Xenharmonic Wiki

Breed family: Difference between revisions

← Older edit
VisualWikitext
Wikispaces>genewardsmith
**Imported revision 205449562 - Original comment: **
m Formatting
 
(68 intermediate revisions by 13 users not shown)
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Technical data page}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
The '''breed family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperament]]s are [[microtemperament]]s which [[tempering out|temper out]] [[2401/2400]].  
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-27 16:20:47 UTC</tt>.<br>
: The original revision id was <tt>205449562</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Breed is a 7-limit microtemperament which tempers 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.


===Vital statistics===
== Breed ==
[[Comma]] c = 2401/2400
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.
7- and 9-limit minimax tuning: 3 and 5 just, 7 1/4c flat
 
[[Eigenmonzo|Eigenmonzos]]: 2, 6/5, 5/4
[[Subgroup]]: 2.3.5.7
Lattice basis: 49/40 length 0.7858 8/7 length 1.1241
 
Angle(49/40, 8/7) = 107.367 degrees
[[Comma list]]: 2401/2400
Map to lattice: [&lt;0 2 -1 0|, &lt;0 0 -2 -1|]
 
Map [&lt;1 1 1 2|, &lt;0 2 1 1|, &lt;0 0 2 1|]
{{Mapping|legend=1| 1 1 1 2 | 0 2 1 1 | 0 0 2 1 }}
[[Generator|Generators]]: 2, 49/40, 10/7
: Mapping generators: ~2, ~49/40, ~10/7
[[edo|EDOs]]: [[441edo|441]], [[612edo|612]], [[2308edo|2308]], [[2749edo|2749]]
 
Badness: 0.0000153
[[Mapping to lattice]]: [{{val| 0 2 -1 0 }}, {{val| 0 0 -2 -1 }}]
 
Lattice basis:
: 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 ET sequence|legend=1| 27, 31, 41, 58, 68, 72, 99, 171, 441, 612, 1966, 2308, 2578, 2749, 3361d }}
 
[[Badness]] (Sintel): 0.0674
 
[[Projection pair]]: <code>3 2401/800</code> to 2.5.7


Scales: [[breed11]]
Scales: [[breed11]]


==Jove, aka Wonder==
; Music
Jove, formerly known as wonder, tempers out 243/242 and 441/440. Wonder has been deprecated as a name due to conflict with another temperament also given that name. 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. 72, 130 and 171 are good edos for jove, and if that doesn't suit there's 476edo.
* ''Bodacious Breed'' (archived 2010) by [[Gene Ward Smith]] – [http://www.archive.org/details/BodaciousBreed details] | [http://www.archive.org/download/BodaciousBreed/Genewardsmith-BodaciousBreed.mp3 play] – breed in 441edo tuning
 
== Jove ==
{{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.
 
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 243/242, 441/440
 
{{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
 
{{Optimal ET sequence|legend=1| 27e, 31, 41, 58, 72, 130, 202 }}
 
[[Badness]] (Sintel): 0.290
 
[[Projection pair]]s: <code>3 242/81, 5 2200/441, 7 440/63, 11 644204/59049</code> to 2.7/5.11/9
 
=== Jovial ===
Subgroup: 2.3.5.7.11.13
 
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:
* 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 ET sequence|legend=0| 27eff, 31f, 41, 58, 72, 130, 243, 301e, 373e }}
 
Badness (Sintel): 0.583
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
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 }}
 
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 ET sequence|legend=0| 27effg, 31fg, 41, 58, 72, 130, 171, 243 }}
 
Badness (Sintel): 0.704
 
==== Heartlandia ====
Subgroup: 2.3.5.7.11.13.17
 
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 generators: ~2, ~119/108, ~27/17
 
Optimal tunings:
* WE: ~2 = 1199.5594{{c}}, ~119/108 = 175.3533{{c}}, ~27/17 = 793.6847{{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): 2.84
 
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
 
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 }}
 
Optimal tunings:
* WE: ~2 = 1199.7333{{c}}, ~21/19 = 175.3472{{c}}, ~19/12 = 793.7794{{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): 2.29
 
=== Jovis ===
Subgroup: 2.3.5.7.11.13
 
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:
* WE: ~2 = 1200.1435{{c}}, ~11/9 = 350.4354{{c}}, ~10/7 = 618.1775{{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 }}
 
Badness (Sintel): 0.507
 
=== Jofur ===
Subgroup: 2.3.5.7.11.13
 
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:
* WE: ~2 = 1198.9534{{c}}, ~11/9 = 351.1412{{c}}, ~10/7 = 618.3494{{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 }}
 
Badness (Sintel): 0.701
 
== Agni ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 385/384, 1375/1372
 
{{Mapping|legend=1| 1 1 1 2 5 | 0 2 1 1 0 | 0 0 2 1 -3 }}
 
Mapping to lattice: [{{val| 0 2 1 1 0 }}, {{val| 0 0 2 1 -3 }}]
 
Lattice basis:
: 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
 
{{Optimal ET sequence|legend=1| 27, 31, 41, 68, 72, 140, 171e, 212, 284, 496ce, 527cee, 739cdeee, 811ccdeee, 1023ccdeee }}
 
[[Badness]] (Sintel): 0.593
 
=== 13-limit ===
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:
* WE: ~2 = 1200.4413{{c}}, ~49/40 = 350.8092{{c}}, ~10/7 = 617.3718{{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 }}
 
Badness (Sintel): 0.863
 
== Zisa ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 2401/2400, 5632/5625
 
{{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]] (Sintel): 0.769
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
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 }}
 
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 (Sintel): 0.776
 
== 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.
 
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.
 
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 2401/2400, 131072/130977
 
{{Mapping|legend=1| 1 1 1 2 8 | 0 2 1 1 -12 | 0 0 2 1 -2 }}
 
[[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]] (Sintel): 0.953
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
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 }}
 
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 (Sintel): 0.542
 
=== 2.3.5.7.11.13.19 subgroup ===
Subgroup: 2.3.5.7.11.13.19
 
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 }}
 
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 (Sintel): 0.488
 
== Baldur ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 2401/2400, 9801/9800
 
{{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
 
{{Optimal ET sequence|legend=1| 58, 72, 130, 198, 212, 270, 342, 612, 954, 1084, 1354, 1696, 4004de, 5700de }}
 
[[Badness]] (Sintel): 0.200
 
[[Projection pair]]s: <code>2 9801/4900, 3 117649/39204, 7 9801/1400, 11 913517247483640899/83082326424002500</code> to 5.7/2.99/4
 
=== Greenland ===
Subgroup: 2.3.5.7.11.13
 
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:
* WE: ~99/70 = 599.9868{{c}}, ~26/15 = 951.0538{{c}}, ~10/7 = 617.8062{{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 }}
 
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
 
==== Midnatssol ====
Subgroup: 2.3.5.7.11.13.17
 
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 }}
 
Optimal tunings:
* WE: ~17/12 = 600.1118{{c}}, ~26/15 = 951.1907{{c}}, ~10/7 = 617.6100{{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
 
== 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.
 
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 2401/2400, 3025/3024
 
{{Mapping|legend=1| 1 1 -1 1 5 | 0 2 3 2 1 | 0 0 4 2 -3 }}
: 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]] [[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]] (Sintel): 0.204
 
[[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.
 
Subgroup: 2.3.5.7.11.13
 
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 }}
 
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 (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
 
=== 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.
 
Subgroup: 2.3.5.7.11.13
 
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 }}
 
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 (Sintel): 0.543
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
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 }}
 
Badness (Sintel): 0.665
 
==== 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}}
* 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 (Sintel): 0.712
 
=== 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.
 
Subgroup: 2.3.5.7.11.13
 
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 }}
 
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}}
 
{{Optimal ET sequence|legend=0| 31, 72, 103, 167, 198, 270, 571, 643, 913f }}
 
Badness (Sintel): 0.562
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


11-limit
Comma list: 715/714, 936/935, 1001/1000, 1225/1224, 1716/1715
[[Comma|Commas]]: 243/242, 441/440


[[Minimax tuning]]
Mapping: {{mapping| 1 1 -1 1 5 -6 -5 | 0 2 3 2 1 6 6 | 0 0 4 2 -3 13 12 }}
[|1 0 0 0 0&gt;, |1/5 0 0 0 2/5&gt;,
|13/5 0 2 -2 1/5&gt;, |13/5 0 1 -1 1/5&gt;,
|0 0 0 0 1&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 7/5, 11/8


Map: [&lt;1 1 1 2 2|, &lt;0 2 1 1 5|, &lt;0 0 2 1 0|]
Optimal tunings:
EDOs: 31, 41, 58, 72, 130, 202
* WE: ~2 = 1200.0446{{c}}, ~49/40 = 350.9662{{c}}, ~26/17 = 733.3826{{c}}
Badness: 0.000241
* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 350.9724{{c}}, ~26/17 = 733.3515{{c}}


===13-limit===
{{Optimal ET sequence|legend=0| 31, 64be, 72, 103, 167, 198g, 239, 270 }}
[[Comma|Commas]]: 243/242, 441/440, 364/363


13-limit minimax
Badness (Sintel): 0.789
[|1 0 0 0 0 0&gt;, |17/11 -12/11 2/11 0 0 4/11&gt;, |34/11 -46/11 15/11 0 0 8/11&gt;,
|35/11 -26/11 8/11 0 0 5/11&gt;,
|37/11 -30/11 5/11 0 0 10/11&gt;,
|34/11 -46/11 4/11 0 0 19/11&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 13/9


15-limit minimax
== Vili ==
[|1 0 0 0 0 0&gt;, |2 -1/4 1/2 -3/4 0 1/4&gt;,
[[Subgroup]]: 2.3.5.7.11
|7/2 -1/8 9/4 -19/8 0 1/8&gt;,
|7/2 -1/8 5/4 -11/8 0 1/8&gt;,
|9/2 -5/8 5/4 -15/8 0 5/8&gt;,
|11/2 -11/8 7/4 -25/8 0 11/8&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 15/13, 7/5


Map: [&lt;1 1 1 2 2 1|, &lt;0 2 1 1 5 11|, &lt;0 2 1 1 0 -1|]
[[Comma list]]: 2401/2400, 391314/390625
EDOs: 41, 58, 72, 130, 243
Badness: 0.000624


===Jofur===
{{Mapping|legend=1| 1 1 -1 1 -4 | 0 2 3 2 6 | 0 0 6 3 14 }}
Commas: 243/242, 441/440, 144/143
: Mapping generators: ~2, ~49/40, ~175/132


Map: [&lt;1 1 1 2 2 4|, &lt;0 2 1 1 5 -1|, &lt;0 0 2 1 0 0|]
[[Optimal tuning]]s:
EDOs: 10, 31, 41, 58
* [[WE]]: ~2 = 1199.9872{{c}}, ~49/40 = 350.9740{{c}}, ~175/132 = 488.9418{{c}}
Badness: 0.000749
: [[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 }}


====17-limit====
{{Optimal ET sequence|legend=1| 27e, 64be, 76e, 93, 103, 130, 233, 243e, 270, 643, 670, 913, 1043, 1313, 1583 }}
Commas: 243/242, 441/440, 364/363, 595/594


17-limit minimax
[[Badness]] (Sintel): 1.51
[|1 0 0 0 0 0 0&gt;, |3/7 -2 6/7 0 0 0 4/7&gt;,
|3/7 -3 13/7 0 0 0 4/7&gt;, |11/7 -2 8/7 0 0 0 3/7&gt;,
|4/7 -5 15/7 0 0 0 10/7&gt;, |-2 -10 4 0 0 0 3&gt;,
|6/7 -6 12/7 0 0 0 15/7&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 18/17, 6/5


Map: [&lt;1 1 1 2 2 1 3|, &lt;0 2 1 1 5 11 9|, &lt;0 0 2 1 0 -1 -3|]
=== 13-limit ===
[[Generator|Generators]]: 2, 11/9, 10/7
Subgroup: 2.3.5.7.11.13
[[edo|Edos]]: 41, 58, [[72edo|72]], [[130edo|130]], [[171edo|171]], [[243edo|243]], [[274edo|274]], [[346edo|346]], [[435edo|435]], [[476edo|476]]
Badness: 0.000741


==Freya==
Comma list: 1001/1000, 1716/1715, 4225/4224
11-limit
[[Comma|Commas]]: 2401/2400, 3025/3024


11-limit minimax
Mapping: {{mapping| 1 1 -1 1 -4 3 | 0 2 3 2 6 1 | 0 0 6 3 14 1 }}
[|1 0 0 0 0&gt;, |0 1 0 0 0&gt;,
|11/10 11/10 0 4/5 -4/5&gt;,
|9/5 4/5 0 2/5 -2/5&gt;, |9/5 4/5 0 -3/5 3/5&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 14/11, 4/3


Map: [&lt;1 1 3 3 2|, &lt;0 2 3 2 1|, &lt;0 0 -4 -3 2|]
Optimal tunings:
EDOs: 10, 31, 41, 72, 167, 198, 239, 270, 342, 612, 954, 1566
* WE: ~2 = 1200.0597{{c}}, ~49/40 = 350.9419{{c}}, ~65/49 = 488.9741{{c}}
Badness: 0.000170
* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 350.9441{{c}}, ~65/49 = 488.9475{{c}}


===13-limit===
{{Optimal ET sequence|legend=0| 27e, 37, 64be, 76e, 93, 103, 130, 233, 243e, 270, 643, 913f }}
Commas: 2401/2400, 3025/3024, 4096/4095


Map: [&lt;1 1 3 3 2|, &lt;0 2 3 2 1|, &lt;0 0 -4 -2 3|]
Badness (Sintel): 0.690
[[Generator|Generators]]: 2, 49/40, 55/42
[[edo|Edos]]: 10, 31, 41, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615
Badness: 0.000855


==Baldur==
== Frigg ==
[[Comma|Commas]]: 2401/2400, 9801/9800
[[Subgroup]]: 2.3.5.7.11


11-limit minimax
[[Comma list]]: 2401/2400, 644204/643125
[|1 0 0 0 0&gt;, |3/4 0 1/2 1/2 -1/2&gt;,
|0 0 1 0 0&gt;, |23/16 0 5/8 1/8 -1/8&gt;,
|23/16 0 5/8 -7/8 7/8&gt;]
[[Eigenmonzo|Eigenmonzos]]: 5/4, 14/11


Map: [&lt;2 0 1 3 7|, &lt;0 2 1 1 -2|, &lt;0 0 2 1 3|]
{{Mapping|legend=1| 1 1 -7 -2 -7 | 0 2 3 2 4 | 0 0 10 5 11 }}
[[Generator|Generators]]: 99/70, 343/198, 10/7
: Mapping generators: ~2, ~49/40, ~88/49
EDOs: 58, 72, 130, 198, 212, 270, 342, 612, 954, 1084, 1354, 1696
Badness: 0.000166


===13-limit===
[[Optimal tuning]]s:
Commas: 2401/2400, 9801/9800, 1001/1000
* [[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 }}


Map: [&lt;2 0 1 3 7 -1|, &lt;0 2 1 1 -2 4|, &lt;0 0 2 1 3 2|]
{{Optimal ET sequence|legend=1| 45e, 58, 103, 161, 212, 270, 643, 913, 1183e }}
[[edo|Edos]]: 58, 72, 130, 198, 270, 940
Badness: 0.000433


==Agni==
[[Badness]] (Sintel): 2.15
[[Comma|Commas]]: 385/384, 1375/1372


11-limit minimax
=== 13-limit ===
[|1 0 0 0 0&gt;, |0 1 0 0 0&gt;,
Subgroup: 2.3.5.7.11.13
|23/10 3/10 2/5 0 -2/5&gt;,
|12/5 2/5 1/5 0 -1/5&gt;,
|23/10 3/10 -3/5 0 3/5&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 4/3, 11/10


Lattice basis: 49/40 length 0.756, 10/7 length 0.819
Comma list: 1001/1000, 1716/1715, 10648/10647
Angle(49/40, 10/7) = 106.460 degrees
Map to lattice: [&lt;0 2 1 1 0|, &lt;0 0 2 1 -3|]


Map: [&lt;1 1 1 2 5|, &lt;0 2 1 1 0|, &lt;0 0 2 1 -3|]
Mapping: {{mapping| 1 1 -7 -2 -7 -9 | 0 2 3 2 4 3 | 0 0 10 5 11 14 }}
[[Generator|Generators]]: 2, 49/40, 10/7
[[edo|Edos]]: 27, 31, 41, 68, 72, 140, 181, [[212edo|212]], [[284edo|284]]
Badness: 0.000494


===13-limit===
Optimal tunings:
Commas: 385/384, 1375/1372, 625/624
* 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}}


Map: [&lt;1 1 1 2 5 -1|, &lt;0 2 1 1 0 2|, &lt;0 0 2 1 -3 8|]
{{Optimal ET sequence|legend=0| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} *
EDOs: 31, 68, 72, 103, 140, 212
Badness: 0.000923


==Vili==
<nowiki/>* optimal patent val: [[1241edo|1241]]
Commas: 2401/2400, 391314/390625


Map: [&lt;1 1 5 4 10|, &lt;0 2 3 2 6|, &lt;0 0 -6 -3 -14|]
Badness (Sintel): 0.873
EDOs: 37, 93, 103, 130, 233, 270, 643, 670, 913, 1043, 1313, 1583
Badness: 0.00126


===13-limit===
== Ennealimmic ==
Commas: 2401/2400, 10985/10976, 1001/1000
{{Distinguish|Ennealimnic}}


Map: [&lt;1 1 5 4 10 4|, &lt;0 2 3 2 6 1|, &lt;0 0 -6 -3 -14 -1|]
[[Subgroup]]: 2.3.5.7.11
EDOs: 37, 93, 103, 130, 233, 270, 643
Badness: 0.000738


==Zisa==
[[Comma list]]: 2401/2400, 4375/4374
Commas: 2401/2400, 5632/5625


Map: [&lt;1 1 1 2 -3|, &lt;0 2 1 1 8|, &lt;0 0 2 1 8|]
{{Mapping|legend=1| 9 1 1 12 0 | 0 2 3 2 0 | 0 0 0 0 1 }}
EDOs: 21, 31, 109, 130, 239, 270, 670, 940, 1210
: Mapping generators: ~27/25, ~5/3, ~11
Badness: 0.000640


===13-limit===
[[Optimal tuning]]s:
Commas: 2401/2400, 5632/5625, 4096/4095
* [[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 }}


Map: [&lt;1 1 1 2 -3 7|, &lt;0 2 1 1 8 -6|, &lt;0 0 2 1 8 -3|]
{{Optimal ET sequence|legend=1| 72, 171(e), 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd, 6903dd }}
EDOs: 21, 31, 109, 130, 239, 270, 571, 701, 841, 971, 1241
Badness: 0.000830


==Frigg==
[[Badness]] (Sintel): 0.330
Commas: 2401/2400, 644204/643125


Map: [&lt;1 1 3 3 4|, &lt;0 2 3 2 4|, &lt;0 0 -10 -5 -11|]
=== 13-limit ===
EDOs: 51, 58, 103, 161, 212, 270, 643, 913
Subgroup: 2.3.5.7.11.13
Badness: 0.00179


===13-limit===
Comma list: 2080/2079, 2401/2400, 4375/4374
Commas: 2401/2400, 10648/10647, 1001/1000


Map: [&lt;1 1 3 3 4 5|, &lt;0 2 3 2 4 3|, &lt;0 0 -10 -5 -11 -14|]
Mapping: {{mapping| 9 1 1 12 0 -31 | 0 2 3 2 0 5 | 0 0 0 0 1 1 }}
EDOs: 58, 103, 161, 212, 270, 643, 1241, 1344
Badness: 0.000934


==Ennealimmic==
Optimal tunings:
Commas: 2401/2400, 4375/4374
* 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}}


Map: [&lt;9 1 1 12 0|, &lt;0 2 3 2 0|, &lt;0 0 0 0 1|]
{{Optimal ET sequence|legend=0| 72, 171(ef), 198, 270, 639, 711, 981, 1692e }}
Generators: 27/25, 5/3, 11
EDOs: 27, 45, 72, 171, 198, 270, 342, 612, 1323, 1395, 1665, 2007, 2277, 2619
Badness: 0.000275


===13-limit===
Badness (Sintel): 0.706
Commas: 2080/2079, 2401/2400, 4375/4374


Map: [&lt;9 1 1 12 0 -31|, &lt;0 2 3 2 0 5|, &lt;0 0 0 0 1 1|]
[[Category:Temperament families]]
EDOs: 27, 72, 171, 198, 270, 639, 711, 981
[[Category:Breed family| ]] <!-- main article -->
Badness: 0.000755</pre></div>
[[Category:Rank 3]]
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Breed family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Breed is a 7-limit microtemperament which tempers 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 &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; 2749et will certainly do the trick.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;a name="x--Vital statistics"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Vital statistics&lt;/h3&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt; c = 2401/2400&lt;br /&gt;
7- and 9-limit minimax tuning: 3 and 5 just, 7 1/4c flat&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 6/5, 5/4&lt;br /&gt;
Lattice basis: 49/40 length 0.7858 8/7 length 1.1241&lt;br /&gt;
Angle(49/40, 8/7) = 107.367 degrees&lt;br /&gt;
Map to lattice: [&amp;lt;0 2 -1 0|, &amp;lt;0 0 -2 -1|]&lt;br /&gt;
Map [&amp;lt;1 1 1 2|, &amp;lt;0 2 1 1|, &amp;lt;0 0 2 1|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 49/40, 10/7&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;EDOs&lt;/a&gt;: &lt;a class="wiki_link" href="/441edo"&gt;441&lt;/a&gt;, &lt;a class="wiki_link" href="/612edo"&gt;612&lt;/a&gt;, &lt;a class="wiki_link" href="/2308edo"&gt;2308&lt;/a&gt;, &lt;a class="wiki_link" href="/2749edo"&gt;2749&lt;/a&gt;&lt;br /&gt;
Badness: 0.0000153&lt;br /&gt;
&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/breed11"&gt;breed11&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Jove, aka Wonder"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Jove, aka Wonder&lt;/h2&gt;
Jove, formerly known as wonder, tempers out 243/242 and 441/440. Wonder has been deprecated as a name due to conflict with another temperament also given that name. 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. 72, 130 and 171 are good edos for jove, and if that doesn't suit there's 476edo.&lt;br /&gt;
&lt;br /&gt;
11-limit&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 243/242, 441/440&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |1/5 0 0 0 2/5&amp;gt;, &lt;br /&gt;
|13/5 0 2 -2 1/5&amp;gt;, |13/5 0 1 -1 1/5&amp;gt;, &lt;br /&gt;
|0 0 0 0 1&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 7/5, 11/8&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 1 2 2|, &amp;lt;0 2 1 1 5|, &amp;lt;0 0 2 1 0|]&lt;br /&gt;
EDOs: 31, 41, 58, 72, 130, 202&lt;br /&gt;
Badness: 0.000241&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Jove, aka Wonder-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h3&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 243/242, 441/440, 364/363&lt;br /&gt;
&lt;br /&gt;
13-limit minimax&lt;br /&gt;
[|1 0 0 0 0 0&amp;gt;, |17/11 -12/11 2/11 0 0 4/11&amp;gt;, |34/11 -46/11 15/11 0 0 8/11&amp;gt;, &lt;br /&gt;
|35/11 -26/11 8/11 0 0 5/11&amp;gt;, &lt;br /&gt;
|37/11 -30/11 5/11 0 0 10/11&amp;gt;, &lt;br /&gt;
|34/11 -46/11 4/11 0 0 19/11&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 10/9, 13/9&lt;br /&gt;
&lt;br /&gt;
15-limit minimax&lt;br /&gt;
[|1 0 0 0 0 0&amp;gt;, |2 -1/4 1/2 -3/4 0 1/4&amp;gt;, &lt;br /&gt;
|7/2 -1/8 9/4 -19/8 0 1/8&amp;gt;, &lt;br /&gt;
|7/2 -1/8 5/4 -11/8 0 1/8&amp;gt;, &lt;br /&gt;
|9/2 -5/8 5/4 -15/8 0 5/8&amp;gt;,&lt;br /&gt;
|11/2 -11/8 7/4 -25/8 0 11/8&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 15/13, 7/5&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 1 2 2 1|, &amp;lt;0 2 1 1 5 11|, &amp;lt;0 2 1 1 0 -1|]&lt;br /&gt;
EDOs: 41, 58, 72, 130, 243&lt;br /&gt;
Badness: 0.000624&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Jove, aka Wonder-Jofur"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Jofur&lt;/h3&gt;
Commas: 243/242, 441/440, 144/143&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 1 2 2 4|, &amp;lt;0 2 1 1 5 -1|, &amp;lt;0 0 2 1 0 0|]&lt;br /&gt;
EDOs: 10, 31, 41, 58&lt;br /&gt;
Badness: 0.000749&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc4"&gt;&lt;a name="x-Jove, aka Wonder-Jofur-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;17-limit&lt;/h4&gt;
Commas: 243/242, 441/440, 364/363, 595/594&lt;br /&gt;
&lt;br /&gt;
17-limit minimax&lt;br /&gt;
[|1 0 0 0 0 0 0&amp;gt;, |3/7 -2 6/7 0 0 0 4/7&amp;gt;, &lt;br /&gt;
|3/7 -3 13/7 0 0 0 4/7&amp;gt;, |11/7 -2 8/7 0 0 0 3/7&amp;gt;, &lt;br /&gt;
|4/7 -5 15/7 0 0 0 10/7&amp;gt;, |-2 -10 4 0 0 0 3&amp;gt;, &lt;br /&gt;
|6/7 -6 12/7 0 0 0 15/7&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 18/17, 6/5&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 1 2 2 1 3|, &amp;lt;0 2 1 1 5 11 9|, &amp;lt;0 0 2 1 0 -1 -3|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 11/9, 10/7&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: 41, 58, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/130edo"&gt;130&lt;/a&gt;, &lt;a class="wiki_link" href="/171edo"&gt;171&lt;/a&gt;, &lt;a class="wiki_link" href="/243edo"&gt;243&lt;/a&gt;, &lt;a class="wiki_link" href="/274edo"&gt;274&lt;/a&gt;, &lt;a class="wiki_link" href="/346edo"&gt;346&lt;/a&gt;, &lt;a class="wiki_link" href="/435edo"&gt;435&lt;/a&gt;, &lt;a class="wiki_link" href="/476edo"&gt;476&lt;/a&gt;&lt;br /&gt;
Badness: 0.000741&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x-Freya"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Freya&lt;/h2&gt;
11-limit&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 2401/2400, 3025/3024&lt;br /&gt;
&lt;br /&gt;
11-limit minimax&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |0 1 0 0 0&amp;gt;, &lt;br /&gt;
|11/10 11/10 0 4/5 -4/5&amp;gt;, &lt;br /&gt;
|9/5 4/5 0 2/5 -2/5&amp;gt;, |9/5 4/5 0 -3/5 3/5&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 14/11, 4/3&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3 3 2|, &amp;lt;0 2 3 2 1|, &amp;lt;0 0 -4 -3 2|]&lt;br /&gt;
EDOs: 10, 31, 41, 72, 167, 198, 239, 270, 342, 612, 954, 1566&lt;br /&gt;
Badness: 0.000170&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="x-Freya-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;13-limit&lt;/h3&gt;
Commas: 2401/2400, 3025/3024, 4096/4095&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3 3 2|, &amp;lt;0 2 3 2 1|, &amp;lt;0 0 -4 -2 3|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 49/40, 55/42&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: 10, 31, 41, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615&lt;br /&gt;
Badness: 0.000855&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="x-Baldur"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Baldur&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 2401/2400, 9801/9800&lt;br /&gt;
&lt;br /&gt;
11-limit minimax&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |3/4 0 1/2 1/2 -1/2&amp;gt;, &lt;br /&gt;
|0 0 1 0 0&amp;gt;, |23/16 0 5/8 1/8 -1/8&amp;gt;, &lt;br /&gt;
|23/16 0 5/8 -7/8 7/8&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 5/4, 14/11&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 1 3 7|, &amp;lt;0 2 1 1 -2|, &amp;lt;0 0 2 1 3|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 99/70, 343/198, 10/7&lt;br /&gt;
EDOs: 58, 72, 130, 198, 212, 270, 342, 612, 954, 1084, 1354, 1696&lt;br /&gt;
Badness: 0.000166&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="x-Baldur-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;13-limit&lt;/h3&gt;
Commas: 2401/2400, 9801/9800, 1001/1000&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 1 3 7 -1|, &amp;lt;0 2 1 1 -2 4|, &amp;lt;0 0 2 1 3 2|]&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: 58, 72, 130, 198, 270, 940&lt;br /&gt;
Badness: 0.000433&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="x-Agni"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Agni&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 385/384, 1375/1372&lt;br /&gt;
&lt;br /&gt;
11-limit minimax&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |0 1 0 0 0&amp;gt;, &lt;br /&gt;
|23/10 3/10 2/5 0 -2/5&amp;gt;, &lt;br /&gt;
|12/5 2/5 1/5 0 -1/5&amp;gt;, &lt;br /&gt;
|23/10 3/10 -3/5 0 3/5&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 4/3, 11/10&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 49/40 length 0.756, 10/7 length 0.819&lt;br /&gt;
Angle(49/40, 10/7) = 106.460 degrees&lt;br /&gt;
Map to lattice: [&amp;lt;0 2 1 1 0|, &amp;lt;0 0 2 1 -3|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 1 2 5|, &amp;lt;0 2 1 1 0|, &amp;lt;0 0 2 1 -3|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 49/40, 10/7&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: 27, 31, 41, 68, 72, 140, 181, &lt;a class="wiki_link" href="/212edo"&gt;212&lt;/a&gt;, &lt;a class="wiki_link" href="/284edo"&gt;284&lt;/a&gt;&lt;br /&gt;
Badness: 0.000494&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="x-Agni-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;13-limit&lt;/h3&gt;
Commas: 385/384, 1375/1372, 625/624&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 1 2 5 -1|, &amp;lt;0 2 1 1 0 2|, &amp;lt;0 0 2 1 -3 8|]&lt;br /&gt;
EDOs: 31, 68, 72, 103, 140, 212&lt;br /&gt;
Badness: 0.000923&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="x-Vili"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Vili&lt;/h2&gt;
Commas: 2401/2400, 391314/390625&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 5 4 10|, &amp;lt;0 2 3 2 6|, &amp;lt;0 0 -6 -3 -14|]&lt;br /&gt;
EDOs: 37, 93, 103, 130, 233, 270, 643, 670, 913, 1043, 1313, 1583&lt;br /&gt;
Badness: 0.00126&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="x-Vili-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;13-limit&lt;/h3&gt;
Commas: 2401/2400, 10985/10976, 1001/1000&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 5 4 10 4|, &amp;lt;0 2 3 2 6 1|, &amp;lt;0 0 -6 -3 -14 -1|]&lt;br /&gt;
EDOs: 37, 93, 103, 130, 233, 270, 643&lt;br /&gt;
Badness: 0.000738&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="x-Zisa"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Zisa&lt;/h2&gt;
Commas: 2401/2400, 5632/5625&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 1 2 -3|, &amp;lt;0 2 1 1 8|, &amp;lt;0 0 2 1 8|]&lt;br /&gt;
EDOs: 21, 31, 109, 130, 239, 270, 670, 940, 1210&lt;br /&gt;
Badness: 0.000640&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc14"&gt;&lt;a name="x-Zisa-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;13-limit&lt;/h3&gt;
Commas: 2401/2400, 5632/5625, 4096/4095&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 1 2 -3 7|, &amp;lt;0 2 1 1 8 -6|, &amp;lt;0 0 2 1 8 -3|]&lt;br /&gt;
EDOs: 21, 31, 109, 130, 239, 270, 571, 701, 841, 971, 1241&lt;br /&gt;
Badness: 0.000830&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="x-Frigg"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Frigg&lt;/h2&gt;
Commas: 2401/2400, 644204/643125&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3 3 4|, &amp;lt;0 2 3 2 4|, &amp;lt;0 0 -10 -5 -11|]&lt;br /&gt;
EDOs: 51, 58, 103, 161, 212, 270, 643, 913&lt;br /&gt;
Badness: 0.00179&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc16"&gt;&lt;a name="x-Frigg-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;13-limit&lt;/h3&gt;
Commas: 2401/2400, 10648/10647, 1001/1000&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3 3 4 5|, &amp;lt;0 2 3 2 4 3|, &amp;lt;0 0 -10 -5 -11 -14|]&lt;br /&gt;
EDOs: 58, 103, 161, 212, 270, 643, 1241, 1344&lt;br /&gt;
Badness: 0.000934&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="x-Ennealimmic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Ennealimmic&lt;/h2&gt;
Commas: 2401/2400, 4375/4374&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;9 1 1 12 0|, &amp;lt;0 2 3 2 0|, &amp;lt;0 0 0 0 1|]&lt;br /&gt;
Generators: 27/25, 5/3, 11&lt;br /&gt;
EDOs: 27, 45, 72, 171, 198, 270, 342, 612, 1323, 1395, 1665, 2007, 2277, 2619&lt;br /&gt;
Badness: 0.000275&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc18"&gt;&lt;a name="x-Ennealimmic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;13-limit&lt;/h3&gt;
Commas: 2080/2079, 2401/2400, 4375/4374&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;9 1 1 12 0 -31|, &amp;lt;0 2 3 2 0 5|, &amp;lt;0 0 0 0 1 1|]&lt;br /&gt;
EDOs: 27, 72, 171, 198, 270, 639, 711, 981&lt;br /&gt;
Badness: 0.000755&lt;/body&gt;&lt;/html&gt;</pre></div>
Retrieved from "https://en.xen.wiki/w/Breed_family"