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Wikispaces>phylingual **Imported revision 339321122 - 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: | : This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-05-24 20:25:42 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>339321122</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> | ||
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<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">37edo is a scale derived from dividing the octave into 37 equal steps of approximately 32.43 cents each. It is the 12th [[xenharmonic/prime numbers|prime]] edo, following [[xenharmonic/31edo|31edo]] and coming before [[xenharmonic/41edo|41edo]]. | <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">37edo is a scale derived from dividing the octave into 37 equal steps of approximately 32.43 cents each. It is the 12th [[xenharmonic/prime numbers|prime]] edo, following [[xenharmonic/31edo|31edo]] and coming before [[xenharmonic/41edo|41edo]]. | ||
Using its best (and sharp) fifth, 37edo tempers out 250/243, making it a variant of [[xenharmonic/porcupine|porcupine]] temperament. Using its alternative flat fifth, it tempers out 16875/16384, making it a [[xenharmonic/negri|negri]] tuning. It also tempers out 2187/2000, resulting in a temperament where three minor whole tones make up a fifth ([[xenharmonic/gorgo|gorgo]]/[[xenharmonic/laconic|laconic]]). | Using its best (and sharp) fifth, 37edo tempers out 250/243, making it a variant of [[xenharmonic/porcupine|porcupine]] temperament. (It is the optimal patent val for [[Porcupine family#Porcupinefish|porcupinefish]], which is about as accurate as "13-limit porcupine" will be.) Using its alternative flat fifth, it tempers out 16875/16384, making it a [[xenharmonic/negri|negri]] tuning. It also tempers out 2187/2000, resulting in a temperament where three minor whole tones make up a fifth ([[xenharmonic/gorgo|gorgo]]/[[xenharmonic/laconic|laconic]]). | ||
37 edo is also a very accurate equal tuning for Undecimation Temperament, which has a generator of about 519 cents; 2 generators lead to 29/16; 3 generators to 32/13; 6 generators to a 10 cent sharp 6/1; 8 generators to a very accurate 11/1 and 10 generators to 20/1. It has a 7L+2s nonatonic MOS, which in 37-edo scale degrees is 0, 1, 6, 11, 16, 17, 22, 27, 32, a scale structure reminiscent of mavila; as well as a 16 note MOS. | 37 edo is also a very accurate equal tuning for Undecimation Temperament, which has a generator of about 519 cents; 2 generators lead to 29/16; 3 generators to 32/13; 6 generators to a 10 cent sharp 6/1; 8 generators to a very accurate 11/1 and 10 generators to 20/1. It has a 7L+2s nonatonic MOS, which in 37-edo scale degrees is 0, 1, 6, 11, 16, 17, 22, 27, 32, a scale structure reminiscent of mavila; as well as a 16 note MOS. | ||
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<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>37edo</title></head><body>37edo is a scale derived from dividing the octave into 37 equal steps of approximately 32.43 cents each. It is the 12th <a class="wiki_link" href="http://xenharmonic.wikispaces.com/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="http://xenharmonic.wikispaces.com/31edo">31edo</a> and coming before <a class="wiki_link" href="http://xenharmonic.wikispaces.com/41edo">41edo</a>.<br /> | <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>37edo</title></head><body>37edo is a scale derived from dividing the octave into 37 equal steps of approximately 32.43 cents each. It is the 12th <a class="wiki_link" href="http://xenharmonic.wikispaces.com/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="http://xenharmonic.wikispaces.com/31edo">31edo</a> and coming before <a class="wiki_link" href="http://xenharmonic.wikispaces.com/41edo">41edo</a>.<br /> | ||
<br /> | <br /> | ||
Using its best (and sharp) fifth, 37edo tempers out 250/243, making it a variant of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/porcupine">porcupine</a> temperament. Using its alternative flat fifth, it tempers out 16875/16384, making it a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/negri">negri</a> tuning. It also tempers out 2187/2000, resulting in a temperament where three minor whole tones make up a fifth (<a class="wiki_link" href="http://xenharmonic.wikispaces.com/gorgo">gorgo</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/laconic">laconic</a>).<br /> | Using its best (and sharp) fifth, 37edo tempers out 250/243, making it a variant of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/porcupine">porcupine</a> temperament. (It is the optimal patent val for <a class="wiki_link" href="/Porcupine%20family#Porcupinefish">porcupinefish</a>, which is about as accurate as &quot;13-limit porcupine&quot; will be.) Using its alternative flat fifth, it tempers out 16875/16384, making it a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/negri">negri</a> tuning. It also tempers out 2187/2000, resulting in a temperament where three minor whole tones make up a fifth (<a class="wiki_link" href="http://xenharmonic.wikispaces.com/gorgo">gorgo</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/laconic">laconic</a>).<br /> | ||
<br /> | <br /> | ||
37 edo is also a very accurate equal tuning for Undecimation Temperament, which has a generator of about 519 cents; 2 generators lead to 29/16; 3 generators to 32/13; 6 generators to a 10 cent sharp 6/1; 8 generators to a very accurate 11/1 and 10 generators to 20/1. It has a 7L+2s nonatonic MOS, which in 37-edo scale degrees is 0, 1, 6, 11, 16, 17, 22, 27, 32, a scale structure reminiscent of mavila; as well as a 16 note MOS.<br /> | 37 edo is also a very accurate equal tuning for Undecimation Temperament, which has a generator of about 519 cents; 2 generators lead to 29/16; 3 generators to 32/13; 6 generators to a 10 cent sharp 6/1; 8 generators to a very accurate 11/1 and 10 generators to 20/1. It has a 7L+2s nonatonic MOS, which in 37-edo scale degrees is 0, 1, 6, 11, 16, 17, 22, 27, 32, a scale structure reminiscent of mavila; as well as a 16 note MOS.<br /> |
Revision as of 20:25, 24 May 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 phylingual and made on 2012-05-24 20:25:42 UTC.
- The original revision id was 339321122.
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37edo is a scale derived from dividing the octave into 37 equal steps of approximately 32.43 cents each. It is the 12th [[xenharmonic/prime numbers|prime]] edo, following [[xenharmonic/31edo|31edo]] and coming before [[xenharmonic/41edo|41edo]]. Using its best (and sharp) fifth, 37edo tempers out 250/243, making it a variant of [[xenharmonic/porcupine|porcupine]] temperament. (It is the optimal patent val for [[Porcupine family#Porcupinefish|porcupinefish]], which is about as accurate as "13-limit porcupine" will be.) Using its alternative flat fifth, it tempers out 16875/16384, making it a [[xenharmonic/negri|negri]] tuning. It also tempers out 2187/2000, resulting in a temperament where three minor whole tones make up a fifth ([[xenharmonic/gorgo|gorgo]]/[[xenharmonic/laconic|laconic]]). 37 edo is also a very accurate equal tuning for Undecimation Temperament, which has a generator of about 519 cents; 2 generators lead to 29/16; 3 generators to 32/13; 6 generators to a 10 cent sharp 6/1; 8 generators to a very accurate 11/1 and 10 generators to 20/1. It has a 7L+2s nonatonic MOS, which in 37-edo scale degrees is 0, 1, 6, 11, 16, 17, 22, 27, 32, a scale structure reminiscent of mavila; as well as a 16 note MOS. [[toc|flat]] ---- =Subgroups= 37edo offers close approximations to [[xenharmonic/OverToneSeries|harmonics]] 5, 7, 11, and 13 [and a usable approximation of 9 as well]. 12\37 = 389.2 cents 30\37 = 973.0 cents 17\37 = 551.4 cents 26\37 = 843.2 cents [6\37edo = 194.6 cents] This means 37 is quite accurate on the 2.5.7.11.13 subgroup, where it shares the same tuning as 111et. In fact, on the larger [[xenharmonic/k*N subgroups|3*37 subgroup]] 2.27.5.7.11.13.51.57 subgroup not only shares the same tuning as 19-limit 111et, it tempers out the same commas. A simpler but less accurate approach is to use the 2*37-subgroup, 2.9.7.11.13.17.19, on which it has the same tuning and commas as 74et. =The Two Fifths= The just [[xenharmonic/perfect fifth|perfect fifth]] of frequency ratio 3:2 is not well-approximated, and falls between two intervals in 37edo: The flat fifth is 21\37 = 681.1 cents The sharp fifth is 22\37 = 713.5 cents 21\37 generates an anti-diatonic, or mavila, scale: 5 5 6 5 5 5 6 "minor third" = 10\37 = 324.3 cents "major third" = 11\37 = 356.8 cents 22\37 generates an extreme superpythagorean scale: 7 7 1 7 7 7 1 "minor third" = 8\37 = 259.5 cents "major third" = 14\37 = 454.1 cents If the minor third of 259.5 cents is mapped to 7/6, this superpythagorean scale can be thought of as a variant of [[xenharmonic/The Biosphere|Biome]] temperament. Interestingly, the "major thirds" of both systems are not 12\37 = 389.2¢, the closest approximation to 5/4 available in 37edo. 37edo has great potential as a near-just xenharmonic system, with high-prime chords such as 8:10:11:13:14 with no perfect fifths available for common terrestrial progressions. The 9/8 approximation is usable but introduces error. One may choose to treat either of the intervals close to 3/2 as 3/2, introducing additional approximations with considerable error (see interval table below). =Intervals= ||~ Degrees of 37edo ||~ Cents Value ||~ Approximate Ratios of 2.5.7.11.13.27 subgroup ||~ Ratios of 3 with a sharp 3/2 ||~ Ratios of 3 with a flat 3/2 ||~ Ratios of 9 with 194.59¢ 9/8 ||~ Ratios of 9 with 227.03¢ 9/8 (two sharp 3/2's) || || 0 || 0.00 || 1/1 || || || || || || 1 || 32.43 || || || || || || || 2 || 64.86 || 28/27, 27/26 || || || || || || 3 || 97.30 || || || || || || || 4 || 129.73 || 14/13 || 13/12 || 12/11 || || || || 5 || 162.16 || 11/10 || 12/11 || 13/12 || || 10/9 || || 6 || 194.59 || || || || 9/8, 10/9 || || || 7 || 227.03 || 8/7 || || || || 9/8 || || 8 || 259.46 || || 7/6 || || || || || 9 || 291.89 || 13/11, 32/27 || || 6/5, 7/6 || || || || 10 || 324.32 || || 6/5 || || || 11/9 || || 11 || 356.76 || 16/13, 27/22 || || || 11/9 || || || 12 || 389.19 || 5/4 || || || || || || 13 || 421.62 || 14/11 || || || 9/7 || || || 14 || 454.05 || 13/10 || || || || 9/7 || || 15 || 486.49 || || 4/3 || || || || || 16 || 518.92 || 27/20 || || 4/3 || || || || 17 || 551.35 || 11/8 || || || 18/13 || || || 18 || 583.78 || 7/5 || || || || 18/13 || || 19 || 616.22 || 10/7 || || || || 13/9 || || 20 || 648.65 || 16/11 || || || 13/9 || || || 21 || 681.08 || 40/27 || || 3/2 || || || || 22 || 713.51 || || 3/2 || || || || || 23 || 745.95 || 20/13 || || || || 14/9 || || 24 || 778.38 || 11/7 || || || 14/9 || || || 25 || 810.81 || 8/5 || || || || || || 26 || 843.24 || 13/8, 44/27 || || || 18/11 || || || 27 || 875.68 || || 5/3 || || || 18/11 || || 28 || 908.11 || 22/13, 27/16 || || 5/3, 12/7 || || || || 29 || 940.54 || || 12/7 || || || || || 30 || 972.97 || 7/4 || || || || 16/9 || || 31 || 1005.41 || || || || 16/9, 9/5 || || || 32 || 1037.84 || 20/11 || 11/6 || 24/13 || || 9/5 || || 33 || 1070.27 || 13/7 || 24/13 || 11/6 || || || || 34 || 1102.70 || || || || || || || 35 || 1135.14 || 27/14, 52/27 || || || || || || 36 || 1167.57 || || || || || || =Scales= [[xenharmonic/MOS Scales of 37edo|MOS Scales of 37edo]] [[xenharmonic/roulette6|roulette6]] [[xenharmonic/roulette7|roulette7]] [[xenharmonic/roulette13|roulette13]] [[xenharmonic/roulette19|roulette19]] [[xenharmonic/Chromatic pairs#Shoe|Shoe]] [[xenharmonic/37ED4|37ED4]] [[xenharmonic/square root of 13 over 10|The Square Root of 13/10]] =Linear temperaments= [[List of 37et rank two temperaments by badness]] ||~ Generator ||~ "Sharp 3/2" temperaments ||~ "Flat 3/2" temperaments (37b val) || || 1\37 || || || || 2\37 || [[xenharmonic/Sycamore family|Sycamore]] || || || 3\37 || [[xenharmonic/Passion|Passion]] || || || 4\37 || [[xenharmonic/Twothirdtonic|Twothirdtonic]] || [[xenharmonic/Negri|Negri]] || || 5\37 || [[xenharmonic/Porcupine|Porcupine]]/[[xenharmonic/The Biosphere#Oceanfront-Oceanfront%20Children-Porcupinefish|porcupinefish]] || || || 6\37 |||| [[xenharmonic/Chromatic pairs#Roulette|Roulette]] || || 7\37 || [[xenharmonic/Semaja|Semaja]] || [[xenharmonic/Gorgo|Gorgo]]/[[xenharmonic/Laconic|Laconic]] || || 8\37 || || || || 9\37 || || || || 10\37 || || || || 11\37 || [[xenharmonic/Beatles|Beatles]] || || || 12\37 || [[xenharmonic/Würschmidt|Würschmidt]] (out-of-tune) || || || 13\37 || || || || 14\37 || [[xenharmonic/Ammonite|Ammonite]] || || || 15\37 || [[The Biosphere#Oceanfront-Oceanfront%20Children-Ultrapyth|Ultrapyth]], **not** [[xenharmonic/superpyth|superpyth]] || || || 16\37 || || **Not** [[xenharmonic/mavila|mavila]] (this is "undecimation") || || 17\37 || [[xenharmonic/Emka|Emka]] || || || 18\37 || || || ==Music in 37edo== [[http://www.akjmusic.com/audio/toccata_bianca_37edo.mp3|Toccata Bianca 37edo]] by [[http://www.akjmusic.com/|Aaron Krister Johnson]] [[@http://andrewheathwaite.bandcamp.com/track/shorn-brown|Shorn Brown]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2002%20Shorn%20Brown.mp3|play]] and [[@http://andrewheathwaite.bandcamp.com/track/jellybear|Jellybear]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2003%20Jellybear.mp3|play]] by [[xenharmonic/Andrew Heathwaite|Andrew Heathwaite]] ==Links== [[http://tonalsoft.com/enc/number/37-edo/37edo.aspx|37edo at Tonalsoft]]
Original HTML content:
<html><head><title>37edo</title></head><body>37edo is a scale derived from dividing the octave into 37 equal steps of approximately 32.43 cents each. It is the 12th <a class="wiki_link" href="http://xenharmonic.wikispaces.com/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="http://xenharmonic.wikispaces.com/31edo">31edo</a> and coming before <a class="wiki_link" href="http://xenharmonic.wikispaces.com/41edo">41edo</a>.<br /> <br /> Using its best (and sharp) fifth, 37edo tempers out 250/243, making it a variant of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/porcupine">porcupine</a> temperament. (It is the optimal patent val for <a class="wiki_link" href="/Porcupine%20family#Porcupinefish">porcupinefish</a>, which is about as accurate as "13-limit porcupine" will be.) Using its alternative flat fifth, it tempers out 16875/16384, making it a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/negri">negri</a> tuning. It also tempers out 2187/2000, resulting in a temperament where three minor whole tones make up a fifth (<a class="wiki_link" href="http://xenharmonic.wikispaces.com/gorgo">gorgo</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/laconic">laconic</a>).<br /> <br /> 37 edo is also a very accurate equal tuning for Undecimation Temperament, which has a generator of about 519 cents; 2 generators lead to 29/16; 3 generators to 32/13; 6 generators to a 10 cent sharp 6/1; 8 generators to a very accurate 11/1 and 10 generators to 20/1. It has a 7L+2s nonatonic MOS, which in 37-edo scale degrees is 0, 1, 6, 11, 16, 17, 22, 27, 32, a scale structure reminiscent of mavila; as well as a 16 note MOS.<br /> <br /> <br /> <!-- ws:start:WikiTextTocRule:14:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><a href="#Subgroups">Subgroups</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#The Two Fifths">The Two Fifths</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Scales">Scales</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Linear temperaments">Linear temperaments</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> <!-- ws:end:WikiTextTocRule:22 --><hr /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Subgroups"></a><!-- ws:end:WikiTextHeadingRule:0 -->Subgroups</h1> 37edo offers close approximations to <a class="wiki_link" href="http://xenharmonic.wikispaces.com/OverToneSeries">harmonics</a> 5, 7, 11, and 13 [and a usable approximation of 9 as well].<br /> <br /> 12\37 = 389.2 cents<br /> 30\37 = 973.0 cents<br /> 17\37 = 551.4 cents<br /> 26\37 = 843.2 cents<br /> [6\37edo = 194.6 cents]<br /> <br /> This means 37 is quite accurate on the 2.5.7.11.13 subgroup, where it shares the same tuning as 111et. In fact, on the larger <a class="wiki_link" href="http://xenharmonic.wikispaces.com/k%2AN%20subgroups">3*37 subgroup</a> 2.27.5.7.11.13.51.57 subgroup not only shares the same tuning as 19-limit 111et, it tempers out the same commas. A simpler but less accurate approach is to use the 2*37-subgroup, 2.9.7.11.13.17.19, on which it has the same tuning and commas as 74et.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="The Two Fifths"></a><!-- ws:end:WikiTextHeadingRule:2 -->The Two Fifths</h1> The just <a class="wiki_link" href="http://xenharmonic.wikispaces.com/perfect%20fifth">perfect fifth</a> of frequency ratio 3:2 is not well-approximated, and falls between two intervals in 37edo:<br /> <br /> The flat fifth is 21\37 = 681.1 cents<br /> The sharp fifth is 22\37 = 713.5 cents<br /> <br /> 21\37 generates an anti-diatonic, or mavila, scale: 5 5 6 5 5 5 6<br /> "minor third" = 10\37 = 324.3 cents<br /> "major third" = 11\37 = 356.8 cents<br /> <br /> 22\37 generates an extreme superpythagorean scale: 7 7 1 7 7 7 1<br /> "minor third" = 8\37 = 259.5 cents<br /> "major third" = 14\37 = 454.1 cents<br /> <br /> If the minor third of 259.5 cents is mapped to 7/6, this superpythagorean scale can be thought of as a variant of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Biosphere">Biome</a> temperament.<br /> <br /> Interestingly, the "major thirds" of both systems are not 12\37 = 389.2¢, the closest approximation to 5/4 available in 37edo.<br /> <br /> 37edo has great potential as a near-just xenharmonic system, with high-prime chords such as 8:10:11:13:14 with no perfect fifths available for common terrestrial progressions. The 9/8 approximation is usable but introduces error. One may choose to treat either of the intervals close to 3/2 as 3/2, introducing additional approximations with considerable error (see interval table below).<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h1> <table class="wiki_table"> <tr> <th>Degrees of 37edo<br /> </th> <th>Cents Value<br /> </th> <th>Approximate Ratios<br /> of 2.5.7.11.13.27 subgroup<br /> </th> <th>Ratios of 3 with<br /> a sharp 3/2<br /> </th> <th>Ratios of 3 with<br /> a flat 3/2<br /> </th> <th>Ratios of 9 with<br /> 194.59¢ 9/8<br /> </th> <th>Ratios of 9 with<br /> 227.03¢ 9/8<br /> (two sharp<br /> 3/2's)<br /> </th> </tr> <tr> <td>0<br /> </td> <td>0.00<br /> </td> <td>1/1<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>1<br /> </td> <td>32.43<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>2<br /> </td> <td>64.86<br /> </td> <td>28/27, 27/26<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>3<br /> </td> <td>97.30<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>4<br /> </td> <td>129.73<br /> </td> <td>14/13<br /> </td> <td>13/12<br /> </td> <td>12/11<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>5<br /> </td> <td>162.16<br /> </td> <td>11/10<br /> </td> <td>12/11<br /> </td> <td>13/12<br /> </td> <td><br /> </td> <td>10/9<br /> </td> </tr> <tr> <td>6<br /> </td> <td>194.59<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>9/8, 10/9<br /> </td> <td><br /> </td> </tr> <tr> <td>7<br /> </td> <td>227.03<br /> </td> <td>8/7<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>9/8<br /> </td> </tr> <tr> <td>8<br /> </td> <td>259.46<br /> </td> <td><br /> </td> <td>7/6<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>9<br /> </td> <td>291.89<br /> </td> <td>13/11, 32/27<br /> </td> <td><br /> </td> <td>6/5, 7/6<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>10<br /> </td> <td>324.32<br /> </td> <td><br /> </td> <td>6/5<br /> </td> <td><br /> </td> <td><br /> </td> <td>11/9<br /> </td> </tr> <tr> <td>11<br /> </td> <td>356.76<br /> </td> <td>16/13, 27/22<br /> </td> <td><br /> </td> <td><br /> </td> <td>11/9<br /> </td> <td><br /> </td> </tr> <tr> <td>12<br /> </td> <td>389.19<br /> </td> <td>5/4<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>13<br /> </td> <td>421.62<br /> </td> <td>14/11<br /> </td> <td><br /> </td> <td><br /> </td> <td>9/7<br /> </td> <td><br /> </td> </tr> <tr> <td>14<br /> </td> <td>454.05<br /> </td> <td>13/10<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>9/7<br /> </td> </tr> <tr> <td>15<br /> </td> <td>486.49<br /> </td> <td><br /> </td> <td>4/3<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>16<br /> </td> <td>518.92<br /> </td> <td>27/20<br /> </td> <td><br /> </td> <td>4/3<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>17<br /> </td> <td>551.35<br /> </td> <td>11/8<br /> </td> <td><br /> </td> <td><br /> </td> <td>18/13<br /> </td> <td><br /> </td> </tr> <tr> <td>18<br /> </td> <td>583.78<br /> </td> <td>7/5<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>18/13<br /> </td> </tr> <tr> <td>19<br /> </td> <td>616.22<br /> </td> <td>10/7<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>13/9<br /> </td> </tr> <tr> <td>20<br /> </td> <td>648.65<br /> </td> <td>16/11<br /> </td> <td><br /> </td> <td><br /> </td> <td>13/9<br /> </td> <td><br /> </td> </tr> <tr> <td>21<br /> </td> <td>681.08<br /> </td> <td>40/27<br /> </td> <td><br /> </td> <td>3/2<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>22<br /> </td> <td>713.51<br /> </td> <td><br /> </td> <td>3/2<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>23<br /> </td> <td>745.95<br /> </td> <td>20/13<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>14/9<br /> </td> </tr> <tr> <td>24<br /> </td> <td>778.38<br /> </td> <td>11/7<br /> </td> <td><br /> </td> <td><br /> </td> <td>14/9<br /> </td> <td><br /> </td> </tr> <tr> <td>25<br /> </td> <td>810.81<br /> </td> <td>8/5<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>26<br /> </td> <td>843.24<br /> </td> <td>13/8, 44/27<br /> </td> <td><br /> </td> <td><br /> </td> <td>18/11<br /> </td> <td><br /> </td> </tr> <tr> <td>27<br /> </td> <td>875.68<br /> </td> <td><br /> </td> <td>5/3<br /> </td> <td><br /> </td> <td><br /> </td> <td>18/11<br /> </td> </tr> <tr> <td>28<br /> </td> <td>908.11<br /> </td> <td>22/13, 27/16<br /> </td> <td><br /> </td> <td>5/3, 12/7<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>29<br /> </td> <td>940.54<br /> </td> <td><br /> </td> <td>12/7<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>30<br /> </td> <td>972.97<br /> </td> <td>7/4<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>16/9<br /> </td> </tr> <tr> <td>31<br /> </td> <td>1005.41<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>16/9, 9/5<br /> </td> <td><br /> </td> </tr> <tr> <td>32<br /> </td> <td>1037.84<br /> </td> <td>20/11<br /> </td> <td>11/6<br /> </td> <td>24/13<br /> </td> <td><br /> </td> <td>9/5<br /> </td> </tr> <tr> <td>33<br /> </td> <td>1070.27<br /> </td> <td>13/7<br /> </td> <td>24/13<br /> </td> <td>11/6<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>34<br /> </td> <td>1102.70<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>35<br /> </td> <td>1135.14<br /> </td> <td>27/14, 52/27<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>36<br /> </td> <td>1167.57<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> </table> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:6 -->Scales</h1> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOS%20Scales%20of%2037edo">MOS Scales of 37edo</a><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/roulette6">roulette6</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/roulette7">roulette7</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/roulette13">roulette13</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/roulette19">roulette19</a><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Chromatic%20pairs#Shoe">Shoe</a><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/37ED4">37ED4</a><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/square%20root%20of%2013%20over%2010">The Square Root of 13/10</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="Linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:8 -->Linear temperaments</h1> <a class="wiki_link" href="/List%20of%2037et%20rank%20two%20temperaments%20by%20badness">List of 37et rank two temperaments by badness</a><br /> <br /> <table class="wiki_table"> <tr> <th>Generator<br /> </th> <th>"Sharp 3/2" temperaments<br /> </th> <th>"Flat 3/2" temperaments (37b val)<br /> </th> </tr> <tr> <td>1\37<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>2\37<br /> </td> <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Sycamore%20family">Sycamore</a><br /> </td> <td><br /> </td> </tr> <tr> <td>3\37<br /> </td> <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Passion">Passion</a><br /> </td> <td><br /> </td> </tr> <tr> <td>4\37<br /> </td> <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Twothirdtonic">Twothirdtonic</a><br /> </td> <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Negri">Negri</a><br /> </td> </tr> <tr> <td>5\37<br /> </td> <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Porcupine">Porcupine</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Biosphere#Oceanfront-Oceanfront%20Children-Porcupinefish">porcupinefish</a><br /> </td> <td><br /> </td> </tr> <tr> <td>6\37<br /> </td> <td colspan="2"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Chromatic%20pairs#Roulette">Roulette</a><br /> </td> </tr> <tr> <td>7\37<br /> </td> <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Semaja">Semaja</a><br /> </td> <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Gorgo">Gorgo</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Laconic">Laconic</a><br /> </td> </tr> <tr> <td>8\37<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>9\37<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>10\37<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>11\37<br /> </td> <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Beatles">Beatles</a><br /> </td> <td><br /> </td> </tr> <tr> <td>12\37<br /> </td> <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/W%C3%BCrschmidt">Würschmidt</a> (out-of-tune)<br /> </td> <td><br /> </td> </tr> <tr> <td>13\37<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>14\37<br /> </td> <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ammonite">Ammonite</a><br /> </td> <td><br /> </td> </tr> <tr> <td>15\37<br /> </td> <td><a class="wiki_link" href="/The%20Biosphere#Oceanfront-Oceanfront%20Children-Ultrapyth">Ultrapyth</a>, <strong>not</strong> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/superpyth">superpyth</a><br /> </td> <td><br /> </td> </tr> <tr> <td>16\37<br /> </td> <td><br /> </td> <td><strong>Not</strong> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/mavila">mavila</a> (this is "undecimation")<br /> </td> </tr> <tr> <td>17\37<br /> </td> <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Emka">Emka</a><br /> </td> <td><br /> </td> </tr> <tr> <td>18\37<br /> </td> <td><br /> </td> <td><br /> </td> </tr> </table> <br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Linear temperaments-Music in 37edo"></a><!-- ws:end:WikiTextHeadingRule:10 -->Music in 37edo</h2> <a class="wiki_link_ext" href="http://www.akjmusic.com/audio/toccata_bianca_37edo.mp3" rel="nofollow">Toccata Bianca 37edo</a> by <a class="wiki_link_ext" href="http://www.akjmusic.com/" rel="nofollow">Aaron Krister Johnson</a><br /> <a class="wiki_link_ext" href="http://andrewheathwaite.bandcamp.com/track/shorn-brown" rel="nofollow" target="_blank">Shorn Brown</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2002%20Shorn%20Brown.mp3" rel="nofollow">play</a> and <a class="wiki_link_ext" href="http://andrewheathwaite.bandcamp.com/track/jellybear" rel="nofollow" target="_blank">Jellybear</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2003%20Jellybear.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Andrew%20Heathwaite">Andrew Heathwaite</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Linear temperaments-Links"></a><!-- ws:end:WikiTextHeadingRule:12 -->Links</h2> <a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/37-edo/37edo.aspx" rel="nofollow">37edo at Tonalsoft</a></body></html>