24edo: Difference between revisions

Wikispaces>k9assassin
**Imported revision 530434830 - Original comment: **
Wikispaces>k9assassin
**Imported revision 531565190 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:k9assassin|k9assassin]] and made on <tt>2014-11-10 21:18:00 UTC</tt>.<br>
: This revision was by author [[User:k9assassin|k9assassin]] and made on <tt>2014-11-18 12:00:15 UTC</tt>.<br>
: The original revision id was <tt>530434830</tt>.<br>
: The original revision id was <tt>531565190</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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|| 22 || 1100 ||= 17/9, 32/17 ||
|| 22 || 1100 ||= 17/9, 32/17 ||
|| 23 || 1150 ||= 33/17, 64/33 ||
|| 23 || 1150 ||= 33/17, 64/33 ||
|| 24 || 1200 ||= 2/1 ||
||   ||   ||=   ||
*based on treating 24-EDO as a 2.3.11.17.19 subgroup; other approaches are possible.
*based on treating 24-EDO as a 2.3.11.17.19 subgroup; other approaches are possible.


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===Commas===  
===Commas===  
24 EDO tempers out the following commas. (Note: This assumes val &lt; 24 38 56 67 83 89 |.)
24 EDO tempers out the following commas. (Note: This assumes val &lt; [[tel:24 38 56 67 83 89|24 38 56 67 83 89]] |.)
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
||= 531441/524288 || | -19 12 &gt; ||&gt; 23.46 ||= Pythagorean Comma ||=  ||  ||
||= [[tel:531441/524288|531441/524288]] || | -19 12 &gt; ||&gt; 23.46 ||= Pythagorean Comma ||=  ||  ||
||= 648/625 || | 3 4 -4 &gt; ||&gt; 62.57 ||= Major Diesis ||= Diminished Comma ||  ||
||= 648/625 || | 3 4 -4 &gt; ||&gt; 62.57 ||= Major Diesis ||= Diminished Comma ||  ||
||= 128/125 || | 7 0 -3 &gt; ||&gt; 41.06 ||= Diesis ||= Augmented Comma ||  ||
||= 128/125 || | 7 0 -3 &gt; ||&gt; 41.06 ||= Diesis ||= Augmented Comma ||  ||
||= 81/80 || | -4 4 -1 &gt; ||&gt; 21.51 ||= Syntonic Comma ||= Didymos Comma || Meantone Comma ||
||= 81/80 || | -4 4 -1 &gt; ||&gt; 21.51 ||= Syntonic Comma ||= Didymos Comma || Meantone Comma ||
||= 2048/2025 || | 11 -4 -2 &gt; ||&gt; 19.55 ||= Diaschisma ||=  ||  ||
||= 2048/2025 || | 11 -4 -2 &gt; ||&gt; 19.55 ||= Diaschisma ||=  ||  ||
||= 5201701/5149091 || | 26 -12 -3 &gt; ||&gt; 17.60 ||= Misty Comma ||=  ||  ||
||= [[tel:5201701/5149091|5201701/5149091]] || | 26 -12 -3 &gt; ||&gt; 17.60 ||= Misty Comma ||=  ||  ||
||= 32805/32768 || | -15 8 1 &gt; ||&gt; 1.95 ||= Schisma ||=  ||  ||
||= 32805/32768 || | -15 8 1 &gt; ||&gt; 1.95 ||= Schisma ||=  ||  ||
||= 1465155/1465142 || | 161 -84 -12 &gt; ||&gt; 0.02 ||= Atom ||=  ||  ||
||= [[tel:1465155/1465142|1465155/1465142]] || | 161 -84 -12 &gt; ||&gt; 0.02 ||= Atom ||=  ||  ||
||= 49/48 || | -4 -1 0 2 &gt; ||&gt; 35.70 ||= Slendro Diesis ||=  ||  ||
||= 49/48 || | -4 -1 0 2 &gt; ||&gt; 35.70 ||= Slendro Diesis ||=  ||  ||
||= 245/243 || | 0 -5 1 2 &gt; ||&gt; 14.19 ||= Sensamagic ||=  ||  ||
||= 245/243 || | 0 -5 1 2 &gt; ||&gt; 14.19 ||= Sensamagic ||=  ||  ||
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||= 676/675 || | 2 -3 -2 0 0 2 &gt; ||&gt; 2.56 ||= Parizeksma ||=  ||  ||
||= 676/675 || | 2 -3 -2 0 0 2 &gt; ||&gt; 2.56 ||= Parizeksma ||=  ||  ||
=Intervals=  
=Intervals=  
The twelve new intervals (quartertones) in 24edo that are not found in 12edo are:
|| 24 || 1200 ||= 2/1 ||
[[24 EDO Interval names and Harmonies|See full article on 24 Edo intervals.]]
||||~ The twelve new intervals in 24edo ||||||~ some nearby JI intervals ||
||||~ The twelve new intervals in 24edo ||||||~ some nearby JI intervals ||
||~ cents ||~ common names ||~ frequency ratio ||~ cents ||~ common name ||
||~ cents ||~ common names ||~ frequency ratio ||~ cents ||~ common name ||
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[[image:http://www.swordguitars.com/Sword_quartertone_stratsm.jpg width="406" height="195"]]24-tone "1/4-tone" Guitar by Ron Sword / Sword guitars
[[image:http://www.swordguitars.com/Sword_quartertone_stratsm.jpg width="406" height="195"]]24-tone "1/4-tone" Guitar by Ron Sword / Sword guitars


Hidekazu Wakabayashi tuned a piano and harp to where the normal sharps and flats are tuned 50 cents higher in which he called "Iceface" tuning.  
Hidekazu Wakabayashi tuned a piano and harp to where the normal sharps and flats are tuned 50 cents higher in which he called "Iceface" tuning.
Read about Iceface tuning here.  
Read about Iceface tuning here.


=Compositions=  
=Compositions=  
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;24&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1200&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;2/1&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x24edo as a temperament--Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt;Commas&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x24edo as a temperament--Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt;Commas&lt;/h3&gt;
  24 EDO tempers out the following commas. (Note: This assumes val &amp;lt; 24 38 56 67 83 89 |.)&lt;br /&gt;
  24 EDO tempers out the following commas. (Note: This assumes val &amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/24%2038%2056%2067%2083%2089"&gt;24 38 56 67 83 89&lt;/a&gt; |.)&lt;br /&gt;




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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td style="text-align: center;"&gt;531441/524288&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;[[tel:531441/524288|531441/524288]]&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;| -19 12 &amp;gt;&lt;br /&gt;
         &lt;td&gt;| -19 12 &amp;gt;&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td style="text-align: center;"&gt;5201701/5149091&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;[[tel:5201701/5149091|5201701/5149091]]&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;| 26 -12 -3 &amp;gt;&lt;br /&gt;
         &lt;td&gt;| 26 -12 -3 &amp;gt;&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td style="text-align: center;"&gt;1465155/1465142&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;[[tel:1465155/1465142|1465155/1465142]]&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;| 161 -84 -12 &amp;gt;&lt;br /&gt;
         &lt;td&gt;| 161 -84 -12 &amp;gt;&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;Intervals&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;Intervals&lt;/h1&gt;
  The twelve new intervals (quartertones) in 24edo that are not found in 12edo are:&lt;br /&gt;
   
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1200&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2/1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;a class="wiki_link" href="/24%20EDO%20Interval%20names%20and%20Harmonies"&gt;See full article on 24 Edo intervals.&lt;/a&gt;&lt;br /&gt;




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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.&lt;br /&gt;
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.&lt;br /&gt;
&lt;strong&gt;Mainstream Quartertone Notation&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;Mainstream Quartertone Notation&lt;/strong&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1532:&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:1532 --&gt; or ^ = quarter-tone sharp or &amp;quot;Jump&amp;quot;&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1542:&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:1542 --&gt; or ^ = quarter-tone sharp or &amp;quot;Jump&amp;quot;&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1533:&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:1533 --&gt; or #^ = three-quarter-tone sharp or &amp;quot;Jump-Sharp&amp;quot;&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1543:&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:1543 --&gt; or #^ = three-quarter-tone sharp or &amp;quot;Jump-Sharp&amp;quot;&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1534:&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:1534 --&gt; or v = quarter-tone flat or &amp;quot;Drop&amp;quot;&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1544:&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:1544 --&gt; or v = quarter-tone flat or &amp;quot;Drop&amp;quot;&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1535:&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:1535 --&gt; or bv = three-quarter-tone flat or &amp;quot;Drop-Flat&amp;quot;&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1545:&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:1545 --&gt; or bv = three-quarter-tone flat or &amp;quot;Drop-Flat&amp;quot;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Pros: Familiar, fairly easy to learn&lt;br /&gt;
Pros: Familiar, fairly easy to learn&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;Alternate Quartertone Accidentals&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;Alternate Quartertone Accidentals&lt;/strong&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1536:&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:1536 --&gt; = quarter-tone sharp or Jump&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1546:&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:1546 --&gt; = quarter-tone sharp or Jump&lt;br /&gt;
††† (the horizontal line should connect all three vertical lines) = three quarter-tones sharp or Jump-Sharp&lt;br /&gt;
††† (the horizontal line should connect all three vertical lines) = three quarter-tones sharp or Jump-Sharp&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1537:&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:1537 --&gt; = quarter-tone flat or Drop&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1547:&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:1547 --&gt; = quarter-tone flat or Drop&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1538:&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:1538 --&gt; = three quarter-tones flat or drop-flat&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1548:&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:1548 --&gt; = three quarter-tones flat or drop-flat&lt;br /&gt;
For example, the scale 0-5-10-15-20 is written as C-D&lt;!-- ws:start:WikiTextRemoteImageRule:1539:&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:1539 --&gt; (or E&lt;!-- ws:start:WikiTextRemoteImageRule:1540:&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:1540 --&gt;) F G&lt;!-- ws:start:WikiTextRemoteImageRule:1541:&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:1541 --&gt; (or A&lt;!-- ws:start:WikiTextRemoteImageRule:1542:&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:1542 --&gt;) Bb.&lt;br /&gt;
For example, the scale 0-5-10-15-20 is written as C-D&lt;!-- ws:start:WikiTextRemoteImageRule:1549:&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:1549 --&gt; (or E&lt;!-- ws:start:WikiTextRemoteImageRule:1550:&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:1550 --&gt;) F G&lt;!-- ws:start:WikiTextRemoteImageRule:1551:&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:1551 --&gt; (or A&lt;!-- ws:start:WikiTextRemoteImageRule:1552:&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:1552 --&gt;) Bb.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Pros: Very easy to distinguish accidentals from one another&lt;br /&gt;
Pros: Very easy to distinguish accidentals from one another&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;&lt;span style="line-height: 1.5;"&gt;And in Persian music&lt;/span&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;&lt;span style="line-height: 1.5;"&gt;And in Persian music&lt;/span&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1543:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 25px; width: 12px;&amp;quot; /&amp;gt; --&gt;&lt;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;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1543 --&gt;Koron (&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Koron_%28music%29" rel="nofollow"&gt;en&lt;/a&gt; | &lt;a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86" rel="nofollow"&gt;fa&lt;/a&gt;) = quarter-tone flat or Jump&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1553:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 25px; width: 12px;&amp;quot; /&amp;gt; --&gt;&lt;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;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1553 --&gt;Koron (&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Koron_%28music%29" rel="nofollow"&gt;en&lt;/a&gt; | &lt;a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86" rel="nofollow"&gt;fa&lt;/a&gt;) = quarter-tone flat or Jump&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1544:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 25px; width: 15px;&amp;quot; /&amp;gt; --&gt;&lt;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;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1544 --&gt;Sori (&lt;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"&gt;fa&lt;/a&gt;) = quarter-tone sharp or Drop&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1554:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 25px; width: 15px;&amp;quot; /&amp;gt; --&gt;&lt;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;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1554 --&gt;Sori (&lt;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"&gt;fa&lt;/a&gt;) = quarter-tone sharp or Drop&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Pros: Easy to read&lt;br /&gt;
Pros: Easy to read&lt;br /&gt;
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A possibility for the best approach would be to not use traditional sharps and flats altogether and replace them&lt;br /&gt;
A possibility for the best approach would be to not use traditional sharps and flats altogether and replace them&lt;br /&gt;
with Sagittal signs for sharp and flat.&lt;br /&gt;
with Sagittal signs for sharp and flat.&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:1530:&amp;lt;img src=&amp;quot;/file/view/sagittal%2024.PNG/500168246/sagittal%2024.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/sagittal%2024.PNG/500168246/sagittal%2024.PNG" alt="sagittal 24.PNG" title="sagittal 24.PNG" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1530 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:1540:&amp;lt;img src=&amp;quot;/file/view/sagittal%2024.PNG/500168246/sagittal%2024.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/sagittal%2024.PNG/500168246/sagittal%2024.PNG" alt="sagittal 24.PNG" title="sagittal 24.PNG" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1540 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:15:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Interval Alterations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:15 --&gt;Interval Alterations&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:15:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Interval Alterations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:15 --&gt;Interval Alterations&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
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William Lynch considers these as some possible good tetrads:&lt;br /&gt;
William Lynch considers these as some possible good tetrads:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:1531:&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:1531 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:1541:&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:1541 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;


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&lt;!-- ws:start:WikiTextHeadingRule:41:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Instruments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:41 --&gt;Instruments&lt;!-- ws:start:WikiTextAnchorRule:80:&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:80 --&gt;&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:41:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Instruments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:41 --&gt;Instruments&lt;!-- ws:start:WikiTextAnchorRule:80:&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:80 --&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:1545:&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:1545 --&gt;24-tone &amp;quot;1/4-tone&amp;quot; Guitar by Ron Sword / Sword guitars&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1555:&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:1555 --&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;
Hidekazu Wakabayashi tuned a piano and harp to where the normal sharps and flats are tuned 50 cents higher in which he called &amp;quot;Iceface&amp;quot; tuning. &lt;br /&gt;
Hidekazu Wakabayashi tuned a piano and harp to where the normal sharps and flats are tuned 50 cents higher in which he called &amp;quot;Iceface&amp;quot; tuning.&lt;br /&gt;
Read about Iceface tuning here. &lt;br /&gt;
Read about Iceface tuning here.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:43:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc20"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:43 --&gt;Compositions&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:43:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc20"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:43 --&gt;Compositions&lt;/h1&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:49:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc23"&gt;&lt;a name="Practical Theory / Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:49 --&gt;Practical Theory / Books&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:49:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc23"&gt;&lt;a name="Practical Theory / Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:49 --&gt;Practical Theory / Books&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:1546:&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:1546 --&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:1556:&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:1556 --&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:51:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc24"&gt;&lt;a name="External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:51 --&gt;External links&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:51:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc24"&gt;&lt;a name="External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:51 --&gt;External links&lt;/h1&gt;