24edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

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: This revision was by author [[User:cookiemeows|cookiemeows]] and made on <tt>2014-02-13 18:22:00 UTC</tt>.<br>

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

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

||= 50 ||= subminor second, quartertone ||= [[36_35|36/35]]

||= 50 ||= subminor second, quartertone

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

[[35_34|35/34]]

[[34_33|34/33]]

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33rd harmonic ||

||= 150 ||= neutral second ||= [[12_11|12/11]] ||= 150.637 ||= large undecimal neutral second ||

||= 250 ||= supermajor second, subminor third ||= [[144_125|144/125]]

||= 250 ||= supermajor second, tendo second,

subminor third, <span style="line-height: 1.5;">arto third</span> ||= [[144_125|144/125]]

[[15_13|15/13]]

[[52_45|52/45]] ||= 244.969

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

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

||= 750 ||= major fifth, subminor sixth, superfifth ||= [[20_13|20/13]]

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

superfifth, tendo seventh ||= [[20_13|20/13]]

[[54_35|54/35]]

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

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..

undecimal neutral sixth ||

||= 950 ||= supermajor sixth, subminor seventh ||= [[45_26|45/26]]

||= 950 ||= supermajor sixth, tendo sixth, subminor seventh, arto seventh ||= [[45_26|45/26]]

[[26_15|26/15]]

[[125_72|125/72]] ||= 949.696

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.. ||

||= 1050 ||= neutral seventh ||= [[11_6|11/6]] ||= 1049.363 ||= undecimal neutral seventh ||

||= 1150 ||= minor octave, supermajor seventh ||= [[31_16|31/16]]

||= 1150 ||= minor octave, supermajor seventh, tendo seventh ||= [[31_16|31/16]]

[[33_17|33/17]]

[[35_18|35/18]] ||= 1145.036

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[[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]]

=Interval Alterations=

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

Supermajor or "**Tendo**" is a major interval raised a quarter tone

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 **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

"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.

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

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 that is built off of a triad containing a quarter tone. 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.

=Rank two temperaments=

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=Compositions=

==Music==

<span class="ymp-btn-page-play ymp-media-eb56a917c62000140296c2e1a6d89911">~~////~~[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex3.mp3|Microhex3]]~~////~~</span> <span class="ymp-btn-page-play ymp-media-750620955011dabb8bc98c7c8830cbb8">~~////~~[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex4.mp3|Microhex4]]~~////~~</span> and <span class="ymp-btn-page-play ymp-media-4aeb7c299c23983ba8081a591562e704">~~////~~[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex5.mp3|Microhex5]]~~////~~</span> by [[http://www.96edo.com/About_me.html|Shaahin Mohajeri]]

<span class="ymp-btn-page-play ymp-media-eb56a917c62000140296c2e1a6d89911">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex3.mp3|Microhex3]]</span> <span class="ymp-btn-page-play ymp-media-750620955011dabb8bc98c7c8830cbb8">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex4.mp3|Microhex4]]</span> and <span class="ymp-btn-page-play ymp-media-4aeb7c299c23983ba8081a591562e704">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex5.mp3|Microhex5]]</span> by [[http://www.96edo.com/About_me.html|Shaahin Mohajeri]]

<span class="ymp-btn-page-play ymp-media-30832be5610668b4b42451c8ce82dc80">~~////~~[[http://micro.soonlabel.com/24et/quarterpicnic.mp3|Quarterpicnic]]~~////~~</span> by [[Chris Vaisvil]]

<span class="ymp-btn-page-play ymp-media-30832be5610668b4b42451c8ce82dc80">[[http://micro.soonlabel.com/24et/quarterpicnic.mp3|Quarterpicnic]]</span> by [[Chris Vaisvil]]

~~////~~[[http://micro.soonlabel.com/gene_ward_smith/Others/BeDell/Quarter%20Tone%20Prelude%20for%20two%20Harps.mp3|Quarter Tone Prelude For Two Harps]]~~////~~ by [[http://soundcloud.com/cerbeus-1/quarter-tone-prelude-for-two|Nathan BeDell]]

[[http://micro.soonlabel.com/gene_ward_smith/Others/BeDell/Quarter%20Tone%20Prelude%20for%20two%20Harps.mp3|Quarter Tone Prelude For Two Harps]] by [[http://soundcloud.com/cerbeus-1/quarter-tone-prelude-for-two|Nathan BeDell]]

<span class="ymp-btn-page-play ymp-media-2738730931ba168a7364a84b5417488d">~~////~~[[http://micro.soonlabel.com/24et/daily20111021-fretless-1.mp3|Fretless Chrome 1]]~~////~~</span> and <span class="ymp-btn-page-play ymp-media-d35cb71128e927701930058ebd16b778">~~////~~[[http://micro.soonlabel.com/24et/daily20111021-fretless-2.mp3|Fretless Chrome 2]]~~////~~</span> by [[@http://chrisvaisvil.com/?p=1477|Chris Vaisvil]]

<span class="ymp-btn-page-play ymp-media-2738730931ba168a7364a84b5417488d">[[http://micro.soonlabel.com/24et/daily20111021-fretless-1.mp3|Fretless Chrome 1]]</span> and <span class="ymp-btn-page-play ymp-media-d35cb71128e927701930058ebd16b778">[[http://micro.soonlabel.com/24et/daily20111021-fretless-2.mp3|Fretless Chrome 2]]</span> by [[@http://chrisvaisvil.com/?p=1477|Chris Vaisvil]]

~~////~~[[http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/Lament.mp3|Lament]]~~////~~ by [[http://soundcloud.com/jdfreivald/lament|Jake Freivald]]. In the [[freivaldneutral24]] scale.

[[http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/Lament.mp3|Lament]] by [[http://soundcloud.com/jdfreivald/lament|Jake Freivald]]. In the [[freivaldneutral24]] scale.

~~////~~[[https://soundcloud.com/jdfreivald/mo-happy-happy|Mo - Happy - Happy]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3|play]]~~////~~ by Jake Freivald in Neutraltet[7] (2.3.11 mohajira), 24et tuning

[[https://soundcloud.com/jdfreivald/mo-happy-happy|Mo - Happy - Happy]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3|play]] by Jake Freivald in Neutraltet[7] (2.3.11 mohajira), 24et tuning

==About==

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<h4>Original HTML content:</h4>

</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="#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="#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;">subminor second, quartertone<br />

arto second<br />

</td>

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</td>

<td style="text-align: center;">supermajor second, subminor third<br />

<td style="text-align: center;">supermajor second, tendo second, <br />

subminor third, <span style="line-height: 1.5;">arto third</span><br />

</td>

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</td>

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

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

superfifth, tendo seventh<br />

</td>

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</td>

<td style="text-align: center;">supermajor sixth, subminor seventh<br />

<td style="text-align: center;">supermajor sixth, tendo sixth, subminor seventh, arto seventh<br />

</td>

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</td>

<td style="text-align: center;">minor octave, supermajor seventh<br />

<td style="text-align: center;">minor octave, supermajor seventh, tendo seventh<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" /> = 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" /> = 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" /> = 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" /> = 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" /> = 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" /> = 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" /> = 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" /> = three-quarter-tone flat<br />

<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" /> can be used as a quarter-tone sharp,<br />

††† (the horizontal line should connect all three vertical lines) can be used as a three-quartertone 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" /> = quartertone 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" /> can be used as a three-quarter-tone 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 />

<br />

<h1 id="toc5"><a name="Rank two temperaments"></a>Rank two temperaments</h1>

<h1 id="toc5"><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 />

<br />

Supermajor or &quot;<strong>Tendo</strong>&quot; is a major interval raised a quarter tone <br />

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>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 />

&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 />

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 />

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 that is built off of a triad containing a quarter tone. 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 />

<br />

<h1 id="toc7"><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="~~toc6~~"><a name="Scales / Modes"></a>Scales / Modes</h1>

<h1 id="toc8"><a name="Scales / Modes"></a>Scales / Modes</h1>

<br />

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<tr>

<td colspan="2"><h4 id="~~toc7~~"><a name="Scales / Modes---24 tone modes:"></a>24 tone modes:</h4>

<td colspan="2"><h4 id="toc9"><a name="Scales / Modes---24 tone modes:"></a>24 tone modes:</h4>

</td>

</tr>

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<br />

<h1 id="~~toc8~~"><a name="Instruments"></a>Instruments<a name="instruments"></a></h1>

<h1 id="toc10"><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="~~toc9~~"><a name="Compositions"></a>Compositions</h1>

<h1 id="toc11"><a name="Compositions"></a>Compositions</h1>

<h2 id="~~toc10~~"><a name="Compositions-Music"></a>Music</h2>

<h2 id="toc12"><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 />

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<a class="wiki_link_ext" href="https://soundcloud.com/jdfreivald/mo-happy-happy" rel="nofollow">Mo - Happy - Happy</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3" rel="nofollow">play</a> by Jake Freivald in Neutraltet[7] (2.3.11 mohajira), 24et tuning<br />

<br />

<h2 id="~~toc11~~"><a name="Compositions-About"></a>About</h2>

<h2 id="toc13"><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="~~toc12~~"><a name="Practical Theory / Books"></a>Practical Theory / Books</h1>

<h1 id="toc14"><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="~~toc13~~"><a name="External links"></a>External links</h1>

<h1 id="toc15"><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:genewardsmith|genewardsmith]] and made on <tt>2013-10-10 19:37:57 UTC</tt>.<br>
+: This revision was by author [[User:cookiemeows|cookiemeows]] and made on <tt>2014-02-13 18:22:00 UTC</tt>.<br>
-: The original revision id was <tt>458723990</tt>.<br>
+: The original revision id was <tt>489397400</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 79: / Line 79: @@
 ||||~ The twelve new intervals in 24edo ||||||~ some nearby JI intervals ||
 ||~ cents ||~ common name ||~ frequency ratio ||~ cents ||~ common name ||
-||= 50 ||= subminor second, quartertone ||= [[36_35|36/35]]
+||= 50 ||= subminor second, quartertone
+arto second ||= [[36_35|36/35]]
 [[35_34|35/34]]
 [[34_33|34/33]]
@@ Line 90: / Line 91: @@
 rd harmonic ||
 ||= 150 ||= neutral second ||= [[12_11|12/11]] ||= 150.637 ||= large undecimal neutral second ||
-||= 250 ||= supermajor second, subminor third ||= [[144_125|144/125]]
+||= 250 ||= supermajor second, tendo second,
+subminor third, &lt;span style="line-height: 1.5;"&gt;arto third&lt;/span&gt; ||= [[144_125|144/125]]
 [[15_13|15/13]]
 [[52_45|52/45]] ||= 244.969
@@ Line 113: / Line 115: @@
 ||= 550 ||= major fourth, superfourth ||= [[11_8|11/8]] ||= 551.318 ||= undecimal superfourth, harmonic 11th ||
 ||= 650 ||= minor fifth, subfifth ||= [[16_11|16/11]] ||= 648.682 ||= undecimal subfifth, 11th subharmonic ||
-||= 750 ||= major fifth, subminor sixth, superfifth ||= [[20_13|20/13]]
+||= 750 ||= major fifth, subminor sixth, arto sixth
+superfifth, tendo seventh ||= [[20_13|20/13]]
 [[54_35|54/35]]
 [[17_11|17/11]] ||= 745.786
@@ Line 127: / Line 130: @@
 ..
 undecimal neutral sixth ||
-||= 950 ||= supermajor sixth, subminor seventh ||= [[45_26|45/26]]
+||= 950 ||= supermajor sixth, tendo sixth, subminor seventh, arto seventh ||= [[45_26|45/26]]
 [[26_15|26/15]]
 [[125_72|125/72]] ||= 949.696
@@ Line 135: / Line 138: @@
 .. ||
 ||= 1050 ||= neutral seventh ||= [[11_6|11/6]] ||= 1049.363 ||= undecimal neutral seventh ||
-||= 1150 ||= minor octave, supermajor seventh ||= [[31_16|31/16]]
+||= 1150 ||= minor octave, supermajor seventh, tendo seventh ||= [[31_16|31/16]]
 [[33_17|33/17]]
 [[35_18|35/18]] ||= 1145.036
@@ Line 158: / Line 161: @@
 [[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]]
+=Interval Alterations=
+The special alterations of the intervals and chords of 12 equal can be notated like this:
+Supermajor or "**Tendo**" is a major interval raised a quarter tone
+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 **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
+"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.
+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
+-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 that is built off of a triad containing a quarter tone. 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.
 =Rank two temperaments=
@@ Line 283: / Line 309: @@
 =Compositions=
 ==Music==
-&lt;span class="ymp-btn-page-play ymp-media-eb56a917c62000140296c2e1a6d89911"&gt;////[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex3.mp3|Microhex3]]////&lt;/span&gt; &lt;span class="ymp-btn-page-play ymp-media-750620955011dabb8bc98c7c8830cbb8"&gt;////[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex4.mp3|Microhex4]]////&lt;/span&gt; and &lt;span class="ymp-btn-page-play ymp-media-4aeb7c299c23983ba8081a591562e704"&gt;////[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex5.mp3|Microhex5]]////&lt;/span&gt; by [[http://www.96edo.com/About_me.html|Shaahin Mohajeri]]
+&lt;span class="ymp-btn-page-play ymp-media-eb56a917c62000140296c2e1a6d89911"&gt;[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex3.mp3|Microhex3]]&lt;/span&gt; &lt;span class="ymp-btn-page-play ymp-media-750620955011dabb8bc98c7c8830cbb8"&gt;[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex4.mp3|Microhex4]]&lt;/span&gt; and &lt;span class="ymp-btn-page-play ymp-media-4aeb7c299c23983ba8081a591562e704"&gt;[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex5.mp3|Microhex5]]&lt;/span&gt; by [[http://www.96edo.com/About_me.html|Shaahin Mohajeri]]
-&lt;span class="ymp-btn-page-play ymp-media-30832be5610668b4b42451c8ce82dc80"&gt;////[[http://micro.soonlabel.com/24et/quarterpicnic.mp3|Quarterpicnic]]////&lt;/span&gt; by [[Chris Vaisvil]]
+&lt;span class="ymp-btn-page-play ymp-media-30832be5610668b4b42451c8ce82dc80"&gt;[[http://micro.soonlabel.com/24et/quarterpicnic.mp3|Quarterpicnic]]&lt;/span&gt; by [[Chris Vaisvil]]
-////[[http://micro.soonlabel.com/gene_ward_smith/Others/BeDell/Quarter%20Tone%20Prelude%20for%20two%20Harps.mp3|Quarter Tone Prelude For Two Harps]]//// by [[http://soundcloud.com/cerbeus-1/quarter-tone-prelude-for-two|Nathan BeDell]]
+[[http://micro.soonlabel.com/gene_ward_smith/Others/BeDell/Quarter%20Tone%20Prelude%20for%20two%20Harps.mp3|Quarter Tone Prelude For Two Harps]] by [[http://soundcloud.com/cerbeus-1/quarter-tone-prelude-for-two|Nathan BeDell]]
-&lt;span class="ymp-btn-page-play ymp-media-2738730931ba168a7364a84b5417488d"&gt;////[[http://micro.soonlabel.com/24et/daily20111021-fretless-1.mp3|Fretless Chrome 1]]////&lt;/span&gt; and &lt;span class="ymp-btn-page-play ymp-media-d35cb71128e927701930058ebd16b778"&gt;////[[http://micro.soonlabel.com/24et/daily20111021-fretless-2.mp3|Fretless Chrome 2]]////&lt;/span&gt; by [[@http://chrisvaisvil.com/?p=1477|Chris Vaisvil]]
+&lt;span class="ymp-btn-page-play ymp-media-2738730931ba168a7364a84b5417488d"&gt;[[http://micro.soonlabel.com/24et/daily20111021-fretless-1.mp3|Fretless Chrome 1]]&lt;/span&gt; and &lt;span class="ymp-btn-page-play ymp-media-d35cb71128e927701930058ebd16b778"&gt;[[http://micro.soonlabel.com/24et/daily20111021-fretless-2.mp3|Fretless Chrome 2]]&lt;/span&gt; by [[@http://chrisvaisvil.com/?p=1477|Chris Vaisvil]]
-////[[http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/Lament.mp3|Lament]]//// by [[http://soundcloud.com/jdfreivald/lament|Jake Freivald]]. In the [[freivaldneutral24]] scale.
+[[http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/Lament.mp3|Lament]] by [[http://soundcloud.com/jdfreivald/lament|Jake Freivald]]. In the [[freivaldneutral24]] scale.
-////[[https://soundcloud.com/jdfreivald/mo-happy-happy|Mo - Happy - Happy]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3|play]]//// by Jake Freivald in Neutraltet[7] (2.3.11 mohajira), 24et tuning
+[[https://soundcloud.com/jdfreivald/mo-happy-happy|Mo - Happy - Happy]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3|play]] by Jake Freivald in Neutraltet[7] (2.3.11 mohajira), 24et tuning
 ==About==
@@ Line 305: / Line 331: @@
 <h4>Original HTML content:</h4>
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;24edo&lt;/title&gt;&lt;/head&gt;&lt;body&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:29:&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:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt;&lt;a href="#Basics"&gt;Basics&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt; | &lt;a href="#x24edo as a temperament"&gt;24edo as a temperament&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt; | &lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt; | &lt;a href="#Notation"&gt;Notation&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt; | &lt;a href="#Rank two temperaments"&gt;Rank two temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt; | &lt;a href="#Scales / Modes"&gt;Scales / Modes&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt;&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&gt; | &lt;a href="#Instruments"&gt;Instruments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt; | &lt;a href="#Compositions"&gt;Compositions&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;!-- ws:end:WikiTextTocRule:41 --&gt;&lt;!-- ws:start:WikiTextTocRule:42: --&gt; | &lt;a href="#Practical Theory / Books"&gt;Practical Theory / Books&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&gt; | &lt;a href="#External links"&gt;External links&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:43 --&gt;&lt;!-- ws:start:WikiTextTocRule:44: --&gt;
+&lt;/script&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt;&lt;!-- ws:start:WikiTextTocRule:33:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt;&lt;a href="#Basics"&gt;Basics&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt; | &lt;a href="#x24edo as a temperament"&gt;24edo as a temperament&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt; | &lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&gt; | &lt;a href="#Notation"&gt;Notation&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt; | &lt;a href="#Interval Alterations"&gt;Interval Alterations&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&gt; | &lt;a href="#Chord Structures"&gt;Chord Structures&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:40 --&gt;&lt;!-- ws:start:WikiTextTocRule:41: --&gt; | &lt;a href="#Rank two temperaments"&gt;Rank two temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:41 --&gt;&lt;!-- ws:start:WikiTextTocRule:42: --&gt; | &lt;a href="#Scales / Modes"&gt;Scales / Modes&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&gt;&lt;!-- ws:end:WikiTextTocRule:43 --&gt;&lt;!-- ws:start:WikiTextTocRule:44: --&gt; | &lt;a href="#Instruments"&gt;Instruments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:44 --&gt;&lt;!-- ws:start:WikiTextTocRule:45: --&gt; | &lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:45 --&gt;&lt;!-- ws:start:WikiTextTocRule:46: --&gt;&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt;&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt; | &lt;a href="#Practical Theory / Books"&gt;Practical Theory / Books&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt; | &lt;a href="#External links"&gt;External links&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:44 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;br /&gt;
 &lt;hr /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Basics"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt;Basics&lt;/h1&gt;
@@ Line 867: / Line 893: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;subminor second, quartertone&lt;br /&gt;
+arto second&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/36_35"&gt;36/35&lt;/a&gt;&lt;br /&gt;
@@ Line 899: / Line 926: @@
          &lt;td style="text-align: center;"&gt;250&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;supermajor second, subminor third&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;supermajor second, tendo second, &lt;br /&gt;
+subminor third, &lt;span style="line-height: 1.5;"&gt;arto third&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/144_125"&gt;144/125&lt;/a&gt;&lt;br /&gt;
@@ Line 977: / Line 1,005: @@
          &lt;td style="text-align: center;"&gt;750&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;major fifth, subminor sixth, superfifth&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;major fifth, subminor sixth, arto sixth&lt;br /&gt;
+superfifth, tendo seventh&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 1,013: / Line 1,042: @@
          &lt;td style="text-align: center;"&gt;950&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;supermajor sixth, subminor seventh&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;supermajor sixth, tendo sixth, subminor seventh, arto seventh&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/45_26"&gt;45/26&lt;/a&gt;&lt;br /&gt;
@@ Line 1,043: / Line 1,072: @@
          &lt;td style="text-align: center;"&gt;1150&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;minor octave, supermajor seventh&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;minor octave, supermajor seventh, tendo seventh&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/31_16"&gt;31/16&lt;/a&gt;&lt;br /&gt;
@@ Line 1,062: / Line 1,091: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;Notation&lt;/h1&gt;
-  &lt;!-- ws:start:WikiTextRemoteImageRule:1411:&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:1411 --&gt; = quarter-tone sharp&lt;br /&gt;
+  &lt;!-- ws:start:WikiTextRemoteImageRule:1417:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/s14_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/s14_blue.gif" alt="external image s14_blue.gif" title="external image s14_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1417 --&gt; = quarter-tone sharp&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1412:&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:1412 --&gt; = three-quarter-tone sharp&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1418:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/s34_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/s34_blue.gif" alt="external image s34_blue.gif" title="external image s34_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1418 --&gt; = three-quarter-tone sharp&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1413:&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:1413 --&gt; = quarter-tone flat&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1419:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/f14_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/f14_blue.gif" alt="external image f14_blue.gif" title="external image f14_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1419 --&gt; = quarter-tone flat&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1414:&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:1414 --&gt; = three-quarter-tone flat&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1420:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/f34_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/f34_blue.gif" alt="external image f34_blue.gif" title="external image f34_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1420 --&gt; = three-quarter-tone flat&lt;br /&gt;
 &lt;br /&gt;
 Alternately, in another notation system,&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1415:&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:1415 --&gt; can be used as a quarter-tone sharp,&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1421:&amp;lt;img src=&amp;quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1421 --&gt; can be used as a quarter-tone sharp,&lt;br /&gt;
 ††† (the horizontal line should connect all three vertical lines) can be used as a three-quartertone sharp,&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1416:&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:1416 --&gt; = quartertone flat,&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1422:&amp;lt;img src=&amp;quot;http://www.dolmetsch.com/onequarterflat.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.dolmetsch.com/onequarterflat.gif" alt="external image onequarterflat.gif" title="external image onequarterflat.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1422 --&gt; = quartertone flat,&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1417:&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:1417 --&gt; can be used as a three-quarter-tone flat.&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1423:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1423 --&gt; can be used as a three-quarter-tone flat.&lt;br /&gt;
-For example, the scale 0-5-10-15-20 is written as C-D&lt;!-- ws:start:WikiTextRemoteImageRule:1418:&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:1418 --&gt; (or E&lt;!-- ws:start:WikiTextRemoteImageRule:1419:&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:1419 --&gt;) F G&lt;!-- ws:start:WikiTextRemoteImageRule:1420:&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:1420 --&gt; (or A&lt;!-- ws:start:WikiTextRemoteImageRule:1421:&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:1421 --&gt;) Bb.&lt;br /&gt;
+For example, the scale 0-5-10-15-20 is written as C-D&lt;!-- ws:start:WikiTextRemoteImageRule:1424:&amp;lt;img src=&amp;quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1424 --&gt; (or E&lt;!-- ws:start:WikiTextRemoteImageRule:1425:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1425 --&gt;) F G&lt;!-- ws:start:WikiTextRemoteImageRule:1426:&amp;lt;img src=&amp;quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1426 --&gt; (or A&lt;!-- ws:start:WikiTextRemoteImageRule:1427:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1427 --&gt;) Bb.&lt;br /&gt;
 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;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Rank two temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;Rank two temperaments&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Interval Alterations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&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;
+&lt;br /&gt;
+Supermajor or &amp;quot;&lt;strong&gt;Tendo&lt;/strong&gt;&amp;quot; is a major interval raised a quarter tone &lt;br /&gt;
+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;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;
+&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:13:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Chord Structures"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:13 --&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;
+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;
+-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 that is built off of a triad containing a quarter tone. In addition, the arto tetrad can have the arto 7th added to it but the chord tends to work better when a minor 7th is used in place of an arto seventh forming the arto tetrad: 0-5-14-20. The Tendo tetrad can also be made by attatching an arto seventh to tendo triad 0-9-14-19. Although the &amp;quot;Super-Tendo&amp;quot; chord can be made by attatching the tendo seventh to the chord, this chord is very dissonant, and therefore it is not considered a resolved sonority, although the sound of 0-9-14-23 is very cool in many context. &lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:15:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Rank two temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:15 --&gt;Rank two temperaments&lt;/h1&gt;
   &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 1,190: / Line 1,242: @@
 &lt;/table&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:13:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Scales / Modes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:13 --&gt;Scales / Modes&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:17:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Scales / Modes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:17 --&gt;Scales / Modes&lt;/h1&gt;
   &lt;br /&gt;
@@ Line 1,196: / Line 1,248: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;td colspan="2"&gt;&lt;!-- ws:start:WikiTextHeadingRule:15:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc7"&gt;&lt;a name="Scales / Modes---24 tone modes:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:15 --&gt;24 tone modes:&lt;/h4&gt;
+         &lt;td colspan="2"&gt;&lt;!-- ws:start:WikiTextHeadingRule:19:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc9"&gt;&lt;a name="Scales / Modes---24 tone modes:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:19 --&gt;24 tone modes:&lt;/h4&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 1,784: / Line 1,836: @@
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:17:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Instruments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:17 --&gt;Instruments&lt;!-- ws:start:WikiTextAnchorRule:45:&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:45 --&gt;&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:21:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Instruments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:21 --&gt;Instruments&lt;!-- ws:start:WikiTextAnchorRule:51:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@instruments&amp;quot; title=&amp;quot;Anchor: instruments&amp;quot;/&amp;gt; --&gt;&lt;a name="instruments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:51 --&gt;&lt;/h1&gt;
   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:1422:&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:1422 --&gt;24-tone &amp;quot;1/4-tone&amp;quot; Guitar by Ron Sword / Sword guitars&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1428:&amp;lt;img src=&amp;quot;http://www.swordguitars.com/Sword_quartertone_stratsm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 195px; width: 406px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.swordguitars.com/Sword_quartertone_stratsm.jpg" alt="external image Sword_quartertone_stratsm.jpg" title="external image Sword_quartertone_stratsm.jpg" style="height: 195px; width: 406px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1428 --&gt;24-tone &amp;quot;1/4-tone&amp;quot; Guitar by Ron Sword / Sword guitars&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:19:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:19 --&gt;Compositions&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:23:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:23 --&gt;Compositions&lt;/h1&gt;
-  &lt;!-- ws:start:WikiTextHeadingRule:21:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Compositions-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:21 --&gt;Music&lt;/h2&gt;
+  &lt;!-- ws:start:WikiTextHeadingRule:25:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Compositions-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:25 --&gt;Music&lt;/h2&gt;
   &lt;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 1,797: / Line 1,849: @@
 &lt;a class="wiki_link_ext" href="https://soundcloud.com/jdfreivald/mo-happy-happy" rel="nofollow"&gt;Mo - Happy - Happy&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3" rel="nofollow"&gt;play&lt;/a&gt; by Jake Freivald in Neutraltet[7] (2.3.11 mohajira), 24et tuning&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:23:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Compositions-About"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:23 --&gt;About&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:27:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Compositions-About"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:27 --&gt;About&lt;/h2&gt;
   &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:25:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Practical Theory / Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:25 --&gt;Practical Theory / Books&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:29:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Practical Theory / Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:29 --&gt;Practical Theory / Books&lt;/h1&gt;
   &lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1423:&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:1423 --&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:1429:&amp;lt;img src=&amp;quot;http://ronsword.com/images/24_tet_Coversm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 236px; width: 179px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://ronsword.com/images/24_tet_Coversm.jpg" alt="external image 24_tet_Coversm.jpg" title="external image 24_tet_Coversm.jpg" style="height: 236px; width: 179px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1429 --&gt;&lt;strong&gt;&amp;quot;Icosakaiteraphonic Scales for Guitar&amp;quot;&lt;/strong&gt; - A Book for Twenty-Four Equal Divisions of the Octave on guitar, or 'Quarter-tones'. Features a practical approach to understanding the tuning, and over 550 Scale Examples on Nine-String finger board charts, which allows for both symmetrical tuning visualization and standard guitar tuning- helpful for bassists and large range guitarists as well. Includes MOS, DE, and *all* the Scales / Modes from the list above.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:27:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc13"&gt;&lt;a name="External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:27 --&gt;External links&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:31:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:31 --&gt;External links&lt;/h1&gt;
   &lt;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>