24edo: Difference between revisions
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: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2015-10-16 02: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2015-10-16 02:49:11 UTC</tt>.<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"><span style="display: block; text-align: right;">[[xenharmonie/24edo|Deutsch]] - [[24平均律|日本語]] | <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"><span style="display: block; text-align: right;">[[xenharmonie/24edo|Deutsch]] - [[24平均律|日本語]] | ||
</span> | </span> | ||
[[toc]] | |||
=Basics= | =Basics= | ||
The 24edo system divides the octave into 24 equal parts of exactly 50 cents each. It is also known as **quarter-tone tuning**, since it evenly divides the 12-tone equal tempered semitone in two. Quarter-tones are the most commonly used microtonal tuning due to its retention of the familiar 12 tones and since it is the smallest microtonal equal temperament that contains all the 12 notes, and also because of its use in theory and occasionally in practice in [[Arabic, Turkish, Persian|Arabic]] music. It is easy to jump into this tuning and make microtonal music right away using common 12 equal software and even instruments - [[DIY Quartertone Composition with 12 equal tools|see this page]]. | The 24edo system divides the octave into 24 equal parts of exactly 50 cents each. It is also known as **quarter-tone tuning**, since it evenly divides the 12-tone equal tempered semitone in two. Quarter-tones are the most commonly used microtonal tuning due to its retention of the familiar 12 tones and since it is the smallest microtonal equal temperament that contains all the 12 notes, and also because of its use in theory and occasionally in practice in [[Arabic, Turkish, Persian|Arabic]] music. It is easy to jump into this tuning and make microtonal music right away using common 12 equal software and even instruments - [[DIY Quartertone Composition with 12 equal tools|see this page]]. | ||
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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>24edo</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/24edo">Deutsch</a> - <a class="wiki_link" href="/24%E5%B9%B3%E5%9D%87%E5%BE%8B">日本語</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>24edo</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/24edo">Deutsch</a> - <a class="wiki_link" href="/24%E5%B9%B3%E5%9D%87%E5%BE%8B">日本語</a><br /> | ||
</span><br /> | </span><br /> | ||
<!-- ws:start: | <!-- ws:start:WikiTextTocRule:58:&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:58 --><!-- ws:start:WikiTextTocRule:59: --><div style="margin-left: 1em;"><a href="#Basics">Basics</a></div> | ||
</ | <!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><div style="margin-left: 1em;"><a href="#x24edo as a temperament">24edo as a temperament</a></div> | ||
< | <!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><div style="margin-left: 3em;"><a href="#x24edo as a temperament--Commas">Commas</a></div> | ||
< | <!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><div style="margin-left: 1em;"><a href="#Intervals">Intervals</a></div> | ||
< | <!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><div style="margin-left: 1em;"><a href="#Notation">Notation</a></div> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --><div style="margin-left: 2em;"><a href="#Notation-Mainstream Quartertone Notation">Mainstream Quartertone Notation</a></div> | ||
<!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><div style="margin-left: 2em;"><a href="#Notation-Alternate Quartertone Accidentals">Alternate Quartertone Accidentals</a></div> | |||
<!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --><div style="margin-left: 2em;"><a href="#Notation-And in Persian music">And in Persian music</a></div> | |||
<!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><div style="margin-left: 2em;"><a href="#Notation-Sagittal Notation">Sagittal Notation</a></div> | |||
<!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --><div style="margin-left: 1em;"><a href="#Interval Alterations">Interval Alterations</a></div> | |||
<!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><div style="margin-left: 1em;"><a href="#Chord Structures">Chord Structures</a></div> | |||
<!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --><div style="margin-left: 1em;"><a href="#Naming Chords in 24edo">Naming Chords in 24edo</a></div> | |||
<!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><div style="margin-left: 1em;"><a href="#Rank two temperaments">Rank two temperaments</a></div> | |||
<!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --><div style="margin-left: 1em;"><a href="#Scales / Modes">Scales / Modes</a></div> | |||
<!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><div style="margin-left: 4em;"><a href="#Scales / Modes---Pentatonic:">Pentatonic:</a></div> | |||
<!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><div style="margin-left: 4em;"><a href="#Scales / Modes---Hexatonic:">Hexatonic:</a></div> | |||
<!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><div style="margin-left: 4em;"><a href="#Scales / Modes---Heptatonic:">Heptatonic:</a></div> | |||
<!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><div style="margin-left: 4em;"><a href="#Scales / Modes---Octatonic:">Octatonic:</a></div> | |||
<!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><div style="margin-left: 4em;"><a href="#Scales / Modes---Enneatonic:">Enneatonic:</a></div> | |||
<!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><div style="margin-left: 4em;"><a href="#Scales / Modes---Decatonic:">Decatonic:</a></div> | |||
<!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><div style="margin-left: 4em;"><a href="#Scales / Modes---Hendecatonic:">Hendecatonic:</a></div> | |||
<!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><div style="margin-left: 4em;"><a href="#Scales / Modes---Tridecatonic:">Tridecatonic:</a></div> | |||
<!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><div style="margin-left: 1em;"><a href="#Instruments">Instruments</a></div> | |||
<!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --><div style="margin-left: 1em;"><a href="#Compositions">Compositions</a></div> | |||
<!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><div style="margin-left: 2em;"><a href="#Compositions-Music">Music</a></div> | |||
<!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><div style="margin-left: 2em;"><a href="#Compositions-About">About</a></div> | |||
<!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --><div style="margin-left: 1em;"><a href="#Practical Theory / Books">Practical Theory / Books</a></div> | |||
<!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><div style="margin-left: 1em;"><a href="#External links">External links</a></div> | |||
<!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --></div> | |||
<!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc0"><a name="Basics"></a><!-- ws:end:WikiTextHeadingRule:2 -->Basics</h1> | |||
The 24edo system divides the octave into 24 equal parts of exactly 50 cents each. It is also known as <strong>quarter-tone tuning</strong>, since it evenly divides the 12-tone equal tempered semitone in two. Quarter-tones are the most commonly used microtonal tuning due to its retention of the familiar 12 tones and since it is the smallest microtonal equal temperament that contains all the 12 notes, and also because of its use in theory and occasionally in practice in <a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">Arabic</a> music. It is easy to jump into this tuning and make microtonal music right away using common 12 equal software and even instruments - <a class="wiki_link" href="/DIY%20Quartertone%20Composition%20with%2012%20equal%20tools">see this page</a>.<br /> | The 24edo system divides the octave into 24 equal parts of exactly 50 cents each. It is also known as <strong>quarter-tone tuning</strong>, since it evenly divides the 12-tone equal tempered semitone in two. Quarter-tones are the most commonly used microtonal tuning due to its retention of the familiar 12 tones and since it is the smallest microtonal equal temperament that contains all the 12 notes, and also because of its use in theory and occasionally in practice in <a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">Arabic</a> music. It is easy to jump into this tuning and make microtonal music right away using common 12 equal software and even instruments - <a class="wiki_link" href="/DIY%20Quartertone%20Composition%20with%2012%20equal%20tools">see this page</a>.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc1"><a name="x24edo as a temperament"></a><!-- ws:end:WikiTextHeadingRule:4 -->24edo as a temperament</h1> | ||
The <a class="wiki_link" href="/Harmonic%20Limit">5-limit</a> approximations in 24-tone equal temperament are the same as those in 12-tone equal temperament, therefore 24-tone equal temperament offers nothing new as far as approximating the 5-limit is concerned. The 7th harmonic-based intervals (7:4, 7:5 and 7:6) are just as bad in 24-tET as in 12-tET, although they are approximated by different intervals. To achieve a satisfactory level of approximation while maintaining the 12 notes of 12-tET requires high-degree tunings like 72-tET, 84-tET or 156-tET.<br /> | The <a class="wiki_link" href="/Harmonic%20Limit">5-limit</a> approximations in 24-tone equal temperament are the same as those in 12-tone equal temperament, therefore 24-tone equal temperament offers nothing new as far as approximating the 5-limit is concerned. The 7th harmonic-based intervals (7:4, 7:5 and 7:6) are just as bad in 24-tET as in 12-tET, although they are approximated by different intervals. To achieve a satisfactory level of approximation while maintaining the 12 notes of 12-tET requires high-degree tunings like 72-tET, 84-tET or 156-tET.<br /> | ||
<br /> | <br /> | ||
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0-5-10 (another kind of &quot;neutral&quot;, splitting the fourth in two. The 0-5-10 can be extended into a pentatonic scale, 0-5-10-14-19-24 (<a class="wiki_link" href="/godzilla">godzilla</a>), that is [[#|close]] to equi-pentatonic and also close to several Indonesian šlêndros. In a similar way 0-7-14 extends to 0-4-7-11-14-18-21-24 (<a class="wiki_link" href="/mohajira">mohajira</a>), a heptatonic scale close to several Arabic scales.)<br /> | 0-5-10 (another kind of &quot;neutral&quot;, splitting the fourth in two. The 0-5-10 can be extended into a pentatonic scale, 0-5-10-14-19-24 (<a class="wiki_link" href="/godzilla">godzilla</a>), that is [[#|close]] to equi-pentatonic and also close to several Indonesian šlêndros. In a similar way 0-7-14 extends to 0-4-7-11-14-18-21-24 (<a class="wiki_link" href="/mohajira">mohajira</a>), a heptatonic scale close to several Arabic scales.)<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc2"><a name="x24edo as a temperament--Commas"></a><!-- ws:end:WikiTextHeadingRule:6 -->Commas</h3> | ||
24 EDO tempers out the following commas. (Note: This assumes val &lt; <a class="wiki_link" href="http://tel.wikispaces.com/24%2038%2056%2067%2083%2089">24 38 56 67 83 89</a> |.)<br /> | 24 EDO tempers out the following commas. (Note: This assumes val &lt; <a class="wiki_link" href="http://tel.wikispaces.com/24%2038%2056%2067%2083%2089">24 38 56 67 83 89</a> |.)<br /> | ||
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</table> | </table> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc3"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:8 -->Intervals</h1> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc4"><a name="Notation"></a><!-- ws:end:WikiTextHeadingRule:10 -->Notation</h1> | ||
There have been disputes about disadvantages of various systems for notating quarter tones. Here are some of the few systems along with pros and cons.<br /> | There have been disputes about disadvantages of various systems for notating quarter tones. Here are some of the few systems along with pros and cons.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc5"><a name="Notation-Mainstream Quartertone Notation"></a><!-- ws:end:WikiTextHeadingRule:12 -->Mainstream Quartertone Notation</h2> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:1541:&lt;img src=&quot;http://www.wfg.woodwind.org/n/s14_blue.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://www.wfg.woodwind.org/n/s14_blue.gif" alt="external image s14_blue.gif" title="external image s14_blue.gif" /><!-- ws:end:WikiTextRemoteImageRule:1541 --> or ^ = quarter-tone sharp or &quot;Jump&quot;<br /> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:1542:&lt;img src=&quot;http://www.wfg.woodwind.org/n/s34_blue.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://www.wfg.woodwind.org/n/s34_blue.gif" alt="external image s34_blue.gif" title="external image s34_blue.gif" /><!-- ws:end:WikiTextRemoteImageRule:1542 --> or #^ = three-quarter-tone sharp or &quot;Jump-Sharp&quot;<br /> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:1543:&lt;img src=&quot;http://www.wfg.woodwind.org/n/f14_blue.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://www.wfg.woodwind.org/n/f14_blue.gif" alt="external image f14_blue.gif" title="external image f14_blue.gif" /><!-- ws:end:WikiTextRemoteImageRule:1543 --> or v = quarter-tone flat or &quot;Drop&quot;<br /> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:1544:&lt;img src=&quot;http://www.wfg.woodwind.org/n/f34_blue.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://www.wfg.woodwind.org/n/f34_blue.gif" alt="external image f34_blue.gif" title="external image f34_blue.gif" /><!-- ws:end:WikiTextRemoteImageRule:1544 --> or bv = three-quarter-tone flat or &quot;Drop-Flat&quot;<br /> | ||
<br /> | <br /> | ||
Pros: Familiar, fairly easy to learn<br /> | Pros: Familiar, fairly easy to learn<br /> | ||
Cons: Clutters a score easily, can get confusing when sight read at faster paces<br /> | Cons: Clutters a score easily, can get confusing when sight read at faster paces<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc6"><a name="Notation-Alternate Quartertone Accidentals"></a><!-- ws:end:WikiTextHeadingRule:14 -->Alternate Quartertone Accidentals</h2> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:1545:&lt;img src=&quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /><!-- ws:end:WikiTextRemoteImageRule:1545 --> = quarter-tone sharp or Jump<br /> | ||
††† (the horizontal line should connect all three vertical lines) = three quarter-tones sharp or Jump-Sharp<br /> | ††† (the horizontal line should connect all three vertical lines) = three quarter-tones sharp or Jump-Sharp<br /> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:1546:&lt;img src=&quot;http://www.dolmetsch.com/onequarterflat.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://www.dolmetsch.com/onequarterflat.gif" alt="external image onequarterflat.gif" title="external image onequarterflat.gif" /><!-- ws:end:WikiTextRemoteImageRule:1546 --> = quarter-tone flat or Drop<br /> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:1547:&lt;img src=&quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /><!-- ws:end:WikiTextRemoteImageRule:1547 --> = three quarter-tones flat or drop-flat<br /> | ||
For example, the scale 0-5-10-15-20 is written as C-D<!-- ws:start:WikiTextRemoteImageRule: | For example, the scale 0-5-10-15-20 is written as C-D<!-- ws:start:WikiTextRemoteImageRule:1548:&lt;img src=&quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /><!-- ws:end:WikiTextRemoteImageRule:1548 --> (or E<!-- ws:start:WikiTextRemoteImageRule:1549:&lt;img src=&quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /><!-- ws:end:WikiTextRemoteImageRule:1549 -->) F G<!-- ws:start:WikiTextRemoteImageRule:1550:&lt;img src=&quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /><!-- ws:end:WikiTextRemoteImageRule:1550 --> (or A<!-- ws:start:WikiTextRemoteImageRule:1551:&lt;img src=&quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /><!-- ws:end:WikiTextRemoteImageRule:1551 -->) Bb.<br /> | ||
<br /> | <br /> | ||
Pros: Very easy to distinguish accidentals from one another<br /> | Pros: Very easy to distinguish accidentals from one another<br /> | ||
Cons: Not practical, tends to clutter a score<br /> | Cons: Not practical, tends to clutter a score<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc7"><a name="Notation-And in Persian music"></a><!-- ws:end:WikiTextHeadingRule:16 --><span style="line-height: 1.5;">And in Persian music</span></h2> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:1552:&lt;img src=&quot;http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 25px; width: 12px;&quot; /&gt; --><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png" alt="external image 200px-Koron_sign.svg.png" title="external image 200px-Koron_sign.svg.png" style="height: 25px; width: 12px;" /><!-- ws:end:WikiTextRemoteImageRule:1552 -->Koron (<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Koron_%28music%29" rel="nofollow">en</a> | <a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86" rel="nofollow">fa</a>) = quarter-tone flat or Jump<br /> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:1553:&lt;img src=&quot;http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 25px; width: 15px;&quot; /&gt; --><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png" alt="external image 200px-Sori_sign.svg.png" title="external image 200px-Sori_sign.svg.png" style="height: 25px; width: 15px;" /><!-- ws:end:WikiTextRemoteImageRule:1553 -->Sori (<a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%D8%B3%D8%B1%DB%8C_%28%D9%85%D9%88%D8%B3%DB%8C%D9%82%DB%8C%29" rel="nofollow">fa</a>) = quarter-tone sharp or Drop<br /> | ||
<br /> | <br /> | ||
Pros: Easy to read<br /> | Pros: Easy to read<br /> | ||
Cons: Hard to write on a computer, doesn't fit with standard notation well<br /> | Cons: Hard to write on a computer, doesn't fit with standard notation well<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc8"><a name="Notation-Sagittal Notation"></a><!-- ws:end:WikiTextHeadingRule:18 -->Sagittal Notation</h2> | ||
<a class="wiki_link" href="/Sagittal%20notation">Sagittal notation</a> works extremely well for 24 Edo notation as well as other systems.<br /> | <a class="wiki_link" href="/Sagittal%20notation">Sagittal notation</a> works extremely well for 24 Edo notation as well as other systems.<br /> | ||
It's easy on the eyes, easy to recognize the various symbols and keeps a score looking tidy and neat.<br /> | It's easy on the eyes, easy to recognize the various symbols and keeps a score looking tidy and neat.<br /> | ||
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with Sagittal signs for sharp and flat.<br /> | with Sagittal signs for sharp and flat.<br /> | ||
<br /> | <br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc9"><a name="Interval Alterations"></a><!-- ws:end:WikiTextHeadingRule:20 -->Interval Alterations</h1> | ||
The special alterations of the intervals and chords of 12 equal can be notated like this:<br /> | The special alterations of the intervals and chords of 12 equal can be notated like this:<br /> | ||
<br /> | <br /> | ||
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The Latin words &quot;tendo&quot; (meaning &quot;expand&quot;) and &quot;arto&quot; (meaning &quot;contract&quot;) can be used to replace the words &quot;supermajor&quot; and &quot;subminor&quot; in order to shorten the names of the intervals.<br /> | The Latin words &quot;tendo&quot; (meaning &quot;expand&quot;) and &quot;arto&quot; (meaning &quot;contract&quot;) can be used to replace the words &quot;supermajor&quot; and &quot;subminor&quot; in order to shorten the names of the intervals.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc10"><a name="Chord Structures"></a><!-- ws:end:WikiTextHeadingRule:22 -->Chord Structures</h1> | ||
24edo features a rich variety on not only new chords, but also alterations that can be used with regular 12 Edo chords. For example, an approximation of the ninth, eleventh, and thirteenth harmonic can be added to a major triad to create a sort of super-extended chord structure of a major chord: 4:5:6:9:11:13.<br /> | 24edo features a rich variety on not only new chords, but also alterations that can be used with regular 12 Edo chords. For example, an approximation of the ninth, eleventh, and thirteenth harmonic can be added to a major triad to create a sort of super-extended chord structure of a major chord: 4:5:6:9:11:13.<br /> | ||
<br /> | <br /> | ||
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William Lynch considers these as some possible good tetrads:<br /> | William Lynch considers these as some possible good tetrads:<br /> | ||
<br /> | <br /> | ||
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<td>1 v3 5 v7<br /> | <td>1 v3 5 v7<br /> | ||
</td> | </td> | ||
<td><!-- ws:start:WikiTextMediaRule: | <td><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/Neutral%20Tetrad%20on%20C.mp3?h=30&amp;w=200&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;Neutral Tetrad on C.mp3&amp;quot; width=&amp;quot;200&amp;quot; height=&amp;quot;30&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;30&quot; width=&quot;200&quot;/&gt; --><embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="200" height="30" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252FNeutral%252BTetrad%252Bon%252BC.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=200&height=30"></embed><!-- ws:end:WikiTextMediaRule:0 --><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>1 bv3 5 b7<br /> | <td>1 bv3 5 b7<br /> | ||
</td> | </td> | ||
<td><!-- ws:start:WikiTextMediaRule: | <td><!-- ws:start:WikiTextMediaRule:1:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/arto%20tetrad%20on%20C.mp3?h=30&amp;w=200&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;arto tetrad on C.mp3&amp;quot; width=&amp;quot;200&amp;quot; height=&amp;quot;30&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;30&quot; width=&quot;200&quot;/&gt; --><embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="200" height="30" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Farto%252Btetrad%252Bon%252BC.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=200&height=30"></embed><!-- ws:end:WikiTextMediaRule:1 --><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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Due to convenience, the names Arto and tendo have been changed to Ultra and Infra.<br /> | Due to convenience, the names Arto and tendo have been changed to Ultra and Infra.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc11"><a name="Naming Chords in 24edo"></a><!-- ws:end:WikiTextHeadingRule:24 -->Naming Chords in 24edo</h1> | ||
Naming chords in 24edo can be achieved by adding a few things to the already [[#|existing]] set of terms that are used to name 12edo chords.<br /> | Naming chords in 24edo can be achieved by adding a few things to the already [[#|existing]] set of terms that are used to name 12edo chords.<br /> | ||
They are:<br /> | They are:<br /> | ||
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<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc12"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:26 -->Rank two temperaments</h1> | ||
<a class="wiki_link" href="/List%20of%2024et%20rank%20two%20temperaments%20by%20badness">List of 24et rank two temperaments by badness</a><br /> | <a class="wiki_link" href="/List%20of%2024et%20rank%20two%20temperaments%20by%20badness">List of 24et rank two temperaments by badness</a><br /> | ||
<a class="wiki_link" href="/List%20of%20edo-distinct%2024et%20rank%20two%20temperaments">List of edo-distinct 24et rank two temperaments</a><br /> | <a class="wiki_link" href="/List%20of%20edo-distinct%2024et%20rank%20two%20temperaments">List of edo-distinct 24et rank two temperaments</a><br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc13"><a name="Scales / Modes"></a><!-- ws:end:WikiTextHeadingRule:28 -->Scales / Modes</h1> | ||
<br /> | <br /> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td colspan="2"><!-- ws:start:WikiTextHeadingRule: | <td colspan="2"><!-- ws:start:WikiTextHeadingRule:30:&lt;h4&gt; --><h4 id="toc14"><a name="Scales / Modes---Pentatonic:"></a><!-- ws:end:WikiTextHeadingRule:30 -->Pentatonic:</h4> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td colspan="2"><!-- ws:start:WikiTextHeadingRule: | <td colspan="2"><!-- ws:start:WikiTextHeadingRule:32:&lt;h4&gt; --><h4 id="toc15"><a name="Scales / Modes---Hexatonic:"></a><!-- ws:end:WikiTextHeadingRule:32 -->Hexatonic:</h4> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td colspan="2"><!-- ws:start:WikiTextHeadingRule: | <td colspan="2"><!-- ws:start:WikiTextHeadingRule:34:&lt;h4&gt; --><h4 id="toc16"><a name="Scales / Modes---Heptatonic:"></a><!-- ws:end:WikiTextHeadingRule:34 -->Heptatonic:</h4> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td colspan="2"><!-- ws:start:WikiTextHeadingRule: | <td colspan="2"><!-- ws:start:WikiTextHeadingRule:36:&lt;h4&gt; --><h4 id="toc17"><a name="Scales / Modes---Octatonic:"></a><!-- ws:end:WikiTextHeadingRule:36 -->Octatonic:</h4> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td colspan="2"><!-- ws:start:WikiTextHeadingRule: | <td colspan="2"><!-- ws:start:WikiTextHeadingRule:38:&lt;h4&gt; --><h4 id="toc18"><a name="Scales / Modes---Enneatonic:"></a><!-- ws:end:WikiTextHeadingRule:38 -->Enneatonic:</h4> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td colspan="2"><!-- ws:start:WikiTextHeadingRule: | <td colspan="2"><!-- ws:start:WikiTextHeadingRule:40:&lt;h4&gt; --><h4 id="toc19"><a name="Scales / Modes---Decatonic:"></a><!-- ws:end:WikiTextHeadingRule:40 -->Decatonic:</h4> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td colspan="2"><!-- ws:start:WikiTextHeadingRule: | <td colspan="2"><!-- ws:start:WikiTextHeadingRule:42:&lt;h4&gt; --><h4 id="toc20"><a name="Scales / Modes---Hendecatonic:"></a><!-- ws:end:WikiTextHeadingRule:42 -->Hendecatonic:</h4> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td colspan="2"><!-- ws:start:WikiTextHeadingRule: | <td colspan="2"><!-- ws:start:WikiTextHeadingRule:44:&lt;h4&gt; --><h4 id="toc21"><a name="Scales / Modes---Tridecatonic:"></a><!-- ws:end:WikiTextHeadingRule:44 -->Tridecatonic:</h4> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:46:&lt;h1&gt; --><h1 id="toc22"><a name="Instruments"></a><!-- ws:end:WikiTextHeadingRule:46 -->Instruments<!-- ws:start:WikiTextAnchorRule:88:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@instruments&quot; title=&quot;Anchor: instruments&quot;/&gt; --><a name="instruments"></a><!-- ws:end:WikiTextAnchorRule:88 --></h1> | ||
The ever-arising question in microtonal music, how to play it on instruments designed for 12edo, has a relatively simple answer in the case of 24edo: use two standard instruments tuned a quartertone apart. This <a class="wiki_link" href="/Microtonal%20Keyboards#twelvenoteoctavescales">&quot;12 note octave scales&quot;</a> approach is used in a wide part of the existing literature - see below.<br /> | The ever-arising question in microtonal music, how to play it on instruments designed for 12edo, has a relatively simple answer in the case of 24edo: use two standard instruments tuned a quartertone apart. This <a class="wiki_link" href="/Microtonal%20Keyboards#twelvenoteoctavescales">&quot;12 note octave scales&quot;</a> approach is used in a wide part of the existing literature - see below.<br /> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:1554:&lt;img src=&quot;http://www.swordguitars.com/Sword_quartertone_stratsm.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 195px; width: 406px;&quot; /&gt; --><img src="http://www.swordguitars.com/Sword_quartertone_stratsm.jpg" alt="external image Sword_quartertone_stratsm.jpg" title="external image Sword_quartertone_stratsm.jpg" style="height: 195px; width: 406px;" /><!-- ws:end:WikiTextRemoteImageRule:1554 -->24-tone &quot;1/4-tone&quot; Guitar by Ron Sword / Sword guitars<br /> | ||
<br /> | <br /> | ||
Hidekazu Wakabayashi tuned a piano and harp to where the normal sharps and flats are tuned 50 cents higher in which he called <a class="wiki_link" href="/Iceface%20Tuning">Iceface tuning</a>.<br /> | Hidekazu Wakabayashi tuned a piano and harp to where the normal sharps and flats are tuned 50 cents higher in which he called <a class="wiki_link" href="/Iceface%20Tuning">Iceface tuning</a>.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:48:&lt;h1&gt; --><h1 id="toc23"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:48 -->Compositions</h1> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc24"><a name="Compositions-Music"></a><!-- ws:end:WikiTextHeadingRule:50 -->Music</h2> | ||
<span class="ymp-btn-page-play ymp-media-eb56a917c62000140296c2e1a6d89911"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex3.mp3" rel="nofollow">Microhex3</a></span> <span class="ymp-btn-page-play ymp-media-750620955011dabb8bc98c7c8830cbb8"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex4.mp3" rel="nofollow">Microhex4</a></span> and <span class="ymp-btn-page-play ymp-media-4aeb7c299c23983ba8081a591562e704"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex5.mp3" rel="nofollow">Microhex5</a></span> by <a class="wiki_link_ext" href="http://www.96edo.com/About_me.html" rel="nofollow">Shaahin Mohajeri</a><br /> | <span class="ymp-btn-page-play ymp-media-eb56a917c62000140296c2e1a6d89911"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex3.mp3" rel="nofollow">Microhex3</a></span> <span class="ymp-btn-page-play ymp-media-750620955011dabb8bc98c7c8830cbb8"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex4.mp3" rel="nofollow">Microhex4</a></span> and <span class="ymp-btn-page-play ymp-media-4aeb7c299c23983ba8081a591562e704"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex5.mp3" rel="nofollow">Microhex5</a></span> by <a class="wiki_link_ext" href="http://www.96edo.com/About_me.html" rel="nofollow">Shaahin Mohajeri</a><br /> | ||
<span class="ymp-btn-page-play ymp-media-30832be5610668b4b42451c8ce82dc80"><a class="wiki_link_ext" href="http://micro.soonlabel.com/24et/quarterpicnic.mp3" rel="nofollow">Quarterpicnic</a></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> | <span class="ymp-btn-page-play ymp-media-30832be5610668b4b42451c8ce82dc80"><a class="wiki_link_ext" href="http://micro.soonlabel.com/24et/quarterpicnic.mp3" rel="nofollow">Quarterpicnic</a></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> | ||
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<a class="wiki_link_ext" href="http://www.youtube.com/watch?v=q1Lp8AtKK9o" rel="nofollow">Autumn Winds</a>, <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=Igxe3DwbFJ4&amp;feature=c4-overview&amp;list=UUvq5bg-LvOS6adpB5efPTyQ" rel="nofollow">Easter Time at Nine</a>, <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=z_3uhA9Cq08&amp;list=UUvq5bg-LvOS6adpB5efPTyQ" rel="nofollow">Waters of Persia</a> by William Lynch in mohajira, 24et tuning.<br /> | <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=q1Lp8AtKK9o" rel="nofollow">Autumn Winds</a>, <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=Igxe3DwbFJ4&amp;feature=c4-overview&amp;list=UUvq5bg-LvOS6adpB5efPTyQ" rel="nofollow">Easter Time at Nine</a>, <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=z_3uhA9Cq08&amp;list=UUvq5bg-LvOS6adpB5efPTyQ" rel="nofollow">Waters of Persia</a> by William Lynch in mohajira, 24et tuning.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc25"><a name="Compositions-About"></a><!-- ws:end:WikiTextHeadingRule:52 -->About</h2> | ||
&quot;Prométhée enchaîné&quot; by <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Fromental_Hal%C3%A9vy" rel="nofollow">Fromental Halévy</a> (considered the first mainstream western orchestral composition to use quarter tones.)<br /> | &quot;Prométhée enchaîné&quot; by <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Fromental_Hal%C3%A9vy" rel="nofollow">Fromental Halévy</a> (considered the first mainstream western orchestral composition to use quarter tones.)<br /> | ||
&quot;3 Hommages&quot; by <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Georg_Friedrich_Haas" rel="nofollow">Georg Friedrich Haas</a><br /> | &quot;3 Hommages&quot; by <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Georg_Friedrich_Haas" rel="nofollow">Georg Friedrich Haas</a><br /> | ||
<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/List_of_quarter_tone_pieces" rel="nofollow">List of quartertone pieces on Wikipedia</a><br /> | <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/List_of_quarter_tone_pieces" rel="nofollow">List of quartertone pieces on Wikipedia</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:54:&lt;h1&gt; --><h1 id="toc26"><a name="Practical Theory / Books"></a><!-- ws:end:WikiTextHeadingRule:54 -->Practical Theory / Books</h1> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:1555:&lt;img src=&quot;http://ronsword.com/images/24_tet_Coversm.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 236px; width: 179px;&quot; /&gt; --><img src="http://ronsword.com/images/24_tet_Coversm.jpg" alt="external image 24_tet_Coversm.jpg" title="external image 24_tet_Coversm.jpg" style="height: 236px; width: 179px;" /><!-- ws:end:WikiTextRemoteImageRule:1555 --><strong>&quot;Icosakaiteraphonic Scales for Guitar&quot;</strong> - A Book for Twenty-Four Equal Divisions of the Octave on guitar, or 'Quarter-tones'. Features a practical approach to understanding the tuning, and over 550 Scale Examples on Nine-String finger board charts, which allows for both symmetrical tuning visualization and standard guitar tuning- helpful for bassists and large range guitarists as well. Includes MOS, DE, and *all* the Scales / Modes from the list above.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:56:&lt;h1&gt; --><h1 id="toc27"><a name="External links"></a><!-- ws:end:WikiTextHeadingRule:56 -->External links</h1> | ||
<a class="wiki_link_ext" href="http://tonalsoft.com/enc/q/quarter-tone.aspx" rel="nofollow">quarter-tone / 24-edo - Encyclopedia of Microtonal Music Theory</a> <a class="wiki_link_ext" href="http://www.webcitation.org/5xeFMH6cd" rel="nofollow">Permalink</a><br /> | <a class="wiki_link_ext" href="http://tonalsoft.com/enc/q/quarter-tone.aspx" rel="nofollow">quarter-tone / 24-edo - Encyclopedia of Microtonal Music Theory</a> <a class="wiki_link_ext" href="http://www.webcitation.org/5xeFMH6cd" rel="nofollow">Permalink</a><br /> | ||
<a class="wiki_link_ext" href="http://www.96edo.com/24_EDO.html" rel="nofollow">About 24-EDO</a> by Shaahin Mohajeri <a class="wiki_link_ext" href="http://www.webcitation.org/5xeFBNdQW" rel="nofollow">Permalink</a><br /> | <a class="wiki_link_ext" href="http://www.96edo.com/24_EDO.html" rel="nofollow">About 24-EDO</a> by Shaahin Mohajeri <a class="wiki_link_ext" href="http://www.webcitation.org/5xeFBNdQW" rel="nofollow">Permalink</a><br /> | ||
<a class="wiki_link_ext" href="https://docs.google.com/file/d/0Bzrl-iLY6DeEVkl1VjBGdEJlOTg/edit" rel="nofollow">Notation and Chord Names for 24-EDO</a> by William Lynch<br /> | <a class="wiki_link_ext" href="https://docs.google.com/file/d/0Bzrl-iLY6DeEVkl1VjBGdEJlOTg/edit" rel="nofollow">Notation and Chord Names for 24-EDO</a> by William Lynch<br /> | ||
<a class="wiki_link_ext" href="http://sonic-arts.org/darreg/contents.htm" rel="nofollow">The place of QUARTERTONES in Today's Xenharmonics</a> by <a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a> <a class="wiki_link_ext" href="http://sonic-arts.org/darreg/dar8.htm" rel="nofollow">Permalink</a></body></html></pre></div> | <a class="wiki_link_ext" href="http://sonic-arts.org/darreg/contents.htm" rel="nofollow">The place of QUARTERTONES in Today's Xenharmonics</a> by <a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a> <a class="wiki_link_ext" href="http://sonic-arts.org/darreg/dar8.htm" rel="nofollow">Permalink</a></body></html></pre></div> | ||