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:

: This revision was by author [[User:~~hstraub~~|~~hstraub~~]] and made on <tt>2010-10-~~27 07~~:15:26 UTC</tt>.

: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2010-10-28 12:43:29 UTC</tt>.

: The original revision id was <tt>~~174008781~~</tt>.

: The original revision id was <tt>174473737</tt>.

: The revision comment was: <tt></tt>

: The revision comment was: <tt>table with nearby JI intervals</tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

<h4>Original Wikitext content:</h4>

Line 16:

The twelve new intervals in quartertones are:

50 ~~cents -~~ subminor second

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

150 ~~cents -~~ neutral second

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

250 ~~cents -~~ supermajor second, subminor third

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

350 ~~cents -~~ neutral third

[[35_34|35/34]]

450 ~~cents -~~ minor fourth, supermajor third

[[34_33|34/33]]

550 ~~cents -~~ major fourth

[[33_32|33/32]] ||= 48.770

650 ~~cents -~~ minor fifth

50.184

750 ~~cents -~~ major fifth, subminor sixth

51.682

850 ~~cents -~~ neutral sixth

53.273 ||= large septimal quarter-tone (Archytas)

950 ~~cents -~~ supermajor sixth, subminor seventh

large 17-limit quartertone

1050 ~~cents -~~ neutral seventh

small 17-limit quartertone

1150 ~~cents -~~ minor octave, supermajor seventh

33rd harmonic ||

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

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

[[15_13|15/13]]

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

247.741

250.304 ||= diminished third (6/5 x 24/25) ||

||= 350 ||= neutral third ||= [[11_9|11/9]]

[[27_22|27/22]]

[[16_13|16/13]] ||= 347.408

354.547

359.472 ||= undecimal neutral third

tridecimal neutral third ||

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

[[35_27|35/27]]

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

449.275

454.214 ||= 17-limit supermajor third

tridecimal subfourth ||

||= 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]]

[[54_35|54/35]]

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

750.725

753.637 ||= tridecimal superfifth

17-limit subminor sixth ||

||= 850 ||= neutral sixth ||= [[13_8|13/8]]

[[44_27|44/27]]

[[18_11|18/11]] ||= 840.528

845.453

852.592 ||= overtone sixth, 13th harmonic

undecimal neutral sixth ||

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

[[26_15|26/15]]

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

952.259

955.031 ||= ||

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

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

[[33_17|33/17]]

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

1148.318

1151.230 ||= 31st harmonic ||

==As a temperament==

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The twelve new intervals in quartertones are:

50 ~~cents~~ - subminor second

150 ~~cents~~ - neutral second

250 ~~cents~~ - supermajor second, subminor third

350 ~~cents~~ - neutral third

<tr>

450 ~~cents~~ - minor fourth, supermajor third

<th colspan="2">The twelve new intervals in 24edo

550 ~~cents~~ - major fourth

</th>

650 ~~cents~~ - minor fifth

<th colspan="3">some nearby JI intervals

750 ~~cents~~ - major fifth, subminor sixth

</th>

850 ~~cents~~ - neutral sixth

</tr>

950 ~~cents~~ - supermajor sixth, subminor seventh

<tr>

1050 ~~cents~~ - neutral seventh

<th>cents

1150 ~~cents~~ - minor octave, supermajor seventh

</th>

<th>common name

</th>

<th>frequency ratio

</th>

<th>cents

</th>

<th>common name

</th>

</tr>

<tr>

<td style="text-align: center;">50

</td>

<td style="text-align: center;">subminor second, quartertone

</td>

</td>

<td style="text-align: center;">48.770

50.184

51.682

53.273

</td>

<td style="text-align: center;">large septimal quarter-tone (Archytas)

large 17-limit quartertone

small 17-limit quartertone

33rd harmonic

</td>

</tr>

<tr>

<td style="text-align: center;">150

</td>

<td style="text-align: center;">neutral second

</td>

</td>

<td style="text-align: center;">150.637

</td>

<td style="text-align: center;">large undecimal neutral second

</td>

</tr>

<tr>

<td style="text-align: center;">250

</td>

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

</td>

</td>

<td style="text-align: center;">244.969

247.741

250.304

</td>

<td style="text-align: center;">diminished third (6/5 x 24/25)

</td>

</tr>

<tr>

<td style="text-align: center;">350

</td>

<td style="text-align: center;">neutral third

</td>

</td>

<td style="text-align: center;">347.408

354.547

359.472

</td>

<td style="text-align: center;">undecimal neutral third

tridecimal neutral third

</td>

</tr>

<tr>

<td style="text-align: center;">450

</td>

<td style="text-align: center;">minor fourth, supermajor third, subfourth

</td>

</td>

<td style="text-align: center;">446.363

449.275

454.214

</td>

<td style="text-align: center;">17-limit supermajor third

tridecimal subfourth

</td>

</tr>

<tr>

<td style="text-align: center;">550

</td>

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

</td>

</td>

<td style="text-align: center;">551.318

</td>

<td style="text-align: center;">undecimal superfourth, harmonic 11th

</td>

</tr>

<tr>

<td style="text-align: center;">650

</td>

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

</td>

</td>

<td style="text-align: center;">648.682

</td>

<td style="text-align: center;">undecimal subfifth, 11th subharmonic

</td>

</tr>

<tr>

<td style="text-align: center;">750

</td>

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

</td>

</td>

<td style="text-align: center;">745.786

750.725

753.637

</td>

<td style="text-align: center;">tridecimal superfifth

17-limit subminor sixth

</td>

</tr>

<tr>

<td style="text-align: center;">850

</td>

<td style="text-align: center;">neutral sixth

</td>

</td>

<td style="text-align: center;">840.528

845.453

852.592

</td>

<td style="text-align: center;">overtone sixth, 13th harmonic

undecimal neutral sixth

</td>

</tr>

<tr>

<td style="text-align: center;">950

</td>

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

</td>

</td>

<td style="text-align: center;">949.696

952.259

955.031

</td>

</td>

</tr>

<tr>

<td style="text-align: center;">1050

</td>

<td style="text-align: center;">neutral seventh

</td>

</td>

<td style="text-align: center;">1049.363

</td>

<td style="text-align: center;">undecimal neutral seventh

</td>

</tr>

<tr>

<td style="text-align: center;">1150

</td>

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

</td>

</td>

<td style="text-align: center;">1145.036

1148.318

1151.230

</td>

<td style="text-align: center;">31st harmonic

</td>

</tr>

</table>

<h2 id="toc2"><a name="Theory-As a temperament"></a>As a temperament</h2>

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<h1 id="toc3"><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

<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

<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

<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

<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

<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

<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

<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

Alternately, in another notation system,

<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,

<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,

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

<img src="http://www.dolmetsch.com/onequarterflat.gif" alt="external image onequarterflat.gif" title="external image onequarterflat.gif" /> = quartertone flat,

<img src="http://www.dolmetsch.com/onequarterflat.gif" alt="external image onequarterflat.gif" title="external image onequarterflat.gif" /> = quartertone flat,

<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.

<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.

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.

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.

And in persian music:

<table class="captionBox"><tr><td class="captionedImage"><a href="/24edo"><img src="http://240edo.googlepages.com/2.jpg/2-custom;size:430,120.jpg" alt="Sori,Koron" title="Sori,Koron" /></a></td></tr><tr><td class="imageCaption">Sori,Koron</td></tr></table>

<table class="captionBox"><tr><td class="captionedImage"><a href="/24edo"><img src="http://240edo.googlepages.com/2.jpg/2-custom;size:430,120.jpg" alt="Sori,Koron" title="Sori,Koron" /></a></td></tr><tr><td class="imageCaption">Sori,Koron</td></tr></table>

<h1 id="toc4"><a name="Scales / Modes"></a>Scales / Modes</h1>

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Line 1,071:

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.

<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

<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

<h1 id="toc7"><a name="Compositions"></a>Compositions</h1>

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Line 1,082:

<h1 id="toc8"><a name="Practical Theory / Books"></a>Practical Theory / Books</h1>

<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;" />&quot;Icosakaiteraphonic Scales for Guitar&quot; - 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.

<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;" />&quot;Icosakaiteraphonic Scales for Guitar&quot; - 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.

<h1 id="toc9"><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.96edo.com/24_EDO.html" rel="nofollow">About 24-EDO</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:hstraub|hstraub]] and made on <tt>2010-10-27 07:15:26 UTC</tt>.<br>
+: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2010-10-28 12:43:29 UTC</tt>.<br>
-: The original revision id was <tt>174008781</tt>.<br>
+: The original revision id was <tt>174473737</tt>.<br>
-: The revision comment was: <tt></tt><br>
+: The revision comment was: <tt>table with nearby JI intervals</tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
@@ Line 16: / Line 16: @@
 The twelve new intervals in quartertones are:
-cents - subminor second
+||||~ The twelve new intervals in 24edo ||||||~ some nearby JI intervals ||
-cents - neutral second
+||~ cents ||~ common name ||~ frequency ratio ||~ cents ||~ common name ||
-cents - supermajor second, subminor third
+||= 50 ||= subminor second, quartertone ||= [[36_35|36/35]]
-cents - neutral third
+[[35_34|35/34]]
-cents - minor fourth, supermajor third
+[[34_33|34/33]]
-cents - major fourth
+[[33_32|33/32]] ||= 48.770
-cents - minor fifth
+.184
-cents - major fifth, subminor sixth
+.682
-cents - neutral sixth
+.273 ||= large septimal quarter-tone (Archytas)
-cents - supermajor sixth, subminor seventh
+large 17-limit quartertone
-cents - neutral seventh
+small 17-limit quartertone
-cents - minor octave, supermajor seventh
+rd harmonic ||
+||= 150 ||= neutral second ||= [[12_11|12/11]] ||= 150.637 ||= large undecimal neutral second ||
+||= 250 ||= supermajor second, subminor third ||= [[144|125|144/125]]
+[[15_13|15/13]]
+[[52_45|52/45]] ||= 244.969
+.741
+.304 ||= diminished third (6/5 x 24/25) ||
+||= 350 ||= neutral third ||= [[11_9|11/9]]
+[[27_22|27/22]]
+[[16_13|16/13]] ||= 347.408
+.547
+.472 ||= undecimal neutral third
+tridecimal neutral third ||
+||= 450 ||= minor fourth, supermajor third, subfourth ||= [[22_17|22/17]]
+[[35_27|35/27]]
+[[13_10|13/10]] ||= 446.363
+.275
+.214 ||= 17-limit supermajor third
+tridecimal subfourth ||
+||= 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]]
+[[54_35|54/35]]
+[[17_11|17/11]] ||= 745.786
+.725
+.637 ||= tridecimal superfifth
+-limit subminor sixth ||
+||= 850 ||= neutral sixth ||= [[13_8|13/8]]
+[[44_27|44/27]]
+[[18_11|18/11]] ||= 840.528
+.453
+.592 ||= overtone sixth, 13th harmonic
+undecimal neutral sixth ||
+||= 950 ||= supermajor sixth, subminor seventh ||= [[45_26|45/26]]
+[[26_15|26/15]]
+[[125_72|125/72]] ||= 949.696
+.259
+.031 ||=   ||
+||= 1050 ||= neutral seventh ||= [[11_6|11/6]] ||= 1049.363 ||= undecimal neutral seventh ||
+||= 1150 ||= minor octave, supermajor seventh ||= [[31_16|31/16]]
+[[33_17|33/17]]
+[[35_18|35/18]] ||= 1145.036
+.318
+.230 ||= 31st harmonic ||
 ==As a temperament==
@@ Line 187: / Line 234: @@
 The twelve new intervals in quartertones are:&lt;br /&gt;
 &lt;br /&gt;
-cents - subminor second&lt;br /&gt;
-cents - neutral second&lt;br /&gt;
-cents - supermajor second, subminor third&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
-cents - neutral third&lt;br /&gt;
+    &lt;tr&gt;
-cents - minor fourth, supermajor third&lt;br /&gt;
+        &lt;th colspan="2"&gt;The twelve new intervals in 24edo&lt;br /&gt;
-cents - major fourth&lt;br /&gt;
+&lt;/th&gt;
-cents - minor fifth&lt;br /&gt;
+        &lt;th colspan="3"&gt;some nearby JI intervals&lt;br /&gt;
-cents - major fifth, subminor sixth&lt;br /&gt;
+&lt;/th&gt;
-cents - neutral sixth&lt;br /&gt;
+    &lt;/tr&gt;
-cents - supermajor sixth, subminor seventh&lt;br /&gt;
+    &lt;tr&gt;
-cents - neutral seventh&lt;br /&gt;
+        &lt;th&gt;cents&lt;br /&gt;
-cents - minor octave, supermajor seventh&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;common name&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;frequency ratio&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;cents&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;common name&lt;br /&gt;
+&lt;/th&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;50&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;subminor second, quartertone&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;
+&lt;a class="wiki_link" href="/35_34"&gt;35/34&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/34_33"&gt;34/33&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/33_32"&gt;33/32&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;48.770&lt;br /&gt;
+.184&lt;br /&gt;
+.682&lt;br /&gt;
+.273&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;large septimal quarter-tone (Archytas)&lt;br /&gt;
+large 17-limit quartertone&lt;br /&gt;
+small 17-limit quartertone&lt;br /&gt;
+rd harmonic&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;150&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;neutral second&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/12_11"&gt;12/11&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;150.637&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;large undecimal neutral second&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &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&gt;
+        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/144"&gt;125|144/125&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/15_13"&gt;15/13&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/52_45"&gt;52/45&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;244.969&lt;br /&gt;
+.741&lt;br /&gt;
+.304&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;diminished third (6/5 x 24/25)&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;350&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;neutral third&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/11_9"&gt;11/9&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/27_22"&gt;27/22&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/16_13"&gt;16/13&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;347.408&lt;br /&gt;
+.547&lt;br /&gt;
+.472&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;undecimal neutral third&lt;br /&gt;
+&lt;br /&gt;
+tridecimal neutral third&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;450&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;minor fourth, supermajor third, subfourth&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/22_17"&gt;22/17&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/35_27"&gt;35/27&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/13_10"&gt;13/10&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;446.363&lt;br /&gt;
+.275&lt;br /&gt;
+.214&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;17-limit supermajor third&lt;br /&gt;
+&lt;br /&gt;
+tridecimal subfourth&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;550&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;major fourth, superfourth&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;551.318&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;undecimal superfourth, harmonic 11th&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;650&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;minor fifth, subfifth&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/16_11"&gt;16/11&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;648.682&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;undecimal subfifth, 11th subharmonic&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &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&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;
+&lt;a class="wiki_link" href="/54_35"&gt;54/35&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/17_11"&gt;17/11&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;745.786&lt;br /&gt;
+.725&lt;br /&gt;
+.637&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;tridecimal superfifth&lt;br /&gt;
+&lt;br /&gt;
+-limit subminor sixth&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;850&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;neutral sixth&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/13_8"&gt;13/8&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/44_27"&gt;44/27&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/18_11"&gt;18/11&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;840.528&lt;br /&gt;
+.453&lt;br /&gt;
+.592&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;overtone sixth, 13th harmonic&lt;br /&gt;
+&lt;br /&gt;
+undecimal neutral sixth&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &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&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;
+&lt;a class="wiki_link" href="/26_15"&gt;26/15&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/125_72"&gt;125/72&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;949.696&lt;br /&gt;
+.259&lt;br /&gt;
+.031&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;1050&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;neutral seventh&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/11_6"&gt;11/6&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;1049.363&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;undecimal neutral seventh&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &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&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;
+&lt;a class="wiki_link" href="/33_17"&gt;33/17&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/35_18"&gt;35/18&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;1145.036&lt;br /&gt;
+.318&lt;br /&gt;
+.230&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;31st harmonic&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Theory-As a temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;As a temperament&lt;/h2&gt;
@@ Line 213: / Line 460: @@
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Notation&lt;/h1&gt;
   &lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:622:&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:622 --&gt; = quarter-tone sharp&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:786:&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:786 --&gt; = quarter-tone sharp&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:623:&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:623 --&gt; = three-quarter-tone sharp&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:787:&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:787 --&gt; = three-quarter-tone sharp&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:624:&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:624 --&gt; = quarter-tone flat&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:788:&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:788 --&gt; = quarter-tone flat&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:625:&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:625 --&gt; = three-quarter-tone flat&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:789:&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:789 --&gt; = three-quarter-tone flat&lt;br /&gt;
 &lt;br /&gt;
 Alternately, in another notation system,&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:626:&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:626 --&gt; can be used as a quarter-tone sharp,&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:790:&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:790 --&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:627:&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:627 --&gt; = quartertone flat,&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:791:&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:791 --&gt; = quartertone flat,&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:628:&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:628 --&gt; can be used as a three-quarter-tone flat.&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:792:&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:792 --&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:629:&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:629 --&gt; (or E&lt;!-- ws:start:WikiTextRemoteImageRule:630:&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:630 --&gt;) F G&lt;!-- ws:start:WikiTextRemoteImageRule:631:&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:631 --&gt; (or A&lt;!-- ws:start:WikiTextRemoteImageRule:632:&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:632 --&gt;) Bb.&lt;br /&gt;
+For example, the scale 0-5-10-15-20 is written as C-D&lt;!-- ws:start:WikiTextRemoteImageRule:793:&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:793 --&gt; (or E&lt;!-- ws:start:WikiTextRemoteImageRule:794:&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:794 --&gt;) F G&lt;!-- ws:start:WikiTextRemoteImageRule:795:&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:795 --&gt; (or A&lt;!-- ws:start:WikiTextRemoteImageRule:796:&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:796 --&gt;) Bb.&lt;br /&gt;
 And in persian music:&lt;br /&gt;
-&lt;span style="display: block; text-align: center;"&gt;&lt;!-- ws:start:WikiTextRemoteImageRule:634:&amp;lt;a href=&amp;quot;/24edo&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;http://240edo.googlepages.com/2.jpg/2-custom;size:430,120.jpg&amp;quot; alt=&amp;quot;Sori,Koron&amp;quot; title=&amp;quot;Sori,Koron&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;a href="/24edo"&gt;&lt;img src="http://240edo.googlepages.com/2.jpg/2-custom;size:430,120.jpg" alt="Sori,Koron" title="Sori,Koron" /&gt;&lt;/a&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;Sori,Koron&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:634 --&gt;&lt;br /&gt;
+&lt;span style="display: block; text-align: center;"&gt;&lt;!-- ws:start:WikiTextRemoteImageRule:798:&amp;lt;a href=&amp;quot;/24edo&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;http://240edo.googlepages.com/2.jpg/2-custom;size:430,120.jpg&amp;quot; alt=&amp;quot;Sori,Koron&amp;quot; title=&amp;quot;Sori,Koron&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;a href="/24edo"&gt;&lt;img src="http://240edo.googlepages.com/2.jpg/2-custom;size:430,120.jpg" alt="Sori,Koron" title="Sori,Koron" /&gt;&lt;/a&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;Sori,Koron&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:798 --&gt;&lt;br /&gt;
 &lt;/span&gt;&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Scales / Modes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Scales / Modes&lt;/h1&gt;
@@ Line 824: / Line 1,071: @@
   &lt;br /&gt;
 The ever-arising question in microtonal music, how to play it on instruments designed for 12edo, has a relatively simple answer in the case of 24edo: use two standard instruments tuned a quartertone apart. This &lt;a class="wiki_link" href="/Microtonal%20Keyboards#twelvenoteoctavescales"&gt;&amp;quot;12 note octave scales&amp;quot;&lt;/a&gt; approach is used in a wide part of the existing literature - see below.&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:635:&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:635 --&gt;24-tone &amp;quot;1/4-tone&amp;quot; Guitar by Ron Sword / Sword guitars&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:799:&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:799 --&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:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Compositions&lt;/h1&gt;
@@ Line 835: / Line 1,082: @@
 &lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Practical Theory / Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Practical Theory / Books&lt;/h1&gt;
   &lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:636:&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:636 --&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:800:&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:800 --&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:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&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;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;&lt;/body&gt;&lt;/html&gt;</pre></div>