24edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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||= 676/675 || | 2 -3 -2 0 0 2 > ||> 2.56 ||= Parizeksma ||= || ||

=Intervals=

The twelve new intervals in ~~quartertones~~ are:

The twelve new intervals (quartertones) in 24edo that are not found in 12edo are:

||||~ The twelve new intervals in 24edo ||||||~ some nearby JI intervals ||

||~ cents ||~ common ~~name~~ ||~ frequency ratio ||~ cents ||~ common name ||

||~ cents ||~ common names ||~ frequency ratio ||~ cents ||~ common name ||

||= 50 ||= subminor second, quartertone

arto second ||= [[36_35|36/35]]

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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/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,

Alternately, in another notation system:

[[image:http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif]] ~~can be used as a~~ quarter-tone sharp,

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

††† (the horizontal line should connect all three vertical lines) ~~can be used as a~~ three-~~quartertone~~ sharp,

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

[[image:http://www.dolmetsch.com/onequarterflat.gif]] = ~~quartertone~~ flat,

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

[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png]] ~~can be used as a~~ three-quarter-~~tone~~ flat.

[[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.

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:~~

[[http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86|~~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|~~Koron~~]]

And in Persian music:

[[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

[[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

=Interval Alterations=

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

The words ~~Tendo~~ meaning "~~Expand~~" and "~~Arto~~" meaning "contract" ~~in Latin~~ can be used to replace the words

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.

"supermajor" and "subminor" in order to shorten the names of the intervals.

=Chord Structures=

~~24 Edo~~ features a rich variety on not only new chords, but also alterations that can be used with regular 12 Edo chords.

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.

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.

As for entirely new chords, ~~24 edo~~ features many possibilities for chords. The most obvious is the neutral triad 0-7-14 however there are other options such as

As for entirely new chords, 24edo features many possibilities for chords. The most obvious is the neutral triad 0-7-14 however there are other options such as

0-9-14 (Tendo Triad) and 0-5-14(Arto Triad), the chord names being based on what kind of third is in the chord.

0-9-14 (Tendo Triad) and 0-5-14 (Arto Triad), the chord names being based on what kind of third is in the chord.

These chords though tend to lack the forcefulness to sound like resolved, tonal sonorities but can be resolved of that issue by using tetrads in place of triads.

For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21 William Lynch considers this chord to be the most beautiful tetrad in ~~24 Edo~~. In addition, the arto tetrad can have the arto 7th added to it but the chord tends to work better when a minor 7th is used in place of an arto seventh forming the arto tetrad: 0-5-14-20. The Tendo tetrad can also be made by ~~attatching~~ an arto seventh to tendo triad 0-9-14-19. Although the "Super-Tendo" chord can be made by ~~attatching~~ the tendo seventh to the chord, this chord is very dissonant, and therefore it is not considered a resolved sonority, although the sound of 0-9-14-23 is very cool in many ~~context~~.

For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21. William Lynch considers this chord to be the most beautiful tetrad in 24edo. In addition, the arto tetrad can have the arto 7th added to it but the chord tends to work better when a minor 7th is used in place of an arto seventh forming the arto tetrad: 0-5-14-20. The Tendo tetrad can also be made by attaching an arto seventh to tendo triad 0-9-14-19. Although the "Super-Tendo" chord can be made by attaching the tendo seventh to the chord, this chord is very dissonant, and therefore it is not considered a resolved sonority, although the sound of 0-9-14-23 is very cool in many contexts.

William Lynch considers these three tetrads to be a good selection for functional harmony in ~~24 Edo~~:

William Lynch considers these three tetrads to be a good selection for functional harmony in 24edo:

[[image:Three chords.PNG]]

~~Neutral~~ 0-7-14-21 or 1, v3, 5, v7[[media type="file" key="Neutral Tetrad on C.mp3" width="~~208~~" height="30"]]

||~ Chord name ||~ Degrees of 24edo ||~ Chord spelling ||~ Audio example ||

~~Arto~~ 0-5-14-20 or 1, bv3, 5, b7[[media type="file" key="arto tetrad on C.mp3" width="~~195~~" height="30"]]

|| neutral || 0 7 14 21 || 1 v3 5 v7 || [[media type="file" key="Neutral Tetrad on C.mp3" width="200" height="30"]] ||

~~Tendo~~ 0-9-14-19 or 1, ^3, 5, bv7

|| arto || 0 5 14 20 || 1 bv3 5 b7 || [[media type="file" key="arto tetrad on C.mp3" width="200" height="30"]] ||

|| tendo || 0 9 14 19 || 1 ^3 5 bv7 || ... ||

=Naming Chords in ~~24 Edo~~=

=Naming Chords in 24edo=

Naming chords in ~~24 edo~~ can be achieved by adding a few things to the already existing set of terms that are used to name ~~12 Edo~~ chords.

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.

They are:

Super + perfect interval such as "perfect fifth" means to raise it by a quarter tone.

Super + perfect interval such as "perfect fifth" means to raise it by a quarter tone

Sub + perfect interval means to lower a quarter tone.

Sub + perfect interval means to lower a quarter tone

Sharp is to raise by one half tone

Flat is to raise by a half tone

Neutral, arto and ~~Tendo~~ refer triads ~~OR also to the tetrad versions~~

Neutral, arto and tendo refer to triads or tetrads

Neutral, ~~Arto~~, or ~~Tendo~~ + interval name of 2nd, 3rd, 6th, or 7th is to alter respectively

Neutral, arto, or tendo + interval name of 2nd, 3rd, 6th, or 7th is to alter respectively

Examples:

Neutral Super Eleventh or neut^11 = C neutral 7th chord with a super 11th thrown on top

Arto Sub Seventh Tendo ~~<span style="line-height: 1.5;">~~Thirteenth or artsub7^13 = Arto tetrad with an arto seventh and a tendo thirteenth on top ~~</span>~~

Arto Sub Seventh Tendo Thirteenth or artsub7^13 = Arto tetrad with an arto seventh and a tendo thirteenth on top Minor Seventh Flat Five Arto Ninth Super Eleventh or m7b5^9^11

~~<span style="line-height: 1.5;">~~Minor Seventh Flat Five Arto Ninth Super Eleventh or m7b5^9^11 ~~</span>~~

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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 ~~24 Edo~~">Naming Chords in ~~24 Edo~~</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 />

<hr />

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<h1 id="toc3"><a name="Intervals"></a>Intervals</h1>

The twelve new intervals in ~~quartertones~~ are:~~<br />~~

The twelve new intervals (quartertones) in 24edo that are not found in 12edo are:<br />

<br />

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<th>cents<br />

</th>

<th>common ~~name~~<br />

<th>common names<br />

</th>

<th>frequency ratio<br />

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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 />

<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 />

<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 />

<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 />

<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 />

<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 />

<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/f34_blue.gif" alt="external image f34_blue.gif" title="external image f34_blue.gif" /> or bv = three-quarter-tone flat<br />

<br />

Alternately, in another notation system,<br />

Alternately, in another notation system:<br />

<img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /> ~~can be used as a~~ quarter-tone sharp,<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 />

††† (the horizontal line should connect all three vertical lines) ~~can be used as a~~ three-~~quartertone~~ sharp,<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" /> = ~~quartertone~~ flat,<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" /> ~~can be used as a~~ three-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 />~~

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 />

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

<br />

<a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86" rel="nofollow">~~Sori~~</a>, <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">~~Koron~~</a><br />

And in Persian music:<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://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 />

<br />

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

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

<br />

The words ~~Tendo~~ meaning &quot;~~Expand~~&quot; and &quot;~~Arto~~&quot; meaning &quot;contract&quot; ~~in Latin~~ can be used to replace the words~~<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 />

&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>

~~24 Edo~~ features a rich variety on not only new chords, but also alterations that can be used with regular 12 Edo chords.~~<br />~~

24edo features a rich variety on not only new chords, but also alterations that can be used with regular 12 Edo chords. For example, an approximation of the ninth, eleventh, and thirteenth harmonic can be added to a major triad to create a sort of super-extended chord structure of a major chord: 4:5:6:9:11:13.<br />

For example, an approximation of the ninth, eleventh, and thirteenth harmonic can be added to a major triad to create a sort of~~<br />~~

super-extended chord structure of a major chord: 4:5:6:9:11:13.<br />

<br />

As for entirely new chords, ~~24 edo~~ features many possibilities for chords. The most obvious is the neutral triad 0-7-14 however there are other options such as<br />

As for entirely new chords, 24edo features many possibilities for chords. The most obvious is the neutral triad 0-7-14 however there are other options such as<br />

0-9-14 (Tendo Triad) and 0-5-14(Arto Triad), the chord names being based on what kind of third is in the chord.<br />

0-9-14 (Tendo Triad) and 0-5-14 (Arto Triad), the chord names being based on what kind of third is in the chord.<br />

These chords though tend to lack the forcefulness to sound like resolved, tonal sonorities but can be resolved of that issue by using tetrads in place of triads.<br />

For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21 William Lynch considers this chord to be the most beautiful tetrad in ~~24 Edo~~. In addition, the arto tetrad can have the arto 7th added to it but the chord tends to work better when a minor 7th is used in place of an arto seventh forming the arto tetrad: 0-5-14-20. The Tendo tetrad can also be made by ~~attatching~~ an arto seventh to tendo triad 0-9-14-19. Although the &quot;Super-Tendo&quot; chord can be made by ~~attatching~~ the tendo seventh to the chord, this chord is very dissonant, and therefore it is not considered a resolved sonority, although the sound of 0-9-14-23 is very cool in many ~~context~~.<br />

For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21. William Lynch considers this chord to be the most beautiful tetrad in 24edo. In addition, the arto tetrad can have the arto 7th added to it but the chord tends to work better when a minor 7th is used in place of an arto seventh forming the arto tetrad: 0-5-14-20. The Tendo tetrad can also be made by attaching an arto seventh to tendo triad 0-9-14-19. Although the &quot;Super-Tendo&quot; chord can be made by attaching the tendo seventh to the chord, this chord is very dissonant, and therefore it is not considered a resolved sonority, although the sound of 0-9-14-23 is very cool in many contexts.<br />

<br />

William Lynch considers these three tetrads to be a good selection for functional harmony in ~~24 Edo~~:<br />

William Lynch considers these three tetrads to be a good selection for functional harmony in 24edo:<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 />

~~Neutral~~ 0-7-14-21 or 1, v3, 5, v7<embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="~~208~~" height="30" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252FNeutral%252BTetrad%252Bon%252BC.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=~~208~~&height=30"></embed><br />

~~Arto~~ 0-5-14-20 or 1, bv3, 5, b7<embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="~~195~~" height="30" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Farto%252Btetrad%252Bon%252BC.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=~~195~~&height=30"></embed><br />

~~Tendo~~ 0-9-14-19 or 1, ^3, 5, bv7<br />

<tr>

<th>Chord name<br />

</th>

<th>Degrees of 24edo<br />

</th>

<th>Chord spelling<br />

</th>

<th>Audio example<br />

</th>

</tr>

<tr>

<td>neutral<br />

</td>

</td>

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

</td>

</tr>

<tr>

<td>tendo<br />

</td>

</td>

</td>

</td>

</tr>

</table>

<br />

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

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

<br />

Naming chords in ~~24 edo~~ can be achieved by adding a few things to the already existing set of terms that are used to name ~~12 Edo~~ chords.<br />

Naming chords in 24edo can be achieved by adding a few things to the already existing set of terms that are used to name 12edo chords.<br />

They are:<br />

Super + perfect interval such as &quot;perfect fifth&quot; means to raise it by a quarter tone.<br />

Super + perfect interval such as &quot;perfect fifth&quot; means to raise it by a quarter tone<br />

Sub + perfect interval means to lower a quarter tone.<br />

Sub + perfect interval means to lower a quarter tone<br />

Sharp is to raise by one half tone<br />

Flat is to raise by a half tone<br />

Neutral, arto and ~~Tendo~~ refer triads ~~OR also to the tetrad versions~~<br />

Neutral, arto and tendo refer to triads or tetrads<br />

Neutral, ~~Arto~~, or ~~Tendo~~ + interval name of 2nd, 3rd, 6th, or 7th is to alter respectively<br />

Neutral, arto, or tendo + interval name of 2nd, 3rd, 6th, or 7th is to alter respectively<br />

<br />

Examples:<br />

Neutral Super Eleventh or neut^11 = C neutral 7th chord with a super 11th thrown on top<br />

Arto Sub Seventh Tendo ~~<span style="line-height: 1.5;">~~Thirteenth or artsub7^13 = Arto tetrad with an arto seventh and a tendo thirteenth on top ~~</span><br />~~

Arto Sub Seventh Tendo Thirteenth or artsub7^13 = Arto tetrad with an arto seventh and a tendo thirteenth on top Minor Seventh Flat Five Arto Ninth Super Eleventh or m7b5^9^11<br />

~~<span style="line-height: 1.5;">~~Minor Seventh Flat Five Arto Ninth Super Eleventh or m7b5^9^11 ~~</span>~~<br />

<br />

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<h1 id="toc11"><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>

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<h1 id="toc15"><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>

@@ 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>2014-02-14 11:06:30 UTC</tt>.<br>
+: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-02-14 18:12:30 UTC</tt>.<br>
-: The original revision id was <tt>489534146</tt>.<br>
+: The original revision id was <tt>489603154</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 77: / Line 77: @@
 ||= 676/675 || | 2 -3 -2 0 0 2 &gt; ||&gt; 2.56 ||= Parizeksma ||=   ||   ||
 =Intervals=
-The twelve new intervals in quartertones are:
+The twelve new intervals (quartertones) in 24edo that are not found in 12edo are:
 ||||~ The twelve new intervals in 24edo ||||||~ some nearby JI intervals ||
-||~ cents ||~ common name ||~ frequency ratio ||~ cents ||~ common name ||
+||~ cents ||~ common names ||~ frequency ratio ||~ cents ||~ common name ||
 ||= 50 ||= subminor second, quartertone
 arto second ||= [[36_35|36/35]]
@@ Line 149: / Line 148: @@
 =Notation=
-[[image:http://www.wfg.woodwind.org/n/s14_blue.gif]] or ^ = quarter-tone sharp ,
+[[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,
+Alternately, in another notation system:
-[[image:http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif]] can be used as a quarter-tone sharp,
+[[image:http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif]] = quarter-tone sharp
-††† (the horizontal line should connect all three vertical lines) can be used as a three-quartertone sharp,
+††† (the horizontal line should connect all three vertical lines) = three quarter-tones sharp
-[[image:http://www.dolmetsch.com/onequarterflat.gif]] = quartertone flat,
+[[image:http://www.dolmetsch.com/onequarterflat.gif]] = quarter-tone flat
-[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png]] can be used as a three-quarter-tone flat.
+[[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.
 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:
-[[http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86|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|Koron]]
+And in Persian music:
+[[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
+[[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
 =Interval Alterations=
@@ Line 174: / Line 174: @@
 The prefix **super** indicates a perfect interval raised by a quarter tone
-The words Tendo meaning "Expand" and "Arto" meaning "contract" in Latin can be used to replace the words
+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.
-"supermajor" and "subminor" in order to shorten the names of the intervals.
 =Chord Structures=
-Edo features a rich variety on not only new chords, but also alterations that can be used with regular 12 Edo chords.
+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.
-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.
-As for entirely new chords, 24 edo features many possibilities for chords. The most obvious is the neutral triad 0-7-14 however there are other options such as
+As for entirely new chords, 24edo features many possibilities for chords. The most obvious is the neutral triad 0-7-14 however there are other options such as
--9-14 (Tendo Triad) and 0-5-14(Arto Triad), the chord names being based on what kind of third is in the chord.
+-9-14 (Tendo Triad) and 0-5-14 (Arto Triad), the chord names being based on what kind of third is in the chord.
 These chords though tend to lack the forcefulness to sound like resolved, tonal sonorities but can be resolved of that issue by using tetrads in place of triads.
-For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21 William Lynch considers this chord to be the most beautiful tetrad in 24 Edo. In addition, the arto tetrad can have the arto 7th added to it but the chord tends to work better when a minor 7th is used in place of an arto seventh forming the arto tetrad: 0-5-14-20. The Tendo tetrad can also be made by attatching an arto seventh to tendo triad 0-9-14-19. Although the "Super-Tendo" chord can be made by attatching the tendo seventh to the chord, this chord is very dissonant, and therefore it is not considered a resolved sonority, although the sound of 0-9-14-23 is very cool in many context.
+For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21. William Lynch considers this chord to be the most beautiful tetrad in 24edo. In addition, the arto tetrad can have the arto 7th added to it but the chord tends to work better when a minor 7th is used in place of an arto seventh forming the arto tetrad: 0-5-14-20. The Tendo tetrad can also be made by attaching an arto seventh to tendo triad 0-9-14-19. Although the "Super-Tendo" chord can be made by attaching the tendo seventh to the chord, this chord is very dissonant, and therefore it is not considered a resolved sonority, although the sound of 0-9-14-23 is very cool in many contexts.
-William Lynch considers these three tetrads to be a good selection for functional harmony in 24 Edo:
+William Lynch considers these three tetrads to be a good selection for functional harmony in 24edo:
 [[image:Three chords.PNG]]
-Neutral 0-7-14-21 or 1, v3, 5, v7[[media type="file" key="Neutral Tetrad on C.mp3" width="208" height="30"]]
+||~ Chord name ||~ Degrees of 24edo ||~ Chord spelling ||~ Audio example ||
-Arto 0-5-14-20 or 1, bv3, 5, b7[[media type="file" key="arto tetrad on C.mp3" width="195" height="30"]]
+|| neutral || 0 7 14 21 || 1 v3 5 v7 || [[media type="file" key="Neutral Tetrad on C.mp3" width="200" height="30"]] ||
-Tendo 0-9-14-19 or 1, ^3, 5, bv7
+|| arto || 0 5 14 20 || 1 bv3 5 b7 || [[media type="file" key="arto tetrad on C.mp3" width="200" height="30"]] ||
+|| tendo || 0 9 14 19 || 1 ^3 5 bv7 || ... ||
-=Naming Chords in 24 Edo=
+=Naming Chords in 24edo=
-Naming chords in 24 edo can be achieved by adding a few things to the already existing set of terms that are used to name 12 Edo chords.
+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.
 They are:
-Super + perfect interval such as "perfect fifth" means to raise it by a quarter tone.
+Super + perfect interval such as "perfect fifth" means to raise it by a quarter tone
-Sub + perfect interval means to lower a quarter tone.
+Sub + perfect interval means to lower a quarter tone
 Sharp is to raise by one half tone
 Flat is to raise by a half tone
-Neutral, arto and Tendo refer triads OR also to the tetrad versions
+Neutral, arto and tendo refer to triads or tetrads
-Neutral, Arto, or Tendo + interval name of 2nd, 3rd, 6th, or 7th is to alter respectively
+Neutral, arto, or tendo + interval name of 2nd, 3rd, 6th, or 7th is to alter respectively
 Examples:
 Neutral Super Eleventh or neut^11 = C neutral 7th chord with a super 11th thrown on top
-Arto Sub Seventh Tendo &lt;span style="line-height: 1.5;"&gt;Thirteenth or artsub7^13 = Arto tetrad with an arto seventh and a tendo thirteenth on top &lt;/span&gt;
+Arto Sub Seventh Tendo Thirteenth or artsub7^13 = Arto tetrad with an arto seventh and a tendo thirteenth on top Minor Seventh Flat Five Arto Ninth Super Eleventh or m7b5^9^11
-&lt;span style="line-height: 1.5;"&gt;Minor Seventh Flat Five Arto Ninth Super Eleventh or m7b5^9^11 &lt;/span&gt;
@@ Line 362: / Line 359: @@
 &lt;/span&gt;&lt;br /&gt;
 &lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/11052600?h=0&amp;amp;w=0&amp;quot; class=&amp;quot;WikiMedia WikiMediaCustom&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;custom&amp;amp;quot; key=&amp;amp;quot;11052600&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;script type="text/javascript" src="http://webplayer.yahooapis.com/player.js"&gt;
-&lt;/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 24 Edo"&gt;Naming Chords in 24 Edo&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: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;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;br /&gt;
 &lt;hr /&gt;
@@ Line 897: / Line 894: @@
 &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 in quartertones are:&lt;br /&gt;
+  The twelve new intervals (quartertones) in 24edo that are not found in 12edo are:&lt;br /&gt;
-&lt;br /&gt;
@@ Line 911: / Line 907: @@
          &lt;th&gt;cents&lt;br /&gt;
 &lt;/th&gt;
-         &lt;th&gt;common name&lt;br /&gt;
+         &lt;th&gt;common names&lt;br /&gt;
 &lt;/th&gt;
          &lt;th&gt;frequency ratio&lt;br /&gt;
@@ Line 1,122: / Line 1,118: @@
 &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:1423:&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:1423 --&gt; or ^ = quarter-tone sharp ,&lt;br /&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;!-- ws:start:WikiTextRemoteImageRule:1424:&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:1424 --&gt; or #^ = three-quarter-tone sharp&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;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1425:&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:1425 --&gt; or v = quarter-tone flat&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;!-- ws:start:WikiTextRemoteImageRule:1426:&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:1426 --&gt; or bv = three-quarter-tone flat&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;br /&gt;
-Alternately, in another notation system,&lt;br /&gt;
+Alternately, in another notation system:&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1427:&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:1427 --&gt; can be used as a quarter-tone sharp,&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;
-††† (the horizontal line should connect all three vertical lines) can be used as a three-quartertone sharp,&lt;br /&gt;
+††† (the horizontal line should connect all three vertical lines) = three quarter-tones sharp&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1428:&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:1428 --&gt; = quartertone flat,&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:1429:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1429 --&gt; can be used as a three-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:1430:&amp;lt;img src=&amp;quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1430 --&gt; (or E&lt;!-- ws:start:WikiTextRemoteImageRule:1431:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1431 --&gt;) F G&lt;!-- ws:start:WikiTextRemoteImageRule:1432:&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:1432 --&gt; (or A&lt;!-- ws:start:WikiTextRemoteImageRule:1433:&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:1433 --&gt;) Bb.&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;
-And in persian music:&lt;br /&gt;
 &lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86" rel="nofollow"&gt;Sori&lt;/a&gt;, &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;Koron&lt;/a&gt;&lt;br /&gt;
+And in Persian music:&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: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;
 &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;
@@ Line 1,147: / Line 1,144: @@
 The prefix &lt;strong&gt;super&lt;/strong&gt; indicates a perfect interval raised by a quarter tone&lt;br /&gt;
 &lt;br /&gt;
-The words Tendo meaning &amp;quot;Expand&amp;quot; and &amp;quot;Arto&amp;quot; meaning &amp;quot;contract&amp;quot; in Latin can be used to replace the words&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;
-&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;
-Edo features a rich variety on not only new chords, but also alterations that can be used with regular 12 Edo chords.&lt;br /&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;
-For example, an approximation of the ninth, eleventh, and thirteenth harmonic can be added to a major triad to create a sort of&lt;br /&gt;
-super-extended chord structure of a major chord: 4:5:6:9:11:13.&lt;br /&gt;
 &lt;br /&gt;
-As for entirely new chords, 24 edo features many possibilities for chords. The most obvious is the neutral triad 0-7-14 however there are other options such as&lt;br /&gt;
+As for entirely new chords, 24edo features many possibilities for chords. The most obvious is the neutral triad 0-7-14 however there are other options such as&lt;br /&gt;
--9-14 (Tendo Triad) and 0-5-14(Arto Triad), the chord names being based on what kind of third is in the chord.&lt;br /&gt;
+-9-14 (Tendo Triad) and 0-5-14 (Arto Triad), the chord names being based on what kind of third is in the chord.&lt;br /&gt;
 These chords though tend to lack the forcefulness to sound like resolved, tonal sonorities but can be resolved of that issue by using tetrads in place of triads.&lt;br /&gt;
-For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21 William Lynch considers this chord to be the most beautiful tetrad in 24 Edo. In addition, the arto tetrad can have the arto 7th added to it but the chord tends to work better when a minor 7th is used in place of an arto seventh forming the arto tetrad: 0-5-14-20. The Tendo tetrad can also be made by attatching an arto seventh to tendo triad 0-9-14-19. Although the &amp;quot;Super-Tendo&amp;quot; chord can be made by attatching the tendo seventh to the chord, this chord is very dissonant, and therefore it is not considered a resolved sonority, although the sound of 0-9-14-23 is very cool in many context.&lt;br /&gt;
+For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21. William Lynch considers this chord to be the most beautiful tetrad in 24edo. In addition, the arto tetrad can have the arto 7th added to it but the chord tends to work better when a minor 7th is used in place of an arto seventh forming the arto tetrad: 0-5-14-20. The Tendo tetrad can also be made by attaching an arto seventh to tendo triad 0-9-14-19. Although the &amp;quot;Super-Tendo&amp;quot; chord can be made by attaching the tendo seventh to the chord, this chord is very dissonant, and therefore it is not considered a resolved sonority, although the sound of 0-9-14-23 is very cool in many contexts.&lt;br /&gt;
 &lt;br /&gt;
-William Lynch considers these three tetrads to be a good selection for functional harmony in 24 Edo:&lt;br /&gt;
+William Lynch considers these three tetrads to be a good selection for functional harmony in 24edo:&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:1422:&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:1422 --&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;br /&gt;
-Neutral 0-7-14-21 or 1, v3, 5, v7&lt;!-- ws:start:WikiTextMediaRule:1:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/Neutral%20Tetrad%20on%20C.mp3?h=30&amp;amp;w=208&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;Neutral Tetrad on C.mp3&amp;amp;quot; width=&amp;amp;quot;208&amp;amp;quot; height=&amp;amp;quot;30&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;30&amp;quot; width=&amp;quot;208&amp;quot;/&amp;gt; --&gt;&lt;embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="208" height="30" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252FNeutral%252BTetrad%252Bon%252BC.mp3?file_extension=mp3&amp;autostart=false&amp;repeat=false&amp;showdigits=true&amp;showfsbutton=false&amp;width=208&amp;height=30"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:1 --&gt;&lt;br /&gt;
-Arto 0-5-14-20 or 1, bv3, 5, b7&lt;!-- ws:start:WikiTextMediaRule:2:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/arto%20tetrad%20on%20C.mp3?h=30&amp;amp;w=195&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;arto tetrad on C.mp3&amp;amp;quot; width=&amp;amp;quot;195&amp;amp;quot; height=&amp;amp;quot;30&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;30&amp;quot; width=&amp;quot;195&amp;quot;/&amp;gt; --&gt;&lt;embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="195" height="30" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Farto%252Btetrad%252Bon%252BC.mp3?file_extension=mp3&amp;autostart=false&amp;repeat=false&amp;showdigits=true&amp;showfsbutton=false&amp;width=195&amp;height=30"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:2 --&gt;&lt;br /&gt;
-Tendo 0-9-14-19 or 1, ^3, 5, bv7&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;th&gt;Chord name&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Degrees of 24edo&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Chord spelling&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Audio example&lt;br /&gt;
+&lt;/th&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;neutral&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0 7 14 21&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1 v3 5 v7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;!-- ws:start:WikiTextMediaRule:1:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/Neutral%20Tetrad%20on%20C.mp3?h=30&amp;amp;w=200&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;Neutral Tetrad on C.mp3&amp;amp;quot; width=&amp;amp;quot;200&amp;amp;quot; height=&amp;amp;quot;30&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;30&amp;quot; width=&amp;quot;200&amp;quot;/&amp;gt; --&gt;&lt;embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="200" height="30" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252FNeutral%252BTetrad%252Bon%252BC.mp3?file_extension=mp3&amp;autostart=false&amp;repeat=false&amp;showdigits=true&amp;showfsbutton=false&amp;width=200&amp;height=30"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:1 --&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;arto&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0 5 14 20&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1 bv3 5 b7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;!-- ws:start:WikiTextMediaRule:2:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/arto%20tetrad%20on%20C.mp3?h=30&amp;amp;w=200&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;arto tetrad on C.mp3&amp;amp;quot; width=&amp;amp;quot;200&amp;amp;quot; height=&amp;amp;quot;30&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;30&amp;quot; width=&amp;quot;200&amp;quot;/&amp;gt; --&gt;&lt;embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="200" height="30" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Farto%252Btetrad%252Bon%252BC.mp3?file_extension=mp3&amp;autostart=false&amp;repeat=false&amp;showdigits=true&amp;showfsbutton=false&amp;width=200&amp;height=30"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:2 --&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;tendo&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0 9 14 19&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1 ^3 5 bv7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;...&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
 &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 24 Edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:17 --&gt;Naming Chords in 24 Edo&lt;/h1&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;br /&gt;
-Naming chords in 24 edo can be achieved by adding a few things to the already existing set of terms that are used to name 12 Edo chords.&lt;br /&gt;
+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;
 They are:&lt;br /&gt;
-Super + perfect interval such as &amp;quot;perfect fifth&amp;quot; means to raise it by a quarter tone.&lt;br /&gt;
+Super + perfect interval such as &amp;quot;perfect fifth&amp;quot; means to raise it by a quarter tone&lt;br /&gt;
-Sub + perfect interval means to lower a quarter tone.&lt;br /&gt;
+Sub + perfect interval means to lower a quarter tone&lt;br /&gt;
 Sharp is to raise by one half tone&lt;br /&gt;
 Flat is to raise by a half tone&lt;br /&gt;
-Neutral, arto and Tendo refer triads OR also to the tetrad versions&lt;br /&gt;
+Neutral, arto and tendo refer to triads or tetrads&lt;br /&gt;
-Neutral, Arto, or Tendo + interval name of 2nd, 3rd, 6th, or 7th is to alter respectively&lt;br /&gt;
+Neutral, arto, or tendo + interval name of 2nd, 3rd, 6th, or 7th is to alter respectively&lt;br /&gt;
 &lt;br /&gt;
 Examples:&lt;br /&gt;
 Neutral Super Eleventh or neut^11 = C neutral 7th chord with a super 11th thrown on top&lt;br /&gt;
-Arto Sub Seventh Tendo &lt;span style="line-height: 1.5;"&gt;Thirteenth or artsub7^13 = Arto tetrad with an arto seventh and a tendo thirteenth on top &lt;/span&gt;&lt;br /&gt;
+Arto Sub Seventh Tendo Thirteenth or artsub7^13 = Arto tetrad with an arto seventh and a tendo thirteenth on top Minor Seventh Flat Five Arto Ninth Super Eleventh or m7b5^9^11&lt;br /&gt;
-&lt;span style="line-height: 1.5;"&gt;Minor Seventh Flat Five Arto Ninth Super Eleventh or m7b5^9^11 &lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,895: / Line 1,930: @@
 &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;
   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:1434:&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:1434 --&gt;24-tone &amp;quot;1/4-tone&amp;quot; Guitar by Ron Sword / Sword guitars&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;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;
@@ Line 1,914: / Line 1,949: @@
 &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;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1435:&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:1435 --&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: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;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;