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:

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: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-03-27 11:33:33 UTC</tt>.

: The original revision id was <tt>~~531567464~~</tt>.

: The original revision id was <tt>545565376</tt>.

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The tunings supplied by 72 cannot be used for all low-limit just intervals, but they can be used on the 17-limit [[k*N subgroups|3*24 subgroup]] 2.3.125.35.11.325.17 [[just intonation subgroup]], making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11 and 17. Another approach would be to treat 24-EDO as a 2.3.11.17.19 subgroup temperament, on which it is quite accurate.

|| [[#|Degree]] || Cents ||= Approximate Ratios* ||

|| [[#|Degree]] || Cents

DMS ||= Approximate Ratios* ||

|| 0 || 0 ||= 1/1 ||

|| 1 || 50 ||= 33/32, 34/33 ||

|| 1 || 50

|| 2 || 100 ||= 17/16, 18/17 ||

15° ||= 33/32, 34/33 ||

|| 3 || 150 ||= 12/11 ||

|| 2 || 100

|| 4 || 200 ||= 9/8 ||

30° ||= 17/16, 18/17 ||

|| 5 || 250 ||= 22/19 ||

|| 3 || 150

|| 6 || 300 ||= 19/16 ||

45° ||= 12/11 ||

|| 7 || 350 ||= 11/9 ||

|| 4 || 200

|| 8 || 400 ||= 24/19 ||

60° ||= 9/8 ||

|| 9 || 450 ||= 22/17 ||

|| 5 || 250

|| 10 || 500 ||= 4/3 ||

75° ||= 22/19 ||

|| 11 || 550 ||= 11/8 ||

|| 6 || 300

|| 12 || 600 ||= 17/12 ||

90° ||= 19/16 ||

|| 13 || 650 ||= 16/11 ||

|| 7 || 350

|| 14 || 700 ||= 3/2 ||

105° ||= 11/9 ||

|| 15 || 750 ||= 17/11 ||

|| 8 || 400

|| 16 || 800 ||= 19/12 ||

120° ||= 24/19 ||

|| 17 || 850 ||= 18/11 ||

|| 9 || 450

|| 18 || 900 ||= 32/19 ||

135° ||= 22/17 ||

|| 19 || 950 ||= 19/11 ||

|| 10 || 500

|| 20 || 1000 ||= 16/9 ||

150° ||= 4/3 ||

|| 21 || 1050 ||= 11/6 ||

|| 11 || 550

|| 22 || 1100 ||= 17/9, 32/17 ||

165° ||= 11/8 ||

|| 23 || 1150 ||= 33/17, 64/33 ||

|| 12 || 600

~~|| || ||=~~ ||

180° ||= 17/12 ||

|| 13 || 650

195° ||= 16/11 ||

|| 14 || 700

210° ||= 3/2 ||

|| 15 || 750

225° ||= 17/11 ||

|| 16 || 800

240* ||= 19/12 ||

|| 17 || 850

255° ||= 18/11 ||

|| 18 || 900

270° ||= 32/19 ||

|| 19 || 950

285° ||= 19/11 ||

|| 20 || 1000

300° ||= 16/9 ||

|| 21 || 1050

315° ||= 11/6 ||

|| 22 || 1100

330° ||= 17/9, 32/17 ||

|| 23 || 1150

345° ||= 33/17, 64/33 ||

*based on treating 24-EDO as a 2.3.11.17.19 subgroup; other approaches are possible.

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|| 24 || 1200 ||= 2/1 ||

24 EDO breaks intervals into two sets of five cartegories. Infra - Minor - Neutral - Major - Ultra for seconds, thirds, sixths, and sevenths; and diminished - narrow - perfect - wide - augmented for

fourths, fifths, unison, and octave. For other strange enharmonics, wide and narrow can be used in conjunction with augmented and diminished intervals such as 550 cents being called a narrow diminished fifth and 850 cents being called a wide augmented fifth.

These are the intervals of 24 EDO that do not exist in 12 EDO: 2

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</td>

<td>Cents

DMS

</td>

<td style="text-align: center;">Approximate Ratios*

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</td>

<td>50

15°

</td>

<td style="text-align: center;">33/32, 34/33

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</td>

<td>100

30°

</td>

<td style="text-align: center;">17/16, 18/17

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</td>

<td>150

45°

</td>

<td style="text-align: center;">12/11

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</td>

<td>200

60°

</td>

<td style="text-align: center;">9/8

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</td>

<td>250

75°

</td>

<td style="text-align: center;">22/19

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</td>

<td>300

90°

</td>

<td style="text-align: center;">19/16

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</td>

<td>350

105°

</td>

<td style="text-align: center;">11/9

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</td>

<td>400

120°

</td>

<td style="text-align: center;">24/19

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</td>

<td>450

135°

</td>

<td style="text-align: center;">22/17

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</td>

<td>500

150°

</td>

<td style="text-align: center;">4/3

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</td>

<td>550

165°

</td>

<td style="text-align: center;">11/8

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</td>

<td>600

180°

</td>

<td style="text-align: center;">17/12

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</td>

<td>650

195°

</td>

<td style="text-align: center;">16/11

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</td>

<td>700

210°

</td>

<td style="text-align: center;">3/2

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</td>

<td>750

225°

</td>

<td style="text-align: center;">17/11

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</td>

<td>800

240*

</td>

<td style="text-align: center;">19/12

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</td>

<td>850

255°

</td>

<td style="text-align: center;">18/11

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</td>

<td>900

270°

</td>

<td style="text-align: center;">32/19

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</td>

<td>950

285°

</td>

<td style="text-align: center;">19/11

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</td>

<td>1000

300°

</td>

<td style="text-align: center;">16/9

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</td>

<td>1050

315°

</td>

<td style="text-align: center;">11/6

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</td>

<td>1100

330°

</td>

<td style="text-align: center;">17/9, 32/17

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</td>

<td>1150

345°

</td>

<td style="text-align: center;">33/17, 64/33

~~</td>~~

~~</tr>~~

~~<tr>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

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

</td>

</tr>

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24 EDO breaks intervals into two sets of five cartegories. Infra - Minor - Neutral - Major - Ultra for seconds, thirds, sixths, and sevenths; and diminished - narrow - perfect - wide - augmented for

fourths, fifths, unison, and octave. For other strange enharmonics, wide and narrow can be used in conjunction with augmented and diminished intervals such as 550 cents being called a narrow diminished fifth and 850 cents being called a wide augmented fifth.

fourths, fifths, unison, and octave. For other strange enharmonics, wide and narrow can be used in conjunction with augmented and diminished intervals such as 550 cents being called a narrow diminished fifth and 850 cents being called a wide augmented fifth.

These are the intervals of 24 EDO that do not exist in 12 EDO: 2

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There have been disputes about disadvantages of various systems for notating quarter tones. Here are some of the few systems along with pros and cons.

Mainstream Quartertone Notation

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

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

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

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

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

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

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

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

Pros: Familiar, fairly easy to learn

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Alternate Quartertone Accidentals

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

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

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

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

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

<img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /> = three quarter-tones flat or drop-flat

<img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /> = three quarter-tones flat or drop-flat

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.

Pros: Very easy to distinguish accidentals from one another

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And in Persian music

<img src="http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png" alt="external image 200px-Koron_sign.svg.png" title="external image 200px-Koron_sign.svg.png" style="height: 25px; width: 12px;" />Koron (<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Koron_%28music%29" rel="nofollow">en</a> | <a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86" rel="nofollow">fa</a>) = quarter-tone flat or Jump

<img src="http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png" alt="external image 200px-Koron_sign.svg.png" title="external image 200px-Koron_sign.svg.png" style="height: 25px; width: 12px;" />Koron (<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Koron_%28music%29" rel="nofollow">en</a> | <a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86" rel="nofollow">fa</a>) = quarter-tone flat or Jump

<img src="http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png" alt="external image 200px-Sori_sign.svg.png" title="external image 200px-Sori_sign.svg.png" style="height: 25px; width: 15px;" />Sori (<a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%D8%B3%D8%B1%DB%8C_%28%D9%85%D9%88%D8%B3%DB%8C%D9%82%DB%8C%29" rel="nofollow">fa</a>) = quarter-tone sharp or Drop

<img src="http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png" alt="external image 200px-Sori_sign.svg.png" title="external image 200px-Sori_sign.svg.png" style="height: 25px; width: 15px;" />Sori (<a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%D8%B3%D8%B1%DB%8C_%28%D9%85%D9%88%D8%B3%DB%8C%D9%82%DB%8C%29" rel="nofollow">fa</a>) = quarter-tone sharp or Drop

Pros: Easy to read

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

with Sagittal signs for sharp and flat.

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

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

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

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William Lynch considers these as some possible good tetrads:

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

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

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<h1 id="toc19"><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.

<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

Hidekazu Wakabayashi tuned a piano and harp to where the normal sharps and flats are tuned 50 cents higher in which he called &quot;Iceface&quot; tuning.

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<h1 id="toc23"><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="toc24"><a name="External links"></a>External links</h1>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:k9assassin|k9assassin]] and made on <tt>2014-11-18 12:13:05 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-03-27 11:33:33 UTC</tt>.<br>
-: The original revision id was <tt>531567464</tt>.<br>
+: The original revision id was <tt>545565376</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 20: / Line 20: @@
 The tunings supplied by 72 cannot be used for all low-limit just intervals, but they can be used on the 17-limit [[k*N subgroups|3*24 subgroup]] 2.3.125.35.11.325.17 [[just intonation subgroup]], making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11 and 17. Another approach would be to treat 24-EDO as a 2.3.11.17.19 subgroup temperament, on which it is quite accurate.
-|| [[#|Degree]] || Cents ||= Approximate Ratios* ||
+|| [[#|Degree]] || Cents
+DMS ||= Approximate Ratios* ||
 || 0 || 0 ||= 1/1 ||
-|| 1 || 50 ||= 33/32, 34/33 ||
+|| 1 || 50
-|| 2 || 100 ||= 17/16, 18/17 ||
+° ||= 33/32, 34/33 ||
-|| 3 || 150 ||= 12/11 ||
+|| 2 || 100
-|| 4 || 200 ||= 9/8 ||
+° ||= 17/16, 18/17 ||
-|| 5 || 250 ||= 22/19 ||
+|| 3 || 150
-|| 6 || 300 ||= 19/16 ||
+° ||= 12/11 ||
-|| 7 || 350 ||= 11/9 ||
+|| 4 || 200
-|| 8 || 400 ||= 24/19 ||
+° ||= 9/8 ||
-|| 9 || 450 ||= 22/17 ||
+|| 5 || 250
-|| 10 || 500 ||= 4/3 ||
+° ||= 22/19 ||
-|| 11 || 550 ||= 11/8 ||
+|| 6 || 300
-|| 12 || 600 ||= 17/12 ||
+° ||= 19/16 ||
-|| 13 || 650 ||= 16/11 ||
+|| 7 || 350
-|| 14 || 700 ||= 3/2 ||
+° ||= 11/9 ||
-|| 15 || 750 ||= 17/11 ||
+|| 8 || 400
-|| 16 || 800 ||= 19/12 ||
+° ||= 24/19 ||
-|| 17 || 850 ||= 18/11 ||
+|| 9 || 450
-|| 18 || 900 ||= 32/19 ||
+° ||= 22/17 ||
-|| 19 || 950 ||= 19/11 ||
+|| 10 || 500
-|| 20 || 1000 ||= 16/9 ||
+° ||= 4/3 ||
-|| 21 || 1050 ||= 11/6 ||
+|| 11 || 550
-|| 22 || 1100 ||= 17/9, 32/17 ||
+° ||= 11/8 ||
-|| 23 || 1150 ||= 33/17, 64/33 ||
+|| 12 || 600
-||   ||   ||=   ||
+° ||= 17/12 ||
+|| 13 || 650
+° ||= 16/11 ||
+|| 14 || 700
+° ||= 3/2 ||
+|| 15 || 750
+° ||= 17/11 ||
+|| 16 || 800
+* ||= 19/12 ||
+|| 17 || 850
+° ||= 18/11 ||
+|| 18 || 900
+° ||= 32/19 ||
+|| 19 || 950
+° ||= 19/11 ||
+|| 20 || 1000
+° ||= 16/9 ||
+|| 21 || 1050
+° ||= 11/6 ||
+|| 22 || 1100
+° ||= 17/9, 32/17 ||
+|| 23 || 1150
+° ||= 33/17, 64/33 ||
 *based on treating 24-EDO as a 2.3.11.17.19 subgroup; other approaches are possible.
@@ Line 81: / Line 104: @@
 || 24 || 1200 ||= 2/1 ||
 EDO breaks intervals into two sets of five cartegories. Infra - Minor - Neutral - Major - Ultra for seconds, thirds, sixths, and sevenths; and diminished - narrow - perfect - wide - augmented for
 fourths, fifths, unison, and octave. For other strange enharmonics, wide and narrow can be used in conjunction with augmented and diminished intervals such as 550 cents being called a narrow diminished fifth and 850 cents being called a wide augmented fifth.
 These are the intervals of 24 EDO that do not exist in 12 EDO: 2
@@ Line 424: / Line 447: @@
 &lt;/td&gt;
          &lt;td&gt;Cents&lt;br /&gt;
+DMS&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Approximate Ratios*&lt;br /&gt;
@@ Line 440: / Line 464: @@
 &lt;/td&gt;
          &lt;td&gt;50&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;33/32, 34/33&lt;br /&gt;
@@ Line 448: / Line 473: @@
 &lt;/td&gt;
          &lt;td&gt;100&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;17/16, 18/17&lt;br /&gt;
@@ Line 456: / Line 482: @@
 &lt;/td&gt;
          &lt;td&gt;150&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;12/11&lt;br /&gt;
@@ Line 464: / Line 491: @@
 &lt;/td&gt;
          &lt;td&gt;200&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;9/8&lt;br /&gt;
@@ Line 472: / Line 500: @@
 &lt;/td&gt;
          &lt;td&gt;250&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;22/19&lt;br /&gt;
@@ Line 480: / Line 509: @@
 &lt;/td&gt;
          &lt;td&gt;300&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;19/16&lt;br /&gt;
@@ Line 488: / Line 518: @@
 &lt;/td&gt;
          &lt;td&gt;350&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/9&lt;br /&gt;
@@ Line 496: / Line 527: @@
 &lt;/td&gt;
          &lt;td&gt;400&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;24/19&lt;br /&gt;
@@ Line 504: / Line 536: @@
 &lt;/td&gt;
          &lt;td&gt;450&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;22/17&lt;br /&gt;
@@ Line 512: / Line 545: @@
 &lt;/td&gt;
          &lt;td&gt;500&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;4/3&lt;br /&gt;
@@ Line 520: / Line 554: @@
 &lt;/td&gt;
          &lt;td&gt;550&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/8&lt;br /&gt;
@@ Line 528: / Line 563: @@
 &lt;/td&gt;
          &lt;td&gt;600&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;17/12&lt;br /&gt;
@@ Line 536: / Line 572: @@
 &lt;/td&gt;
          &lt;td&gt;650&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;16/11&lt;br /&gt;
@@ Line 544: / Line 581: @@
 &lt;/td&gt;
          &lt;td&gt;700&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;3/2&lt;br /&gt;
@@ Line 552: / Line 590: @@
 &lt;/td&gt;
          &lt;td&gt;750&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;17/11&lt;br /&gt;
@@ Line 560: / Line 599: @@
 &lt;/td&gt;
          &lt;td&gt;800&lt;br /&gt;
+*&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;19/12&lt;br /&gt;
@@ Line 568: / Line 608: @@
 &lt;/td&gt;
          &lt;td&gt;850&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;18/11&lt;br /&gt;
@@ Line 576: / Line 617: @@
 &lt;/td&gt;
          &lt;td&gt;900&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;32/19&lt;br /&gt;
@@ Line 584: / Line 626: @@
 &lt;/td&gt;
          &lt;td&gt;950&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;19/11&lt;br /&gt;
@@ Line 592: / Line 635: @@
 &lt;/td&gt;
          &lt;td&gt;1000&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;16/9&lt;br /&gt;
@@ Line 600: / Line 644: @@
 &lt;/td&gt;
          &lt;td&gt;1050&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/6&lt;br /&gt;
@@ Line 608: / Line 653: @@
 &lt;/td&gt;
          &lt;td&gt;1100&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;17/9, 32/17&lt;br /&gt;
@@ Line 616: / Line 662: @@
 &lt;/td&gt;
          &lt;td&gt;1150&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;33/17, 64/33&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 955: / Line 994: @@
 EDO breaks intervals into two sets of five cartegories. Infra - Minor - Neutral - Major - Ultra for seconds, thirds, sixths, and sevenths; and diminished - narrow - perfect - wide - augmented for&lt;br /&gt;
-fourths, fifths, unison, and octave. For other strange enharmonics, wide and narrow can be used in conjunction with augmented and diminished intervals such as 550 cents being called a narrow diminished fifth and 850 cents being called a wide augmented fifth. &lt;br /&gt;
+fourths, fifths, unison, and octave. For other strange enharmonics, wide and narrow can be used in conjunction with augmented and diminished intervals such as 550 cents being called a narrow diminished fifth and 850 cents being called a wide augmented fifth.&lt;br /&gt;
 &lt;br /&gt;
 These are the intervals of 24 EDO that do not exist in 12 EDO: 2&lt;br /&gt;
@@ Line 1,184: / Line 1,223: @@
 There have been disputes about disadvantages of various systems for notating quarter tones. Here are some of the few systems along with pros and cons.&lt;br /&gt;
 &lt;strong&gt;Mainstream Quartertone Notation&lt;/strong&gt;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1542:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/s14_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/s14_blue.gif" alt="external image s14_blue.gif" title="external image s14_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1542 --&gt; or ^ = quarter-tone sharp or &amp;quot;Jump&amp;quot;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1534:&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:1534 --&gt; or ^ = quarter-tone sharp or &amp;quot;Jump&amp;quot;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1543:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/s34_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/s34_blue.gif" alt="external image s34_blue.gif" title="external image s34_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1543 --&gt; or #^ = three-quarter-tone sharp or &amp;quot;Jump-Sharp&amp;quot;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1535:&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:1535 --&gt; or #^ = three-quarter-tone sharp or &amp;quot;Jump-Sharp&amp;quot;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1544:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/f14_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/f14_blue.gif" alt="external image f14_blue.gif" title="external image f14_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1544 --&gt; or v = quarter-tone flat or &amp;quot;Drop&amp;quot;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1536:&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:1536 --&gt; or v = quarter-tone flat or &amp;quot;Drop&amp;quot;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1545:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/f34_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/f34_blue.gif" alt="external image f34_blue.gif" title="external image f34_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1545 --&gt; or bv = three-quarter-tone flat or &amp;quot;Drop-Flat&amp;quot;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1537:&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:1537 --&gt; or bv = three-quarter-tone flat or &amp;quot;Drop-Flat&amp;quot;&lt;br /&gt;
 &lt;br /&gt;
 Pros: Familiar, fairly easy to learn&lt;br /&gt;
@@ Line 1,193: / Line 1,232: @@
 &lt;br /&gt;
 &lt;strong&gt;Alternate Quartertone Accidentals&lt;/strong&gt;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1546:&amp;lt;img src=&amp;quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1546 --&gt; = quarter-tone sharp or Jump&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1538:&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:1538 --&gt; = quarter-tone sharp or Jump&lt;br /&gt;
 ††† (the horizontal line should connect all three vertical lines) = three quarter-tones sharp or Jump-Sharp&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1547:&amp;lt;img src=&amp;quot;http://www.dolmetsch.com/onequarterflat.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.dolmetsch.com/onequarterflat.gif" alt="external image onequarterflat.gif" title="external image onequarterflat.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1547 --&gt; = quarter-tone flat or Drop&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1539:&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:1539 --&gt; = quarter-tone flat or Drop&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1548:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1548 --&gt; = three quarter-tones flat or drop-flat&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1540:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1540 --&gt; = three quarter-tones flat or drop-flat&lt;br /&gt;
-For example, the scale 0-5-10-15-20 is written as C-D&lt;!-- ws:start:WikiTextRemoteImageRule:1549:&amp;lt;img src=&amp;quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1549 --&gt; (or E&lt;!-- ws:start:WikiTextRemoteImageRule:1550:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1550 --&gt;) F G&lt;!-- ws:start:WikiTextRemoteImageRule:1551:&amp;lt;img src=&amp;quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1551 --&gt; (or A&lt;!-- ws:start:WikiTextRemoteImageRule:1552:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1552 --&gt;) Bb.&lt;br /&gt;
+For example, the scale 0-5-10-15-20 is written as C-D&lt;!-- ws:start:WikiTextRemoteImageRule:1541:&amp;lt;img src=&amp;quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1541 --&gt; (or E&lt;!-- ws:start:WikiTextRemoteImageRule:1542:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1542 --&gt;) F G&lt;!-- ws:start:WikiTextRemoteImageRule:1543:&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:1543 --&gt; (or A&lt;!-- ws:start:WikiTextRemoteImageRule:1544:&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:1544 --&gt;) Bb.&lt;br /&gt;
 &lt;br /&gt;
 Pros: Very easy to distinguish accidentals from one another&lt;br /&gt;
@@ Line 1,203: / Line 1,242: @@
 &lt;br /&gt;
 &lt;strong&gt;&lt;span style="line-height: 1.5;"&gt;And in Persian music&lt;/span&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1553:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 25px; width: 12px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png" alt="external image 200px-Koron_sign.svg.png" title="external image 200px-Koron_sign.svg.png" style="height: 25px; width: 12px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1553 --&gt;Koron (&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Koron_%28music%29" rel="nofollow"&gt;en&lt;/a&gt; | &lt;a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86" rel="nofollow"&gt;fa&lt;/a&gt;) = quarter-tone flat or Jump&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1545:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 25px; width: 12px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png" alt="external image 200px-Koron_sign.svg.png" title="external image 200px-Koron_sign.svg.png" style="height: 25px; width: 12px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1545 --&gt;Koron (&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Koron_%28music%29" rel="nofollow"&gt;en&lt;/a&gt; | &lt;a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86" rel="nofollow"&gt;fa&lt;/a&gt;) = quarter-tone flat or Jump&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1554:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 25px; width: 15px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png" alt="external image 200px-Sori_sign.svg.png" title="external image 200px-Sori_sign.svg.png" style="height: 25px; width: 15px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1554 --&gt;Sori (&lt;a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%D8%B3%D8%B1%DB%8C_%28%D9%85%D9%88%D8%B3%DB%8C%D9%82%DB%8C%29" rel="nofollow"&gt;fa&lt;/a&gt;) = quarter-tone sharp or Drop&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1546:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 25px; width: 15px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png" alt="external image 200px-Sori_sign.svg.png" title="external image 200px-Sori_sign.svg.png" style="height: 25px; width: 15px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1546 --&gt;Sori (&lt;a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%D8%B3%D8%B1%DB%8C_%28%D9%85%D9%88%D8%B3%DB%8C%D9%82%DB%8C%29" rel="nofollow"&gt;fa&lt;/a&gt;) = quarter-tone sharp or Drop&lt;br /&gt;
 &lt;br /&gt;
 Pros: Easy to read&lt;br /&gt;
@@ Line 1,215: / Line 1,254: @@
 A possibility for the best approach would be to not use traditional sharps and flats altogether and replace them&lt;br /&gt;
 with Sagittal signs for sharp and flat.&lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:1540:&amp;lt;img src=&amp;quot;/file/view/sagittal%2024.PNG/500168246/sagittal%2024.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/sagittal%2024.PNG/500168246/sagittal%2024.PNG" alt="sagittal 24.PNG" title="sagittal 24.PNG" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1540 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:1532:&amp;lt;img src=&amp;quot;/file/view/sagittal%2024.PNG/500168246/sagittal%2024.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/sagittal%2024.PNG/500168246/sagittal%2024.PNG" alt="sagittal 24.PNG" title="sagittal 24.PNG" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1532 --&gt;&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:15:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Interval Alterations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:15 --&gt;Interval Alterations&lt;/h1&gt;
   &lt;br /&gt;
@@ Line 1,238: / Line 1,277: @@
 William Lynch considers these as some possible good tetrads:&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:1541:&amp;lt;img src=&amp;quot;/file/view/Three%20chords.PNG/489521008/Three%20chords.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Three%20chords.PNG/489521008/Three%20chords.PNG" alt="Three chords.PNG" title="Three chords.PNG" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1541 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:1533:&amp;lt;img src=&amp;quot;/file/view/Three%20chords.PNG/489521008/Three%20chords.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Three%20chords.PNG/489521008/Three%20chords.PNG" alt="Three chords.PNG" title="Three chords.PNG" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1533 --&gt;&lt;br /&gt;
 &lt;br /&gt;
@@ Line 2,084: / Line 2,123: @@
 &lt;!-- ws:start:WikiTextHeadingRule:41:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Instruments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:41 --&gt;Instruments&lt;!-- ws:start:WikiTextAnchorRule:80:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@instruments&amp;quot; title=&amp;quot;Anchor: instruments&amp;quot;/&amp;gt; --&gt;&lt;a name="instruments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:80 --&gt;&lt;/h1&gt;
   The ever-arising question in microtonal music, how to play it on instruments designed for 12edo, has a relatively simple answer in the case of 24edo: use two standard instruments tuned a quartertone apart. This &lt;a class="wiki_link" href="/Microtonal%20Keyboards#twelvenoteoctavescales"&gt;&amp;quot;12 note octave scales&amp;quot;&lt;/a&gt; approach is used in a wide part of the existing literature - see below.&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1555:&amp;lt;img src=&amp;quot;http://www.swordguitars.com/Sword_quartertone_stratsm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 195px; width: 406px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.swordguitars.com/Sword_quartertone_stratsm.jpg" alt="external image Sword_quartertone_stratsm.jpg" title="external image Sword_quartertone_stratsm.jpg" style="height: 195px; width: 406px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1555 --&gt;24-tone &amp;quot;1/4-tone&amp;quot; Guitar by Ron Sword / Sword guitars&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1547:&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:1547 --&gt;24-tone &amp;quot;1/4-tone&amp;quot; Guitar by Ron Sword / Sword guitars&lt;br /&gt;
 &lt;br /&gt;
 Hidekazu Wakabayashi tuned a piano and harp to where the normal sharps and flats are tuned 50 cents higher in which he called &amp;quot;Iceface&amp;quot; tuning.&lt;br /&gt;
@@ Line 2,106: / Line 2,145: @@
 &lt;!-- ws:start:WikiTextHeadingRule:49:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc23"&gt;&lt;a name="Practical Theory / Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:49 --&gt;Practical Theory / Books&lt;/h1&gt;
   &lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1556:&amp;lt;img src=&amp;quot;http://ronsword.com/images/24_tet_Coversm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 236px; width: 179px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://ronsword.com/images/24_tet_Coversm.jpg" alt="external image 24_tet_Coversm.jpg" title="external image 24_tet_Coversm.jpg" style="height: 236px; width: 179px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1556 --&gt;&lt;strong&gt;&amp;quot;Icosakaiteraphonic Scales for Guitar&amp;quot;&lt;/strong&gt; - A Book for Twenty-Four Equal Divisions of the Octave on guitar, or 'Quarter-tones'. Features a practical approach to understanding the tuning, and over 550 Scale Examples on Nine-String finger board charts, which allows for both symmetrical tuning visualization and standard guitar tuning- helpful for bassists and large range guitarists as well. Includes MOS, DE, and *all* the Scales / Modes from the list above.&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1548:&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:1548 --&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:51:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc24"&gt;&lt;a name="External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:51 --&gt;External links&lt;/h1&gt;