13edo: 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:~~TallKite~~|~~TallKite~~]] and made on <tt>2016-12-22 04:01:49 UTC</tt>.

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-22 04:46:38 UTC</tt>.

: The original revision id was <tt>~~602738262~~</tt>.

: The original revision id was <tt>602739096</tt>.

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

: The revision comment was: <tt>table formatting, unified precision of cent values</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>

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As a temperament of 21-odd-limit Just Intonation, 13edo has excellent approximations to the 11th and 21st harmonics, and reasonable approximations to the 5th, 9th, 13th, 17th, and 19th harmonics. For most purposes it does not offer acceptable approximations to the 3rd, 7th, or 15th. The lack of reasonable approximation to the 3rd harmonic makes 13edo unsuitable for common-practice music, but its good approximations to ratios of 11, 13, and 21 make it a very xenharmonic tuning, as these identities are not remotely represented in 12edo. Despite its reputation for dissonance, it is an excellent rank-1 temperament on the 2.5.9.11.13.17.19.21 subgroup, and has a substantial repertoire of complex consonances for its small size.

|| **Degree** || Cents ||= Approximated 21-limit Ratios* || Erv Wilson || Archaeotonic || Oneirotonic || [[26edo]] names || Kentaku ||

||= **Degree** ||= **Cents** ||= **Approximated 21-limit Ratios** * ||= **Erv Wilson** ||= **Archaeotonic** ||= **Oneirotonic** ||= **[[26edo]] names** ||= **Kentaku** ||

|| 0 || 0 ||= 1/1 || H || C || C || C || J ||

||= 0 ||= 0 ||= 1/1 ||= H || C || C || C || J ||

|| 1 || 92.31 ||= 17/16, 18/17, 19/18, 20/19, 21/20, 22/21 || β || C#/Db || C#/Db || Cx/Dbb || J#/Kb ||

||= 1 ||> 92.31 ||= 17/16, 18/17, 19/18, 20/19, 21/20, 22/21 ||= β || C#/Db || C#/Db || Cx/Dbb || J#/Kb ||

|| 2 || 184.~~615~~ ||= 9/8, 10/9, 11/10, 19/17, 21/19 || A || D || D || D || K ||

||= 2 ||> 184.62 ||= 9/8, 10/9, 11/10, 19/17, 21/19 ||= A || D || D || D || K ||

|| 3 || 276.92 ||= 7/6, 13/11, 20/17, 19/16, 22/19 || δ || D#/Eb || D#/Eb || Dx/Ebb || K#/Lb ||

||= 3 ||> 276.92 ||= 7/6, 13/11, 20/17, 19/16, 22/19 ||= δ || D#/Eb || D#/Eb || Dx/Ebb || K#/Lb ||

|| 4 || 369.23 ||= 5/4, 11/9, 16/13, 26/21 || C || E || E || E || L ||

||= 4 ||> 369.23 ||= 5/4, 11/9, 16/13, 26/21 ||= C || E || E || E || L ||

|| 5 || 461.54 ||= 13/10, 17/13, 21/16, 22/17 || B || E#/Fb || F || Ex/Fb || M ||

||= 5 ||> 461.54 ||= 13/10, 17/13, 21/16, 22/17 ||= B || E#/Fb || F || Ex/Fb || M ||

|| 6 || 553.85 ||= 11/8, 18/13, 26/19 || ε || F || F#/Gb || F# || M#/Nb ||

||= 6 ||> 553.85 ||= 11/8, 18/13, 26/19 ||= ε || F || F#/Gb || F# || M#/Nb ||

|| 7 || 646.15 ||= 16/11, 13/9, 19/13 || D || F#/Gb || G || Gb || N ||

||= 7 ||> 646.15 ||= 16/11, 13/9, 19/13 ||= D || F#/Gb || G || Gb || N ||

|| 8 || 738.46 ||= 17/11, 20/13, 26/17, 32/21 || γ || G || G#/Hb || G# || N#/Ob ||

||= 8 ||> 738.46 ||= 17/11, 20/13, 26/17, 32/21 ||= γ || G || G#/Hb || G# || N#/Ob ||

|| 9 || 830.77 ||= 8/5, 13/8, 18/11, 21/13 || F || G#/Ab || H || Ab || O ||

||= 9 ||> 830.77 ||= 8/5, 13/8, 18/11, 21/13 ||= F || G#/Ab || H || Ab || O ||

|| 10 || 923.08 ||= [[17_10|17/10]], [[12_7|12/7]], [[22_13|22/13]], [[19_11|19/11]] || E || A || A || A# || P ||

||= 10 ||> 923.08 ||= [[17_10|17/10]], [[12_7|12/7]], [[22_13|22/13]], [[19_11|19/11]] ||= E || A || A || A# || P ||

|| 11 || 1015.~~385~~ ||= 9/5, 16/9, 20/11, 34/19, 38/21 || α || A#/Bb || A#/Bb || Bb || P#/Qb ||

||= 11 ||> 1015.38 ||= 9/5, 16/9, 20/11, 34/19, 38/21 ||= α || A#/Bb || A#/Bb || Bb || P#/Qb ||

|| 12 || 1107.69 ||= 17/9, 19/10, 21/11, 32/17, 36/19, 40/21 || G || B/Cb || B || B#/Cbb || Q ||

||= 12 ||> 1107.69 ||= 17/9, 19/10, 21/11, 32/17, 36/19, 40/21 ||= G || B/Cb || B || B#/Cbb || Q ||

|| 13 || 1200 ||= 2/1 || H || C/B# || C || C || J ||

||= 13 ||> 1200.00 ||= 2/1 ||= H || C/B# || C || C || J ||

||.............||.............||................................................................||...................||.......................||....................||.......................||................||

*based on treating 13-EDO as a 2.5.9.11.13.21 subgroup temperament; other approaches are possible.

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<tr>

<td>Degree

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

</td>

<td>Cents

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

</td>

<td style="text-align: center;">Approximated 21-limit Ratios*

<td style="text-align: center;">Approximated 21-limit Ratios *

</td>

<td>Erv Wilson

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

</td>

<td>Archaeotonic

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

</td>

<td>Oneirotonic

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

</td>

<td><a class="wiki_link" href="/26edo">26edo</a> names

<td style="text-align: center;"><a class="wiki_link" href="/26edo">26edo</a> names

</td>

<td>Kentaku

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

</td>

</tr>

<tr>

<td>0

<td style="text-align: center;">0

</td>

<td>0

<td style="text-align: center;">0

</td>

<td style="text-align: center;">1/1

</td>

<td>H

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

</td>

<td>C

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</tr>

<tr>

<td>1

<td style="text-align: center;">1

</td>

<td>92.31

<td style="text-align: right;">92.31

</td>

<td style="text-align: center;">17/16, 18/17, 19/18, 20/19, 21/20, 22/21

</td>

<td>β

<td style="text-align: center;">β

</td>

<td>C#/Db

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</tr>

<tr>

<td>2

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

</td>

<td>184.~~615~~

<td style="text-align: right;">184.62

</td>

<td style="text-align: center;">9/8, 10/9, 11/10, 19/17, 21/19

</td>

<td>A

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

</td>

<td>D

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</tr>

<tr>

<td>3

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

</td>

<td>276.92

<td style="text-align: right;">276.92

</td>

<td style="text-align: center;">7/6, 13/11, 20/17, 19/16, 22/19

</td>

<td>δ

<td style="text-align: center;">δ

</td>

<td>D#/Eb

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</tr>

<tr>

<td>4

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

</td>

<td>369.23

<td style="text-align: right;">369.23

</td>

<td style="text-align: center;">5/4, 11/9, 16/13, 26/21

</td>

<td>C

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

</td>

<td>E

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</tr>

<tr>

<td>5

<td style="text-align: center;">5

</td>

<td>461.54

<td style="text-align: right;">461.54

</td>

<td style="text-align: center;">13/10, 17/13, 21/16, 22/17

</td>

<td>B

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

</td>

<td>E#/Fb

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</tr>

<tr>

<td>6

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

</td>

<td>553.85

<td style="text-align: right;">553.85

</td>

<td style="text-align: center;">11/8, 18/13, 26/19

</td>

<td>ε

<td style="text-align: center;">ε

</td>

<td>F

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</tr>

<tr>

<td>7

<td style="text-align: center;">7

</td>

<td>646.15

<td style="text-align: right;">646.15

</td>

<td style="text-align: center;">16/11, 13/9, 19/13

</td>

<td>D

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

</td>

<td>F#/Gb

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</tr>

<tr>

<td>8

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

</td>

<td>738.46

<td style="text-align: right;">738.46

</td>

<td style="text-align: center;">17/11, 20/13, 26/17, 32/21

</td>

<td>γ

<td style="text-align: center;">γ

</td>

<td>G

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</tr>

<tr>

<td>9

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

</td>

<td>830.77

<td style="text-align: right;">830.77

</td>

<td style="text-align: center;">8/5, 13/8, 18/11, 21/13

</td>

<td>F

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

</td>

<td>G#/Ab

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</tr>

<tr>

<td>10

<td style="text-align: center;">10

</td>

<td>923.08

<td style="text-align: right;">923.08

</td>

</td>

<td>E

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

</td>

<td>A

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</tr>

<tr>

<td>11

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

</td>

<td>1015.~~385~~

<td style="text-align: right;">1015.38

</td>

<td style="text-align: center;">9/5, 16/9, 20/11, 34/19, 38/21

</td>

<td>α

<td style="text-align: center;">α

</td>

<td>A#/Bb

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</tr>

<tr>

<td>12

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

</td>

<td>1107.69

<td style="text-align: right;">1107.69

</td>

<td style="text-align: center;">17/9, 19/10, 21/11, 32/17, 36/19, 40/21

</td>

<td>G

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

</td>

<td>B/Cb

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</tr>

<tr>

<td>13

<td style="text-align: center;">13

</td>

<td>1200

<td style="text-align: right;">1200.00

</td>

<td style="text-align: center;">2/1

</td>

<td>H

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

</td>

<td>C/B#

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</td>

<td>J

</td>

</tr>

<tr>

<td>.............

</td>

<td>.............

</td>

<td>................................................................

</td>

<td>...................

</td>

<td>.......................

</td>

<td>....................

</td>

<td>.......................

</td>

<td>................

</td>

</tr>

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<object id="example" type="image/svg+xml" data="http://xenharmonic.wikispaces.com/file/view/13ed2-001.svg">alt : Your browser has no SVG support.</object>

<div class="objectEmbed"><a href="/file/view/13ed2-001.svg/480712008/13ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/13ed2-001.svg/480712008/13ed2-001.svg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="13ed2-001.svg" /></a><div><a href="/file/view/13ed2-001.svg/480712008/13ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/13ed2-001.svg/480712008/13ed2-001.svg');" class="filename" title="13ed2-001.svg">13ed2-001.svg</a> <ul><li><a href="/file/detail/13ed2-001.svg">Details</a></li><li><a href="/file/view/13ed2-001.svg/480712008/13ed2-001.svg">Download</a></li><li style="color: #666">15 KB</li></ul></div></div>

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<h1 id="toc2"><a name="Scales in 13edo"></a>Scales in 13edo</h1>

Due to the prime character of the number 13, 13edo can form several xenharmonic <a class="wiki_link" href="/MOSScales">moment of symmetry scales</a>. The diagram below shows five &quot;families&quot; of MOS scales: those generated by making a chain of 2\13 (two <a class="wiki_link" href="/degree">degree</a>s of 13edo), 3\13, 4\13, 5\13, &amp; 6\13, respectively.

<img src="/file/view/13edo_horograms.jpg/104015789/13edo_horograms.jpg" alt="13edo_horograms.jpg" title="13edo_horograms.jpg" />

<img src="/file/view/13edo_horograms.jpg/104015789/13edo_horograms.jpg" alt="13edo_horograms.jpg" title="13edo_horograms.jpg" />

<div class="objectEmbed"><a href="/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf" onclick="ws.common.trackFileLink('/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf');"><img src="http://www.wikispaces.com/i/mime/32/application/pdf.png" height="32" width="32" alt="13edo horograms.pdf" /></a><div><a href="/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf" onclick="ws.common.trackFileLink('/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf');" class="filename" title="13edo horograms.pdf">13edo horograms.pdf</a> <ul><li><a href="/file/detail/13edo%20horograms.pdf">Details</a></li><li><a href="/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf">Download</a></li><li style="color: #666">242 KB</li></ul></div></div>

<div class="objectEmbed"><a href="/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf" onclick="ws.common.trackFileLink('/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf');"><img src="http://www.wikispaces.com/i/mime/32/application/pdf.png" height="32" width="32" alt="13edo horograms.pdf" /></a><div><a href="/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf" onclick="ws.common.trackFileLink('/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf');" class="filename" title="13edo horograms.pdf">13edo horograms.pdf</a> <ul><li><a href="/file/detail/13edo%20horograms.pdf">Details</a></li><li><a href="/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf">Download</a></li><li style="color: #666">242 KB</li></ul></div></div>

~diagram by Andrew Heathwaite, based on horagrams pioneered by Erv Wilson

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<h3 id="toc6"><a name="Notational and Compositional Approaches to 13edo-The Cryptic Ruse Methods-Modes and Harmony in The Archaeotonic Scale"></a>Modes and Harmony in The Archaeotonic Scale</h3>

A 7-nominal notaiton is proposed, using the letters A-G. The &quot;C natural&quot; scale is proposed to be degrees 0-2-4-6-8-10-12-(13), with the note &quot;C&quot; tuned to a reference pitch of concert middle C. The modes are laid out in the following table, excerpted from an unfinished paper on 13edo.

<img src="/file/view/Archeotonic.png/252639498/Archeotonic.png" alt="Archeotonic.png" title="Archeotonic.png" />

<img src="/file/view/Archeotonic.png/252639498/Archeotonic.png" alt="Archeotonic.png" title="Archeotonic.png" />

Treating 13edo as a temperament as proposed above leads to a chord of degrees 0-2-4-6-9 representing the JI harmony 8:9:10:11:13; two such pentads exist in this scale, on E and F. Smaller harmonic units exist as follows: 8:9:10:11 on C, D, E, and F; 8:9:10:13 on E, F and G; 8:9:10 on C, D, E, F, and G; 8:9:11 on C, D, E, and F; 8:9:13 on E, F, G, and A. Finally, on B we have the relatively-discordant 16:17:21:26 (0-1-5-9, or the notes B-C-E-G), which can be octave-inverted into a more concordant 8:13:17:21.

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<h3 id="toc7"><a name="Notational and Compositional Approaches to 13edo-The Cryptic Ruse Methods-Modes and Harmony in the Oneirotonic Scale"></a>Modes and Harmony in the Oneirotonic Scale</h3>

Here an 8-nominal notation is proposed, using letters A-H. The &quot;C natural&quot; scale is proposed to be degrees 0-2-4-5-7-9-10-12-(13), with the note &quot;C&quot; tuned to concert middle C. The modes are laid out in the following table, excerpted from an unfinished paper on 13edo.

<img src="/file/view/Oneirotonic.png/252639860/Oneirotonic.png" alt="Oneirotonic.png" title="Oneirotonic.png" />

<img src="/file/view/Oneirotonic.png/252639860/Oneirotonic.png" alt="Oneirotonic.png" title="Oneirotonic.png" />

There is a great number of potential consonant harmonies in this scale. A dedicated article on harmony and tonality in the oneirotonic scale is forthcoming.

<h2 id="toc8"> </h2>

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This new approach simply modifies the way 13 edo is systematized and notated but is based on the exact same 8 tone scale that cryptic ruse uses.

<img src="/file/view/13%20edo%20alphabet.PNG/506083616/13%20edo%20alphabet.PNG" alt="13 edo alphabet.PNG" title="13 edo alphabet.PNG" />

<img src="/file/view/13%20edo%20alphabet.PNG/506083616/13%20edo%20alphabet.PNG" alt="13 edo alphabet.PNG" title="13 edo alphabet.PNG" />

Notation written on the staff looks nearly the same as 12 edo notation except that because there are 8 letters instead of 7, the notes offset themselves to where space to space and line to line is now octaves rather than line to space. This actually makes learning the system much, much easier because a letter that is on a line is always on a line.

3 EDO Chromatic Scale in Octatonic Notation:

<img src="/file/view/8%20tone%20scale%2013%20edo.PNG/506382886/8%20tone%20scale%2013%20edo.PNG" alt="8 tone scale 13 edo.PNG" title="8 tone scale 13 edo.PNG" />

<img src="/file/view/8%20tone%20scale%2013%20edo.PNG/506382886/8%20tone%20scale%2013%20edo.PNG" alt="8 tone scale 13 edo.PNG" title="8 tone scale 13 edo.PNG" />

<img src="/file/view/13%20edo%20chromatic%20scale.PNG/506089524/13%20edo%20chromatic%20scale.PNG" alt="13 edo chromatic scale.PNG" title="13 edo chromatic scale.PNG" />

<img src="/file/view/13%20edo%20chromatic%20scale.PNG/506089524/13%20edo%20chromatic%20scale.PNG" alt="13 edo chromatic scale.PNG" title="13 edo chromatic scale.PNG" />

Also, this approach allows for a circle of fourths to be produced:

<img src="http://xenharmonic.wikispaces.com/file/view/13%20ET%20circle%20of%20fourths.PNG/506093224/13%20ET%20circle%20of%20fourths.PNG" alt="13 ET circle of fourths.PNG" title="13 ET circle of fourths.PNG" />

<img src="http://xenharmonic.wikispaces.com/file/view/13%20ET%20circle%20of%20fourths.PNG/506093224/13%20ET%20circle%20of%20fourths.PNG" alt="13 ET circle of fourths.PNG" title="13 ET circle of fourths.PNG" />

Listen to Ryonian on J (F#) <embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+Ryo+mode.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed>

Listen to Dylathian on J: (F#) <embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+8+tone+mode+1.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed>

@@ 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:TallKite|TallKite]] and made on <tt>2016-12-22 04:01:49 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-22 04:46:38 UTC</tt>.<br>
-: The original revision id was <tt>602738262</tt>.<br>
+: The original revision id was <tt>602739096</tt>.<br>
-: The revision comment was: <tt></tt><br>
+: The revision comment was: <tt>table formatting, unified precision of cent values</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 18: / Line 18: @@
 As a temperament of 21-odd-limit Just Intonation, 13edo has excellent approximations to the 11th and 21st harmonics, and reasonable approximations to the 5th, 9th, 13th, 17th, and 19th harmonics. For most purposes it does not offer acceptable approximations to the 3rd, 7th, or 15th. The lack of reasonable approximation to the 3rd harmonic makes 13edo unsuitable for common-practice music, but its good approximations to ratios of 11, 13, and 21 make it a very xenharmonic tuning, as these identities are not remotely represented in 12edo. Despite its reputation for dissonance, it is an excellent rank-1 temperament on the 2.5.9.11.13.17.19.21 subgroup, and has a substantial repertoire of complex consonances for its small size.
-|| **Degree** || Cents ||= Approximated 21-limit Ratios* || Erv Wilson || Archaeotonic || Oneirotonic || [[26edo]] names || Kentaku ||
+||= **Degree** ||= **Cents** ||= **Approximated 21-limit Ratios** * ||= **Erv Wilson** ||= **Archaeotonic** ||= **Oneirotonic** ||= **[[26edo]] names** ||= **Kentaku** ||
-|| 0 || 0 ||= 1/1 || H || C || C || C || J ||
+||= 0 ||= 0 ||= 1/1 ||= H || C || C || C || J ||
-|| 1 || 92.31 ||= 17/16, 18/17, 19/18, 20/19, 21/20, 22/21 || &lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;β&lt;/span&gt; || C#/Db || C#/Db || Cx/Dbb || J#/Kb ||
+||= 1 ||&gt; 92.31 ||= 17/16, 18/17, 19/18, 20/19, 21/20, 22/21 ||= &lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;β&lt;/span&gt; || C#/Db || C#/Db || Cx/Dbb || J#/Kb ||
-|| 2 || 184.615 ||= 9/8, 10/9, 11/10, 19/17, 21/19 || A || D || D || D || K ||
+||= 2 ||&gt; 184.62 ||= 9/8, 10/9, 11/10, 19/17, 21/19 ||= A || D || D || D || K ||
-|| 3 || 276.92 ||= 7/6, 13/11, 20/17, 19/16, 22/19 || &lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;δ&lt;/span&gt; || D#/Eb || D#/Eb || Dx/Ebb || K#/Lb ||
+||= 3 ||&gt; 276.92 ||= 7/6, 13/11, 20/17, 19/16, 22/19 ||= &lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;δ&lt;/span&gt; || D#/Eb || D#/Eb || Dx/Ebb || K#/Lb ||
-|| 4 || 369.23 ||= 5/4, 11/9, 16/13, 26/21 || C || E || E || E || L ||
+||= 4 ||&gt; 369.23 ||= 5/4, 11/9, 16/13, 26/21 ||= C || E || E || E || L ||
-|| 5 || 461.54 ||= 13/10, 17/13, 21/16, 22/17 || B || E#/Fb || F || Ex/Fb || M ||
+||= 5 ||&gt; 461.54 ||= 13/10, 17/13, 21/16, 22/17 ||= B || E#/Fb || F || Ex/Fb || M ||
-|| 6 || 553.85 ||= 11/8, 18/13, 26/19 || &lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;ε&lt;/span&gt; || F || F#/Gb || F# || M#/Nb ||
+||= 6 ||&gt; 553.85 ||= 11/8, 18/13, 26/19 ||= &lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;ε&lt;/span&gt; || F || F#/Gb || F# || M#/Nb ||
-|| 7 || 646.15 ||= 16/11, 13/9, 19/13 || D || F#/Gb || G || Gb || N ||
+||= 7 ||&gt; 646.15 ||= 16/11, 13/9, 19/13 ||= D || F#/Gb || G || Gb || N ||
-|| 8 || 738.46 ||= 17/11, 20/13, 26/17, 32/21 || &lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;γ&lt;/span&gt; || G || G#/Hb || G# || N#/Ob ||
+||= 8 ||&gt; 738.46 ||= 17/11, 20/13, 26/17, 32/21 ||= &lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;γ&lt;/span&gt; || G || G#/Hb || G# || N#/Ob ||
-|| 9 || 830.77 ||= 8/5, 13/8, 18/11, 21/13 || F || G#/Ab || H || Ab || O ||
+||= 9 ||&gt; 830.77 ||= 8/5, 13/8, 18/11, 21/13 ||= F || G#/Ab || H || Ab || O ||
-|| 10 || 923.08 ||= [[17_10|17/10]], [[12_7|12/7]], [[22_13|22/13]], [[19_11|19/11]] || E || A || A || A# || P ||
+||= 10 ||&gt; 923.08 ||= [[17_10|17/10]], [[12_7|12/7]], [[22_13|22/13]], [[19_11|19/11]] ||= E || A || A || A# || P ||
-|| 11 || 1015.385 ||= 9/5, 16/9, 20/11, 34/19, 38/21 || &lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;α&lt;/span&gt; || A#/Bb || A#/Bb || Bb || P#/Qb ||
+||= 11 ||&gt; 1015.38 ||= 9/5, 16/9, 20/11, 34/19, 38/21 ||= &lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;α&lt;/span&gt; || A#/Bb || A#/Bb || Bb || P#/Qb ||
-|| 12 || 1107.69 ||= 17/9, 19/10, 21/11, 32/17, 36/19, 40/21 || G || B/Cb || B || B#/Cbb || Q ||
+||= 12 ||&gt; 1107.69 ||= 17/9, 19/10, 21/11, 32/17, 36/19, 40/21 ||= G || B/Cb || B || B#/Cbb || Q ||
-|| 13 || 1200 ||= 2/1 || H || C/B# || C || C || J ||
+||= 13 ||&gt; 1200.00 ||= 2/1 ||= H || C/B# || C || C || J ||
+||.............||.............||................................................................||...................||.......................||....................||.......................||................||
 *based on treating 13-EDO as a 2.5.9.11.13.21 subgroup temperament; other approaches are possible.
@@ Line 190: / Line 191: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;strong&gt;Degree&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Degree&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Cents&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Cents&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Approximated 21-limit Ratios*&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Approximated 21-limit Ratios&lt;/strong&gt; *&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Erv Wilson&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Erv Wilson&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Archaeotonic&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Archaeotonic&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Oneirotonic&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Oneirotonic&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;a class="wiki_link" href="/26edo"&gt;26edo&lt;/a&gt; names&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/26edo"&gt;26edo&lt;/a&gt; names&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Kentaku&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Kentaku&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;0&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;0&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;1/1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;H&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;H&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;C&lt;br /&gt;
@@ Line 226: / Line 227: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;92.31&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;92.31&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;17/16, 18/17, 19/18, 20/19, 21/20, 22/21&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;β&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;β&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;C#/Db&lt;br /&gt;
@@ Line 244: / Line 245: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;184.615&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;184.62&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;9/8, 10/9, 11/10, 19/17, 21/19&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;A&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;D&lt;br /&gt;
@@ Line 262: / Line 263: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;276.92&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;276.92&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7/6, 13/11, 20/17, 19/16, 22/19&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;δ&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;δ&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;D#/Eb&lt;br /&gt;
@@ Line 280: / Line 281: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;4&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;369.23&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;369.23&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;5/4, 11/9, 16/13, 26/21&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;C&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;E&lt;br /&gt;
@@ Line 298: / Line 299: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;461.54&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;461.54&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;13/10, 17/13, 21/16, 22/17&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;B&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;B&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;E#/Fb&lt;br /&gt;
@@ Line 316: / Line 317: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;6&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;553.85&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;553.85&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/8, 18/13, 26/19&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;ε&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;ε&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;F&lt;br /&gt;
@@ Line 334: / Line 335: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;646.15&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;646.15&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;16/11, 13/9, 19/13&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;D&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;F#/Gb&lt;br /&gt;
@@ Line 352: / Line 353: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;8&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;738.46&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;738.46&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;17/11, 20/13, 26/17, 32/21&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;γ&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;γ&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;G&lt;br /&gt;
@@ Line 370: / Line 371: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;9&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;830.77&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;830.77&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;8/5, 13/8, 18/11, 21/13&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;F&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;G#/Ab&lt;br /&gt;
@@ Line 388: / Line 389: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;10&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;10&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;923.08&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;923.08&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/17_10"&gt;17/10&lt;/a&gt;, &lt;a class="wiki_link" href="/12_7"&gt;12/7&lt;/a&gt;, &lt;a class="wiki_link" href="/22_13"&gt;22/13&lt;/a&gt;, &lt;a class="wiki_link" href="/19_11"&gt;19/11&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;E&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;E&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;A&lt;br /&gt;
@@ Line 406: / Line 407: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;11&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1015.385&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;1015.38&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;9/5, 16/9, 20/11, 34/19, 38/21&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;α&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;α&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;A#/Bb&lt;br /&gt;
@@ Line 424: / Line 425: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;12&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;12&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1107.69&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;1107.69&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;17/9, 19/10, 21/11, 32/17, 36/19, 40/21&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;G&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;G&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;B/Cb&lt;br /&gt;
@@ Line 442: / Line 443: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;13&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1200&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;1200.00&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;2/1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;H&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;H&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;C/B#&lt;br /&gt;
@@ Line 457: / Line 458: @@
 &lt;/td&gt;
          &lt;td&gt;J&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&gt;................................................................&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;...................&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;.......................&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;....................&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;.......................&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;................&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 471: / Line 490: @@
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 &lt;!-- ws:start:WikiTextHeadingRule:13:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Scales in 13edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:13 --&gt;Scales in 13edo&lt;/h1&gt;
   Due to the prime character of the number 13, 13edo can form several xenharmonic &lt;a class="wiki_link" href="/MOSScales"&gt;moment of symmetry scales&lt;/a&gt;. The diagram below shows five &amp;quot;families&amp;quot; of MOS scales: those generated by making a chain of 2\13 (two &lt;u&gt;&lt;a class="wiki_link" href="/degree"&gt;degree&lt;/a&gt;s of&lt;/u&gt; 13edo), 3\13, 4\13, 5\13, &amp;amp; 6\13, respectively.&lt;br /&gt;
 &lt;br /&gt;
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 ~diagram by Andrew Heathwaite, based on horagrams pioneered by Erv Wilson&lt;br /&gt;
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@@ Line 507: / Line 526: @@
 &lt;!-- ws:start:WikiTextHeadingRule:21:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="Notational and Compositional Approaches to 13edo-The Cryptic Ruse Methods-Modes and Harmony in The Archaeotonic Scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:21 --&gt;Modes and Harmony in The Archaeotonic Scale&lt;/h3&gt;
   A 7-nominal notaiton is proposed, using the letters A-G. The &amp;quot;C natural&amp;quot; scale is proposed to be degrees 0-2-4-6-8-10-12-(13), with the note &amp;quot;C&amp;quot; tuned to a reference pitch of concert middle C. The modes are laid out in the following table, excerpted from an unfinished paper on 13edo.&lt;br /&gt;
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 Treating 13edo as a temperament as proposed above leads to a chord of degrees 0-2-4-6-9 representing the JI harmony 8:9:10:11:13; two such pentads exist in this scale, on E and F. Smaller harmonic units exist as follows: 8:9:10:11 on C, D, E, and F; 8:9:10:13 on E, F and G; 8:9:10 on C, D, E, F, and G; 8:9:11 on C, D, E, and F; 8:9:13 on E, F, G, and A. Finally, on B we have the relatively-discordant 16:17:21:26 (0-1-5-9, or the notes B-C-E-G), which can be octave-inverted into a more concordant 8:13:17:21.&lt;br /&gt;
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@@ Line 514: / Line 533: @@
 &lt;!-- ws:start:WikiTextHeadingRule:23:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="Notational and Compositional Approaches to 13edo-The Cryptic Ruse Methods-Modes and Harmony in the Oneirotonic Scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:23 --&gt;Modes and Harmony in the Oneirotonic Scale&lt;/h3&gt;
   Here an 8-nominal notation is proposed, using letters A-H. The &amp;quot;C natural&amp;quot; scale is proposed to be degrees 0-2-4-5-7-9-10-12-(13), with the note &amp;quot;C&amp;quot; tuned to concert middle C. The modes are laid out in the following table, excerpted from an unfinished paper on 13edo.&lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:856:&amp;lt;img src=&amp;quot;/file/view/Oneirotonic.png/252639860/Oneirotonic.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Oneirotonic.png/252639860/Oneirotonic.png" alt="Oneirotonic.png" title="Oneirotonic.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:856 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:874:&amp;lt;img src=&amp;quot;/file/view/Oneirotonic.png/252639860/Oneirotonic.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Oneirotonic.png/252639860/Oneirotonic.png" alt="Oneirotonic.png" title="Oneirotonic.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:874 --&gt;&lt;br /&gt;
 There is a great number of potential consonant harmonies in this scale. A dedicated article on harmony and tonality in the oneirotonic scale is forthcoming.&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:25:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;!-- ws:end:WikiTextHeadingRule:25 --&gt; &lt;/h2&gt;
@@ Line 523: / Line 542: @@
 &lt;br /&gt;
 This new approach simply modifies the way 13 edo is systematized and notated but is based on the exact same 8 tone scale that cryptic ruse uses.&lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:857:&amp;lt;img src=&amp;quot;/file/view/13%20edo%20alphabet.PNG/506083616/13%20edo%20alphabet.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/13%20edo%20alphabet.PNG/506083616/13%20edo%20alphabet.PNG" alt="13 edo alphabet.PNG" title="13 edo alphabet.PNG" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:857 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:875:&amp;lt;img src=&amp;quot;/file/view/13%20edo%20alphabet.PNG/506083616/13%20edo%20alphabet.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/13%20edo%20alphabet.PNG/506083616/13%20edo%20alphabet.PNG" alt="13 edo alphabet.PNG" title="13 edo alphabet.PNG" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:875 --&gt;&lt;br /&gt;
 Notation written on the staff looks nearly the same as 12 edo notation except that because there are 8 letters instead of 7, the notes offset themselves to where space to space and line to line is now octaves rather than line to space. This actually makes learning the system much, much easier because a letter that is on a line is always on a line.&lt;br /&gt;
 &lt;br /&gt;
 EDO Chromatic Scale in Octatonic Notation:&lt;br /&gt;
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 Also, this approach allows for a circle of fourths to be produced:&lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:860:&amp;lt;img src=&amp;quot;http://xenharmonic.wikispaces.com/file/view/13%20ET%20circle%20of%20fourths.PNG/506093224/13%20ET%20circle%20of%20fourths.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://xenharmonic.wikispaces.com/file/view/13%20ET%20circle%20of%20fourths.PNG/506093224/13%20ET%20circle%20of%20fourths.PNG" alt="13 ET circle of fourths.PNG" title="13 ET circle of fourths.PNG" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:860 --&gt;&lt;br /&gt;
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 Listen to Ryonian on J (F#) &lt;!-- ws:start:WikiTextMediaRule:7:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%20Ryo%20mode.wav?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;13 edo Ryo mode.wav&amp;amp;quot; width=&amp;amp;quot;300&amp;amp;quot; height=&amp;amp;quot;50&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+Ryo+mode.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:7 --&gt;&lt;br /&gt;
 Listen to Dylathian on J: (F#) &lt;!-- ws:start:WikiTextMediaRule:8:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%208%20tone%20mode%201.wav?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;13 edo 8 tone mode 1.wav&amp;amp;quot; width=&amp;amp;quot;300&amp;amp;quot; height=&amp;amp;quot;50&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+8+tone+mode+1.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:8 --&gt;&lt;br /&gt;