Breed family: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
__FORCETOC__
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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|optimal patent val]] 2749et will certainly do the trick.
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-21 14:31:48 UTC</tt>.<br>
: The original revision id was <tt>323680962</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">[[toc]]


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=
[[Comma|Comma]] c = 2401/2400


=Vital statistics=
[[Comma]] c = 2401/2400
7- and 9-limit minimax tuning: 3 and 5 just, 7 1/4c flat
7- and 9-limit minimax tuning: 3 and 5 just, 7 1/4c flat
[[Eigenmonzo|Eigenmonzos]]: 2, 6/5, 5/4
[[Eigenmonzo|Eigenmonzos]]: 2, 6/5, 5/4
Lattice basis: 49/40 length 0.7858 8/7 length 1.1241
Lattice basis: 49/40 length 0.7858 8/7 length 1.1241
Angle(49/40, 8/7) = 107.367 degrees
Angle(49/40, 8/7) = 107.367 degrees
Map to lattice: [&lt;0 2 -1 0|, &lt;0 0 -2 -1|]
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|]
Map [&lt;1 1 1 2|, &lt;0 2 1 1|, &lt;0 0 2 1|]
[[Generator|Generators]]: 2, 49/40, 10/7
 
[[edo|EDOs]]: [[31edo|31]], [[41edo|41]], [[58edo|58]], [[68edo|68]], [[72edo|72]], [[171edo|171]], [[441edo|441]], [[612edo|612]], [[2308edo|2308]], [[2578edo|2578]], [[2749edo|2749]], [[3361edo|3361d]]
[[generator|Generators]]: 2, 49/40, 10/7
 
[[EDO|EDOs]]: [[31edo|31]], [[41edo|41]], [[58edo|58]], [[68edo|68]], [[72edo|72]], [[171edo|171]], [[441edo|441]], [[612edo|612]], [[2308edo|2308]], [[2578edo|2578]], [[2749edo|2749]], [[3361edo|3361d]]
 
Badness: 0.0000153
Badness: 0.0000153


[[Projection pair]]: 3 2401/800 to 2.5.7
[[Projection_pair|Projection pair]]: 3 2401/800 to 2.5.7


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


=Jove, aka Wonder=
=Jove, aka Wonder=
Line 30: Line 31:


11-limit
11-limit
[[Comma|Commas]]: 243/242, 441/440
[[Comma|Commas]]: 243/242, 441/440


[[Minimax tuning]]
[[Minimax_tuning|Minimax tuning]]
 
[|1 0 0 0 0&gt;, |1/5 0 0 0 2/5&gt;,  
[|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;,  
|13/5 0 2 -2 1/5&gt;, |13/5 0 1 -1 1/5&gt;,  
|0 0 0 0 1&gt;]
|0 0 0 0 1&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 7/5, 11/8
[[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|]
Map: [&lt;1 1 1 2 2|, &lt;0 2 1 1 5|, &lt;0 0 2 1 0|]
EDOs: 31, 41, 58, 72, 130, 161, 171, 202
EDOs: 31, 41, 58, 72, 130, 161, 171, 202
Badness: 0.000241
Badness: 0.000241


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


[[http://micro.soonlabel.com/hobbit_scales/20120418-jove41.mp3|By Jove!]] in [[jove41]] by Chris Vaisvil
[http://micro.soonlabel.com/hobbit_scales/20120418-jove41.mp3 By Jove!] in [[jove41|jove41]] by Chris Vaisvil


==Jovial==
==Jovial==
Line 50: Line 56:


13-limit minimax
13-limit minimax
[|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;,  
[|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;,  
|35/11 -26/11 8/11 0 0 5/11&gt;,  
|37/11 -30/11 5/11 0 0 10/11&gt;,  
|37/11 -30/11 5/11 0 0 10/11&gt;,  
|34/11 -46/11 4/11 0 0 19/11&gt;]
|34/11 -46/11 4/11 0 0 19/11&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 13/9
[[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 13/9


15-limit minimax
15-limit minimax
[|1 0 0 0 0 0&gt;, |2 -1/4 1/2 -3/4 0 1/4&gt;,  
[|1 0 0 0 0 0&gt;, |2 -1/4 1/2 -3/4 0 1/4&gt;,  
|7/2 -1/8 9/4 -19/8 0 1/8&gt;,  
|7/2 -1/8 9/4 -19/8 0 1/8&gt;,  
Line 62: Line 71:
|9/2 -5/8 5/4 -15/8 0 5/8&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;]
|11/2 -11/8 7/4 -25/8 0 11/8&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 15/13, 7/5
[[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|]
Map: [&lt;1 1 1 2 2 1|, &lt;0 2 1 1 5 11|, &lt;0 2 1 1 0 -1|]
EDOs: 41, 58, 72, 89, 113, 130, 243, 301e, 373e, 503e, 674e
EDOs: 41, 58, 72, 89, 113, 130, 243, 301e, 373e, 503e, 674e
Badness: 0.000624
Badness: 0.000624


Line 72: Line 84:


17-limit minimax
17-limit minimax
[|1 0 0 0 0 0 0&gt;, |3/7 -2 6/7 0 0 0 4/7&gt;,  
[|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;,  
|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;,  
|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;]
|6/7 -6 12/7 0 0 0 15/7&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 18/17, 6/5
[[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|]
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|]
[[Generator|Generators]]: 2, 11/9, 10/7
 
[[edo|Edos]]: 41, 58, [[72edo|72]], [[130edo|130]], [[171edo|171]], [[243edo|243]], [[274edo|274]], [[346edo|346]], [[373edo|373eg]], [[414edo|414e]], [[544edo|540eg]], [[787edo|787eg]]
[[generator|Generators]]: 2, 11/9, 10/7
 
[[EDO|Edos]]: 41, 58, [[72edo|72]], [[130edo|130]], [[171edo|171]], [[243edo|243]], [[274edo|274]], [[346edo|346]], [[373edo|373eg]], [[414edo|414e]], [[544edo|540eg]], [[787edo|787eg]]
 
Badness: 0.000741
Badness: 0.000741


Line 87: Line 104:


Map: [&lt;1 1 1 2 2 4|, &lt;0 2 1 1 5 -1|, &lt;0 0 2 1 0 0|]
Map: [&lt;1 1 1 2 2 4|, &lt;0 2 1 1 5 -1|, &lt;0 0 2 1 0 0|]
EDOs: 31, 41, 58, 89f, 99ef, 157ef
EDOs: 31, 41, 58, 89f, 99ef, 157ef
Badness: 0.000749
Badness: 0.000749


Line 94: Line 113:


Map: [&lt;1 1 1 2 2 2|, &lt;0 2 1 1 5 -3|, &lt;0 0 2 1 0 5|]
Map: [&lt;1 1 1 2 2 2|, &lt;0 2 1 1 5 -3|, &lt;0 0 2 1 0 5|]
EDOs: 31, 58, 72, 103, 130, 233, 363, 798bf, 928bef
EDOs: 31, 58, 72, 103, 130, 233, 363, 798bf, 928bef
Badness: 0.000542
Badness: 0.000542


=Freya=
=Freya=
11-limit
11-limit
[[Comma|Commas]]: 2401/2400, 3025/3024
[[Comma|Commas]]: 2401/2400, 3025/3024


11-limit minimax
11-limit minimax
[|1 0 0 0 0&gt;, |0 1 0 0 0&gt;,  
[|1 0 0 0 0&gt;, |0 1 0 0 0&gt;,  
|11/10 11/10 0 4/5 -4/5&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;]
|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
[[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|]
Map: [&lt;1 1 3 3 2|, &lt;0 2 3 2 1|, &lt;0 0 -4 -3 2|]
EDOs: 31, 41, 72, 167, 188, 198, 229, 239, 270, 342, 612, 954, 1566, 3443de, 4055de, 4397cde
EDOs: 31, 41, 72, 167, 188, 198, 229, 239, 270, 342, 612, 954, 1566, 3443de, 4055de, 4397cde
Badness: 0.000170
Badness: 0.000170


Line 117: Line 143:


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


Line 127: Line 156:


11-limit minimax
11-limit minimax
[|1 0 0 0 0&gt;, |3/4 0 1/2 1/2 -1/2&gt;,  
[|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;,  
|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;]
|23/16 0 5/8 -7/8 7/8&gt;]
[[Eigenmonzo|Eigenmonzos]]: 5/4, 14/11
[[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|]
Map: [&lt;2 0 1 3 7|, &lt;0 2 1 1 -2|, &lt;0 0 2 1 3|]
[[Generator|Generators]]: 99/70, 343/198, 10/7
 
[[generator|Generators]]: 99/70, 343/198, 10/7
 
EDOs: 58, 72, 130, 198, 212, 270, 342, 612, 954, 1084, 1354, 1696, 4004de, 5700de
EDOs: 58, 72, 130, 198, 212, 270, 342, 612, 954, 1084, 1354, 1696, 4004de, 5700de
Badness: 0.000166
Badness: 0.000166


Line 143: Line 177:


Map: [&lt;2 0 1 3 7 -1|, &lt;0 2 1 1 -2 4|, &lt;0 0 2 1 3 2|]
Map: [&lt;2 0 1 3 7 -1|, &lt;0 2 1 1 -2 4|, &lt;0 0 2 1 3 2|]
[[edo|Edos]]: 58, 72, 130, 198, 270, 940, 1210f, 1480cf, 1750cf
 
[[EDO|Edos]]: 58, 72, 130, 198, 270, 940, 1210f, 1480cf, 1750cf
 
Badness: 0.000433
Badness: 0.000433
[[Spectrum of a temperament|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
 
[[Spectrum_of_a_temperament|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: 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
Line 153: Line 190:


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


Lattice basis: 49/40 length 0.756, 10/7 length 0.819
Lattice basis: 49/40 length 0.756, 10/7 length 0.819
Angle(49/40, 10/7) = 106.460 degrees
Angle(49/40, 10/7) = 106.460 degrees
Map to lattice: [&lt;0 2 1 1 0|, &lt;0 0 2 1 -3|]
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|]
Map: [&lt;1 1 1 2 5|, &lt;0 2 1 1 0|, &lt;0 0 2 1 -3|]
[[Generator|Generators]]: 2, 49/40, 10/7
 
[[edo|Edos]]: 27, 31, 41, 68, 72, 140, 171e, 181, [[212edo|212]], [[284edo|284]], [[496edo|496ce]], [[527edo|527ce]]
[[generator|Generators]]: 2, 49/40, 10/7
 
[[EDO|Edos]]: 27, 31, 41, 68, 72, 140, 171e, 181, [[212edo|212]], [[284edo|284]], [[496edo|496ce]], [[527edo|527ce]]
 
Badness: 0.000494
Badness: 0.000494


Line 172: Line 216:


Map: [&lt;1 1 1 2 5 -1|, &lt;0 2 1 1 0 2|, &lt;0 0 2 1 -3 8|]
Map: [&lt;1 1 1 2 5 -1|, &lt;0 2 1 1 0 2|, &lt;0 0 2 1 -3 8|]
EDOs: 31, 68, 72, 103, 140, 212, 243e, 315ef, 455ef
EDOs: 31, 68, 72, 103, 140, 212, 243e, 315ef, 455ef
Badness: 0.000923
Badness: 0.000923


Line 179: Line 225:


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


Line 186: Line 234:


Map: [&lt;1 1 5 4 10 4|, &lt;0 2 3 2 6 1|, &lt;0 0 -6 -3 -14 -1|]
Map: [&lt;1 1 5 4 10 4|, &lt;0 2 3 2 6 1|, &lt;0 0 -6 -3 -14 -1|]
EDOs: 37, 93, 103, 130, 233, 270, 643, 773, 913f, 1956ef
EDOs: 37, 93, 103, 130, 233, 270, 643, 773, 913f, 1956ef
Badness: 0.000738
Badness: 0.000738


Line 193: Line 243:


Map: [&lt;1 1 1 2 -3|, &lt;0 2 1 1 8|, &lt;0 0 2 1 8|]
Map: [&lt;1 1 1 2 -3|, &lt;0 2 1 1 8|, &lt;0 0 2 1 8|]
EDOs: 21, 31, 109, 130, 239, 270, 670, 940, 1210, 2150c
EDOs: 21, 31, 109, 130, 239, 270, 670, 940, 1210, 2150c
Badness: 0.000640
Badness: 0.000640


Line 200: Line 252:


Map: [&lt;1 1 1 2 -3 7|, &lt;0 2 1 1 8 -6|, &lt;0 0 2 1 8 -3|]
Map: [&lt;1 1 1 2 -3 7|, &lt;0 2 1 1 8 -6|, &lt;0 0 2 1 8 -3|]
EDOs: 21, 31, 109, 130, 239, 270, 571, 701, 841, 971, 1241
EDOs: 21, 31, 109, 130, 239, 270, 571, 701, 841, 971, 1241
Badness: 0.000830
Badness: 0.000830


Line 207: Line 261:


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


Line 214: Line 270:


Map: [&lt;1 1 3 3 4 5|, &lt;0 2 3 2 4 3|, &lt;0 0 -10 -5 -11 -14|]
Map: [&lt;1 1 3 3 4 5|, &lt;0 2 3 2 4 3|, &lt;0 0 -10 -5 -11 -14|]
EDOs: 58, 103, 161, 212, 270, 643, 1241, 2082ce, 3053ce, 3323cef
EDOs: 58, 103, 161, 212, 270, 643, 1241, 2082ce, 3053ce, 3323cef
Badness: 0.000934
Badness: 0.000934


Line 221: Line 279:


Map: [&lt;9 1 1 12 0|, &lt;0 2 3 2 0|, &lt;0 0 0 0 1|]
Map: [&lt;9 1 1 12 0|, &lt;0 2 3 2 0|, &lt;0 0 0 0 1|]
Generators: 27/25, 5/3, 11
Generators: 27/25, 5/3, 11
EDOs: 27, 45, 72, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 4896d
EDOs: 27, 45, 72, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 4896d
Badness: 0.000275
Badness: 0.000275


Line 229: Line 290:


Map: [&lt;9 1 1 12 0 -31|, &lt;0 2 3 2 0 5|, &lt;0 0 0 0 1 1|]
Map: [&lt;9 1 1 12 0 -31|, &lt;0 2 3 2 0 5|, &lt;0 0 0 0 1 1|]
EDOs: 27, 72, 171, 198, 270, 639, 711, 981, 1692e, 2673e
EDOs: 27, 72, 171, 198, 270, 639, 711, 981, 1692e, 2673e
Badness: 0.000755</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 0.000755
<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;&lt;!-- ws:start:WikiTextTocRule:40:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:40 --&gt;&lt;!-- ws:start:WikiTextTocRule:41: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Vital statistics"&gt;Vital statistics&lt;/a&gt;&lt;/div&gt;
[[Category:breed]]
&lt;!-- ws:end:WikiTextTocRule:41 --&gt;&lt;!-- ws:start:WikiTextTocRule:42: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Jove, aka Wonder"&gt;Jove, aka Wonder&lt;/a&gt;&lt;/div&gt;
[[Category:family]]
&lt;!-- ws:end:WikiTextTocRule:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Jove, aka Wonder-Jovial"&gt;Jovial&lt;/a&gt;&lt;/div&gt;
[[Category:planar]]
&lt;!-- ws:end:WikiTextTocRule:43 --&gt;&lt;!-- ws:start:WikiTextTocRule:44: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Jove, aka Wonder-Jovial-17-limit"&gt;17-limit&lt;/a&gt;&lt;/div&gt;
[[Category:theory]]
&lt;!-- ws:end:WikiTextTocRule:44 --&gt;&lt;!-- ws:start:WikiTextTocRule:45: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Jove, aka Wonder-Jofur"&gt;Jofur&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:45 --&gt;&lt;!-- ws:start:WikiTextTocRule:46: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Jove, aka Wonder-Jovis"&gt;Jovis&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Freya"&gt;Freya&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Freya-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Baldur"&gt;Baldur&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Baldur-Greenland"&gt;Greenland&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Agni"&gt;Agni&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Agni-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Vili"&gt;Vili&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Vili-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Zisa"&gt;Zisa&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Zisa-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Frigg"&gt;Frigg&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Frigg-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Ennealimmic"&gt;Ennealimmic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Ennealimmic-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;br /&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;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Vital statistics"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Vital statistics&lt;/h1&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="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;, &lt;a class="wiki_link" href="/58edo"&gt;58&lt;/a&gt;, &lt;a class="wiki_link" href="/68edo"&gt;68&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/171edo"&gt;171&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="/2578edo"&gt;2578&lt;/a&gt;, &lt;a class="wiki_link" href="/2749edo"&gt;2749&lt;/a&gt;, &lt;a class="wiki_link" href="/3361edo"&gt;3361d&lt;/a&gt;&lt;br /&gt;
Badness: 0.0000153&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;: 3 2401/800 to 2.5.7&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;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Jove, aka Wonder"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Jove, aka Wonder&lt;/h1&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, 171 and 202 are good edos for jove.&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, 161, 171, 202&lt;br /&gt;
Badness: 0.000241&lt;br /&gt;
&lt;br /&gt;
Projection pairs: 3 242/81 5 2200/441 7 440/63 11 644204/59049 to 2.7/5.11/9&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/hobbit_scales/20120418-jove41.mp3" rel="nofollow"&gt;By Jove!&lt;/a&gt; in &lt;a class="wiki_link" href="/jove41"&gt;jove41&lt;/a&gt; by Chris Vaisvil&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Jove, aka Wonder-Jovial"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Jovial&lt;/h2&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, 89, 113, 130, 243, 301e, 373e, 503e, 674e&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="Jove, aka Wonder-Jovial-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;17-limit&lt;/h3&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="/373edo"&gt;373eg&lt;/a&gt;, &lt;a class="wiki_link" href="/414edo"&gt;414e&lt;/a&gt;, &lt;a class="wiki_link" href="/544edo"&gt;540eg&lt;/a&gt;, &lt;a class="wiki_link" href="/787edo"&gt;787eg&lt;/a&gt;&lt;br /&gt;
Badness: 0.000741&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Jove, aka Wonder-Jofur"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Jofur&lt;/h2&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: 31, 41, 58, 89f, 99ef, 157ef&lt;br /&gt;
Badness: 0.000749&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="Jove, aka Wonder-Jovis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Jovis&lt;/h2&gt;
Commas: 243/242, 351/350, 441/440&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 1 2 2 2|, &amp;lt;0 2 1 1 5 -3|, &amp;lt;0 0 2 1 0 5|]&lt;br /&gt;
EDOs: 31, 58, 72, 103, 130, 233, 363, 798bf, 928bef&lt;br /&gt;
Badness: 0.000542&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Freya"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Freya&lt;/h1&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: 31, 41, 72, 167, 188, 198, 229, 239, 270, 342, 612, 954, 1566, 3443de, 4055de, 4397cde&lt;br /&gt;
Badness: 0.000170&lt;br /&gt;
&lt;br /&gt;
Projection pairs: 3 2401/800 5 22880495169/4575312500 7 1058841/151250 11 33275/3024 to 2.49/5.77/3&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="Freya-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;13-limit&lt;/h2&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;: 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;
Projection pairs: 3 2401/800 5 22880495169/4575312500 7 1058841/151250 11 33275/3024 1814078464000000000000000/139662717676432916098329 to 2.49/5.77/3&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Baldur"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Baldur&lt;/h1&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, 4004de, 5700de&lt;br /&gt;
Badness: 0.000166&lt;br /&gt;
&lt;br /&gt;
Projection pairs: 2 9801/4900 3 117649/39204 7 9801/1400 11  913517247483640899/83082326424002500 to 5.7/2.99/4&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="Baldur-Greenland"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Greenland&lt;/h2&gt;
Commas: 676/675, 1001/1000, 1716/1715&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, 1210f, 1480cf, 1750cf&lt;br /&gt;
Badness: 0.000433&lt;br /&gt;
&lt;a class="wiki_link" href="/Spectrum%20of%20a%20temperament"&gt;Spectrum&lt;/a&gt;: 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&lt;br /&gt;
&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Agni"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Agni&lt;/h1&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, 171e, 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;a class="wiki_link" href="/496edo"&gt;496ce&lt;/a&gt;, &lt;a class="wiki_link" href="/527edo"&gt;527ce&lt;/a&gt;&lt;br /&gt;
Badness: 0.000494&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="Agni-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;13-limit&lt;/h2&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, 243e, 315ef, 455ef&lt;br /&gt;
Badness: 0.000923&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Vili"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Vili&lt;/h1&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:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Vili-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;13-limit&lt;/h2&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, 773, 913f, 1956ef&lt;br /&gt;
Badness: 0.000738&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Zisa"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Zisa&lt;/h1&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, 2150c&lt;br /&gt;
Badness: 0.000640&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="Zisa-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;13-limit&lt;/h2&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:32:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc16"&gt;&lt;a name="Frigg"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Frigg&lt;/h1&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:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Frigg-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;13-limit&lt;/h2&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, 2082ce, 3053ce, 3323cef&lt;br /&gt;
Badness: 0.000934&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Ennealimmic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Ennealimmic&lt;/h1&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, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 4896d&lt;br /&gt;
Badness: 0.000275&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Ennealimmic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;13-limit&lt;/h2&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, 1692e, 2673e&lt;br /&gt;
Badness: 0.000755&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

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

Comma c = 2401/2400

7- and 9-limit minimax tuning: 3 and 5 just, 7 1/4c flat

Eigenmonzos: 2, 6/5, 5/4

Lattice basis: 49/40 length 0.7858 8/7 length 1.1241

Angle(49/40, 8/7) = 107.367 degrees

Map to lattice: [<0 2 -1 0|, <0 0 -2 -1|]

Map [<1 1 1 2|, <0 2 1 1|, <0 0 2 1|]

Generators: 2, 49/40, 10/7

EDOs: 31, 41, 58, 68, 72, 171, 441, 612, 2308, 2578, 2749, 3361d

Badness: 0.0000153

Projection pair: 3 2401/800 to 2.5.7

Scales: breed11

Jove, aka Wonder

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, 171 and 202 are good edos for jove.

11-limit

Commas: 243/242, 441/440

Minimax tuning

[|1 0 0 0 0>, |1/5 0 0 0 2/5>, |13/5 0 2 -2 1/5>, |13/5 0 1 -1 1/5>, |0 0 0 0 1>]

Eigenmonzos: 2, 7/5, 11/8

Map: [<1 1 1 2 2|, <0 2 1 1 5|, <0 0 2 1 0|]

EDOs: 31, 41, 58, 72, 130, 161, 171, 202

Badness: 0.000241

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

By Jove! in jove41 by Chris Vaisvil

Jovial

Commas: 243/242, 441/440, 364/363

13-limit minimax

[|1 0 0 0 0 0>, |17/11 -12/11 2/11 0 0 4/11>, |34/11 -46/11 15/11 0 0 8/11>, |35/11 -26/11 8/11 0 0 5/11>, |37/11 -30/11 5/11 0 0 10/11>, |34/11 -46/11 4/11 0 0 19/11>]

Eigenmonzos: 2, 10/9, 13/9

15-limit minimax

[|1 0 0 0 0 0>, |2 -1/4 1/2 -3/4 0 1/4>, |7/2 -1/8 9/4 -19/8 0 1/8>, |7/2 -1/8 5/4 -11/8 0 1/8>, |9/2 -5/8 5/4 -15/8 0 5/8>, |11/2 -11/8 7/4 -25/8 0 11/8>]

Eigenmonzos: 2, 15/13, 7/5

Map: [<1 1 1 2 2 1|, <0 2 1 1 5 11|, <0 2 1 1 0 -1|]

EDOs: 41, 58, 72, 89, 113, 130, 243, 301e, 373e, 503e, 674e

Badness: 0.000624

17-limit

Commas: 243/242, 441/440, 364/363, 595/594

17-limit minimax

[|1 0 0 0 0 0 0>, |3/7 -2 6/7 0 0 0 4/7>, |3/7 -3 13/7 0 0 0 4/7>, |11/7 -2 8/7 0 0 0 3/7>, |4/7 -5 15/7 0 0 0 10/7>, |-2 -10 4 0 0 0 3>, |6/7 -6 12/7 0 0 0 15/7>]

Eigenmonzos: 2, 18/17, 6/5

Map: [<1 1 1 2 2 1 3|, <0 2 1 1 5 11 9|, <0 0 2 1 0 -1 -3|]

Generators: 2, 11/9, 10/7

Edos: 41, 58, 72, 130, 171, 243, 274, 346, 373eg, 414e, 540eg, 787eg

Badness: 0.000741

Jofur

Commas: 243/242, 441/440, 144/143

Map: [<1 1 1 2 2 4|, <0 2 1 1 5 -1|, <0 0 2 1 0 0|]

EDOs: 31, 41, 58, 89f, 99ef, 157ef

Badness: 0.000749

Jovis

Commas: 243/242, 351/350, 441/440

Map: [<1 1 1 2 2 2|, <0 2 1 1 5 -3|, <0 0 2 1 0 5|]

EDOs: 31, 58, 72, 103, 130, 233, 363, 798bf, 928bef

Badness: 0.000542

Freya

11-limit

Commas: 2401/2400, 3025/3024

11-limit minimax

[|1 0 0 0 0>, |0 1 0 0 0>, |11/10 11/10 0 4/5 -4/5>, |9/5 4/5 0 2/5 -2/5>, |9/5 4/5 0 -3/5 3/5>]

Eigenmonzos: 2, 14/11, 4/3

Map: [<1 1 3 3 2|, <0 2 3 2 1|, <0 0 -4 -3 2|]

EDOs: 31, 41, 72, 167, 188, 198, 229, 239, 270, 342, 612, 954, 1566, 3443de, 4055de, 4397cde

Badness: 0.000170

Projection pairs: 3 2401/800 5 22880495169/4575312500 7 1058841/151250 11 33275/3024 to 2.49/5.77/3

13-limit

Commas: 2401/2400, 3025/3024, 4096/4095

Map: [<1 1 3 3 2|, <0 2 3 2 1|, <0 0 -4 -2 3|]

Generators: 2, 49/40, 55/42

Edos: 31, 41, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615

Badness: 0.000855

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

Baldur

Commas: 2401/2400, 9801/9800

11-limit minimax

[|1 0 0 0 0>, |3/4 0 1/2 1/2 -1/2>, |0 0 1 0 0>, |23/16 0 5/8 1/8 -1/8>, |23/16 0 5/8 -7/8 7/8>]

Eigenmonzos: 5/4, 14/11

Map: [<2 0 1 3 7|, <0 2 1 1 -2|, <0 0 2 1 3|]

Generators: 99/70, 343/198, 10/7

EDOs: 58, 72, 130, 198, 212, 270, 342, 612, 954, 1084, 1354, 1696, 4004de, 5700de

Badness: 0.000166

Projection pairs: 2 9801/4900 3 117649/39204 7 9801/1400 11 913517247483640899/83082326424002500 to 5.7/2.99/4

Greenland

Commas: 676/675, 1001/1000, 1716/1715

Map: [<2 0 1 3 7 -1|, <0 2 1 1 -2 4|, <0 0 2 1 3 2|]

Edos: 58, 72, 130, 198, 270, 940, 1210f, 1480cf, 1750cf

Badness: 0.000433

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

Agni

Commas: 385/384, 1375/1372

11-limit minimax

[|1 0 0 0 0>, |0 1 0 0 0>, |23/10 3/10 2/5 0 -2/5>, |12/5 2/5 1/5 0 -1/5>, |23/10 3/10 -3/5 0 3/5>]

Eigenmonzos: 2, 4/3, 11/10

Lattice basis: 49/40 length 0.756, 10/7 length 0.819

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

Map to lattice: [<0 2 1 1 0|, <0 0 2 1 -3|]

Map: [<1 1 1 2 5|, <0 2 1 1 0|, <0 0 2 1 -3|]

Generators: 2, 49/40, 10/7

Edos: 27, 31, 41, 68, 72, 140, 171e, 181, 212, 284, 496ce, 527ce

Badness: 0.000494

13-limit

Commas: 385/384, 1375/1372, 625/624

Map: [<1 1 1 2 5 -1|, <0 2 1 1 0 2|, <0 0 2 1 -3 8|]

EDOs: 31, 68, 72, 103, 140, 212, 243e, 315ef, 455ef

Badness: 0.000923

Vili

Commas: 2401/2400, 391314/390625

Map: [<1 1 5 4 10|, <0 2 3 2 6|, <0 0 -6 -3 -14|]

EDOs: 37, 93, 103, 130, 233, 270, 643, 670, 913, 1043, 1313, 1583

Badness: 0.00126

13-limit

Commas: 2401/2400, 10985/10976, 1001/1000

Map: [<1 1 5 4 10 4|, <0 2 3 2 6 1|, <0 0 -6 -3 -14 -1|]

EDOs: 37, 93, 103, 130, 233, 270, 643, 773, 913f, 1956ef

Badness: 0.000738

Zisa

Commas: 2401/2400, 5632/5625

Map: [<1 1 1 2 -3|, <0 2 1 1 8|, <0 0 2 1 8|]

EDOs: 21, 31, 109, 130, 239, 270, 670, 940, 1210, 2150c

Badness: 0.000640

13-limit

Commas: 2401/2400, 5632/5625, 4096/4095

Map: [<1 1 1 2 -3 7|, <0 2 1 1 8 -6|, <0 0 2 1 8 -3|]

EDOs: 21, 31, 109, 130, 239, 270, 571, 701, 841, 971, 1241

Badness: 0.000830

Frigg

Commas: 2401/2400, 644204/643125

Map: [<1 1 3 3 4|, <0 2 3 2 4|, <0 0 -10 -5 -11|]

EDOs: 51, 58, 103, 161, 212, 270, 643, 913

Badness: 0.00179

13-limit

Commas: 2401/2400, 10648/10647, 1001/1000

Map: [<1 1 3 3 4 5|, <0 2 3 2 4 3|, <0 0 -10 -5 -11 -14|]

EDOs: 58, 103, 161, 212, 270, 643, 1241, 2082ce, 3053ce, 3323cef

Badness: 0.000934

Ennealimmic

Commas: 2401/2400, 4375/4374

Map: [<9 1 1 12 0|, <0 2 3 2 0|, <0 0 0 0 1|]

Generators: 27/25, 5/3, 11

EDOs: 27, 45, 72, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 4896d

Badness: 0.000275

13-limit

Commas: 2080/2079, 2401/2400, 4375/4374

Map: [<9 1 1 12 0 -31|, <0 2 3 2 0 5|, <0 0 0 0 1 1|]

EDOs: 27, 72, 171, 198, 270, 639, 711, 981, 1692e, 2673e

Badness: 0.000755

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