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Wikispaces>genewardsmith **Imported revision 277304902 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 305116882 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt> | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-25 21:20:54 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>305116882</tt>.<br> | ||
: The revision comment was: <tt></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> | 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> | <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 | <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. | 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. | ||
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Badness: 0.000755</pre></div> | Badness: 0.000755</pre></div> | ||
<h4>Original HTML content:</h4> | <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"><html><head><title>Breed family</title></head><body><!-- ws:start:WikiTextTocRule:40:&lt;img id=&quot;wikitext@@toc@@ | <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"><html><head><title>Breed family</title></head><body><!-- ws:start:WikiTextTocRule:40:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><div style="margin-left: 1em;"><a href="#Vital statistics">Vital statistics</a></div> | ||
<!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><div style="margin-left: 1em;"><a href="#Jove, aka Wonder">Jove, aka Wonder</a></div> | |||
<!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><div style="margin-left: 2em;"><a href="#Jove, aka Wonder-Jovial">Jovial</a></div> | |||
<!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><div style="margin-left: 3em;"><a href="#Jove, aka Wonder-Jovial-17-limit">17-limit</a></div> | |||
<!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><div style="margin-left: 2em;"><a href="#Jove, aka Wonder-Jofur">Jofur</a></div> | |||
<!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --><div style="margin-left: 2em;"><a href="#Jove, aka Wonder-Jovis">Jovis</a></div> | |||
<!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><div style="margin-left: 1em;"><a href="#Freya">Freya</a></div> | |||
<!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><div style="margin-left: 2em;"><a href="#Freya-13-limit">13-limit</a></div> | |||
<!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><div style="margin-left: 1em;"><a href="#Baldur">Baldur</a></div> | |||
<!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><div style="margin-left: 2em;"><a href="#Baldur-Greenland">Greenland</a></div> | |||
<!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><div style="margin-left: 1em;"><a href="#Agni">Agni</a></div> | |||
<!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><div style="margin-left: 2em;"><a href="#Agni-13-limit">13-limit</a></div> | |||
<!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><div style="margin-left: 1em;"><a href="#Vili">Vili</a></div> | |||
<!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><div style="margin-left: 2em;"><a href="#Vili-13-limit">13-limit</a></div> | |||
<!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><div style="margin-left: 1em;"><a href="#Zisa">Zisa</a></div> | |||
<!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><div style="margin-left: 2em;"><a href="#Zisa-13-limit">13-limit</a></div> | |||
<!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><div style="margin-left: 1em;"><a href="#Frigg">Frigg</a></div> | |||
<!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><div style="margin-left: 2em;"><a href="#Frigg-13-limit">13-limit</a></div> | |||
<!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><div style="margin-left: 1em;"><a href="#Ennealimmic">Ennealimmic</a></div> | |||
<!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><div style="margin-left: 2em;"><a href="#Ennealimmic-13-limit">13-limit</a></div> | |||
<!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --></div> | |||
<!-- ws:end:WikiTextTocRule:61 --><br /> | <!-- ws:end:WikiTextTocRule:61 --><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 <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> 2749et will certainly do the trick.<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 <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> 2749et will certainly do the trick.<br /> | ||
Revision as of 21:20, 25 February 2012
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2012-02-25 21:20:54 UTC.
- The original revision id was 305116882.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
[[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]] c = 2401/2400 7- and 9-limit minimax tuning: 3 and 5 just, 7 1/4c flat [[Eigenmonzo|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|] [[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 [[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 [[Comma|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>] [[Eigenmonzo|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 ==Jovial== [[Comma|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>] [[Eigenmonzo|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>] [[Eigenmonzo|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>] [[Eigenmonzo|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|] [[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 ==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 [[Comma|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>] [[Eigenmonzo|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|] [[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 Projection pairs: 3 2401/800 5 22880495169/4575312500 7 1058841/151250 11 33275/3024 1814078464000000000000000/139662717676432916098329 to 2.49/5.77/3 =Baldur= [[Comma|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>] [[Eigenmonzo|Eigenmonzos]]: 5/4, 14/11 Map: [<2 0 1 3 7|, <0 2 1 1 -2|, <0 0 2 1 3|] [[Generator|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|] [[edo|Edos]]: 58, 72, 130, 198, 270, 940, 1210f, 1480cf, 1750cf 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 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= [[Comma|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>] [[Eigenmonzo|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|] [[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 ==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
Original HTML content:
<html><head><title>Breed family</title></head><body><!-- ws:start:WikiTextTocRule:40:<img id="wikitext@@toc@@normal" class="WikiMedia WikiMediaToc" title="Table of Contents" src="/site/embedthumbnail/toc/normal?w=225&h=100"/> --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><div style="margin-left: 1em;"><a href="#Vital statistics">Vital statistics</a></div> <!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><div style="margin-left: 1em;"><a href="#Jove, aka Wonder">Jove, aka Wonder</a></div> <!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><div style="margin-left: 2em;"><a href="#Jove, aka Wonder-Jovial">Jovial</a></div> <!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><div style="margin-left: 3em;"><a href="#Jove, aka Wonder-Jovial-17-limit">17-limit</a></div> <!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><div style="margin-left: 2em;"><a href="#Jove, aka Wonder-Jofur">Jofur</a></div> <!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --><div style="margin-left: 2em;"><a href="#Jove, aka Wonder-Jovis">Jovis</a></div> <!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><div style="margin-left: 1em;"><a href="#Freya">Freya</a></div> <!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><div style="margin-left: 2em;"><a href="#Freya-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><div style="margin-left: 1em;"><a href="#Baldur">Baldur</a></div> <!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><div style="margin-left: 2em;"><a href="#Baldur-Greenland">Greenland</a></div> <!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><div style="margin-left: 1em;"><a href="#Agni">Agni</a></div> <!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><div style="margin-left: 2em;"><a href="#Agni-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><div style="margin-left: 1em;"><a href="#Vili">Vili</a></div> <!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><div style="margin-left: 2em;"><a href="#Vili-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><div style="margin-left: 1em;"><a href="#Zisa">Zisa</a></div> <!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><div style="margin-left: 2em;"><a href="#Zisa-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><div style="margin-left: 1em;"><a href="#Frigg">Frigg</a></div> <!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><div style="margin-left: 2em;"><a href="#Frigg-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><div style="margin-left: 1em;"><a href="#Ennealimmic">Ennealimmic</a></div> <!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><div style="margin-left: 2em;"><a href="#Ennealimmic-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --></div> <!-- ws:end:WikiTextTocRule:61 --><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 <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> 2749et will certainly do the trick.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Vital statistics"></a><!-- ws:end:WikiTextHeadingRule:0 -->Vital statistics</h1> <a class="wiki_link" href="/Comma">Comma</a> c = 2401/2400<br /> 7- and 9-limit minimax tuning: 3 and 5 just, 7 1/4c flat<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 6/5, 5/4<br /> Lattice basis: 49/40 length 0.7858 8/7 length 1.1241<br /> Angle(49/40, 8/7) = 107.367 degrees<br /> Map to lattice: [<0 2 -1 0|, <0 0 -2 -1|]<br /> Map [<1 1 1 2|, <0 2 1 1|, <0 0 2 1|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 49/40, 10/7<br /> <a class="wiki_link" href="/edo">EDOs</a>: <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/41edo">41</a>, <a class="wiki_link" href="/58edo">58</a>, <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/171edo">171</a>, <a class="wiki_link" href="/441edo">441</a>, <a class="wiki_link" href="/612edo">612</a>, <a class="wiki_link" href="/2308edo">2308</a>, <a class="wiki_link" href="/2578edo">2578</a>, <a class="wiki_link" href="/2749edo">2749</a>, <a class="wiki_link" href="/3361edo">3361d</a><br /> Badness: 0.0000153<br /> <br /> <a class="wiki_link" href="/Projection%20pair">Projection pair</a>: 3 2401/800 to 2.5.7<br /> <br /> Scales: <a class="wiki_link" href="/breed11">breed11</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Jove, aka Wonder"></a><!-- ws:end:WikiTextHeadingRule:2 -->Jove, aka Wonder</h1> 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.<br /> <br /> 11-limit<br /> <a class="wiki_link" href="/Comma">Commas</a>: 243/242, 441/440<br /> <br /> <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br /> [|1 0 0 0 0>, |1/5 0 0 0 2/5>, <br /> |13/5 0 2 -2 1/5>, |13/5 0 1 -1 1/5>, <br /> |0 0 0 0 1>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/5, 11/8<br /> <br /> Map: [<1 1 1 2 2|, <0 2 1 1 5|, <0 0 2 1 0|]<br /> EDOs: 31, 41, 58, 72, 130, 161, 171, 202<br /> Badness: 0.000241<br /> <br /> Projection pairs: 3 242/81 5 2200/441 7 440/63 11 644204/59049 to 2.7/5.11/9<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Jove, aka Wonder-Jovial"></a><!-- ws:end:WikiTextHeadingRule:4 -->Jovial</h2> <a class="wiki_link" href="/Comma">Commas</a>: 243/242, 441/440, 364/363<br /> <br /> 13-limit minimax<br /> [|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>, <br /> |35/11 -26/11 8/11 0 0 5/11>, <br /> |37/11 -30/11 5/11 0 0 10/11>, <br /> |34/11 -46/11 4/11 0 0 19/11>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 10/9, 13/9<br /> <br /> 15-limit minimax<br /> [|1 0 0 0 0 0>, |2 -1/4 1/2 -3/4 0 1/4>, <br /> |7/2 -1/8 9/4 -19/8 0 1/8>, <br /> |7/2 -1/8 5/4 -11/8 0 1/8>, <br /> |9/2 -5/8 5/4 -15/8 0 5/8>,<br /> |11/2 -11/8 7/4 -25/8 0 11/8>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 15/13, 7/5<br /> <br /> Map: [<1 1 1 2 2 1|, <0 2 1 1 5 11|, <0 2 1 1 0 -1|]<br /> EDOs: 41, 58, 72, 89, 113, 130, 243, 301e, 373e, 503e, 674e<br /> Badness: 0.000624<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h3> --><h3 id="toc3"><a name="Jove, aka Wonder-Jovial-17-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->17-limit</h3> Commas: 243/242, 441/440, 364/363, 595/594<br /> <br /> 17-limit minimax<br /> [|1 0 0 0 0 0 0>, |3/7 -2 6/7 0 0 0 4/7>, <br /> |3/7 -3 13/7 0 0 0 4/7>, |11/7 -2 8/7 0 0 0 3/7>, <br /> |4/7 -5 15/7 0 0 0 10/7>, |-2 -10 4 0 0 0 3>, <br /> |6/7 -6 12/7 0 0 0 15/7>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 18/17, 6/5<br /> <br /> Map: [<1 1 1 2 2 1 3|, <0 2 1 1 5 11 9|, <0 0 2 1 0 -1 -3|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 11/9, 10/7<br /> <a class="wiki_link" href="/edo">Edos</a>: 41, 58, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/130edo">130</a>, <a class="wiki_link" href="/171edo">171</a>, <a class="wiki_link" href="/243edo">243</a>, <a class="wiki_link" href="/274edo">274</a>, <a class="wiki_link" href="/346edo">346</a>, <a class="wiki_link" href="/373edo">373eg</a>, <a class="wiki_link" href="/414edo">414e</a>, <a class="wiki_link" href="/544edo">540eg</a>, <a class="wiki_link" href="/787edo">787eg</a><br /> Badness: 0.000741<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="Jove, aka Wonder-Jofur"></a><!-- ws:end:WikiTextHeadingRule:8 -->Jofur</h2> Commas: 243/242, 441/440, 144/143<br /> <br /> Map: [<1 1 1 2 2 4|, <0 2 1 1 5 -1|, <0 0 2 1 0 0|]<br /> EDOs: 31, 41, 58, 89f, 99ef, 157ef<br /> Badness: 0.000749<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Jove, aka Wonder-Jovis"></a><!-- ws:end:WikiTextHeadingRule:10 -->Jovis</h2> Commas: 243/242, 351/350, 441/440<br /> <br /> Map: [<1 1 1 2 2 2|, <0 2 1 1 5 -3|, <0 0 2 1 0 5|]<br /> EDOs: 31, 58, 72, 103, 130, 233, 363, 798bf, 928bef<br /> Badness: 0.000542<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc6"><a name="Freya"></a><!-- ws:end:WikiTextHeadingRule:12 -->Freya</h1> 11-limit<br /> <a class="wiki_link" href="/Comma">Commas</a>: 2401/2400, 3025/3024<br /> <br /> 11-limit minimax<br /> [|1 0 0 0 0>, |0 1 0 0 0>, <br /> |11/10 11/10 0 4/5 -4/5>, <br /> |9/5 4/5 0 2/5 -2/5>, |9/5 4/5 0 -3/5 3/5>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 14/11, 4/3<br /> <br /> Map: [<1 1 3 3 2|, <0 2 3 2 1|, <0 0 -4 -3 2|]<br /> EDOs: 31, 41, 72, 167, 188, 198, 229, 239, 270, 342, 612, 954, 1566, 3443de, 4055de, 4397cde<br /> Badness: 0.000170<br /> <br /> Projection pairs: 3 2401/800 5 22880495169/4575312500 7 1058841/151250 11 33275/3024 to 2.49/5.77/3<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="Freya-13-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->13-limit</h2> Commas: 2401/2400, 3025/3024, 4096/4095<br /> <br /> Map: [<1 1 3 3 2|, <0 2 3 2 1|, <0 0 -4 -2 3|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 49/40, 55/42<br /> <a class="wiki_link" href="/edo">Edos</a>: 31, 41, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615<br /> Badness: 0.000855<br /> <br /> Projection pairs: 3 2401/800 5 22880495169/4575312500 7 1058841/151250 11 33275/3024 1814078464000000000000000/139662717676432916098329 to 2.49/5.77/3<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h1> --><h1 id="toc8"><a name="Baldur"></a><!-- ws:end:WikiTextHeadingRule:16 -->Baldur</h1> <a class="wiki_link" href="/Comma">Commas</a>: 2401/2400, 9801/9800<br /> <br /> 11-limit minimax<br /> [|1 0 0 0 0>, |3/4 0 1/2 1/2 -1/2>, <br /> |0 0 1 0 0>, |23/16 0 5/8 1/8 -1/8>, <br /> |23/16 0 5/8 -7/8 7/8>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 5/4, 14/11<br /> <br /> Map: [<2 0 1 3 7|, <0 2 1 1 -2|, <0 0 2 1 3|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 99/70, 343/198, 10/7<br /> EDOs: 58, 72, 130, 198, 212, 270, 342, 612, 954, 1084, 1354, 1696, 4004de, 5700de<br /> Badness: 0.000166<br /> <br /> Projection pairs: 2 9801/4900 3 117649/39204 7 9801/1400 11 913517247483640899/83082326424002500 to 5.7/2.99/4<br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h2> --><h2 id="toc9"><a name="Baldur-Greenland"></a><!-- ws:end:WikiTextHeadingRule:18 -->Greenland</h2> Commas: 676/675, 1001/1000, 1716/1715<br /> <br /> Map: [<2 0 1 3 7 -1|, <0 2 1 1 -2 4|, <0 0 2 1 3 2|]<br /> <a class="wiki_link" href="/edo">Edos</a>: 58, 72, 130, 198, 270, 940, 1210f, 1480cf, 1750cf<br /> Badness: 0.000433<br /> <a class="wiki_link" href="/Spectrum%20of%20a%20temperament">Spectrum</a>: 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<br /> <br /> 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<br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h1> --><h1 id="toc10"><a name="Agni"></a><!-- ws:end:WikiTextHeadingRule:20 -->Agni</h1> <a class="wiki_link" href="/Comma">Commas</a>: 385/384, 1375/1372<br /> <br /> 11-limit minimax<br /> [|1 0 0 0 0>, |0 1 0 0 0>, <br /> |23/10 3/10 2/5 0 -2/5>, <br /> |12/5 2/5 1/5 0 -1/5>, <br /> |23/10 3/10 -3/5 0 3/5>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 4/3, 11/10<br /> <br /> Lattice basis: 49/40 length 0.756, 10/7 length 0.819<br /> Angle(49/40, 10/7) = 106.460 degrees<br /> Map to lattice: [<0 2 1 1 0|, <0 0 2 1 -3|]<br /> <br /> Map: [<1 1 1 2 5|, <0 2 1 1 0|, <0 0 2 1 -3|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 49/40, 10/7<br /> <a class="wiki_link" href="/edo">Edos</a>: 27, 31, 41, 68, 72, 140, 171e, 181, <a class="wiki_link" href="/212edo">212</a>, <a class="wiki_link" href="/284edo">284</a>, <a class="wiki_link" href="/496edo">496ce</a>, <a class="wiki_link" href="/527edo">527ce</a><br /> Badness: 0.000494<br /> <br /> <!-- ws:start:WikiTextHeadingRule:22:<h2> --><h2 id="toc11"><a name="Agni-13-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->13-limit</h2> Commas: 385/384, 1375/1372, 625/624<br /> <br /> Map: [<1 1 1 2 5 -1|, <0 2 1 1 0 2|, <0 0 2 1 -3 8|]<br /> EDOs: 31, 68, 72, 103, 140, 212, 243e, 315ef, 455ef<br /> Badness: 0.000923<br /> <br /> <!-- ws:start:WikiTextHeadingRule:24:<h1> --><h1 id="toc12"><a name="Vili"></a><!-- ws:end:WikiTextHeadingRule:24 -->Vili</h1> Commas: 2401/2400, 391314/390625<br /> <br /> Map: [<1 1 5 4 10|, <0 2 3 2 6|, <0 0 -6 -3 -14|]<br /> EDOs: 37, 93, 103, 130, 233, 270, 643, 670, 913, 1043, 1313, 1583<br /> Badness: 0.00126<br /> <br /> <!-- ws:start:WikiTextHeadingRule:26:<h2> --><h2 id="toc13"><a name="Vili-13-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->13-limit</h2> Commas: 2401/2400, 10985/10976, 1001/1000<br /> <br /> Map: [<1 1 5 4 10 4|, <0 2 3 2 6 1|, <0 0 -6 -3 -14 -1|]<br /> EDOs: 37, 93, 103, 130, 233, 270, 643, 773, 913f, 1956ef<br /> Badness: 0.000738<br /> <br /> <!-- ws:start:WikiTextHeadingRule:28:<h1> --><h1 id="toc14"><a name="Zisa"></a><!-- ws:end:WikiTextHeadingRule:28 -->Zisa</h1> Commas: 2401/2400, 5632/5625<br /> <br /> Map: [<1 1 1 2 -3|, <0 2 1 1 8|, <0 0 2 1 8|]<br /> EDOs: 21, 31, 109, 130, 239, 270, 670, 940, 1210, 2150c<br /> Badness: 0.000640<br /> <br /> <!-- ws:start:WikiTextHeadingRule:30:<h2> --><h2 id="toc15"><a name="Zisa-13-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->13-limit</h2> Commas: 2401/2400, 5632/5625, 4096/4095<br /> <br /> Map: [<1 1 1 2 -3 7|, <0 2 1 1 8 -6|, <0 0 2 1 8 -3|]<br /> EDOs: 21, 31, 109, 130, 239, 270, 571, 701, 841, 971, 1241<br /> Badness: 0.000830<br /> <br /> <!-- ws:start:WikiTextHeadingRule:32:<h1> --><h1 id="toc16"><a name="Frigg"></a><!-- ws:end:WikiTextHeadingRule:32 -->Frigg</h1> Commas: 2401/2400, 644204/643125<br /> <br /> Map: [<1 1 3 3 4|, <0 2 3 2 4|, <0 0 -10 -5 -11|]<br /> EDOs: 51, 58, 103, 161, 212, 270, 643, 913<br /> Badness: 0.00179<br /> <br /> <!-- ws:start:WikiTextHeadingRule:34:<h2> --><h2 id="toc17"><a name="Frigg-13-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->13-limit</h2> Commas: 2401/2400, 10648/10647, 1001/1000<br /> <br /> Map: [<1 1 3 3 4 5|, <0 2 3 2 4 3|, <0 0 -10 -5 -11 -14|]<br /> EDOs: 58, 103, 161, 212, 270, 643, 1241, 2082ce, 3053ce, 3323cef<br /> Badness: 0.000934<br /> <br /> <!-- ws:start:WikiTextHeadingRule:36:<h1> --><h1 id="toc18"><a name="Ennealimmic"></a><!-- ws:end:WikiTextHeadingRule:36 -->Ennealimmic</h1> Commas: 2401/2400, 4375/4374<br /> <br /> Map: [<9 1 1 12 0|, <0 2 3 2 0|, <0 0 0 0 1|]<br /> Generators: 27/25, 5/3, 11<br /> EDOs: 27, 45, 72, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 4896d<br /> Badness: 0.000275<br /> <br /> <!-- ws:start:WikiTextHeadingRule:38:<h2> --><h2 id="toc19"><a name="Ennealimmic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->13-limit</h2> Commas: 2080/2079, 2401/2400, 4375/4374<br /> <br /> Map: [<9 1 1 12 0 -31|, <0 2 3 2 0 5|, <0 0 0 0 1 1|]<br /> EDOs: 27, 72, 171, 198, 270, 639, 711, 981, 1692e, 2673e<br /> Badness: 0.000755</body></html>