41edo: Difference between revisions
Wikispaces>Osmiorisbendi **Imported revision 610818591 - Original comment: ** |
Wikispaces>spt3125 **Imported revision 615832291 - Original comment: added link (deorphaning)** |
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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:spt3125|spt3125]] and made on <tt>2017-07-22 19:56:32 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>615832291</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>added link (deorphaning)</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> | ||
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A possible system to tune keyboards in 41EDO is discussed in [[http://launch.groups.yahoo.com/group/tuning/message/74155]]. | A possible system to tune keyboards in 41EDO is discussed in [[http://launch.groups.yahoo.com/group/tuning/message/74155]]. | ||
=Harmonic Scale= | =Scales and modes= | ||
A list of [[41edo modes]] (MOS and others). | |||
===Harmonic Scale=== | |||
41edo is the first edo to do some justice to Mode 8 of the [[OverToneSeries|harmonic series]], which Dante Rosati calls the "[[overtone scales|Diatonic Harmonic Series Scale]]," consisting of overtones 8 through 16 (sometimes made to repeat at the octave). | 41edo is the first edo to do some justice to Mode 8 of the [[OverToneSeries|harmonic series]], which Dante Rosati calls the "[[overtone scales|Diatonic Harmonic Series Scale]]," consisting of overtones 8 through 16 (sometimes made to repeat at the octave). | ||
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<span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/41edo">Deutsch</a><br /> | <span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/41edo">Deutsch</a><br /> | ||
</span><br /> | </span><br /> | ||
<!-- ws:start:WikiTextTocRule: | <!-- ws:start:WikiTextTocRule:33:&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:33 --><!-- ws:start:WikiTextTocRule:34: --><a href="#Introduction">Introduction</a><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --> | <a href="#Temperaments">Temperaments</a><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --> | <a href="#Instruments">Instruments</a><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | <a href="#Scales and modes">Scales and modes</a><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#Nonoctave Temperaments">Nonoctave Temperaments</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --> | <a href="#Links">Links</a><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:46 --><hr /> | ||
<!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc0"><a name="Introduction"></a><!-- ws:end:WikiTextHeadingRule:9 -->Introduction</h1> | <!-- 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 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 /> | 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 /> | ||
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<!-- ws:start:WikiTextHeadingRule:19:&lt;h1&gt; --><h1 id="toc5"><a name="Instruments"></a><!-- ws:end:WikiTextHeadingRule:19 -->Instruments</h1> | <!-- ws:start:WikiTextHeadingRule:19:&lt;h1&gt; --><h1 id="toc5"><a name="Instruments"></a><!-- ws:end:WikiTextHeadingRule:19 -->Instruments</h1> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:2722:&lt;img src=&quot;/file/view/41-EDD%20elektrische%20gitaar.jpg/610818537/560x745/41-EDD%20elektrische%20gitaar.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 745px; width: 560px;&quot; /&gt; --><img src="/file/view/41-EDD%20elektrische%20gitaar.jpg/610818537/560x745/41-EDD%20elektrische%20gitaar.jpg" alt="41-EDD elektrische gitaar.jpg" title="41-EDD elektrische gitaar.jpg" style="height: 745px; width: 560px;" /><!-- ws:end:WikiTextLocalImageRule:2722 --><br /> | ||
<em>41-EDO Electric guitar, by Gregory Sanchez.</em><br /> | <em>41-EDO Electric guitar, by Gregory Sanchez.</em><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:2723:&lt;img src=&quot;/file/view/Ron_Sword_with_a_41ET_Guitar.jpg/221056094/Ron_Sword_with_a_41ET_Guitar.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/Ron_Sword_with_a_41ET_Guitar.jpg/221056094/Ron_Sword_with_a_41ET_Guitar.jpg" alt="Ron_Sword_with_a_41ET_Guitar.jpg" title="Ron_Sword_with_a_41ET_Guitar.jpg" /><!-- ws:end:WikiTextLocalImageRule:2723 --><br /> | ||
<em>41-EDO Classical guitar, by Ron Sword.</em><br /> | <em>41-EDO Classical guitar, by Ron Sword.</em><br /> | ||
<br /> | <br /> | ||
A possible system to tune keyboards in 41EDO is discussed in <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/74155" rel="nofollow">http://launch.groups.yahoo.com/group/tuning/message/74155</a>.<br /> | A possible system to tune keyboards in 41EDO is discussed in <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/74155" rel="nofollow">http://launch.groups.yahoo.com/group/tuning/message/74155</a>.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:21:&lt;h1&gt; --><h1 id="toc6"><a name="Harmonic Scale"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:21:&lt;h1&gt; --><h1 id="toc6"><a name="Scales and modes"></a><!-- ws:end:WikiTextHeadingRule:21 -->Scales and modes</h1> | ||
<br /> | |||
A list of <a class="wiki_link" href="/41edo%20modes">41edo modes</a> (MOS and others).<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:23:&lt;h3&gt; --><h3 id="toc7"><a name="Scales and modes--Harmonic Scale"></a><!-- ws:end:WikiTextHeadingRule:23 -->Harmonic Scale</h3> | |||
41edo is the first edo to do some justice to Mode 8 of the <a class="wiki_link" href="/OverToneSeries">harmonic series</a>, which Dante Rosati calls the &quot;<a class="wiki_link" href="/overtone%20scales">Diatonic Harmonic Series Scale</a>,&quot; consisting of overtones 8 through 16 (sometimes made to repeat at the octave).<br /> | |||
<br /> | <br /> | ||
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The scale in 41, as adjacent steps, thus goes: 7 6 6 5 5 4 4 4.<br /> | The scale in 41, as adjacent steps, thus goes: 7 6 6 5 5 4 4 4.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:25:&lt;h1&gt; --><h1 id="toc8"><a name="Nonoctave Temperaments"></a><!-- ws:end:WikiTextHeadingRule:25 -->Nonoctave Temperaments</h1> | ||
Taking every third degree of 41edo produces a scale extremely close to <a class="wiki_link" href="/88cET">88cET</a> or 88-cent equal temperament (or the 8th root of 3:2). Likewise, taking every fifth degree produces a scale very close to the equal-tempered <span class="wiki_link_new"><a class="wiki_link" href="/BP">Bohlen-Pierce</a></span><a class="wiki_link" href="/BP"> Scale</a> (or the 13th root of 3). See chart:<br /> | Taking every third degree of 41edo produces a scale extremely close to <a class="wiki_link" href="/88cET">88cET</a> or 88-cent equal temperament (or the 8th root of 3:2). Likewise, taking every fifth degree produces a scale very close to the equal-tempered <span class="wiki_link_new"><a class="wiki_link" href="/BP">Bohlen-Pierce</a></span><a class="wiki_link" href="/BP"> Scale</a> (or the 13th root of 3). See chart:<br /> | ||
<br /> | <br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:27:&lt;h2&gt; --><h2 id="toc9"><a name="Nonoctave Temperaments-Notation"></a><!-- ws:end:WikiTextHeadingRule:27 -->Notation</h2> | ||
<br /> | <br /> | ||
A red-note/blue-note system, similar to the one proposed for <a class="wiki_link" href="/36edo">36edo</a>, is one option for notating 41edo. (This is separate from and not compatible with Kite's <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Kite%27s%20color%20notation">color notation</a>.) We have the &quot;white key&quot; albitonic notes A-G (7 in total), the &quot;black key&quot; sharps and flats (10 in total), a &quot;red&quot; and &quot;blue&quot; version of each albitonic note (14 in total), a &quot;red&quot; (dark red?) version of each sharp and a &quot;blue&quot; (dark blue?) version of each flat (10 in total), adding up to 41. This would result in quite a colorful keyboard! Note that there are no red flats or blue sharps. Using this nomenclature the notes are:<br /> | A red-note/blue-note system, similar to the one proposed for <a class="wiki_link" href="/36edo">36edo</a>, is one option for notating 41edo. (This is separate from and not compatible with Kite's <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Kite%27s%20color%20notation">color notation</a>.) We have the &quot;white key&quot; albitonic notes A-G (7 in total), the &quot;black key&quot; sharps and flats (10 in total), a &quot;red&quot; and &quot;blue&quot; version of each albitonic note (14 in total), a &quot;red&quot; (dark red?) version of each sharp and a &quot;blue&quot; (dark blue?) version of each flat (10 in total), adding up to 41. This would result in quite a colorful keyboard! Note that there are no red flats or blue sharps. Using this nomenclature the notes are:<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:29:&lt;h1&gt; --><h1 id="toc10"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:29 -->Music</h1> | ||
<a class="wiki_link_ext" href="http://soundcloud.com/cameron-bobro/eveninghorizon-cbobro" rel="nofollow">EveningHorizon</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3" rel="nofollow">play</a> by Cameron Bobro<br /> | <a class="wiki_link_ext" href="http://soundcloud.com/cameron-bobro/eveninghorizon-cbobro" rel="nofollow">EveningHorizon</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3" rel="nofollow">play</a> by Cameron Bobro<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:31:&lt;h1&gt; --><h1 id="toc11"><a name="Links"></a><!-- ws:end:WikiTextHeadingRule:31 -->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><li>Taylor, Cam. <a class="wiki_link_ext" href="https://drive.google.com/open?id=0B3wIGTmjY_VZYllwcHI0d3hEc3M" rel="nofollow">Intervals, Scales and Chords in 41EDO</a>, a work in progress using just intonation concepts and simplified Sagittal notation.</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><li>Taylor, Cam. <a class="wiki_link_ext" href="https://drive.google.com/open?id=0B3wIGTmjY_VZYllwcHI0d3hEc3M" rel="nofollow">Intervals, Scales and Chords in 41EDO</a>, a work in progress using just intonation concepts and simplified Sagittal notation.</li></ul><!-- ws:start:WikiTextReferencesRule:4142: --><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 website of <a class="wiki_link" href="/Graham%20Breed">Graham Breed</a></li> | <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:4142 --></body></html></pre></div> | ||