24edo: Difference between revisions

Wikispaces>cookiemeows
**Imported revision 489520654 - Original comment: **
Wikispaces>cookiemeows
**Imported revision 489524488 - Original comment: **
Line 1: Line 1:
<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:cookiemeows|cookiemeows]] and made on <tt>2014-02-14 09:59:59 UTC</tt>.<br>
: This revision was by author [[User:cookiemeows|cookiemeows]] and made on <tt>2014-02-14 10:18:44 UTC</tt>.<br>
: The original revision id was <tt>489520654</tt>.<br>
: The original revision id was <tt>489524488</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>
Line 186: Line 186:
These chords though tend to lack the forcefulness to sound like resolved, tonal sonorities but can be resolved of that issue by using tetrads in place of triads.
These chords though tend to lack the forcefulness to sound like resolved, tonal sonorities but can be resolved of that issue by using tetrads in place of triads.
For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21 William Lynch considers this chord to be the most beautiful tetrad in 24 Edo. In addition, the arto tetrad can have the arto 7th added to it but the chord tends to work better when a minor 7th is used in place of an arto seventh forming the arto tetrad: 0-5-14-20. The Tendo tetrad can also be made by attatching an arto seventh to tendo triad 0-9-14-19. Although the "Super-Tendo" chord can be made by attatching the tendo seventh to the chord, this chord is very dissonant, and therefore it is not considered a resolved sonority, although the sound of 0-9-14-23 is very cool in many context.
For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21 William Lynch considers this chord to be the most beautiful tetrad in 24 Edo. In addition, the arto tetrad can have the arto 7th added to it but the chord tends to work better when a minor 7th is used in place of an arto seventh forming the arto tetrad: 0-5-14-20. The Tendo tetrad can also be made by attatching an arto seventh to tendo triad 0-9-14-19. Although the "Super-Tendo" chord can be made by attatching the tendo seventh to the chord, this chord is very dissonant, and therefore it is not considered a resolved sonority, although the sound of 0-9-14-23 is very cool in many context.
The three most tonal quarter-tone tetrads on C:
[[image:Three chords.PNG]]
Neutral 0-7-14-21 or 1, v3, 5, v7
Arto 0-5-14-20 or 1, bv3, 5, b7
Tendo 0-9-14-19 or 1, ^3, 5, bv7
=Naming Chords in 24 Edo=
Naming chords in 24 edo can be achieved by adding a few things to the already existing set of terms that are used to name 12 Edo chords.
They are:
Super + perfect interval such as "perfect fifth" means to raise it by a quarter tone.
Sub + perfect interval means to lower a quarter tone.
Sharp is to raise by one half tone
Flat is to raise by a half tone
Neutral, arto and Tendo refer triads OR also to the tetrad versions
Neutral, Arto, or Tendo + interval name of 2nd, 3rd, 6th, or 7th is to alter respectively
Examples:
Neutral Super Eleventh or neut^11 = C neutral 7th chord with a super 11th thrown on top
Arto Sub Seventh Tendo &lt;span style="line-height: 1.5;"&gt;Thirteenth or artsub7^13 = Arto tetrad with an arto seventh and a tendo thirteenth on top &lt;/span&gt;
&lt;span style="line-height: 1.5;"&gt;Minor Seventh Flat Five Arto Ninth Super Eleventh or m7b5^9^11 &lt;/span&gt;


=Rank two temperaments=  
=Rank two temperaments=  
Line 336: Line 361:
&lt;/span&gt;&lt;br /&gt;
&lt;/span&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/11052600?h=0&amp;amp;w=0&amp;quot; class=&amp;quot;WikiMedia WikiMediaCustom&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;custom&amp;amp;quot; key=&amp;amp;quot;11052600&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;script type="text/javascript" src="http://webplayer.yahooapis.com/player.js"&gt;
&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/11052600?h=0&amp;amp;w=0&amp;quot; class=&amp;quot;WikiMedia WikiMediaCustom&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;custom&amp;amp;quot; key=&amp;amp;quot;11052600&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;script type="text/javascript" src="http://webplayer.yahooapis.com/player.js"&gt;
&lt;/script&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt;&lt;!-- ws:start:WikiTextTocRule:33:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt;&lt;a href="#Basics"&gt;Basics&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt; | &lt;a href="#x24edo as a temperament"&gt;24edo as a temperament&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt; | &lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&gt; | &lt;a href="#Notation"&gt;Notation&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt; | &lt;a href="#Interval Alterations"&gt;Interval Alterations&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&gt; | &lt;a href="#Chord Structures"&gt;Chord Structures&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:40 --&gt;&lt;!-- ws:start:WikiTextTocRule:41: --&gt; | &lt;a href="#Rank two temperaments"&gt;Rank two temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:41 --&gt;&lt;!-- ws:start:WikiTextTocRule:42: --&gt; | &lt;a href="#Scales / Modes"&gt;Scales / Modes&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&gt;&lt;!-- ws:end:WikiTextTocRule:43 --&gt;&lt;!-- ws:start:WikiTextTocRule:44: --&gt; | &lt;a href="#Instruments"&gt;Instruments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:44 --&gt;&lt;!-- ws:start:WikiTextTocRule:45: --&gt; | &lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:45 --&gt;&lt;!-- ws:start:WikiTextTocRule:46: --&gt;&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt;&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt; | &lt;a href="#Practical Theory / Books"&gt;Practical Theory / Books&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt; | &lt;a href="#External links"&gt;External links&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt;
&lt;/script&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt;&lt;!-- ws:start:WikiTextTocRule:35:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt;&lt;a href="#Basics"&gt;Basics&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt; | &lt;a href="#x24edo as a temperament"&gt;24edo as a temperament&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&gt;&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt; | &lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&gt; | &lt;a href="#Notation"&gt;Notation&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:40 --&gt;&lt;!-- ws:start:WikiTextTocRule:41: --&gt; | &lt;a href="#Interval Alterations"&gt;Interval Alterations&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:41 --&gt;&lt;!-- ws:start:WikiTextTocRule:42: --&gt; | &lt;a href="#Chord Structures"&gt;Chord Structures&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&gt; | &lt;a href="#Naming Chords in 24 Edo"&gt;Naming Chords in 24 Edo&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:43 --&gt;&lt;!-- ws:start:WikiTextTocRule:44: --&gt; | &lt;a href="#Rank two temperaments"&gt;Rank two temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:44 --&gt;&lt;!-- ws:start:WikiTextTocRule:45: --&gt; | &lt;a href="#Scales / Modes"&gt;Scales / Modes&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:45 --&gt;&lt;!-- ws:start:WikiTextTocRule:46: --&gt;&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt; | &lt;a href="#Instruments"&gt;Instruments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt; | &lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt; | &lt;a href="#Practical Theory / Books"&gt;Practical Theory / Books&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt; | &lt;a href="#External links"&gt;External links&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;
&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;br /&gt;
&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;br /&gt;
&lt;hr /&gt;
&lt;hr /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Basics"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt;Basics&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Basics"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt;Basics&lt;/h1&gt;
Line 1,096: Line 1,121:
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;Notation&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;Notation&lt;/h1&gt;
  &lt;!-- ws:start:WikiTextRemoteImageRule:1417:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/s14_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/s14_blue.gif" alt="external image s14_blue.gif" title="external image s14_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1417 --&gt; or ^ = quarter-tone sharp ,&lt;br /&gt;
  &lt;!-- ws:start:WikiTextRemoteImageRule:1421:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/s14_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/s14_blue.gif" alt="external image s14_blue.gif" title="external image s14_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1421 --&gt; or ^ = quarter-tone sharp ,&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1418:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/s34_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/s34_blue.gif" alt="external image s34_blue.gif" title="external image s34_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1418 --&gt; or #^ = three-quarter-tone sharp&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1422:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/s34_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/s34_blue.gif" alt="external image s34_blue.gif" title="external image s34_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1422 --&gt; or #^ = three-quarter-tone sharp&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1419:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/f14_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/f14_blue.gif" alt="external image f14_blue.gif" title="external image f14_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1419 --&gt; or v = quarter-tone flat&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1423:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/f14_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/f14_blue.gif" alt="external image f14_blue.gif" title="external image f14_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1423 --&gt; or v = quarter-tone flat&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1420:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/f34_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/f34_blue.gif" alt="external image f34_blue.gif" title="external image f34_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1420 --&gt; or bv = three-quarter-tone flat&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1424:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/f34_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/f34_blue.gif" alt="external image f34_blue.gif" title="external image f34_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1424 --&gt; or bv = three-quarter-tone flat&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Alternately, in another notation system,&lt;br /&gt;
Alternately, in another notation system,&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1421:&amp;lt;img src=&amp;quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1421 --&gt; can be used as a quarter-tone sharp,&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1425:&amp;lt;img src=&amp;quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1425 --&gt; can be used as a quarter-tone sharp,&lt;br /&gt;
††† (the horizontal line should connect all three vertical lines) can be used as a three-quartertone sharp,&lt;br /&gt;
††† (the horizontal line should connect all three vertical lines) can be used as a three-quartertone sharp,&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1422:&amp;lt;img src=&amp;quot;http://www.dolmetsch.com/onequarterflat.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.dolmetsch.com/onequarterflat.gif" alt="external image onequarterflat.gif" title="external image onequarterflat.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1422 --&gt; = quartertone flat,&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1426:&amp;lt;img src=&amp;quot;http://www.dolmetsch.com/onequarterflat.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.dolmetsch.com/onequarterflat.gif" alt="external image onequarterflat.gif" title="external image onequarterflat.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1426 --&gt; = quartertone flat,&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1423:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;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" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1423 --&gt; can be used as a three-quarter-tone flat.&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1427:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;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" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1427 --&gt; can be used as a three-quarter-tone flat.&lt;br /&gt;
For example, the scale 0-5-10-15-20 is written as C-D&lt;!-- ws:start:WikiTextRemoteImageRule:1424:&amp;lt;img src=&amp;quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1424 --&gt; (or E&lt;!-- ws:start:WikiTextRemoteImageRule:1425:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;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" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1425 --&gt;) F G&lt;!-- ws:start:WikiTextRemoteImageRule:1426:&amp;lt;img src=&amp;quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1426 --&gt; (or A&lt;!-- ws:start:WikiTextRemoteImageRule:1427:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;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" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1427 --&gt;) Bb.&lt;br /&gt;
For example, the scale 0-5-10-15-20 is written as C-D&lt;!-- ws:start:WikiTextRemoteImageRule:1428:&amp;lt;img src=&amp;quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1428 --&gt; (or E&lt;!-- ws:start:WikiTextRemoteImageRule:1429:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;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" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1429 --&gt;) F G&lt;!-- ws:start:WikiTextRemoteImageRule:1430:&amp;lt;img src=&amp;quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1430 --&gt; (or A&lt;!-- ws:start:WikiTextRemoteImageRule:1431:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;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" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1431 --&gt;) Bb.&lt;br /&gt;
And in persian music:&lt;br /&gt;
And in persian music:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 1,134: Line 1,159:
For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21 William Lynch considers this chord to be the most beautiful tetrad in 24 Edo. In addition, the arto tetrad can have the arto 7th added to it but the chord tends to work better when a minor 7th is used in place of an arto seventh forming the arto tetrad: 0-5-14-20. The Tendo tetrad can also be made by attatching an arto seventh to tendo triad 0-9-14-19. Although the &amp;quot;Super-Tendo&amp;quot; chord can be made by attatching the tendo seventh to the chord, this chord is very dissonant, and therefore it is not considered a resolved sonority, although the sound of 0-9-14-23 is very cool in many context.&lt;br /&gt;
For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21 William Lynch considers this chord to be the most beautiful tetrad in 24 Edo. In addition, the arto tetrad can have the arto 7th added to it but the chord tends to work better when a minor 7th is used in place of an arto seventh forming the arto tetrad: 0-5-14-20. The Tendo tetrad can also be made by attatching an arto seventh to tendo triad 0-9-14-19. Although the &amp;quot;Super-Tendo&amp;quot; chord can be made by attatching the tendo seventh to the chord, this chord is very dissonant, and therefore it is not considered a resolved sonority, although the sound of 0-9-14-23 is very cool in many context.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:15:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Rank two temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:15 --&gt;Rank two temperaments&lt;/h1&gt;
The three most tonal quarter-tone tetrads on C:&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:1420:&amp;lt;img src=&amp;quot;/file/view/Three%20chords.PNG/489521008/Three%20chords.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Three%20chords.PNG/489521008/Three%20chords.PNG" alt="Three chords.PNG" title="Three chords.PNG" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1420 --&gt;&lt;br /&gt;
&lt;br /&gt;
Neutral 0-7-14-21 or 1, v3, 5, v7&lt;br /&gt;
Arto 0-5-14-20 or 1, bv3, 5, b7&lt;br /&gt;
Tendo 0-9-14-19 or 1, ^3, 5, bv7 &lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:15:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Naming Chords in 24 Edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:15 --&gt;Naming Chords in 24 Edo&lt;/h1&gt;
&lt;br /&gt;
Naming chords in 24 edo can be achieved by adding a few things to the already existing set of terms that are used to name 12 Edo chords. &lt;br /&gt;
They are:&lt;br /&gt;
Super + perfect interval such as &amp;quot;perfect fifth&amp;quot; means to raise it by a quarter tone. &lt;br /&gt;
Sub + perfect interval means to lower a quarter tone. &lt;br /&gt;
Sharp is to raise by one half tone&lt;br /&gt;
Flat is to raise by a half tone&lt;br /&gt;
Neutral, arto and Tendo refer triads OR also to the tetrad versions &lt;br /&gt;
Neutral, Arto, or Tendo + interval name of 2nd, 3rd, 6th, or 7th is to alter respectively&lt;br /&gt;
&lt;br /&gt;
Examples:&lt;br /&gt;
Neutral Super Eleventh or neut^11 = C neutral 7th chord with a super 11th thrown on top&lt;br /&gt;
Arto Sub Seventh Tendo &lt;span style="line-height: 1.5;"&gt;Thirteenth or artsub7^13 = Arto tetrad with an arto seventh and a tendo thirteenth on top &lt;/span&gt;&lt;br /&gt;
&lt;span style="line-height: 1.5;"&gt;Minor Seventh Flat Five Arto Ninth Super Eleventh or m7b5^9^11 &lt;/span&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:17:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Rank two temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:17 --&gt;Rank two temperaments&lt;/h1&gt;
  &lt;a class="wiki_link" href="/List%20of%2024et%20rank%20two%20temperaments%20by%20badness"&gt;List of 24et rank two temperaments by badness&lt;/a&gt;&lt;br /&gt;
  &lt;a class="wiki_link" href="/List%20of%2024et%20rank%20two%20temperaments%20by%20badness"&gt;List of 24et rank two temperaments by badness&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/List%20of%20edo-distinct%2024et%20rank%20two%20temperaments"&gt;List of edo-distinct 24et rank two temperaments&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/List%20of%20edo-distinct%2024et%20rank%20two%20temperaments"&gt;List of edo-distinct 24et rank two temperaments&lt;/a&gt;&lt;br /&gt;
Line 1,247: Line 1,297:
&lt;/table&gt;
&lt;/table&gt;


&lt;!-- ws:start:WikiTextHeadingRule:17:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Scales / Modes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:17 --&gt;Scales / Modes&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:19:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Scales / Modes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:19 --&gt;Scales / Modes&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;


Line 1,253: Line 1,303:
&lt;table class="wiki_table"&gt;
&lt;table class="wiki_table"&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td colspan="2"&gt;&lt;!-- ws:start:WikiTextHeadingRule:19:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc9"&gt;&lt;a name="Scales / Modes---24 tone modes:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:19 --&gt;24 tone modes:&lt;/h4&gt;
         &lt;td colspan="2"&gt;&lt;!-- ws:start:WikiTextHeadingRule:21:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc10"&gt;&lt;a name="Scales / Modes---24 tone modes:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:21 --&gt;24 tone modes:&lt;/h4&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 1,841: Line 1,891:


&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:21:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Instruments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:21 --&gt;Instruments&lt;!-- ws:start:WikiTextAnchorRule:51:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@instruments&amp;quot; title=&amp;quot;Anchor: instruments&amp;quot;/&amp;gt; --&gt;&lt;a name="instruments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:51 --&gt;&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:23:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Instruments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:23 --&gt;Instruments&lt;!-- ws:start:WikiTextAnchorRule:54:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@instruments&amp;quot; title=&amp;quot;Anchor: instruments&amp;quot;/&amp;gt; --&gt;&lt;a name="instruments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:54 --&gt;&lt;/h1&gt;
  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 &lt;a class="wiki_link" href="/Microtonal%20Keyboards#twelvenoteoctavescales"&gt;&amp;quot;12 note octave scales&amp;quot;&lt;/a&gt; approach is used in a wide part of the existing literature - see below.&lt;br /&gt;
  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 &lt;a class="wiki_link" href="/Microtonal%20Keyboards#twelvenoteoctavescales"&gt;&amp;quot;12 note octave scales&amp;quot;&lt;/a&gt; approach is used in a wide part of the existing literature - see below.&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1428:&amp;lt;img src=&amp;quot;http://www.swordguitars.com/Sword_quartertone_stratsm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 195px; width: 406px;&amp;quot; /&amp;gt; --&gt;&lt;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;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1428 --&gt;24-tone &amp;quot;1/4-tone&amp;quot; Guitar by Ron Sword / Sword guitars&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1432:&amp;lt;img src=&amp;quot;http://www.swordguitars.com/Sword_quartertone_stratsm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 195px; width: 406px;&amp;quot; /&amp;gt; --&gt;&lt;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;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1432 --&gt;24-tone &amp;quot;1/4-tone&amp;quot; Guitar by Ron Sword / Sword guitars&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:23:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:23 --&gt;Compositions&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:25:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:25 --&gt;Compositions&lt;/h1&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:25:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Compositions-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:25 --&gt;Music&lt;/h2&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:27:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Compositions-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:27 --&gt;Music&lt;/h2&gt;
  &lt;span class="ymp-btn-page-play ymp-media-eb56a917c62000140296c2e1a6d89911"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex3.mp3" rel="nofollow"&gt;Microhex3&lt;/a&gt;&lt;/span&gt; &lt;span class="ymp-btn-page-play ymp-media-750620955011dabb8bc98c7c8830cbb8"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex4.mp3" rel="nofollow"&gt;Microhex4&lt;/a&gt;&lt;/span&gt; and &lt;span class="ymp-btn-page-play ymp-media-4aeb7c299c23983ba8081a591562e704"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex5.mp3" rel="nofollow"&gt;Microhex5&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link_ext" href="http://www.96edo.com/About_me.html" rel="nofollow"&gt;Shaahin Mohajeri&lt;/a&gt;&lt;br /&gt;
  &lt;span class="ymp-btn-page-play ymp-media-eb56a917c62000140296c2e1a6d89911"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex3.mp3" rel="nofollow"&gt;Microhex3&lt;/a&gt;&lt;/span&gt; &lt;span class="ymp-btn-page-play ymp-media-750620955011dabb8bc98c7c8830cbb8"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex4.mp3" rel="nofollow"&gt;Microhex4&lt;/a&gt;&lt;/span&gt; and &lt;span class="ymp-btn-page-play ymp-media-4aeb7c299c23983ba8081a591562e704"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex5.mp3" rel="nofollow"&gt;Microhex5&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link_ext" href="http://www.96edo.com/About_me.html" rel="nofollow"&gt;Shaahin Mohajeri&lt;/a&gt;&lt;br /&gt;
&lt;span class="ymp-btn-page-play ymp-media-30832be5610668b4b42451c8ce82dc80"&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/24et/quarterpicnic.mp3" rel="nofollow"&gt;Quarterpicnic&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;br /&gt;
&lt;span class="ymp-btn-page-play ymp-media-30832be5610668b4b42451c8ce82dc80"&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/24et/quarterpicnic.mp3" rel="nofollow"&gt;Quarterpicnic&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;br /&gt;
Line 1,855: Line 1,905:
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=q1Lp8AtKK9o" rel="nofollow"&gt;Autumn Winds&lt;/a&gt;, &lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=Igxe3DwbFJ4&amp;amp;feature=c4-overview&amp;amp;list=UUvq5bg-LvOS6adpB5efPTyQ" rel="nofollow"&gt;Easter Time at Nine&lt;/a&gt;, &lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=z_3uhA9Cq08&amp;amp;list=UUvq5bg-LvOS6adpB5efPTyQ" rel="nofollow"&gt;Waters of Persia&lt;/a&gt; by William Lynch in mohajira, 24et tuning.&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=q1Lp8AtKK9o" rel="nofollow"&gt;Autumn Winds&lt;/a&gt;, &lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=Igxe3DwbFJ4&amp;amp;feature=c4-overview&amp;amp;list=UUvq5bg-LvOS6adpB5efPTyQ" rel="nofollow"&gt;Easter Time at Nine&lt;/a&gt;, &lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=z_3uhA9Cq08&amp;amp;list=UUvq5bg-LvOS6adpB5efPTyQ" rel="nofollow"&gt;Waters of Persia&lt;/a&gt; by William Lynch in mohajira, 24et tuning.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:27:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Compositions-About"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:27 --&gt;About&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:29:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Compositions-About"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:29 --&gt;About&lt;/h2&gt;
  &amp;quot;Prométhée enchaîné&amp;quot; by &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Fromental_Hal%C3%A9vy" rel="nofollow"&gt;Fromental Halévy&lt;/a&gt; (considered the first mainstream western orchestral composition to use quarter tones.)&lt;br /&gt;
  &amp;quot;Prométhée enchaîné&amp;quot; by &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Fromental_Hal%C3%A9vy" rel="nofollow"&gt;Fromental Halévy&lt;/a&gt; (considered the first mainstream western orchestral composition to use quarter tones.)&lt;br /&gt;
&amp;quot;3 Hommages&amp;quot; by &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Georg_Friedrich_Haas" rel="nofollow"&gt;Georg Friedrich Haas&lt;/a&gt;&lt;br /&gt;
&amp;quot;3 Hommages&amp;quot; by &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Georg_Friedrich_Haas" rel="nofollow"&gt;Georg Friedrich Haas&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/List_of_quarter_tone_pieces" rel="nofollow"&gt;List of quartertone pieces on Wikipedia&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/List_of_quarter_tone_pieces" rel="nofollow"&gt;List of quartertone pieces on Wikipedia&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:29:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Practical Theory / Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:29 --&gt;Practical Theory / Books&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:31:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Practical Theory / Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:31 --&gt;Practical Theory / Books&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1429:&amp;lt;img src=&amp;quot;http://ronsword.com/images/24_tet_Coversm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 236px; width: 179px;&amp;quot; /&amp;gt; --&gt;&lt;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;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1429 --&gt;&lt;strong&gt;&amp;quot;Icosakaiteraphonic Scales for Guitar&amp;quot;&lt;/strong&gt; - 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.&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1433:&amp;lt;img src=&amp;quot;http://ronsword.com/images/24_tet_Coversm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 236px; width: 179px;&amp;quot; /&amp;gt; --&gt;&lt;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;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1433 --&gt;&lt;strong&gt;&amp;quot;Icosakaiteraphonic Scales for Guitar&amp;quot;&lt;/strong&gt; - 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.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:31:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:31 --&gt;External links&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:33:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc16"&gt;&lt;a name="External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:33 --&gt;External links&lt;/h1&gt;
  &lt;a class="wiki_link_ext" href="http://tonalsoft.com/enc/q/quarter-tone.aspx" rel="nofollow"&gt;quarter-tone / 24-edo - Encyclopedia of Microtonal Music Theory&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeFMH6cd" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;br /&gt;
  &lt;a class="wiki_link_ext" href="http://tonalsoft.com/enc/q/quarter-tone.aspx" rel="nofollow"&gt;quarter-tone / 24-edo - Encyclopedia of Microtonal Music Theory&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeFMH6cd" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.96edo.com/24_EDO.html" rel="nofollow"&gt;About 24-EDO&lt;/a&gt; by Shaahin Mohajeri &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeFBNdQW" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.96edo.com/24_EDO.html" rel="nofollow"&gt;About 24-EDO&lt;/a&gt; by Shaahin Mohajeri &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeFBNdQW" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://sonic-arts.org/darreg/contents.htm" rel="nofollow"&gt;The place of QUARTERTONES in Today's Xenharmonics&lt;/a&gt; by &lt;a class="wiki_link" href="/Ivor%20Darreg"&gt;Ivor Darreg&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://sonic-arts.org/darreg/dar8.htm" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;a class="wiki_link_ext" href="http://sonic-arts.org/darreg/contents.htm" rel="nofollow"&gt;The place of QUARTERTONES in Today's Xenharmonics&lt;/a&gt; by &lt;a class="wiki_link" href="/Ivor%20Darreg"&gt;Ivor Darreg&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://sonic-arts.org/darreg/dar8.htm" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>