41edo: Difference between revisions
Wikispaces>jdfreivald **Imported revision 395842882 - Original comment: ** |
Wikispaces>Gedankenwelt **Imported revision 440469648 - 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:Gedankenwelt|Gedankenwelt]] and made on <tt>2013-07-04 11:39:07 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>440469648</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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[[toc|flat]] | [[toc|flat]] | ||
=Introduction= | =Introduction= | ||
The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 [[cent]]s, an [[interval]] close in size to [[64_63|64/63]], the [[Septimal comma|septimal comma]]. 41-ET can be seen as a tuning of the //[[Schismatic family#Garibaldi|Garibaldi temperament]]// <ref>[[http://x31eq.com/schismic.htm|"Schismic Temperaments"]] at x31eq.com the | The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 [[cent]]s, an [[interval]] close in size to [[64_63|64/63]], the [[Septimal comma|septimal comma]]. 41-ET can be seen as a tuning of the //[[Schismatic family#Garibaldi|Garibaldi temperament]]// <ref>[[http://x31eq.com/schismic.htm|"Schismic Temperaments"]] at x31eq.com the website of [[Graham Breed]]</ref> , <ref>[[http://x31eq.com/decimal_lattice.htm|"Lattices with Decimal Notation"]] at x31eq.com</ref> , <ref>[[http://en.wikipedia.org/wiki/Schismatic_temperament|Schismatic temperament]]</ref> the //[[Magic family|Magic temperament]]// <ref>[[http://en.wikipedia.org/wiki/Magic_temperament|Magic temperament]]</ref> and the superkleismic (41&26) temperament. It is the second smallest equal temperament (after [[29edo]]) whose perfect fifth is closer to just intonation than that of [[12edo|12-ET]], and is the seventh [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]] after 31; it is not, however, a [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta gap edo]]. This has to do with the fact that it can deal with the [[11-limit]] fairly well, and the [[13-limit]] perhaps close enough for government work, though its [[13_10|13/10]] is 14 cents sharp. Various 13-limit [[magic extensions]] are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo. | ||
41-ET forms the foundation of the [[http://www.h-pi.com/theory/huntsystem1.html|H-System]], which uses the scale degrees of 41-ET as the basic [[13-limit]] intervals requiring fine tuning +/- 1 [[http://www.h-pi.com/theory/huntsystem2.html|average JND]] from the 41-ET circle in [[205edo]]. | 41-ET forms the foundation of the [[http://www.h-pi.com/theory/huntsystem1.html|H-System]], which uses the scale degrees of 41-ET as the basic [[13-limit]] intervals requiring fine tuning +/- 1 [[http://www.h-pi.com/theory/huntsystem2.html|average JND]] from the 41-ET circle in [[205edo]]. | ||
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|| 0 || 0.00 || [[1_1|1/1]] || do || || || | || 0 || 0.00 || [[1_1|1/1]] || do || || || | ||
|| 1 || 29.27 || [[81_80|81/80]] || di || || || | || 1 || 29.27 || [[81_80|81/80]] || di || || || | ||
|| 2 || 58.54 || [[25_24|25/24]], [[28_27|28/27]], [[33_32|33/32]] || ro || | || 2 || 58.54 || [[25_24|25/24]], [[28_27|28/27]], [[33_32|33/32]] || ro || [[Gamelismic clan#Miracle-Hemimiracle|Hemimiracle]] || || | ||
|| 3 || 87.80 || [[21_20|21/20]], [[22_21|22/21]] || rih || 88cET (approx) / [[octacot]] || || | || 3 || 87.80 || [[21_20|21/20]], [[22_21|22/21]] || rih || 88cET (approx) / [[octacot]] || || | ||
|| 4 || 117.07 || [[16_15|16/15]], [[15_14|15/14]] || ra || [[Miracle]] || || | || 4 || 117.07 || [[16_15|16/15]], [[15_14|15/14]] || ra || [[Miracle]] || || | ||
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|| 8 || 234.15 || [[8_7|8/7]] || ri || [[Rodan]]/[[guiron]] || 11-tone MOS: 7 1 7 1 7 1 7 1 1 7 1 || | || 8 || 234.15 || [[8_7|8/7]] || ri || [[Rodan]]/[[guiron]] || 11-tone MOS: 7 1 7 1 7 1 7 1 1 7 1 || | ||
|| 9 || 263.41 || [[7_6|7/6]], [[32_25|32/25]] || ma || [[Septimin]] || 9-tone MOS: 5 4 5 5 4 5 4 5 4 || | || 9 || 263.41 || [[7_6|7/6]], [[32_25|32/25]] || ma || [[Septimin]] || 9-tone MOS: 5 4 5 5 4 5 4 5 4 || | ||
|| 10 || 292.68 || [[32_27|32/27]] || meh || | || 10 || 292.68 || [[32_27|32/27]] || meh || [[Keemic temperaments#Quasitemp|Quasitemp]] || || | ||
|| 11 || 321.95 || [[6_5|6/5]] || me || [[Superkleismic]] || 11-tone MOS: 5 3 5 3 3 5 3 3 5 3 3 || | || 11 || 321.95 || [[6_5|6/5]] || me || [[Superkleismic]] || 11-tone MOS: 5 3 5 3 3 5 3 3 5 3 3 || | ||
|| 12 || 351.22 || [[11_9|11/9]],[[27_22|27/22]] || mu || [[Hemififths]]/[[karadeniz]] || 10-tone MOS: 5 2 5 5 2 5 5 5 2 5 || | || 12 || 351.22 || [[11_9|11/9]],[[27_22|27/22]] || mu || [[Hemififths]]/[[karadeniz]] || 10-tone MOS: 5 2 5 5 2 5 5 5 2 5 || | ||
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|| 14 || 409.76 || [[14_11|14/11]], [[81_64|81/64]] || maa || [[Hocus]] || || | || 14 || 409.76 || [[14_11|14/11]], [[81_64|81/64]] || maa || [[Hocus]] || || | ||
|| 15 || 439.02 || [[9_7|9/7]] || mo || || 11-tone MOS: 4 3 4 4 4 3 4 4 3 4 4 || | || 15 || 439.02 || [[9_7|9/7]] || mo || || 11-tone MOS: 4 3 4 4 4 3 4 4 3 4 4 || | ||
|| 16 || 468.29 || [[21_16|21/16]] || fe || | || 16 || 468.29 || [[21_16|21/16]] || fe || [[Keemic temperaments#Barbad|Barbad]] || || | ||
|| 17 || 497.56 || [[4_3|4/3]] || fa || [[Schismatic]] ([[helmholtz]], [[Garibaldi temperament|garibaldi]], [[cassandra]]) || || | || 17 || 497.56 || [[4_3|4/3]] || fa || [[Schismatic]] ([[helmholtz]], [[Garibaldi temperament|garibaldi]], [[cassandra]]) || || | ||
|| 18 || 526.83 || [[15_11|15/11]], [[27_20|27/20]] || fih || | || 18 || 526.83 || [[15_11|15/11]], [[27_20|27/20]] || fih || [[Magic family#Trismegistus|Trismegistus]] || 9-tone MOS: 5 5 3 5 5 5 5 3 5 || | ||
|| 19 || 556.10 || [[11_8|11/8]] || fu || || || | || 19 || 556.10 || [[11_8|11/8]] || fu || || || | ||
|| 20 || 585.37 || [[7_5|7/5]] || fi || [[Pluto]] || || | || 20 || 585.37 || [[7_5|7/5]] || fi || [[Pluto]] || || | ||
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=Music= | =Music= | ||
[[http://soundcloud.com/cameron-bobro/eveninghorizon-cbobro|EveningHorizon]] | [[http://soundcloud.com/cameron-bobro/eveninghorizon-cbobro|EveningHorizon]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3|play]] by Cameron Bobro | ||
=Links= | =Links= | ||
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* [[Magic22 as srutis#magic22assrutis]] describes a possible use of 41edo for [[indian]] music. | * [[Magic22 as srutis#magic22assrutis]] describes a possible use of 41edo for [[indian]] music. | ||
* see also [[Magic family]] | * see also [[Magic family]] | ||
* Sword, Ron.[[@http://www.ronsword.com| "Tetracontamonophonic Scales for Guitar"]]</pre></div> | * Sword, Ron. [[@http://www.ronsword.com|"Tetracontamonophonic Scales for Guitar"]]</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>41edo</title></head><body><span style="color: #004d25; font-family: 'Times New Roman',Times,serif; font-size: 20px;"><strong>41 Tone Equal Temperament</strong></span><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>41edo</title></head><body><span style="color: #004d25; font-family: 'Times New Roman',Times,serif; font-size: 20px;"><strong>41 Tone Equal Temperament</strong></span><br /> | ||
<!-- ws:start:WikiTextTocRule:27:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><a href="#Introduction">Introduction</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Temperaments">Temperaments</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#Instruments">Instruments</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --> | <a href="#Harmonic Scale">Harmonic Scale</a><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --> | <a href="#Nonoctave Temperaments">Nonoctave Temperaments</a><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --> | <a href="#Links">Links</a><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --> | <!-- ws:start:WikiTextTocRule:27:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><a href="#Introduction">Introduction</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Temperaments">Temperaments</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#Instruments">Instruments</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --> | <a href="#Harmonic Scale">Harmonic Scale</a><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --> | <a href="#Nonoctave Temperaments">Nonoctave Temperaments</a><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --> | <a href="#Links">Links</a><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --> | ||
<!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc0"><a name="Introduction"></a><!-- ws:end:WikiTextHeadingRule:9 -->Introduction</h1> | <!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc0"><a name="Introduction"></a><!-- ws:end:WikiTextHeadingRule:9 -->Introduction</h1> | ||
The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 <a class="wiki_link" href="/cent">cent</a>s, an <a class="wiki_link" href="/interval">interval</a> close in size to <a class="wiki_link" href="/64_63">64/63</a>, the <a class="wiki_link" href="/Septimal%20comma">septimal comma</a>. 41-ET can be seen as a tuning of the <em><a class="wiki_link" href="/Schismatic%20family#Garibaldi">Garibaldi temperament</a></em> <!-- ws:start:WikiTextRefRule:2:&amp;lt;ref&amp;gt;&lt;a class=&quot;wiki_link_ext&quot; href=&quot;http://x31eq.com/schismic.htm&quot; rel=&quot;nofollow&quot;&gt;&amp;quot;Schismic Temperaments&amp;quot;&lt;/a&gt; at x31eq.com the | The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 <a class="wiki_link" href="/cent">cent</a>s, an <a class="wiki_link" href="/interval">interval</a> close in size to <a class="wiki_link" href="/64_63">64/63</a>, the <a class="wiki_link" href="/Septimal%20comma">septimal comma</a>. 41-ET can be seen as a tuning of the <em><a class="wiki_link" href="/Schismatic%20family#Garibaldi">Garibaldi temperament</a></em> <!-- ws:start:WikiTextRefRule:2:&amp;lt;ref&amp;gt;&lt;a class=&quot;wiki_link_ext&quot; href=&quot;http://x31eq.com/schismic.htm&quot; rel=&quot;nofollow&quot;&gt;&amp;quot;Schismic Temperaments&amp;quot;&lt;/a&gt; at x31eq.com the website of &lt;a class=&quot;wiki_link&quot; href=&quot;/Graham%20Breed&quot;&gt;Graham Breed&lt;/a&gt;&amp;lt;/ref&amp;gt; --><sup id="cite_ref-1" class="reference"><a href="#cite_note-1">[1]</a></sup><!-- ws:end:WikiTextRefRule:2 --> , <!-- ws:start:WikiTextRefRule:4:&amp;lt;ref&amp;gt;&lt;a class=&quot;wiki_link_ext&quot; href=&quot;http://x31eq.com/decimal_lattice.htm&quot; rel=&quot;nofollow&quot;&gt;&amp;quot;Lattices with Decimal Notation&amp;quot;&lt;/a&gt; at x31eq.com&amp;lt;/ref&amp;gt; --><sup id="cite_ref-2" class="reference"><a href="#cite_note-2">[2]</a></sup><!-- ws:end:WikiTextRefRule:4 --> , <!-- ws:start:WikiTextRefRule:6:&amp;lt;ref&amp;gt;&lt;a class=&quot;wiki_link_ext&quot; href=&quot;http://en.wikipedia.org/wiki/Schismatic_temperament&quot; rel=&quot;nofollow&quot;&gt;Schismatic temperament&lt;/a&gt;&amp;lt;/ref&amp;gt; --><sup id="cite_ref-3" class="reference"><a href="#cite_note-3">[3]</a></sup><!-- ws:end:WikiTextRefRule:6 --> the <em><a class="wiki_link" href="/Magic%20family">Magic temperament</a></em> <!-- ws:start:WikiTextRefRule:8:&amp;lt;ref&amp;gt;&lt;a class=&quot;wiki_link_ext&quot; href=&quot;http://en.wikipedia.org/wiki/Magic_temperament&quot; rel=&quot;nofollow&quot;&gt;Magic temperament&lt;/a&gt;&amp;lt;/ref&amp;gt; --><sup id="cite_ref-4" class="reference"><a href="#cite_note-4">[4]</a></sup><!-- ws:end:WikiTextRefRule:8 --> and the superkleismic (41&amp;26) temperament. It is the second smallest equal temperament (after <a class="wiki_link" href="/29edo">29edo</a>) whose perfect fifth is closer to just intonation than that of <a class="wiki_link" href="/12edo">12-ET</a>, and is the seventh <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a> after 31; it is not, however, a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta gap edo</a>. This has to do with the fact that it can deal with the <a class="wiki_link" href="/11-limit">11-limit</a> fairly well, and the <a class="wiki_link" href="/13-limit">13-limit</a> perhaps close enough for government work, though its <a class="wiki_link" href="/13_10">13/10</a> is 14 cents sharp. Various 13-limit <a class="wiki_link" href="/magic%20extensions">magic extensions</a> are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo.<br /> | ||
<br /> | <br /> | ||
41-ET forms the foundation of the <a class="wiki_link_ext" href="http://www.h-pi.com/theory/huntsystem1.html" rel="nofollow">H-System</a>, which uses the scale degrees of 41-ET as the basic <a class="wiki_link" href="/13-limit">13-limit</a> intervals requiring fine tuning +/- 1 <a class="wiki_link_ext" href="http://www.h-pi.com/theory/huntsystem2.html" rel="nofollow">average JND</a> from the 41-ET circle in <a class="wiki_link" href="/205edo">205edo</a>.<br /> | 41-ET forms the foundation of the <a class="wiki_link_ext" href="http://www.h-pi.com/theory/huntsystem1.html" rel="nofollow">H-System</a>, which uses the scale degrees of 41-ET as the basic <a class="wiki_link" href="/13-limit">13-limit</a> intervals requiring fine tuning +/- 1 <a class="wiki_link_ext" href="http://www.h-pi.com/theory/huntsystem2.html" rel="nofollow">average JND</a> from the 41-ET circle in <a class="wiki_link" href="/205edo">205edo</a>.<br /> | ||
| Line 888: | Line 888: | ||
<td>ro<br /> | <td>ro<br /> | ||
</td> | </td> | ||
<td><br /> | <td><a class="wiki_link" href="/Gamelismic%20clan#Miracle-Hemimiracle">Hemimiracle</a><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,000: | Line 1,000: | ||
<td>meh<br /> | <td>meh<br /> | ||
</td> | </td> | ||
<td><br /> | <td><a class="wiki_link" href="/Keemic%20temperaments#Quasitemp">Quasitemp</a><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,084: | Line 1,084: | ||
<td>fe<br /> | <td>fe<br /> | ||
</td> | </td> | ||
<td><br /> | <td><a class="wiki_link" href="/Keemic%20temperaments#Barbad">Barbad</a><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,112: | Line 1,112: | ||
<td>fih<br /> | <td>fih<br /> | ||
</td> | </td> | ||
<td><br /> | <td><a class="wiki_link" href="/Magic%20family#Trismegistus">Trismegistus</a><br /> | ||
</td> | </td> | ||
<td>9-tone MOS: 5 5 3 5 5 5 5 3 5<br /> | <td>9-tone MOS: 5 5 3 5 5 5 5 3 5<br /> | ||
| Line 2,520: | Line 2,520: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:25:&lt;h1&gt; --><h1 id="toc8"><a name="Links"></a><!-- ws:end:WikiTextHeadingRule:25 -->Links</h1> | <!-- ws:start:WikiTextHeadingRule:25:&lt;h1&gt; --><h1 id="toc8"><a name="Links"></a><!-- ws:end:WikiTextHeadingRule:25 -->Links</h1> | ||
<ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/41_equal_temperament" rel="nofollow">Wikipedia article on 41edo</a></li><li><a class="wiki_link" href="/Magic22%20as%20srutis#magic22assrutis">Magic22 as srutis</a> describes a possible use of 41edo for <a class="wiki_link" href="/indian">indian</a> music.</li><li>see also <a class="wiki_link" href="/Magic%20family">Magic family</a></li><li>Sword, Ron.<a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow" target="_blank"> &quot;Tetracontamonophonic Scales for Guitar&quot;</a></li></ul><!-- ws:start:WikiTextReferencesRule: | <ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/41_equal_temperament" rel="nofollow">Wikipedia article on 41edo</a></li><li><a class="wiki_link" href="/Magic22%20as%20srutis#magic22assrutis">Magic22 as srutis</a> describes a possible use of 41edo for <a class="wiki_link" href="/indian">indian</a> music.</li><li>see also <a class="wiki_link" href="/Magic%20family">Magic family</a></li><li>Sword, Ron. <a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow" target="_blank">&quot;Tetracontamonophonic Scales for Guitar&quot;</a></li></ul><!-- ws:start:WikiTextReferencesRule:3405: --><hr class="references" /><ol class="references"> | ||
<li id="cite_note-1"><a href="#cite_ref-1">^</a> <a class="wiki_link_ext" href="http://x31eq.com/schismic.htm" rel="nofollow">&quot;Schismic Temperaments&quot;</a> at x31eq.com the | <li id="cite_note-1"><a href="#cite_ref-1">^</a> <a class="wiki_link_ext" href="http://x31eq.com/schismic.htm" rel="nofollow">&quot;Schismic Temperaments&quot;</a> at x31eq.com the website of <a class="wiki_link" href="/Graham%20Breed">Graham Breed</a></li> | ||
<li id="cite_note-2"><a href="#cite_ref-2">^</a> <a class="wiki_link_ext" href="http://x31eq.com/decimal_lattice.htm" rel="nofollow">&quot;Lattices with Decimal Notation&quot;</a> at x31eq.com</li> | <li id="cite_note-2"><a href="#cite_ref-2">^</a> <a class="wiki_link_ext" href="http://x31eq.com/decimal_lattice.htm" rel="nofollow">&quot;Lattices with Decimal Notation&quot;</a> at x31eq.com</li> | ||
<li id="cite_note-3"><a href="#cite_ref-3">^</a> <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Schismatic_temperament" rel="nofollow">Schismatic temperament</a></li> | <li id="cite_note-3"><a href="#cite_ref-3">^</a> <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Schismatic_temperament" rel="nofollow">Schismatic temperament</a></li> | ||
<li id="cite_note-4"><a href="#cite_ref-4">^</a> <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Magic_temperament" rel="nofollow">Magic temperament</a></li> | <li id="cite_note-4"><a href="#cite_ref-4">^</a> <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Magic_temperament" rel="nofollow">Magic temperament</a></li> | ||
</ol><!-- ws:end:WikiTextReferencesRule: | </ol><!-- ws:end:WikiTextReferencesRule:3405 --></body></html></pre></div> | ||