}
 Optimal tunings:
@@ Line 278: / Line 313: @@
 Comma list: 1216/1215, 1729/1728, 2080/2079, 2401/2400
-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 }}
+{{Mapping|legend=2| 1 1 1 2 8 7 0 | 0 2 1 1 -12 -6 11 | 0 0 2 1 -2 -3 2 }}
 Optimal tunings:
@@ Line 287: / Line 322: @@
 Badness (Sintel): 0.488
+== Freyr ==
+Freyr tempers out the [[symbiotic comma]], so that the [[rastma]] is split in halves with each part standing in not only for [[441/440]][[~]][[540/539]], but the [[5120/5103|aberschisma]]. Freyr easily extends to the [[13-limit]], equating the [[352/351|major minthma]] with the aberschisma, and the no-17 [[19-limit]], equating the [[513/512|undevicesimal schisma]] with it too.
+It can be notated with [[neutral chain-of-fifths notation]] with two additional sets of accidentals, one for the generic comma step, and the other for the generic aberschisma step.
+This temperament was named by [[Flora Canou]] in 2026, under the impression that it functions as a counterpart of [[#Freya|freya]].
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 2401/2400, 19712/19683
+{{Mapping|legend=1| 1 1 1 2 -1 | 0 2 1 1 17 | 0 0 2 1 -1 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9474{{c}}, ~49/40 = 351.1064{{c}}, ~10/7 = 617.6483{{c}}
+: [[error map]]: {{val| -0.053 +0.205 +0.037 -0.176 -0.104 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.1156{{c}}, ~10/7 = 617.6499{{c}}
+: error map: {{val| 0.000 +0.276 +0.102 -0.060 -0.003 }}
+{{Optimal ET sequence|legend=1| 41, 58, 99e, 171e, 212, 270, 581, 851, 1121, 1972, 2881bc }}
+[[Badness]] (Sintel): 1.23
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 2080/2079, 2401/2400, 10648/10647
+{{Mapping|legend=0| 1 1 1 2 -1 -2 | 0 2 1 1 17 23 | 0 0 2 1 -1 -2 }}
+Optimal tunings:
+* WE: ~2 = 1199.9432{{c}}, ~49/40 = 351.1128{{c}}, ~10/7 = 617.6419{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1232{{c}}, ~10/7 = 617.6431{{c}}
+{{Optimal ET sequence|legend=0| 41, 58, 99ef, 154cef, 171ef, 212, 270, 581, 851, 1490, 1760, 2071be, 2341b }}
+Badness (Sintel): 0.760
+=== 2.3.5.7.11.13.19 subgroup ===
+Subgroup: 2.3.5.7.11.13.19
+Comma list: 1216/1215, 1540/1539, 2080/2079, 2401/2400
+{{Mapping|legend=0| 1 1 1 2 -1 -2 0 | 0 2 1 1 17 23 11 | 0 0 2 1 -1 -2 2 }}
+Optimal tunings:
+* WE: ~2 = 1199.9435{{c}}, ~49/40 = 351.1127{{c}}, ~10/7 = 617.6404{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1236{{c}}, ~10/7 = 617.6459{{c}}
+{{Optimal ET sequence|legend=0| 41, 58h, 99ef, 171ef, 212h, 270, 581, 851, 1490h, 1760h, 2071beh, 2341bh }}
+Badness (Sintel): 0.523
 == Baldur ==
@@ Line 318: / Line 406: @@
 Comma list: 676/675, 1001/1000, 1716/1715
-Mapping: {{mapping| 2 0 1 3 7 -1 | 0 2 1 1 -2 4 | 0 0 2 1 3 2 }}
+{{Mapping|legend=0| 2 0 1 3 7 -1 | 0 2 1 1 -2 4 | 0 0 2 1 3 2 }}
 Optimal tunings:
@@ Line 327: / Line 415: @@
 Badness (Sintel): 0.415
-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: <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
@@ Line 337: / Line 423: @@
 Comma list: 289/288, 442/441, 561/560, 676/675
-Mapping: {{mapping| 2 0 1 3 7 -1 5 | 0 2 1 1 -2 4 2 | 0 0 2 1 3 2 0 }}
+{{Mapping|legend=0| 2 0 1 3 7 -1 5 | 0 2 1 1 -2 4 2 | 0 0 2 1 3 2 0 }}
 Optimal tunings:
@@ Line 348: / Line 434: @@
 == Freya ==
-Freya tempers out [[3025/3024]] and [[41503/41472]], so it splits breed's [[28/27]] into two [[55/54]]~[[56/55]]'s and [[8/7]] into two [[77/72]]'s. It also takes the [[225/224]][[~]][[1029/1024]] [[kleisma (interval region)|kleisma]] to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament.
+Freya tempers out [[3025/3024]] and [[41503/41472]], so it splits breed's [[28/27]] into two [[55/54]]~[[56/55]]'s and [[8/7]] into two [[77/72]]'s. It also takes the [[225/224]][[~]][[1029/1024]] [[kleisma #As an interval region|kleisma]] to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament.
 [[Subgroup]]: 2.3.5.7.11
@@ Line 370: / Line 456: @@
 [[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
+[[Projection pair]]s: <code>3 2401/800, 5 22880495169/4575312500, 7 1058841/151250, 11 33275/3024</code> to 2.49/5.77/3
 === 13-limit ===
-Freya's canonical 13-limit extension maps [[352/351]] to the half-kleisma. It has [[miraculous]] as a sub-temperament.
+Tridecimal freya maps [[352/351]] to the half-kleisma. It has [[miraculous]] as a sub-temperament.
 Subgroup: 2.3.5.7.11.13
@@ Line 379: / Line 465: @@
 Comma list: 2401/2400, 3025/3024, 4096/4095
-Mapping: {{mapping| 1 1 -1 1 5 10 | 0 2 3 2 1 -9 | 0 0 4 2 -3 -6 }}
+{{Mapping|legend=0| 1 1 -1 1 5 10 | 0 2 3 2 1 -9 | 0 0 4 2 -3 -6 }}
 Optimal tunings:
@@ Line 392: / Line 478: @@
 === Eir ===
-[[User:VIxen|VIxen]] named this extension after a healer goddess or valkyrie from the Norse mythology, as it is an extension of freya with the [[ibnsinma]] that evokes associations with medicine. It maps [[325/324]], [[364/363]], and [[729/728]] to the half-kleisma and has [[manna]] as a sub-temperament.
+Eir maps [[325/324]], [[364/363]], and [[729/728]] to the half-kleisma and has [[manna]] as a sub-temperament. {{U|VIxen}} named this extension after a healer goddess or valkyrie from the Norse mythology, as it extends freya via the [[ibnsinma]], which evokes associations with medicine.
 Subgroup: 2.3.5.7.11.13
@@ Line 398: / Line 484: @@
 Comma list: 2080/2079, 2401/2400, 3025/3024
-Mapping: {{mapping| 1 1 -1 1 5 5 | 0 2 3 2 1 6 | 0 0 4 2 -3 -5 }}
+{{Mapping|legend=0| 1 1 -1 1 5 5 | 0 2 3 2 1 6 | 0 0 4 2 -3 -5 }}
 Optimal tunings:
@@ Line 404: / Line 490: @@
 * 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 }}
+{{Optimal ET sequence|legend=0| 41, 72, 157, 185cf, 198, 270, 581, 851, 1504, 1774f, 2085, 2355f }}
 Badness (Sintel): 0.543
-==== 17-limit ====
+==== 2.3.5.7.11.13.19 subgroup ====
-Subgroup: 2.3.5.7.11.13.17
+Subgroup: 2.3.5.7.11.13.19
-Comma list: 1225/1224, 2058/2057, 2080/2079, 2401/2400
-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 }}
+Comma list: 1540/1539, 2080/2079, 2401/2400, 3025/3024
-Badness (Sintel): 0.665
+{{Mapping|legend=2| 1 1 -1 1 5 5 3 | 0 2 3 2 1 6 -2 | 0 0 4 2 -3 -5 3 }}
-==== 19-limit ====
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 1225/1224, 1540/1539, 2080/2079, 3136/3135, 4200/4199
-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 }}
 Optimal tunings:
-* WE: ~2 = 1200.0015{{c}}, ~49/40 = 351.0770{{c}}, ~84/55 = 733.2252{{c}}
+* WE: ~2 = 1199.9951{{c}}, ~49/40 = 351.0906{{c}}, ~84/55 = 733.2475{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0768{{c}}, ~84/55 = 733.2243{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0913{{c}}, ~84/55 = 733.2473{{c}}
-{{Optimal ET sequence|legend=0| 41g, 72, 198g, 239f, 270, 311, 581, 1234, 1815 }}
+{{Optimal ET sequence|legend=0| 41, 72, 113, 157, 198, 270, 581, 851, 2085, 2355f }}
-Badness (Sintel): 0.712
+Badness (Sintel): 0.500
 === Heimlaug ===
-VIxen named this extension after a völva (seeress) from the Gull-Þóris saga of Icelanders. It is an extension of freya with the [[1001/1000|fairytale comma]] and the [[936/935|ainisma]], both adding to the mystical theme. The one of prophecy is bolstered by that this extension has [[benediction]] as a subtemperament. It maps [[351/350]] and [[625/624]] to the half-kleisma.
+Heimlaug maps [[351/350]] and [[625/624]] to the half-kleisma and has [[benediction]] as a subtemperament. VIxen named this extension after a völva (seeress) from the Gull-Þóris saga of Icelanders, as it extends freya via the [[1001/1000|fairytale comma]], adding to the mystical theme.
 Subgroup: 2.3.5.7.11.13
@@ Line 445: / Line 516: @@
 Comma list: 1001/1000, 1716/1715, 3025/3024
-Mapping: {{mapping| 1 1 -1 1 5 -6 | 0 2 3 2 1 6 | 0 0 4 2 -3 13 }}
+{{Mapping|legend=0| 1 1 -1 1 5 -6 | 0 2 3 2 1 6 | 0 0 4 2 -3 13 }}
 Optimal tunings:
@@ Line 454: / Line 525: @@
 Badness (Sintel): 0.562
-==== 17-limit ====
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 715/714, 936/935, 1001/1000, 1225/1224, 1716/1715
-Mapping: {{mapping| 1 1 -1 1 5 -6 -5 | 0 2 3 2 1 6 6 | 0 0 4 2 -3 13 12 }}
-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}}
-{{Optimal ET sequence|legend=0| 31, 64be, 72, 103, 167, 198g, 239, 270 }}
-Badness (Sintel): 0.789
 == Vili ==
@@ Line 493: / Line 549: @@
 Comma list: 1001/1000, 1716/1715, 4225/4224
-Mapping: {{mapping| 1 1 -1 1 -4 3 | 0 2 3 2 6 1 | 0 0 6 3 14 1 }}
+{{Mapping|legend=0| 1 1 -1 1 -4 3 | 0 2 3 2 6 1 | 0 0 6 3 14 1 }}
 Optimal tunings:
@@ Line 526: / Line 582: @@
 Comma list: 1001/1000, 1716/1715, 10648/10647
-Mapping: {{mapping| 1 1 -7 -2 -7 -9 | 0 2 3 2 4 3 | 0 0 10 5 11 14 }}
+{{Mapping|legend=0| 1 1 -7 -2 -7 -9 | 0 2 3 2 4 3 | 0 0 10 5 11 14 }}
 Optimal tunings:
@@ Line 532: / Line 588: @@
 * 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>
+{{Optimal ET sequence|legend=0| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} *
-<nowiki>*</nowiki> [[optimal patent val]]: [[1241edo|1241]]
+<nowiki/>* optimal patent val: [[1241edo|1241]]
 Badness (Sintel): 0.873
@@ Line 562: / Line 619: @@
 Comma list: 2080/2079, 2401/2400, 4375/4374
-Mapping: {{mapping| 9 1 1 12 0 -31 | 0 2 3 2 0 5 | 0 0 0 0 1 1 }}
+{{Mapping|legend=0| 9 1 1 12 0 -31 | 0 2 3 2 0 5 | 0 0 0 0 1 1 }}
 Optimal tunings:
@@ Line 572: / Line 629: @@
 Badness (Sintel): 0.706
+[[Category:Breed family| ]] <!-- main article -->
+[[Category:Breed| ]] <!-- key article -->
 [[Category:Temperament families]]
-[[Category:Breed family| ]] <!-- main article -->
+[[Category:Catalogs of rank-3 temperaments]]
-[[Category:Rank 3]]