24edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:cookiemeows|cookiemeows]] and made on <tt>2014-04-02 17:18:36 UTC</tt>.<br>

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..

tridecimal neutral third ||

||= 450 ||= minor fourth, supermajor third, ~~subfourth~~, Tendo Third ||= [[22_17|22/17]]

||= 450 ||= minor fourth, supermajor third, Under-fourth, Tendo Third ||= [[22_17|22/17]]

[[35_27|35/27]]

[[13_10|13/10]] ||= 446.363

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..

tridecimal subfourth ||

||= 550 ||= major fourth, ~~superfourth~~ ||= [[11_8|11/8]] ||= 551.318 ||= undecimal superfourth, harmonic 11th ||

||= 550 ||= major fourth, over-fourth ||= [[11_8|11/8]] ||= 551.318 ||= undecimal superfourth, harmonic 11th ||

||= 650 ||= minor fifth, ~~subfifth~~ ||= [[16_11|16/11]] ||= 648.682 ||= undecimal subfifth, 11th subharmonic ||

||= 650 ||= minor fifth, Under-Fifth ||= [[16_11|16/11]] ||= 648.682 ||= undecimal subfifth, 11th subharmonic ||

||= 750 ||= major fifth, subminor sixth, arto sixth

~~superfifth~~, ||= [[20_13|20/13]]

Over-fifth, ||= [[20_13|20/13]]

[[54_35|54/35]]

[[17_11|17/11]] ||= 745.786

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=Notation=

~~[[image:http://www.wfg.woodwind.org/n/s14_blue.gif]] or ^ = quarter-tone sharp~~

~~[[image:http://www.wfg.woodwind.org/n/s34_blue.gif]] or #^ = three-quarter-tone sharp~~

~~[[image:http://www.wfg.woodwind.org/n/f14_blue.gif]] or v = quarter-tone flat~~

~~[[image:http://www.wfg.woodwind.org/n/f34_blue.gif]] or bv = three-quarter-tone flat~~

~~Alternately~~, ~~in another notation system~~:

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.

[[image:http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif]] = quarter-tone sharp

**Mainstream Quartertone Notation**

††† (the horizontal line should connect all three vertical lines) = three quarter-tones sharp

[[image:http://www.wfg.woodwind.org/n/s14_blue.gif]] or ^ = quarter-tone sharp or "Jump"

[[image:http://www.dolmetsch.com/onequarterflat.gif]] = quarter-tone flat

[[image:http://www.wfg.woodwind.org/n/s34_blue.gif]] or #^ = three-quarter-tone sharp or "Jump-Sharp"

[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png]] = three quarter-tones flat.

[[image:http://www.wfg.woodwind.org/n/f14_blue.gif]] or v = quarter-tone flat or "Drop"

[[image:http://www.wfg.woodwind.org/n/f34_blue.gif]] or bv = three-quarter-tone flat or "Drop-Flat"

Pros: Familiar, fairly easy to learn

Cons: Clutters a score easily, can get confusing when sight read at faster paces

**Alternate Quartertone Accidentals**

[[image:http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif]] = quarter-tone sharp or Jump

††† (the horizontal line should connect all three vertical lines) = three quarter-tones sharp or Jump-Sharp

[[image:http://www.dolmetsch.com/onequarterflat.gif]] = quarter-tone flat or Drop

[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png]] = three quarter-tones flat or drop-flat

For example, the scale 0-5-10-15-20 is written as C-D[[image:http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif]] (or E[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png]]) F G[[image:http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif]] (or A[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png]]) Bb.

And in Persian music:

Pros: Very easy to distinguish accidentals from one another

[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png width="12" height="25"]]Koron ([[http://en.wikipedia.org/wiki/Koron_%28music%29|en]] | [[http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86|fa]]) = quarter-tone flat

Cons: Not practical, tends to clutter a score

[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png width="15" height="25"]]Sori ([[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|fa]]) = quarter-tone sharp

**<span style="line-height: 1.5;">And in Persian music</span>**

[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png width="12" height="25"]]Koron ([[http://en.wikipedia.org/wiki/Koron_%28music%29|en]] | [[http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86|fa]]) = quarter-tone flat or Jump

[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png width="15" height="25"]]Sori ([[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|fa]]) = quarter-tone sharp or Drop

Pros: Easy to read

Cons: Hard to write on a computer, doesn't fit with standard notation well

==Sagittal Notation==

Sagittal notation works extremely well for 24 Edo notation as well as other systems

It's easy on the eyes, easy to recognize the various symbols and keeps a score looking tidy and neat.

A possibility for the best approach would be to not use traditional sharps and flats altogether and replace them

with Sagittal signs for sharp and flat.

[[image:sagittal 24.PNG]]

=Interval Alterations=

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Subminor or "**Arto**" is a minor interval lowered a quarter tone

Neutral are intervals that exist between the major and minor version of an interval

The prefix **~~sub~~** indicates a perfect interval lowered by one quarter tone

The prefix **under** indicates a perfect interval lowered by one quarter tone

The prefix **~~super~~** indicates a perfect interval raised by a quarter tone

The prefix **over** indicates a perfect interval raised by a quarter tone

The Latin words "tendo" (meaning "expand") and "arto" (meaning "contract") can be used to replace the words "supermajor" and "subminor" in order to shorten the names of the intervals.

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</span><br />

<script type="text/javascript" src="http://webplayer.yahooapis.com/player.js">

</script><a href="#Basics">Basics</a> | <a href="#x24edo as a temperament">24edo as a temperament</a> | <a href="#Intervals">Intervals</a> | <a href="#Notation">Notation</a> | <a href="#Interval Alterations">Interval Alterations</a> | <a href="#Chord Structures">Chord Structures</a> | <a href="#Naming Chords in 24edo">Naming Chords in 24edo</a> | <a href="#Rank two temperaments">Rank two temperaments</a> | <a href="#Scales / Modes">Scales / Modes</a> | <a href="#Instruments">Instruments</a> | <a href="#Compositions">Compositions</a> | <a href="#Practical Theory / Books">Practical Theory / Books</a> | <a href="#External links">External links</a>

</script><a href="#Basics">Basics</a> | <a href="#x24edo as a temperament">24edo as a temperament</a> | <a href="#Intervals">Intervals</a> | <a href="#Notation">Notation</a> | <a href="#Interval Alterations">Interval Alterations</a> | <a href="#Chord Structures">Chord Structures</a> | <a href="#Naming Chords in 24edo">Naming Chords in 24edo</a> | <a href="#Rank two temperaments">Rank two temperaments</a> | <a href="#Scales / Modes">Scales / Modes</a> | <a href="#Instruments">Instruments</a> | <a href="#Compositions">Compositions</a> | <a href="#Practical Theory / Books">Practical Theory / Books</a> | <a href="#External links">External links</a>

<br />

<br />

<hr />

<h1 id="toc0"><a name="Basics"></a>Basics</h1>

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</td>

<td style="text-align: center;">minor fourth, supermajor third, ~~subfourth~~, Tendo Third<br />

<td style="text-align: center;">minor fourth, supermajor third, Under-fourth, Tendo Third<br />

</td>

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</td>

<td style="text-align: center;">major fourth, ~~superfourth~~<br />

<td style="text-align: center;">major fourth, over-fourth<br />

</td>

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</td>

<td style="text-align: center;">minor fifth, ~~subfifth~~<br />

<td style="text-align: center;">minor fifth, Under-Fifth<br />

</td>

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</td>

<td style="text-align: center;">major fifth, subminor sixth, arto sixth<br />

~~superfifth~~,<br />

Over-fifth,<br />

</td>

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<br />

<h1 id="toc4"><a name="Notation"></a>Notation</h1>

<img src="http://www.wfg.woodwind.org/n/s14_blue.gif" alt="external image s14_blue.gif" title="external image s14_blue.gif" /> or ^ = quarter-tone sharp<br />

<br />

<img src="http://www.wfg.woodwind.org/n/s34_blue.gif" alt="external image s34_blue.gif" title="external image s34_blue.gif" /> or #^ = three-quarter-tone sharp<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 />

<img src="http://www.wfg.woodwind.org/n/f14_blue.gif" alt="external image f14_blue.gif" title="external image f14_blue.gif" /> or v = quarter-tone flat<br />

<strong>Mainstream Quartertone Notation</strong><br />

<img src="http://www.wfg.woodwind.org/n/f34_blue.gif" alt="external image f34_blue.gif" title="external image f34_blue.gif" /> or bv = three-quarter-tone flat<br />

<img src="http://www.wfg.woodwind.org/n/s14_blue.gif" alt="external image s14_blue.gif" title="external image s14_blue.gif" /> or ^ = quarter-tone sharp or &quot;Jump&quot;<br />

<img src="http://www.wfg.woodwind.org/n/s34_blue.gif" alt="external image s34_blue.gif" title="external image s34_blue.gif" /> or #^ = three-quarter-tone sharp or &quot;Jump-Sharp&quot;<br />

<img src="http://www.wfg.woodwind.org/n/f14_blue.gif" alt="external image f14_blue.gif" title="external image f14_blue.gif" /> or v = quarter-tone flat or &quot;Drop&quot;<br />

<img src="http://www.wfg.woodwind.org/n/f34_blue.gif" alt="external image f34_blue.gif" title="external image f34_blue.gif" /> or bv = three-quarter-tone flat or &quot;Drop-Flat&quot;<br />

<br />

~~Alternately~~, ~~in another notation system:<br />~~

Pros: Familiar, fairly easy to learn<br />

<img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /> = quarter-tone sharp<br />

Cons: Clutters a score easily, can get confusing when sight read at faster paces<br />

~~††† (the horizontal line should connect all three vertical lines) = three quarter-tones sharp<br />~~

<img src="http://www.dolmetsch.com/onequarterflat.gif" alt="external image onequarterflat.gif" title="external image onequarterflat.gif" /> = quarter-tone flat<br />

<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" /> = three quarter-tones flat.<br />

~~For example~~, the scale 0-5-10-15-20 is written as C-D<img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /> (or E<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" />) F G<img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /> (or A<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" />) Bb.<br />

<br />

~~And in Persian music:~~<br />

<strong>Alternate Quartertone Accidentals</strong><br />

<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;~~" />~~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<br /~~>

<img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /> = quarter-tone sharp or Jump<br />

<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;~~" />~~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~~<br />

††† (the horizontal line should connect all three vertical lines) = three quarter-tones sharp or Jump-Sharp<br />

<img src="http://www.dolmetsch.com/onequarterflat.gif" alt="external image onequarterflat.gif" title="external image onequarterflat.gif" /> = quarter-tone flat or Drop<br />

<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" /> = three quarter-tones flat or drop-flat<br />

For example, the scale 0-5-10-15-20 is written as C-D<img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /> (or E<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" />) F G<img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /> (or A<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" />) Bb.<br />

<br />

<h1 id="~~toc5~~"><a name="Interval Alterations"></a>Interval Alterations</h1>

Pros: Very easy to distinguish accidentals from one another<br />

Cons: Not practical, tends to clutter a score<br />

<br />

<strong><span style="line-height: 1.5;">And in Persian music</span></strong><br />

<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;" />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 />

<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;" />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 />

Pros: Easy to read<br />

Cons: Hard to write on a computer, doesn't fit with standard notation well<br />

<br />

<h2 id="toc5"><a name="Notation-Sagittal Notation"></a>Sagittal Notation</h2>

<br />

Sagittal notation 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 />

A possibility for the best approach would be to not use traditional sharps and flats altogether and replace them <br />

with Sagittal signs for sharp and flat. <br />

<img src="/file/view/sagittal%2024.PNG/500168246/sagittal%2024.PNG" alt="sagittal 24.PNG" title="sagittal 24.PNG" /><br />

<h1 id="toc6"><a name="Interval Alterations"></a>Interval Alterations</h1>

<br />

The special alterations of the intervals and chords of 12 equal can be notated like this:<br />

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Subminor or &quot;<strong>Arto</strong>&quot; is a minor interval lowered a quarter tone<br />

Neutral are intervals that exist between the major and minor version of an interval<br />

The prefix <strong>~~sub~~</strong> indicates a perfect interval lowered by one quarter tone<br />

The prefix <strong>under</strong> indicates a perfect interval lowered by one quarter tone<br />

The prefix <strong>~~super~~</strong> indicates a perfect interval raised by a quarter tone<br />

The prefix <strong>over</strong> indicates a perfect interval raised by a quarter tone<br />

<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 />

<h1 id="~~toc6~~"><a name="Chord Structures"></a>Chord Structures</h1>

<h1 id="toc7"><a name="Chord Structures"></a>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 />

<br />

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William Lynch considers these as some possible good tetrads:<br />

<br />

<img src="/file/view/Three%20chords.PNG/489521008/Three%20chords.PNG" alt="Three chords.PNG" title="Three chords.PNG" /><br />

<img src="/file/view/Three%20chords.PNG/489521008/Three%20chords.PNG" alt="Three chords.PNG" title="Three chords.PNG" /><br />

<br />

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<br />

<h1 id="~~toc7~~"><a name="Naming Chords in 24edo"></a>Naming Chords in 24edo</h1>

<h1 id="toc8"><a name="Naming Chords in 24edo"></a>Naming Chords in 24edo</h1>

<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 />

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<br />

<h1 id="~~toc8~~"><a name="Rank two temperaments"></a>Rank two temperaments</h1>

<h1 id="toc9"><a name="Rank two temperaments"></a>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%20edo-distinct%2024et%20rank%20two%20temperaments">List of edo-distinct 24et rank two temperaments</a><br />

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</table>

<h1 id="~~toc9~~"><a name="Scales / Modes"></a>Scales / Modes</h1>

<h1 id="toc10"><a name="Scales / Modes"></a>Scales / Modes</h1>

<br />

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<tr>

<td colspan="2"><h4 id="~~toc10~~"><a name="Scales / Modes---24 tone modes:"></a>24 tone modes:</h4>

<td colspan="2"><h4 id="toc11"><a name="Scales / Modes---24 tone modes:"></a>24 tone modes:</h4>

</td>

</tr>

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<br />

<h1 id="~~toc11~~"><a name="Instruments"></a>Instruments<a name="instruments"></a></h1>

<h1 id="toc12"><a name="Instruments"></a>Instruments<a name="instruments"></a></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 />

<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;" />24-tone &quot;1/4-tone&quot; Guitar by Ron Sword / Sword guitars<br />

<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;" />24-tone &quot;1/4-tone&quot; Guitar by Ron Sword / Sword guitars<br />

<br />

<h1 id="~~toc12~~"><a name="Compositions"></a>Compositions</h1>

<h1 id="toc13"><a name="Compositions"></a>Compositions</h1>

<h2 id="~~toc13~~"><a name="Compositions-Music"></a>Music</h2>

<h2 id="toc14"><a name="Compositions-Music"></a>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-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 />

Line 1,942:

Line 1,980:

<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 />

<h2 id="~~toc14~~"><a name="Compositions-About"></a>About</h2>

<h2 id="toc15"><a name="Compositions-About"></a>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;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 />

<br />

<h1 id="~~toc15~~"><a name="Practical Theory / Books"></a>Practical Theory / Books</h1>

<h1 id="toc16"><a name="Practical Theory / Books"></a>Practical Theory / Books</h1>

<br />

<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;" /><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 />

<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;" /><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 />

<br />

<h1 id="~~toc16~~"><a name="External links"></a>External links</h1>

<h1 id="toc17"><a name="External links"></a>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://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://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>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2014-02-24 20:16:08 UTC</tt>.<br>
+: This revision was by author [[User:cookiemeows|cookiemeows]] and made on <tt>2014-04-02 17:18:36 UTC</tt>.<br>
-: The original revision id was <tt>491724360</tt>.<br>
+: The original revision id was <tt>500168940</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>
@@ Line 107: / Line 107: @@
 ..
 tridecimal neutral third ||
-||= 450 ||= minor fourth, supermajor third, subfourth, Tendo Third ||= [[22_17|22/17]]
+||= 450 ||= minor fourth, supermajor third, Under-fourth, Tendo Third ||= [[22_17|22/17]]
 [[35_27|35/27]]
 [[13_10|13/10]] ||= 446.363
@@ Line 114: / Line 114: @@
 ..
 tridecimal subfourth ||
-||= 550 ||= major fourth, superfourth ||= [[11_8|11/8]] ||= 551.318 ||= undecimal superfourth, harmonic 11th ||
+||= 550 ||= major fourth, over-fourth ||= [[11_8|11/8]] ||= 551.318 ||= undecimal superfourth, harmonic 11th ||
-||= 650 ||= minor fifth, subfifth ||= [[16_11|16/11]] ||= 648.682 ||= undecimal subfifth, 11th subharmonic ||
+||= 650 ||= minor fifth, Under-Fifth ||= [[16_11|16/11]] ||= 648.682 ||= undecimal subfifth, 11th subharmonic ||
 ||= 750 ||= major fifth, subminor sixth, arto sixth
-superfifth, ||= [[20_13|20/13]]
+Over-fifth, ||= [[20_13|20/13]]
 [[54_35|54/35]]
 [[17_11|17/11]] ||= 745.786
@@ Line 148: / Line 148: @@
 =Notation=
-[[image:http://www.wfg.woodwind.org/n/s14_blue.gif]] or ^ = quarter-tone sharp
-[[image:http://www.wfg.woodwind.org/n/s34_blue.gif]] or #^ = three-quarter-tone sharp
-[[image:http://www.wfg.woodwind.org/n/f14_blue.gif]] or v = quarter-tone flat
-[[image:http://www.wfg.woodwind.org/n/f34_blue.gif]] or bv = three-quarter-tone flat
-Alternately, in another notation system:
+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.
-[[image:http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif]] = quarter-tone sharp
+**Mainstream Quartertone Notation**
-††† (the horizontal line should connect all three vertical lines) = three quarter-tones sharp
+[[image:http://www.wfg.woodwind.org/n/s14_blue.gif]] or ^ = quarter-tone sharp or "Jump"
-[[image:http://www.dolmetsch.com/onequarterflat.gif]] = quarter-tone flat
+[[image:http://www.wfg.woodwind.org/n/s34_blue.gif]] or #^ = three-quarter-tone sharp or "Jump-Sharp"
-[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png]] = three quarter-tones flat.
+[[image:http://www.wfg.woodwind.org/n/f14_blue.gif]] or v = quarter-tone flat or "Drop"
+[[image:http://www.wfg.woodwind.org/n/f34_blue.gif]] or bv = three-quarter-tone flat or "Drop-Flat"
+Pros: Familiar, fairly easy to learn
+Cons: Clutters a score easily, can get confusing when sight read at faster paces
+**Alternate Quartertone Accidentals**
+[[image:http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif]] = quarter-tone sharp or Jump
+††† (the horizontal line should connect all three vertical lines) = three quarter-tones sharp or Jump-Sharp
+[[image:http://www.dolmetsch.com/onequarterflat.gif]] = quarter-tone flat or Drop
+[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png]] = three quarter-tones flat or drop-flat
 For example, the scale 0-5-10-15-20 is written as C-D[[image:http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif]] (or E[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png]]) F G[[image:http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif]] (or A[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png]]) Bb.
-And in Persian music:
+Pros: Very easy to distinguish accidentals from one another
-[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png width="12" height="25"]]Koron ([[http://en.wikipedia.org/wiki/Koron_%28music%29|en]] | [[http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86|fa]]) = quarter-tone flat
+Cons: Not practical, tends to clutter a score
-[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png width="15" height="25"]]Sori ([[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|fa]]) = quarter-tone sharp
+**&lt;span style="line-height: 1.5;"&gt;And in Persian music&lt;/span&gt;**
+[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png width="12" height="25"]]Koron ([[http://en.wikipedia.org/wiki/Koron_%28music%29|en]] | [[http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86|fa]]) = quarter-tone flat or Jump
+[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png width="15" height="25"]]Sori ([[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|fa]]) = quarter-tone sharp or Drop
+Pros: Easy to read
+Cons: Hard to write on a computer, doesn't fit with standard notation well
+==Sagittal Notation==
+Sagittal notation works extremely well for 24 Edo notation as well as other systems
+It's easy on the eyes, easy to recognize the various symbols and keeps a score looking tidy and neat.
+A possibility for the best approach would be to not use traditional sharps and flats altogether and replace them
+with Sagittal signs for sharp and flat.
+[[image:sagittal 24.PNG]]
 =Interval Alterations=
@@ Line 171: / Line 190: @@
 Subminor or "**Arto**" is a minor interval lowered a quarter tone
 Neutral are intervals that exist between the major and minor version of an interval
-The prefix **sub** indicates a perfect interval lowered by one quarter tone
+The prefix **under** indicates a perfect interval lowered by one quarter tone
-The prefix **super** indicates a perfect interval raised by a quarter tone
+The prefix **over** indicates a perfect interval raised by a quarter tone
 The Latin words "tendo" (meaning "expand") and "arto" (meaning "contract") can be used to replace the words "supermajor" and "subminor" in order to shorten the names of the intervals.
@@ Line 359: / Line 378: @@
 &lt;/span&gt;&lt;br /&gt;
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-&lt;/script&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt;&lt;!-- ws:start:WikiTextTocRule:37:&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:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&gt;&lt;a href="#Basics"&gt;Basics&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt; | &lt;a href="#x24edo as a temperament"&gt;24edo as a temperament&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&gt;&lt;!-- ws:end:WikiTextTocRule:40 --&gt;&lt;!-- ws:start:WikiTextTocRule:41: --&gt; | &lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:41 --&gt;&lt;!-- ws:start:WikiTextTocRule:42: --&gt; | &lt;a href="#Notation"&gt;Notation&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&gt; | &lt;a href="#Interval Alterations"&gt;Interval Alterations&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:43 --&gt;&lt;!-- ws:start:WikiTextTocRule:44: --&gt; | &lt;a href="#Chord Structures"&gt;Chord Structures&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:44 --&gt;&lt;!-- ws:start:WikiTextTocRule:45: --&gt; | &lt;a href="#Naming Chords in 24edo"&gt;Naming Chords in 24edo&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:45 --&gt;&lt;!-- ws:start:WikiTextTocRule:46: --&gt; | &lt;a href="#Rank two temperaments"&gt;Rank two temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt; | &lt;a href="#Scales / Modes"&gt;Scales / Modes&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt;&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt; | &lt;a href="#Instruments"&gt;Instruments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt; | &lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt; | &lt;a href="#Practical Theory / Books"&gt;Practical Theory / Books&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt; | &lt;a href="#External links"&gt;External links&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;
+&lt;/script&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt;&lt;!-- ws:start:WikiTextTocRule:39:&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:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&gt;&lt;a href="#Basics"&gt;Basics&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:40 --&gt;&lt;!-- ws:start:WikiTextTocRule:41: --&gt; | &lt;a href="#x24edo as a temperament"&gt;24edo as a temperament&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:41 --&gt;&lt;!-- ws:start:WikiTextTocRule:42: --&gt;&lt;!-- ws:end:WikiTextTocRule:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&gt; | &lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:43 --&gt;&lt;!-- ws:start:WikiTextTocRule:44: --&gt; | &lt;a href="#Notation"&gt;Notation&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:44 --&gt;&lt;!-- ws:start:WikiTextTocRule:45: --&gt;&lt;!-- ws:end:WikiTextTocRule:45 --&gt;&lt;!-- ws:start:WikiTextTocRule:46: --&gt; | &lt;a href="#Interval Alterations"&gt;Interval Alterations&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt; | &lt;a href="#Chord Structures"&gt;Chord Structures&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt; | &lt;a href="#Naming Chords in 24edo"&gt;Naming Chords in 24edo&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt; | &lt;a href="#Rank two temperaments"&gt;Rank two temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt; | &lt;a href="#Scales / Modes"&gt;Scales / Modes&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt; | &lt;a href="#Instruments"&gt;Instruments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt; | &lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt; | &lt;a href="#Practical Theory / Books"&gt;Practical Theory / Books&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt; | &lt;a href="#External links"&gt;External links&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;br /&gt;
 &lt;hr /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Basics"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt;Basics&lt;/h1&gt;
@@ Line 990: / Line 1,009: @@
          &lt;td style="text-align: center;"&gt;450&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;minor fourth, supermajor third, subfourth, Tendo Third&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;minor fourth, supermajor third, Under-fourth, Tendo Third&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/22_17"&gt;22/17&lt;/a&gt;&lt;br /&gt;
@@ Line 1,008: / Line 1,027: @@
          &lt;td style="text-align: center;"&gt;550&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;major fourth, superfourth&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;major fourth, over-fourth&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt;&lt;br /&gt;
@@ Line 1,020: / Line 1,039: @@
          &lt;td style="text-align: center;"&gt;650&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;minor fifth, subfifth&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;minor fifth, Under-Fifth&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/16_11"&gt;16/11&lt;/a&gt;&lt;br /&gt;
@@ Line 1,033: / Line 1,052: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;major fifth, subminor sixth, arto sixth&lt;br /&gt;
-superfifth,&lt;br /&gt;
+Over-fifth,&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/20_13"&gt;20/13&lt;/a&gt;&lt;br /&gt;
@@ Line 1,118: / Line 1,137: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;Notation&lt;/h1&gt;
-  &lt;!-- ws:start:WikiTextRemoteImageRule:1465:&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:1465 --&gt; or ^ = quarter-tone sharp&lt;br /&gt;
+  &lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1466:&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:1466 --&gt; or #^ = three-quarter-tone sharp&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;!-- ws:start:WikiTextRemoteImageRule:1467:&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:1467 --&gt; or v = quarter-tone flat&lt;br /&gt;
+&lt;strong&gt;Mainstream Quartertone Notation&lt;/strong&gt;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1468:&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:1468 --&gt; or bv = three-quarter-tone flat&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1469:&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:1469 --&gt; or ^ = quarter-tone sharp or &amp;quot;Jump&amp;quot;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1470:&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:1470 --&gt; or #^ = three-quarter-tone sharp or &amp;quot;Jump-Sharp&amp;quot;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1471:&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:1471 --&gt; or v = quarter-tone flat or &amp;quot;Drop&amp;quot;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1472:&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:1472 --&gt; or bv = three-quarter-tone flat or &amp;quot;Drop-Flat&amp;quot;&lt;br /&gt;
 &lt;br /&gt;
-Alternately, in another notation system:&lt;br /&gt;
+Pros: Familiar, fairly easy to learn&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1469:&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:1469 --&gt; = quarter-tone sharp&lt;br /&gt;
+Cons: Clutters a score easily, can get confusing when sight read at faster paces&lt;br /&gt;
-††† (the horizontal line should connect all three vertical lines) = three quarter-tones sharp&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1470:&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:1470 --&gt; = quarter-tone flat&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1471:&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:1471 --&gt; = three quarter-tones flat.&lt;br /&gt;
-For example, the scale 0-5-10-15-20 is written as C-D&lt;!-- ws:start:WikiTextRemoteImageRule:1472:&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:1472 --&gt; (or E&lt;!-- ws:start:WikiTextRemoteImageRule:1473:&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:1473 --&gt;) F G&lt;!-- ws:start:WikiTextRemoteImageRule:1474:&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:1474 --&gt; (or A&lt;!-- ws:start:WikiTextRemoteImageRule:1475:&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:1475 --&gt;) Bb.&lt;br /&gt;
 &lt;br /&gt;
-And in Persian music:&lt;br /&gt;
+&lt;strong&gt;Alternate Quartertone Accidentals&lt;/strong&gt;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1476:&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:1476 --&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&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1473:&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:1473 --&gt; = quarter-tone sharp or Jump&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1477:&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:1477 --&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&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:1474:&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:1474 --&gt; = quarter-tone flat or Drop&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1475:&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:1475 --&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:1476:&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:1476 --&gt; (or E&lt;!-- ws:start:WikiTextRemoteImageRule:1477:&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:1477 --&gt;) F G&lt;!-- ws:start:WikiTextRemoteImageRule:1478:&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:1478 --&gt; (or A&lt;!-- ws:start:WikiTextRemoteImageRule:1479:&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:1479 --&gt;) Bb.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:13:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Interval Alterations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:13 --&gt;Interval Alterations&lt;/h1&gt;
+Pros: Very easy to distinguish accidentals from one another&lt;br /&gt;
+Cons: Not practical, tends to clutter a score&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;!-- ws:start:WikiTextRemoteImageRule:1480:&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:1480 --&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:1481:&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:1481 --&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;
+Pros: Easy to read&lt;br /&gt;
+Cons: Hard to write on a computer, doesn't fit with standard notation well&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:13:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Notation-Sagittal Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:13 --&gt;Sagittal Notation&lt;/h2&gt;
+ &lt;br /&gt;
+Sagittal notation works extremely well for 24 Edo notation as well as other systems&lt;br /&gt;
+It's easy on the eyes, easy to recognize the various symbols and keeps a score looking tidy and neat.&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;
+&lt;!-- ws:start:WikiTextLocalImageRule:1467:&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:1467 --&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;br /&gt;
 The special alterations of the intervals and chords of 12 equal can be notated like this:&lt;br /&gt;
@@ Line 1,141: / Line 1,179: @@
 Subminor or &amp;quot;&lt;strong&gt;Arto&lt;/strong&gt;&amp;quot; is a minor interval lowered a quarter tone&lt;br /&gt;
 Neutral are intervals that exist between the major and minor version of an interval&lt;br /&gt;
-The prefix &lt;strong&gt;sub&lt;/strong&gt; indicates a perfect interval lowered by one quarter tone&lt;br /&gt;
+The prefix &lt;strong&gt;under&lt;/strong&gt; indicates a perfect interval lowered by one quarter tone&lt;br /&gt;
-The prefix &lt;strong&gt;super&lt;/strong&gt; indicates a perfect interval raised by a quarter tone&lt;br /&gt;
+The prefix &lt;strong&gt;over&lt;/strong&gt; indicates a perfect interval raised by a quarter tone&lt;br /&gt;
 &lt;br /&gt;
 The Latin words &amp;quot;tendo&amp;quot; (meaning &amp;quot;expand&amp;quot;) and &amp;quot;arto&amp;quot; (meaning &amp;quot;contract&amp;quot;) can be used to replace the words &amp;quot;supermajor&amp;quot; and &amp;quot;subminor&amp;quot; in order to shorten the names of the intervals.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:15:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Chord Structures"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:15 --&gt;Chord Structures&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:17:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Chord Structures"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:17 --&gt;Chord Structures&lt;/h1&gt;
 edo 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.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,156: / Line 1,194: @@
 William Lynch considers these as some possible good tetrads:&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:1464:&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:1464 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:1468:&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:1468 --&gt;&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,205: / Line 1,243: @@
 &lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:17:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Naming Chords in 24edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:17 --&gt;Naming Chords in 24edo&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:19:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Naming Chords in 24edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:19 --&gt;Naming Chords in 24edo&lt;/h1&gt;
   &lt;br /&gt;
 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.&lt;br /&gt;
@@ Line 1,221: / Line 1,259: @@
 &lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:19:&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:19 --&gt;Rank two temperaments&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:21:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Rank two temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:21 --&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%20edo-distinct%2024et%20rank%20two%20temperaments"&gt;List of edo-distinct 24et rank two temperaments&lt;/a&gt;&lt;br /&gt;
@@ Line 1,334: / Line 1,372: @@
 &lt;/table&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:21:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Scales / Modes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:21 --&gt;Scales / Modes&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:23:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Scales / Modes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:23 --&gt;Scales / Modes&lt;/h1&gt;
   &lt;br /&gt;
@@ Line 1,340: / Line 1,378: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;td colspan="2"&gt;&lt;!-- ws:start:WikiTextHeadingRule:23:&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:23 --&gt;24 tone modes:&lt;/h4&gt;
+         &lt;td colspan="2"&gt;&lt;!-- ws:start:WikiTextHeadingRule:25:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc11"&gt;&lt;a name="Scales / Modes---24 tone modes:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:25 --&gt;24 tone modes:&lt;/h4&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 1,928: / Line 1,966: @@
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:25:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Instruments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:25 --&gt;Instruments&lt;!-- ws:start:WikiTextAnchorRule:56:&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:56 --&gt;&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:27:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Instruments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:27 --&gt;Instruments&lt;!-- ws:start:WikiTextAnchorRule:59:&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:59 --&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;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1478:&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:1478 --&gt;24-tone &amp;quot;1/4-tone&amp;quot; Guitar by Ron Sword / Sword guitars&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1482:&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:1482 --&gt;24-tone &amp;quot;1/4-tone&amp;quot; Guitar by Ron Sword / Sword guitars&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:27:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:27 --&gt;Compositions&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:29:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc13"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:29 --&gt;Compositions&lt;/h1&gt;
-  &lt;!-- ws:start:WikiTextHeadingRule:29:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Compositions-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:29 --&gt;Music&lt;/h2&gt;
+  &lt;!-- ws:start:WikiTextHeadingRule:31:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Compositions-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:31 --&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-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 1,942: / Line 1,980: @@
 &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;!-- ws:start:WikiTextHeadingRule:31:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Compositions-About"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:31 --&gt;About&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:33:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Compositions-About"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:33 --&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;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;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:33:&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:33 --&gt;Practical Theory / Books&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:35:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc16"&gt;&lt;a name="Practical Theory / Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:35 --&gt;Practical Theory / Books&lt;/h1&gt;
   &lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1479:&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:1479 --&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:1483:&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:1483 --&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;!-- ws:start:WikiTextHeadingRule:35:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc16"&gt;&lt;a name="External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:35 --&gt;External links&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:37:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc17"&gt;&lt;a name="External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:37 --&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://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>