22edo: 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:~~spt3125~~|~~spt3125~~]] and made on <tt>2017-07-~~22 21~~:58:22 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-11 17:42:37 UTC</tt>.

: The original revision id was <tt>~~615833805~~</tt>.

: The original revision id was <tt>621459943</tt>.

: The revision comment was: <tt>~~added link (deorphaning), some cleanup~~</tt>

: The revision comment was: <tt></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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||= 21 ||= 1145 ||= major 7th ||= M7 ||= C# ||= dim 8ve ||= d8 ||= Db ||= dim octave ||= d8 ||= Db ||

||= 22 ||= 1200 ||= perfect octave ||= P8 ||= D ||= perfect octave ||= P8 ||= D ||= perfect octave ||= P8 ||= D ||

Combining ups and downs notation with [[Kite's color notation|color notation]], qualities can be associated with colors (higher prime content):

||~ quality ||~ color ||~ monzo ||~ examples ||

||= minor ||= blue ||= {a, b, 0, c}, c = 1 ||= 7/6, 7/4 ||

||= " ||= fourthward white ||= {a, b}, b < -1 ||= 16/9, 32/27 ||

||= upminor ||= green ||= {a, b, c}, c = -1 ||= 6/5, 9/5 ||

||= downmajor ||= yellow ||= {a, b, c}, c = 1 ||= 5/4, 5/3 ||

||= major ||= fifthward white ||= {a, b}, b > 1 ||= 9/8, 27/16 ||

||= " ||= red ||= {a, b, 0, c}, c = -1 ||= 9/7, 12/7 ||

=Chord Names=

22edo chords can be named using ups and downs notation.

All 22edo chords can be named using ups and downs notation. Here are the blue, green, yellow and red triads:

||~ color of the 3rd ||~ JI chord ||~ notes as edosteps ||~ notes of C chord ||~ written name ||~ spoken name ||

0-8-13 = C E G = C = "C~~" or "~~C ~~major"~~

||= blue ||= 6:7:9 ||= 0-5-13 ||= C Eb G ||= Cm ||= C minor ||

0-7-13 = C Ev G = C.v = "C downmajor" or "C dot down"

||= green ||= 10:12:15 ||= 0-6-13 ||= C Eb^ G ||= C.^m ||= C upminor ||

~~The~~ period is needed because "Cv", spoken as "C down", is either a note, or a major chord Cv Ev Gv.

||= yellow ||= 4:5:6 ||= 0-7-13 ||= C Ev G ||= C.v ||= C downmajor or C dot down ||

~~0-6-13 = C Eb^ G = C.^m = "C upminor"~~

||= red ||= 14:18:27 ||= 0-8-13 ||= C E G ||= C ||= C major or C ||

~~0-5-13 = C Eb G = Cm = "C minor"~~

For C.v, the period is needed because "Cv", spoken as "C down", is either a note, or a major chord Cv Ev Gv.

The period isn't needed in ~~the last chord name~~ because there's no ups or downs immediately after the note name.

The period isn't needed in Cm because there's no ups or downs immediately after the note name.

0-8-13-18 = C E G Bb = C7 = "C seven"

0-7-13-18 = C Ev G Bb = C7(v3) = "C seven, down third"

0-8-13-21 = C E G B = CM7 = "C major seven"

0-7-13-20 = C Ev G Bv = C.vM7 = "C downmajor seven" (the down symbol ~~affects~~ both the 3rd and the 7th)

0-7-13-20 = C Ev G Bv = C.vM7 = "C downmajor seven" (the down symbol applies to both the 3rd and the 7th)

0-3-13 = C Dv G = ~~Csusv2~~

0-3-13 = C Dv G = C(v2)

0-4-13 = C D G = ~~Csus2~~

0-4-13 = C D G = C2

~~0-5-13 = C Eb G = Cm~~

0-9-13 = C F G = C4

~~0-6-13 = C Eb^ G = C.^m~~

0-10-13 = C F^ G = C(^4)

~~0-7-13 = C Ev G = C.v~~

~~0-8-13 = C E G = C~~

0-9-13 = C F G = ~~Csus4~~

0-10-13 = C F^ G = ~~Csus~~^4

0-5-10 = C Eb Gb = Cdim

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0-5-11-14 = C Eb Gb^ Bbbv = Cdim7(^5,v7)

0-6-11-15 = C Eb^ Gb^ Bbb = Cdim7(^3,^5)

0-6-11-16 = C Eb^ Gb^ Bbb^ = C.^dim7 (the up symbol applies to ~~m3, d5~~ and d7)

0-6-11-16 = C Eb^ Gb^ Bbb^ = C.^dim7(^5) (the up symbol applies to both the 3rd and the 7th)

0-5-13-17 = C Eb G A = Cm6

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0-5-13-18 = C Eb G Bb = Cm7

0-6-13-19 = C Eb^ G Bb^ = C.^m7

0-8-13-21 = C E G B = CM7

0-7-13-20 = C Ev G Bv = C.vM7

~~0-8-13-21 = C E G B = CM7~~

0-5-13-16 = C Eb G Av = Cm(v6)

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Paul Erlich's "Tibia" in G, with independent ups and downs:

[[image:Tibia in G for the book-1.png width="800" height="956"]]

[[image:Tibia in G for the book-2.png width="800" height="889"]]

=The Decatonic System=

The decatonic system is an approach of notation based on Paul Erlich's decatonic scales. Unlike typical notation, the decatonic system is based on a scale of 10 tones rather than 7. This approach requires an entire re-learning of chords, intervals, and notation, but it allows 22EDO to be notated using only one pair of accidentals, and gives the opportunity to escape a heptatonic thinking pattern

==[[#TOC-Decatonic-Alphabet]]Decatonic Alphabet==

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==Internal links==

* [[William Lynch's Thoughts on Septimal Harmony and 22 EDO]]

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<~~!-- ws:start:WikiTextHeadingRule:10:~~&~~amp~~;lt;h1&~~amp~~;gt; --><~~h1 id~~="~~toc4~~"><~~a name="Chord Names"~~></a><~~!-- ws:end:WikiTextHeadingRule:10 --~~>~~Chord Names~~</h1>

Combining ups and downs notation with <a class="wiki_link" href="/Kite%27s%20color%20notation">color notation</a>, qualities can be associated with colors (higher prime content):

~~22edo chords can be named using ups and downs notation.~~

~~0-8-13 = C E G = C =~~ &~~amp~~;~~quot~~;C&~~amp~~;~~quot~~; or &~~amp~~;~~quot~~;~~C major~~&~~amp~~;~~quot~~;

<tr>

~~0-7-13 = C Ev G = C.v =~~ &~~amp~~;~~quot~~;~~C downmajor~~&~~amp~~;~~quot~~; or &~~amp~~;~~quot~~;~~C dot down~~&~~amp;quot~~;

<th>quality

~~The period is needed because~~ &~~amp~~;~~quot~~;Cv&~~amp~~;~~quot~~;~~, spoken as~~ &~~amp~~;~~quot~~;~~C down~~&~~amp~~;~~quot~~;, ~~is either a note~~, ~~or a major chord Cv Ev Gv.~~

</th>

0-6~~-13 = C Eb^ G = C.^m =~~ &~~amp~~;~~quot~~;~~C upminor~~&~~amp~~;~~quot~~;

<th>color

0-~~5-13 = C Eb G = Cm =~~ &quot;~~C minor~~&~~amp~~;~~quot~~;

</th>

~~The period isn't needed in the last chord name because there's no ups or downs immediately after the note name.~~

<th>monzo

</th>

0-~~8-13-18 = C E G Bb = C7 =~~ &~~quot~~;~~C seven~~&~~amp~~;~~quot~~;

<th>examples

0-~~7-13-18 = C Ev G Bb = C7(v3) =~~ &~~amp~~;~~quot~~;~~C seven, down third~~&~~amp~~;~~quot~~;

</th>

~~0-8-13-21 = C E G B = CM7 =~~ &~~amp~~;~~quot~~;~~C major seven~~&~~amp~~;~~quot~~;

</tr>

~~0-7-13-20 = C Ev G Bv = C.vM7 =~~ &~~amp~~;~~quot~~;~~C downmajor seven~~&~~amp~~;~~quot~~; ~~(the down symbol affects both the 3rd and the 7th)~~

<tr>

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

0-3-~~13 = C Dv G = Csusv2~~

</td>

~~0-4-13 = C D G = Csus2~~

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

0-5~~-13 = C Eb G = Cm~~

</td>

~~0-6-13 = C Eb^ G = C.^m~~

<td style="text-align: center;">{a, b, 0, c}, c = 1

~~0-7-13 = C Ev G = C.v~~

</td>

0-~~8-13 = C E G = C~~

<td style="text-align: center;">7/6, 7/4

~~0-9-13 = C F G = Csus4~~

</td>

0-~~10-13 = C F^ G = Csus^4~~

</tr>

<tr>

0-~~5-10~~ = ~~C Eb Gb = Cdim~~

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

0-5~~-11 = C Eb Gb^ = Cdim(^~~5)

</td>

0-~~5-12 = C Eb Gv = Cm(v5)~~

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

</td>

0-~~5-10-15 = C Eb Gb Bbb = Cdim7~~

<td style="text-align: center;">{a, b}, b &lt; -1

0-~~5-11-14 = C Eb Gb^ Bbbv = Cdim7(^5~~,~~v7)~~

</td>

0-~~6-11-15 = C Eb^ Gb^ Bbb = Cdim7(^3~~,~~^5)~~

<td style="text-align: center;">16/9, 32/27

~~0-6-11-16 = C Eb^ Gb^ Bbb^ = C.^dim7 (the up symbol applies to m3, d5 and d7)~~

</td>

0-~~5-13-17 = C Eb G A = Cm6~~

</tr>

<tr>

~~Sometimes doubled ups/downs are unavoidable~~:

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

0-~~6-12-15 = C Eb^ Gv Avv = Cm6(^3~~,v5,~~vv6)~~, ~~or C Eb^ Gb^^ Bbb~~ = ~~Cdim7(^3,^^5)~~

</td>

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

0-~~8-13-17 = C E G A = C6~~

</td>

~~0-8-13-16 = C E G Av = C(v6)~~

<td style="text-align: center;">{a, b, c}, c = -1

~~0-7-13-17 = C Ev G A = C6(v3)~~

</td>

~~0-7-13-16 = C Ev G Av = C.v6 (the down symbol applies to both the 3rd and the 6th)~~

<td style="text-align: center;">6/5, 9/5

</td>

</tr>

<tr>

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

</td>

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

</td>

<td style="text-align: center;">{a, b, c}, c = 1

</td>

<td style="text-align: center;">5/4, 5/3

</td>

</tr>

<tr>

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

</td>

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

</td>

<td style="text-align: center;">{a, b}, b &gt; 1

</td>

<td style="text-align: center;">9/8, 27/16

</td>

</tr>

<tr>

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

</td>

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

</td>

<td style="text-align: center;">{a, b, 0, c}, c = -1

</td>

<td style="text-align: center;">9/7, 12/7

</td>

</tr>

</table>

0-5-13-~~18 =~~ C Eb G Bb = ~~Cm7~~

<h1 id="toc4"><a name="Chord Names"></a>Chord Names</h1>

0-6-13-~~19 =~~ C Eb^ G Bb^ = C.~~^m7~~

0-7-13-20 = C Ev G Bv = C.vM7

All 22edo chords can be named using ups and downs notation. Here are the blue, green, yellow and red triads:

<tr>

<th>color of the 3rd

</th>

<th>JI chord

</th>

<th>notes as edosteps

</th>

<th>notes of C chord

</th>

<th>written name

</th>

<th>spoken name

</th>

</tr>

<tr>

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

</td>

<td style="text-align: center;">6:7:9

</td>

<td style="text-align: center;">0-5-13

</td>

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

</td>

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

</td>

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

</td>

</tr>

<tr>

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

</td>

<td style="text-align: center;">10:12:15

</td>

<td style="text-align: center;">0-6-13

</td>

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

</td>

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

</td>

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

</td>

</tr>

<tr>

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

</td>

<td style="text-align: center;">4:5:6

</td>

<td style="text-align: center;">0-7-13

</td>

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

</td>

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

</td>

<td style="text-align: center;">C downmajor or C dot down

</td>

</tr>

<tr>

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

</td>

<td style="text-align: center;">14:18:27

</td>

<td style="text-align: center;">0-8-13

</td>

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

</td>

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

</td>

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

</td>

</tr>

</table>

For C.v, the period is needed because &quot;Cv&quot;, spoken as &quot;C down&quot;, is either a note, or a major chord Cv Ev Gv.

The period isn't needed in Cm because there's no ups or downs immediately after the note name.

0-8-13-18 = C E G Bb = C7 = &quot;C seven&quot;

0-7-13-18 = C Ev G Bb = C7(v3) = &quot;C seven, down third&quot;

0-8-13-21 = C E G B = CM7 = &quot;C major seven&quot;

0-7-13-20 = C Ev G Bv = C.vM7 = &quot;C downmajor seven&quot; (the down symbol applies to both the 3rd and the 7th)

0-3-13 = C Dv G = C(v2)

0-4-13 = C D G = C2

0-9-13 = C F G = C4

0-10-13 = C F^ G = C(^4)

0-5-10 = C Eb Gb = Cdim

0-5-11 = C Eb Gb^ = Cdim(^5)

0-5-12 = C Eb Gv = Cm(v5)

0-5-10-15 = C Eb Gb Bbb = Cdim7

0-5-11-14 = C Eb Gb^ Bbbv = Cdim7(^5,v7)

0-6-11-15 = C Eb^ Gb^ Bbb = Cdim7(^3,^5)

0-6-11-16 = C Eb^ Gb^ Bbb^ = C.^dim7(^5) (the up symbol applies to both the 3rd and the 7th)

0-5-13-17 = C Eb G A = Cm6

Sometimes doubled ups/downs are unavoidable:

0-6-12-15 = C Eb^ Gv Avv = Cm6(^3,v5,vv6), or C Eb^ Gb^^ Bbb = Cdim7(^3,^^5)

0-8-13-17 = C E G A = C6

0-8-13-16 = C E G Av = C(v6)

0-7-13-17 = C Ev G A = C6(v3)

0-7-13-16 = C Ev G Av = C.v6 (the down symbol applies to both the 3rd and the 6th)

0-5-13-18 = C Eb G Bb = Cm7

0-6-13-19 = C Eb^ G Bb^ = C.^m7

0-8-13-21 = C E G B = CM7

0-7-13-20 = C Ev G Bv = C.vM7

0-5-13-16 = C Eb G Av = Cm(v6)

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See also: <a class="wiki_link" href="/22edo%20Solfege">22edo Solfege</a>, <a class="wiki_link" href="/22edo%20Tetrachords">22edo Tetrachords</a>, <a class="wiki_link" href="/22%20EDO%20Chords">22 EDO Chords</a>, <a class="wiki_link" href="/22edo%20Modes">22edo Modes</a>

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When 22edo is treated as generated by a cycle of its fifths, the naturals F C G D A E B represent a chain of those 13\22 fifths; consequently, the whole tone comes out to four degrees and the apotome (pythagorean sharp/flat) comes out to three degrees. Three pairs of sagittal symbols, dividing that apotome into three parts, are all that is necessary, and offer plenty of enharmonic equivalents:

<img src="/file/view/22edo.png/269078624/22edo.png" alt="22edo.png" title="22edo.png" />

<img src="/file/view/22edo.png/269078624/22edo.png" alt="22edo.png" title="22edo.png" />

This notation is consistent with Sagittal's notation of 5-limit JI harmony: &quot;major&quot; 3rds and 6ths appear as (super)pythagorean intervals flattened by a syntonic comma.

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Treating <a class="wiki_link" href="/Ups%20and%20Downs%20Notation">ups and downs</a> as &quot;fused&quot; with sharps and flats, and never appearing separately:

<img src="/file/view/Tibia%2022edo%20ups%20and%20downs%20guide%201.png/602422384/800x147/Tibia%2022edo%20ups%20and%20downs%20guide%201.png" alt="Tibia 22edo ups and downs guide 1.png" title="Tibia 22edo ups and downs guide 1.png" style="height: 147px; width: 800px;" />

<img src="/file/view/Tibia%2022edo%20ups%20and%20downs%20guide%201.png/602422384/800x147/Tibia%2022edo%20ups%20and%20downs%20guide%201.png" alt="Tibia 22edo ups and downs guide 1.png" title="Tibia 22edo ups and downs guide 1.png" style="height: 147px; width: 800px;" />

Treating ups and downs as independent of sharps and flats, and sometimes appearing separately:

<img src="/file/view/Tibia%2022edo%20ups%20and%20downs%20guide%202.png/602422386/800x150/Tibia%2022edo%20ups%20and%20downs%20guide%202.png" alt="Tibia 22edo ups and downs guide 2.png" title="Tibia 22edo ups and downs guide 2.png" style="height: 150px; width: 800px;" />

<img src="/file/view/Tibia%2022edo%20ups%20and%20downs%20guide%202.png/602422386/800x150/Tibia%2022edo%20ups%20and%20downs%20guide%202.png" alt="Tibia 22edo ups and downs guide 2.png" title="Tibia 22edo ups and downs guide 2.png" style="height: 150px; width: 800px;" />

A D downmajor scale with mandatory accidentals (no key signature), with minimal accidentals (only when needed to override the key signature), and with independent ups and downs.

<img src="/file/view/Tibia%2022edo%20guide%20D%20major.png/602422382/800x68/Tibia%2022edo%20guide%20D%20major.png" alt="Tibia 22edo guide D major.png" title="Tibia 22edo guide D major.png" style="height: 68px; width: 800px;" />

<img src="/file/view/Tibia%2022edo%20guide%20D%20major.png/602422382/800x68/Tibia%2022edo%20guide%20D%20major.png" alt="Tibia 22edo guide D major.png" title="Tibia 22edo guide D major.png" style="height: 68px; width: 800px;" />

Paul Erlich's &quot;Tibia&quot; in G, with independent ups and downs:

<img src="/file/view/Tibia%20in%20G%20for%20the%20book-1.png/623289179/800x956/Tibia%20in%20G%20for%20the%20book-1.png" alt="Tibia in G for the book-1.png" title="Tibia in G for the book-1.png" style="height: 956px; width: 800px;" />

<img src="/file/view/Tibia%20in%20G%20for%20the%20book-1.png/623289179/800x956/Tibia%20in%20G%20for%20the%20book-1.png" alt="Tibia in G for the book-1.png" title="Tibia in G for the book-1.png" style="height: 956px; width: 800px;" />

<img src="/file/view/Tibia%20in%20G%20for%20the%20book-2.png/623289195/800x889/Tibia%20in%20G%20for%20the%20book-2.png" alt="Tibia in G for the book-2.png" title="Tibia in G for the book-2.png" style="height: 889px; width: 800px;" />

<img src="/file/view/Tibia%20in%20G%20for%20the%20book-2.png/623289195/800x889/Tibia%20in%20G%20for%20the%20book-2.png" alt="Tibia in G for the book-2.png" title="Tibia in G for the book-2.png" style="height: 889px; width: 800px;" />

<h1 id="toc11"><a name="The Decatonic System"></a>The Decatonic System</h1>

The decatonic system is an approach of notation based on Paul Erlich's decatonic scales. Unlike typical notation, the decatonic system is based on a scale of 10 tones rather than 7. This approach requires an entire re-learning of chords, intervals, and notation, but it allows 22EDO to be notated using only one pair of accidentals, and gives the opportunity to escape a heptatonic thinking pattern

<h2 id="toc12"><a name="The Decatonic System-Decatonic Alphabet"></a><a name="TOC-Decatonic-Alphabet"></a>Decatonic Alphabet</h2>

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<h2 id="toc13"><a name="The Decatonic System-Internal links"></a>Internal links</h2>

<ul><li><a class="wiki_link" href="/William%20Lynch%27s%20Thoughts%20on%20Septimal%20Harmony%20and%2022%20EDO">William Lynch's Thoughts on Septimal Harmony and 22 EDO</a></li></ul>

<h2 id="toc14"><a name="The Decatonic System-External links"></a>External links</h2>

<ul><li><a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/erlich-decatonic.pdf" rel="nofollow">Erlich, Paul, ''Tuning, Tonality, and Twenty-Two Tone Temperament''</a></li><li><a class="wiki_link_ext" href="http://porcupinemusic.weebly.com/" rel="nofollow">&quot;Porcupine Music&quot; - Website Focused on the Development of 22 EDO music </a></li></ul>

@@ 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:spt3125|spt3125]] and made on <tt>2017-07-22 21:58:22 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-11 17:42:37 UTC</tt>.<br>
-: The original revision id was <tt>615833805</tt>.<br>
+: The original revision id was <tt>621459943</tt>.<br>
-: The revision comment was: <tt>added link (deorphaning), some cleanup</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>
 <h4>Original Wikitext content:</h4>
@@ Line 105: / Line 105: @@
 ||= 21 ||= 1145 ||= major 7th ||= M7 ||= C# ||= dim 8ve ||= d8 ||= Db ||= dim octave ||= d8 ||= Db ||
 ||= 22 ||= 1200 ||= perfect octave ||= P8 ||= D ||= perfect octave ||= P8 ||= D ||= perfect octave ||= P8 ||= D ||
+Combining ups and downs notation with [[Kite's color notation|color notation]], qualities can be associated with colors (higher prime content):
+||~ quality ||~ color ||~ monzo ||~ examples ||
+||= minor ||= blue ||= {a, b, 0, c}, c = 1 ||= 7/6, 7/4 ||
+||= " ||= fourthward white ||= {a, b}, b &lt; -1 ||= 16/9, 32/27 ||
+||= upminor ||= green ||= {a, b, c}, c = -1 ||= 6/5, 9/5 ||
+||= downmajor ||= yellow ||= {a, b, c}, c = 1 ||= 5/4, 5/3 ||
+||= major ||= fifthward white ||= {a, b}, b &gt; 1 ||= 9/8, 27/16 ||
+||= " ||= red ||= {a, b, 0, c}, c = -1 ||= 9/7, 12/7 ||
 =Chord Names=
-edo chords can be named using ups and downs notation.
+All 22edo chords can be named using ups and downs notation. Here are the blue, green, yellow and red triads:
+||~ color of the 3rd ||~ JI chord ||~ notes as edosteps ||~ notes of C chord ||~ written name ||~ spoken name ||
--8-13 = C E G = C = "C" or "C major"
+||= blue ||= 6:7:9 ||= 0-5-13 ||= C Eb G ||= Cm ||= C minor ||
--7-13 = C Ev G = C.v = "C downmajor" or "C dot down"
+||= green ||= 10:12:15 ||= 0-6-13 ||= C Eb^ G ||= C.^m ||= C upminor ||
-The period is needed because "Cv", spoken as "C down", is either a note, or a major chord Cv Ev Gv.
+||= yellow ||= 4:5:6 ||= 0-7-13 ||= C Ev G ||= C.v ||= C downmajor or C dot down ||
--6-13 = C Eb^ G = C.^m = "C upminor"
+||= red ||= 14:18:27 ||= 0-8-13 ||= C E G ||= C ||= C major or C ||
--5-13 = C Eb G = Cm = "C minor"
+For C.v, the period is needed because "Cv", spoken as "C down", is either a note, or a major chord Cv Ev Gv.
-The period isn't needed in the last chord name because there's no ups or downs immediately after the note name.
+The period isn't needed in Cm because there's no ups or downs immediately after the note name.
 -8-13-18 = C E G Bb = C7 = "C seven"
 -7-13-18 = C Ev G Bb = C7(v3) = "C seven, down third"
 -8-13-21 = C E G B = CM7 = "C major seven"
--7-13-20 = C Ev G Bv = C.vM7 = "C downmajor seven" (the down symbol affects both the 3rd and the 7th)
+-7-13-20 = C Ev G Bv = C.vM7 = "C downmajor seven" (the down symbol applies to both the 3rd and the 7th)
--3-13 = C Dv G = Csusv2
+-3-13 = C Dv G = C(v2)
--4-13 = C D G = Csus2
+-4-13 = C D G = C2
--5-13 = C Eb G = Cm
+-9-13 = C F G = C4
--6-13 = C Eb^ G = C.^m
+-10-13 = C F^ G = C(^4)
--7-13 = C Ev G = C.v
--8-13 = C E G = C
--9-13 = C F G = Csus4
--10-13 = C F^ G = Csus^4
 -5-10 = C Eb Gb = Cdim
@@ Line 138: / Line 143: @@
 -5-11-14 = C Eb Gb^ Bbbv = Cdim7(^5,v7)
 -6-11-15 = C Eb^ Gb^ Bbb = Cdim7(^3,^5)
--6-11-16 = C Eb^ Gb^ Bbb^ = C.^dim7 (the up symbol applies to m3, d5 and d7)
+-6-11-16 = C Eb^ Gb^ Bbb^ = C.^dim7(^5) (the up symbol applies to both the 3rd and the 7th)
 -5-13-17 = C Eb G A = Cm6
@@ Line 151: / Line 156: @@
 -5-13-18 = C Eb G Bb = Cm7
 -6-13-19 = C Eb^ G Bb^ = C.^m7
+-8-13-21 = C E G B = CM7
 -7-13-20 = C Ev G Bv = C.vM7
--8-13-21 = C E G B = CM7
 -5-13-16 = C Eb G Av = Cm(v6)
@@ Line 283: / Line 288: @@
 Paul Erlich's "Tibia" in G, with independent ups and downs:
 [[image:Tibia in G for the book-1.png width="800" height="956"]]
 [[image:Tibia in G for the book-2.png width="800" height="889"]]
 =The Decatonic System=
-The decatonic system is an approach of notation based on Paul Erlich's decatonic scales. Unlike typical notation, the decatonic system is based on a scale of 10 tones rather than 7.  This approach requires an entire re-learning of chords, intervals, and notation, but  it allows 22EDO to be notated using only one pair of accidentals, and gives the opportunity to escape a heptatonic thinking pattern
+The decatonic system is an approach of notation based on Paul Erlich's decatonic scales. Unlike typical notation, the decatonic system is based on a scale of 10 tones rather than 7. This approach requires an entire re-learning of chords, intervals, and notation, but it allows 22EDO to be notated using only one pair of accidentals, and gives the opportunity to escape a heptatonic thinking pattern
 ==[[#TOC-Decatonic-Alphabet]]Decatonic Alphabet==
@@ Line 300: / Line 305: @@
 ==Internal links==
 * [[William Lynch's Thoughts on Septimal Harmony and 22 EDO]]
@@ Line 1,244: / Line 1,249: @@
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Chord Names"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Chord Names&lt;/h1&gt;
+Combining ups and downs notation with &lt;a class="wiki_link" href="/Kite%27s%20color%20notation"&gt;color notation&lt;/a&gt;, qualities can be associated with colors (higher prime content):&lt;br /&gt;
- &lt;br /&gt;
-edo chords can be named using ups and downs notation.&lt;br /&gt;
-&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
--8-13 = C E G = C = &amp;quot;C&amp;quot; or &amp;quot;C major&amp;quot;&lt;br /&gt;
+    &lt;tr&gt;
--7-13 = C Ev G = C.v = &amp;quot;C downmajor&amp;quot; or &amp;quot;C dot down&amp;quot;&lt;br /&gt;
+        &lt;th&gt;quality&lt;br /&gt;
-The period is needed because &amp;quot;Cv&amp;quot;, spoken as &amp;quot;C down&amp;quot;, is either a note, or a major chord Cv Ev Gv.&lt;br /&gt;
+&lt;/th&gt;
--6-13 = C Eb^ G = C.^m = &amp;quot;C upminor&amp;quot;&lt;br /&gt;
+        &lt;th&gt;color&lt;br /&gt;
--5-13 = C Eb G = Cm = &amp;quot;C minor&amp;quot;&lt;br /&gt;
+&lt;/th&gt;
-The period isn't needed in the last chord name because there's no ups or downs immediately after the note name.&lt;br /&gt;
+        &lt;th&gt;monzo&lt;br /&gt;
-&lt;br /&gt;
+&lt;/th&gt;
--8-13-18 = C E G Bb = C7 = &amp;quot;C seven&amp;quot;&lt;br /&gt;
+        &lt;th&gt;examples&lt;br /&gt;
--7-13-18 = C Ev G Bb = C7(v3) = &amp;quot;C seven, down third&amp;quot;&lt;br /&gt;
+&lt;/th&gt;
--8-13-21 = C E G B = CM7 = &amp;quot;C major seven&amp;quot;&lt;br /&gt;
+    &lt;/tr&gt;
--7-13-20 = C Ev G Bv = C.vM7 = &amp;quot;C downmajor seven&amp;quot; (the down symbol affects both the 3rd and the 7th)&lt;br /&gt;
+    &lt;tr&gt;
-&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;minor&lt;br /&gt;
--3-13 = C Dv G = Csusv2&lt;br /&gt;
+&lt;/td&gt;
--4-13 = C D G = Csus2&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;blue&lt;br /&gt;
--5-13 = C Eb G = Cm&lt;br /&gt;
+&lt;/td&gt;
--6-13 = C Eb^ G = C.^m&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;{a, b, 0, c}, c = 1&lt;br /&gt;
--7-13 = C Ev G = C.v&lt;br /&gt;
+&lt;/td&gt;
--8-13 = C E G = C&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;7/6, 7/4&lt;br /&gt;
--9-13 = C F G = Csus4&lt;br /&gt;
+&lt;/td&gt;
--10-13 = C F^ G = Csus^4&lt;br /&gt;
+    &lt;/tr&gt;
-&lt;br /&gt;
+    &lt;tr&gt;
--5-10 = C Eb Gb = Cdim&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;&amp;quot;&lt;br /&gt;
--5-11 = C Eb Gb^ = Cdim(^5)&lt;br /&gt;
+&lt;/td&gt;
--5-12 = C Eb Gv = Cm(v5)&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;fourthward white&lt;br /&gt;
-&lt;br /&gt;
+&lt;/td&gt;
--5-10-15 = C Eb Gb Bbb = Cdim7&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;{a, b}, b &amp;lt; -1&lt;br /&gt;
--5-11-14 = C Eb Gb^ Bbbv = Cdim7(^5,v7)&lt;br /&gt;
+&lt;/td&gt;
--6-11-15 = C Eb^ Gb^ Bbb = Cdim7(^3,^5)&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;16/9, 32/27&lt;br /&gt;
--6-11-16 = C Eb^ Gb^ Bbb^ = C.^dim7 (the up symbol applies to m3, d5 and d7)&lt;br /&gt;
+&lt;/td&gt;
--5-13-17 = C Eb G A = Cm6&lt;br /&gt;
+    &lt;/tr&gt;
-&lt;br /&gt;
+    &lt;tr&gt;
-Sometimes doubled ups/downs are unavoidable:&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;upminor&lt;br /&gt;
--6-12-15 = C Eb^ Gv Avv = Cm6(^3,v5,vv6), or C Eb^ Gb^^ Bbb = Cdim7(^3,^^5)&lt;br /&gt;
+&lt;/td&gt;
-&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;green&lt;br /&gt;
--8-13-17 = C E G A = C6&lt;br /&gt;
+&lt;/td&gt;
--8-13-16 = C E G Av = C(v6)&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;{a, b, c}, c = -1&lt;br /&gt;
--7-13-17 = C Ev G A = C6(v3)&lt;br /&gt;
+&lt;/td&gt;
--7-13-16 = C Ev G Av = C.v6 (the down symbol applies to both the 3rd and the 6th)&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;6/5, 9/5&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;downmajor&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;yellow&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;{a, b, c}, c = 1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;5/4, 5/3&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;major&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;fifthward white&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;{a, b}, b &amp;gt; 1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;9/8, 27/16&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;&amp;quot;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;red&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;{a, b, 0, c}, c = -1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;9/7, 12/7&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
 &lt;br /&gt;
--5-13-18 = C Eb G Bb = Cm7&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Chord Names"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Chord Names&lt;/h1&gt;
--6-13-19 = C Eb^ G Bb^ = C.^m7&lt;br /&gt;
+ &lt;br /&gt;
--7-13-20 = C Ev G Bv = C.vM7&lt;br /&gt;
+All 22edo chords can be named using ups and downs notation. Here are the blue, green, yellow and red triads:&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;th&gt;color of the 3rd&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;JI chord&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;notes as edosteps&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;notes of C chord&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;written name&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;spoken name&lt;br /&gt;
+&lt;/th&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;blue&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;6:7:9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;0-5-13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C Eb G&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Cm&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C minor&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;green&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;10:12:15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;0-6-13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C Eb^ G&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C.^m&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C upminor&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;yellow&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;4:5:6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;0-7-13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C Ev G&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C.v&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C downmajor or C dot down&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;red&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;14:18:27&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;0-8-13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C E G&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C major or C&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+For C.v, the period is needed because &amp;quot;Cv&amp;quot;, spoken as &amp;quot;C down&amp;quot;, is either a note, or a major chord Cv Ev Gv.&lt;br /&gt;
+The period isn't needed in Cm because there's no ups or downs immediately after the note name.&lt;br /&gt;
+&lt;br /&gt;
+-8-13-18 = C E G Bb = C7 = &amp;quot;C seven&amp;quot;&lt;br /&gt;
+-7-13-18 = C Ev G Bb = C7(v3) = &amp;quot;C seven, down third&amp;quot;&lt;br /&gt;
+-8-13-21 = C E G B = CM7 = &amp;quot;C major seven&amp;quot;&lt;br /&gt;
+-7-13-20 = C Ev G Bv = C.vM7 = &amp;quot;C downmajor seven&amp;quot; (the down symbol applies to both the 3rd and the 7th)&lt;br /&gt;
+&lt;br /&gt;
+-3-13 = C Dv G = C(v2)&lt;br /&gt;
+-4-13 = C D G = C2&lt;br /&gt;
+-9-13 = C F G = C4&lt;br /&gt;
+-10-13 = C F^ G = C(^4)&lt;br /&gt;
+&lt;br /&gt;
+-5-10 = C Eb Gb = Cdim&lt;br /&gt;
+-5-11 = C Eb Gb^ = Cdim(^5)&lt;br /&gt;
+-5-12 = C Eb Gv = Cm(v5)&lt;br /&gt;
+&lt;br /&gt;
+-5-10-15 = C Eb Gb Bbb = Cdim7&lt;br /&gt;
+-5-11-14 = C Eb Gb^ Bbbv = Cdim7(^5,v7)&lt;br /&gt;
+-6-11-15 = C Eb^ Gb^ Bbb = Cdim7(^3,^5)&lt;br /&gt;
+-6-11-16 = C Eb^ Gb^ Bbb^ = C.^dim7(^5) (the up symbol applies to both the 3rd and the 7th)&lt;br /&gt;
+-5-13-17 = C Eb G A = Cm6&lt;br /&gt;
+&lt;br /&gt;
+Sometimes doubled ups/downs are unavoidable:&lt;br /&gt;
+-6-12-15 = C Eb^ Gv Avv = Cm6(^3,v5,vv6), or C Eb^ Gb^^ Bbb = Cdim7(^3,^^5)&lt;br /&gt;
+&lt;br /&gt;
+-8-13-17 = C E G A = C6&lt;br /&gt;
+-8-13-16 = C E G Av = C(v6)&lt;br /&gt;
+-7-13-17 = C Ev G A = C6(v3)&lt;br /&gt;
+-7-13-16 = C Ev G Av = C.v6 (the down symbol applies to both the 3rd and the 6th)&lt;br /&gt;
+&lt;br /&gt;
+-5-13-18 = C Eb G Bb = Cm7&lt;br /&gt;
+-6-13-19 = C Eb^ G Bb^ = C.^m7&lt;br /&gt;
 -8-13-21 = C E G B = CM7&lt;br /&gt;
+-7-13-20 = C Ev G Bv = C.vM7&lt;br /&gt;
 &lt;br /&gt;
 -5-13-16 = C Eb G Av = Cm(v6)&lt;br /&gt;
@@ Line 1,459: / Line 1,607: @@
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 See also: &lt;a class="wiki_link" href="/22edo%20Solfege"&gt;22edo Solfege&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo%20Tetrachords"&gt;22edo Tetrachords&lt;/a&gt;, &lt;a class="wiki_link" href="/22%20EDO%20Chords"&gt;22 EDO Chords&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo%20Modes"&gt;22edo Modes&lt;/a&gt;&lt;br /&gt;
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 When 22edo is treated as generated by a cycle of its fifths, the naturals F C G D A E B represent a chain of those 13\22 fifths; consequently, the whole tone comes out to four degrees and the apotome (pythagorean sharp/flat) comes out to three degrees. Three pairs of sagittal symbols, dividing that apotome into three parts, are all that is necessary, and offer plenty of enharmonic equivalents:&lt;br /&gt;
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+&lt;!-- ws:start:WikiTextLocalImageRule:1789:&amp;lt;img src=&amp;quot;/file/view/22edo.png/269078624/22edo.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/22edo.png/269078624/22edo.png" alt="22edo.png" title="22edo.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1789 --&gt;&lt;br /&gt;
 This notation is consistent with Sagittal's notation of 5-limit JI harmony: &amp;quot;major&amp;quot; 3rds and 6ths appear as (super)pythagorean intervals flattened by a syntonic comma.&lt;br /&gt;
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 Treating &lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;ups and downs&lt;/a&gt; as &amp;quot;fused&amp;quot; with sharps and flats, and never appearing separately:&lt;br /&gt;
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+&lt;!-- ws:start:WikiTextLocalImageRule:1790:&amp;lt;img src=&amp;quot;/file/view/Tibia%2022edo%20ups%20and%20downs%20guide%201.png/602422384/800x147/Tibia%2022edo%20ups%20and%20downs%20guide%201.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 147px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Tibia%2022edo%20ups%20and%20downs%20guide%201.png/602422384/800x147/Tibia%2022edo%20ups%20and%20downs%20guide%201.png" alt="Tibia 22edo ups and downs guide 1.png" title="Tibia 22edo ups and downs guide 1.png" style="height: 147px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1790 --&gt;&lt;br /&gt;
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 Treating ups and downs as independent of sharps and flats, and sometimes appearing separately:&lt;br /&gt;
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+&lt;!-- ws:start:WikiTextLocalImageRule:1791:&amp;lt;img src=&amp;quot;/file/view/Tibia%2022edo%20ups%20and%20downs%20guide%202.png/602422386/800x150/Tibia%2022edo%20ups%20and%20downs%20guide%202.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 150px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Tibia%2022edo%20ups%20and%20downs%20guide%202.png/602422386/800x150/Tibia%2022edo%20ups%20and%20downs%20guide%202.png" alt="Tibia 22edo ups and downs guide 2.png" title="Tibia 22edo ups and downs guide 2.png" style="height: 150px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1791 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 A D downmajor scale with mandatory accidentals (no key signature), with minimal accidentals (only when needed to override the key signature), and with independent ups and downs.&lt;br /&gt;
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+&lt;!-- ws:start:WikiTextLocalImageRule:1792:&amp;lt;img src=&amp;quot;/file/view/Tibia%2022edo%20guide%20D%20major.png/602422382/800x68/Tibia%2022edo%20guide%20D%20major.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 68px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Tibia%2022edo%20guide%20D%20major.png/602422382/800x68/Tibia%2022edo%20guide%20D%20major.png" alt="Tibia 22edo guide D major.png" title="Tibia 22edo guide D major.png" style="height: 68px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1792 --&gt;&lt;br /&gt;
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 Paul Erlich's &amp;quot;Tibia&amp;quot; in G, with independent ups and downs:&lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:1649:&amp;lt;img src=&amp;quot;/file/view/Tibia%20in%20G%20for%20the%20book-1.png/623289179/800x956/Tibia%20in%20G%20for%20the%20book-1.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 956px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Tibia%20in%20G%20for%20the%20book-1.png/623289179/800x956/Tibia%20in%20G%20for%20the%20book-1.png" alt="Tibia in G for the book-1.png" title="Tibia in G for the book-1.png" style="height: 956px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1649 --&gt; &lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:1793:&amp;lt;img src=&amp;quot;/file/view/Tibia%20in%20G%20for%20the%20book-1.png/623289179/800x956/Tibia%20in%20G%20for%20the%20book-1.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 956px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Tibia%20in%20G%20for%20the%20book-1.png/623289179/800x956/Tibia%20in%20G%20for%20the%20book-1.png" alt="Tibia in G for the book-1.png" title="Tibia in G for the book-1.png" style="height: 956px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1793 --&gt;&lt;br /&gt;
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+&lt;!-- ws:start:WikiTextLocalImageRule:1794:&amp;lt;img src=&amp;quot;/file/view/Tibia%20in%20G%20for%20the%20book-2.png/623289195/800x889/Tibia%20in%20G%20for%20the%20book-2.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 889px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Tibia%20in%20G%20for%20the%20book-2.png/623289195/800x889/Tibia%20in%20G%20for%20the%20book-2.png" alt="Tibia in G for the book-2.png" title="Tibia in G for the book-2.png" style="height: 889px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1794 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="The Decatonic System"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;The Decatonic System&lt;/h1&gt;
-  The decatonic system is an approach of notation based on Paul Erlich's decatonic scales. Unlike typical notation, the decatonic system is based on a scale of 10 tones rather than 7.  This approach requires an entire re-learning of chords, intervals, and notation, but  it allows 22EDO to be notated using only one pair of accidentals, and gives the opportunity to escape a heptatonic thinking pattern&lt;br /&gt;
+  The decatonic system is an approach of notation based on Paul Erlich's decatonic scales. Unlike typical notation, the decatonic system is based on a scale of 10 tones rather than 7. This approach requires an entire re-learning of chords, intervals, and notation, but it allows 22EDO to be notated using only one pair of accidentals, and gives the opportunity to escape a heptatonic thinking pattern&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="The Decatonic System-Decatonic Alphabet"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:55:&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@@TOC-Decatonic-Alphabet&amp;quot; title=&amp;quot;Anchor: TOC-Decatonic-Alphabet&amp;quot;/&amp;gt; --&gt;&lt;a name="TOC-Decatonic-Alphabet"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:55 --&gt;Decatonic Alphabet&lt;/h2&gt;
@@ Line 2,053: / Line 2,201: @@
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 &lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="The Decatonic System-Internal links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Internal links&lt;/h2&gt;
-&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/William%20Lynch%27s%20Thoughts%20on%20Septimal%20Harmony%20and%2022%20EDO"&gt;William Lynch's Thoughts on Septimal Harmony and 22 EDO&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+ &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/William%20Lynch%27s%20Thoughts%20on%20Septimal%20Harmony%20and%2022%20EDO"&gt;William Lynch's Thoughts on Septimal Harmony and 22 EDO&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="The Decatonic System-External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;External links&lt;/h2&gt;
   &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/erlich-decatonic.pdf" rel="nofollow"&gt;Erlich, Paul, ''Tuning, Tonality, and Twenty-Two Tone Temperament''&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://porcupinemusic.weebly.com/" rel="nofollow"&gt;&amp;quot;Porcupine Music&amp;quot; - Website Focused on the Development of 22 EDO music &lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;