22edo: Difference between revisions

Line 1:

<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:~~vaisvil~~|~~vaisvil~~]] and made on <tt>2016-09-~~02 23~~:03:30 UTC</tt>.

: This revision was by author [[User:hearneg|hearneg]] and made on <tt>2016-09-08 11:42:40 UTC</tt>.

: The original revision id was <tt>~~590991010~~</tt>.

: The original revision id was <tt>591425126</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.

Line 29:

Ratios* ||

|| 0 || Natural Unison, 1 || 0 ||= 1/1 ||

|| 1 || s-minor second, sm2 || 54.55

|| 1 || s-minor second, sm2 || 54.55 ||= 33/32, 34/33, 32/31 ||

~~16°21'49"~~ ||= 33/32, 34/33, 32/31 ||

|| 2 || p-diminished second, pd2 || 109.09 ||= 18/17, 17/16, 16/15, 15/14 ||

|| 2 || p-diminished second, pd2 || 109.09

|| 3 || p-minor second, pm2 || 163.64 ||= 11/10, 10/9, 32/29 ||

~~32°43'38"~~ ||= 18/17, 17/16, 16/15, 15/14 ||

|| 4 || (s/p) Major second, M2 || 218.18 ||= 9/8, 8/7, 17/15 ||

|| 3 || p-minor second, pm2 || 163.64

|| 5 || s-minor third, sm3 || 272.73 ||= [[7_6|7/6]], [[20_17|20/17]] ||

~~49°5'27"~~ ||= 11/10, 10/9, 32/29 ||

|| 6 || p-minor third, pm3 || 327.27 ||= 6/5, 17/14, 11/9, 29/24 ||

|| 4 || (s/p) Major second, M2 || 218.18

|| 7 || p-Major third, pM3 || 381.82 ||= 5/4 ||

~~65°27'16"~~ ||= 9/8, 8/7, 17/15 ||

|| 8 || s-Major third, sM3 || 436.36 ||= 9/7, 14/11, 22/17 ||

|| 5 || s-minor third, sm3 || 272.73

|| 9 || Natural Fourth, 4, N4 || 490.91 ||= 4/3 ||

~~81°49'5"~~ ||= [[7_6|7/6]], [[20_17|20/17]] ||

|| 6 || p-minor third, pm3 || 327.27

~~98°10'55"~~ ||= 6/5, 17/14, 11/9, 29/24 ||

|| 7 || p-Major third, pM3 || 381.82

~~114°31'44"~~ ||= 5/4 ||

|| 8 || s-Major third, sM3 || 436.36

~~130°54'33"~~ ||= 9/7, 14/11, 22/17 ||

|| 9 || Natural Fourth, 4, N4 || 490.91

~~147°16'22"~~ ||= 4/3 ||

|| 10 || p-Major Fourth, pM4

s-dim fifth || 545.45

s-dim fifth || 545.45 ||= 11/8, 15/11 ||

~~163°38'11"~~ ||= 11/8, 15/11 ||

|| 11 || Augmented Fourth, A4,

Half-Octave, HO || 600

Half-Octave, HO || 600 ||= 7/5, 10/7, 17/12, 24/17 ||

~~180°~~ ||= 7/5, 10/7, 17/12, 24/17 ||

|| 12 || p-minor Fifth, pm5

s-aug fourth || 654.55

s-aug fourth || 654.55 ||= 16/11, 22/15 ||

~~196°21'49"~~ ||= 16/11, 22/15 ||

|| 13 || Natural Fifth, 5, N5 || 709.09 ||= 3/2 ||

|| 13 || Natural Fifth, 5, N5 || 709.09

|| 14 || s-minor sixth, sm6 || 763.64 ||= 11/7, 14/9, 17/11 ||

~~212°43'38"~~ ||= 3/2 ||

|| 15 || p-minor sixth, pm6 || 818.18 ||= 8/5 ||

|| 14 || s-minor sixth, sm6 || 763.64

|| 16 || p-Major sixth, pM6 || 872.73 ||= 5/3, 18/11, 28/17 ||

~~229°5'27"~~ ||= 11/7, 14/9, 17/11 ||

|| 17 || s-Major sixth, sM6 || 927.27 ||= [[12_7|12/7]], [[17_10|17/10]] ||

|| 15 || p-minor sixth, pm6 || 818.18

|| 18 || (s/p) minor seventh, m7 || 981.82 ||= 7/4, 16/9, 30/17 ||

~~245°16'22"~~ ||= 8/5 ||

|| 19 || p-Major seventh, pM7 || 1036.36 ||= 20/11, 9/5, 29/16 ||

|| 16 || p-Major sixth, pM6 || 872.73

|| 20 || p-Augmented Seventh || 1090.91 ||= 15/8, 32/17, 17/9, 28/15 ||

~~261°49'5"~~ ||= 5/3, 18/11, 28/17 ||

|| 21 || s-Major Seventh, sM7 || 1145.45 ||= 33/17, 64/33, 31/16 ||

|| 17 || s-Major sixth, sM6 || 927.27

|| 22 || Octave, 8 || 1200 ||= 2/1 ||

~~278°10'55"~~ ||= [[12_7|12/7]], [[17_10|17/10]] ||

|| 18 || (s/p) minor seventh, m7 || 981.82

~~294°31'44"~~ ||= 7/4, 16/9, 30/17 ||

|| 19 || p-Major seventh, pM7 || 1036.36

~~310°54'33"~~ ||= 20/11, 9/5, 29/16 ||

|| 20 || p-Augmented Seventh || 1090.91

~~327°16'22"~~ ||= 15/8, 32/17, 17/9, 28/15 ||

|| 21 || s-Major Seventh, sM7 || 1145.45

~~343°38'11"~~ ||= 33/17, 64/33, 31/16 ||

|| 22 || Octave, 8 || 1200

~~360°~~ ||= 2/1 ||

22edo intervals can also be notated using [[Ups and Downs Notation|ups and downs]]: The keyboard runs C * * * D * * * E F * * * G * * * A * * * B C.

Line 274:

Line 252:

=The Decatonic System=

The decatonic system is an approach of notation based on Paul Erlich's decatonic scales. Unlike typical notation, the decatonic system bases music into a 10 tone scale rather than 7.

The decatonic system is an approach of notation based on Paul Erlich's decatonic scales. Unlike typical notation, the decatonic system bases music into a 10 tone scale rather than 7.

This approach requires an entire re-learning of chords, intervals, and notation but the advantage is that it allows 22 EDO to be notated using only one pair of accidentals, as well asgives the opportunity to escape a heptatonic thinking pattern.

This approach requires an entire re-learning of chords, intervals, and notation but the advantage is that it allows 22 EDO to be notated using only one pair of accidentals, as well asgives the opportunity to escape a heptatonic thinking pattern.

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

The system is based on two chains of fifths. One represented by latin letters, the other greek. The two chains can be looked at as two juxtaposed pentatonic scales.

The system is based on two chains of fifths. One represented by latin letters, the other greek. The two chains can be looked at as two juxtaposed pentatonic scales.

Chain 1: C G D A EChain 2: γ δ α ε β

Chain 1: C G D A EChain 2: γ δ α ε β

The alphabet is ascending order: C δ D ε E γ G α A β C

The alphabet is ascending order: C δ D ε E γ G α A β C

In this alphabet, a chain of fifths is preserved because equivalent greek letters also represent fifths if they are the same as their latin counter parts. For example G D is a fifth as well as γ δ.

In this alphabet, a chain of fifths is preserved because equivalent greek letters also represent fifths if they are the same as their latin counter parts. For example G D is a fifth as well as γ δ.

= =

|| **Mode Name** || Notes || Step Structure ||

Line 297:

Line 275:

|| Yesod || || ||

|| Malkuth || || ||

==External links==

Line 425:

Line 403:

</td>

<td>54.55

~~16°21'49&quot; ~~

</td>

<td style="text-align: center;">33/32, 34/33, 32/31

Line 436:

Line 413:

</td>

<td>109.09

~~32°43'38&quot; ~~

</td>

<td style="text-align: center;">18/17, 17/16, 16/15, 15/14

Line 447:

Line 423:

</td>

<td>163.64

~~49°5'27&quot; ~~

</td>

<td style="text-align: center;">11/10, 10/9, 32/29

Line 458:

Line 433:

</td>

<td>218.18

~~65°27'16&quot; ~~

</td>

<td style="text-align: center;">9/8, 8/7, 17/15

Line 469:

Line 443:

</td>

<td>272.73

~~81°49'5&quot; ~~

</td>

Line 480:

Line 453:

</td>

<td>327.27

~~98°10'55&quot; ~~

</td>

<td style="text-align: center;">6/5, 17/14, 11/9, 29/24

Line 491:

Line 463:

</td>

<td>381.82

~~114°31'44&quot; ~~

</td>

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

Line 502:

Line 473:

</td>

<td>436.36

~~130°54'33&quot; ~~

</td>

<td style="text-align: center;">9/7, 14/11, 22/17

Line 513:

Line 483:

</td>

<td>490.91

~~147°16'22&quot; ~~

</td>

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

Line 525:

Line 494:

</td>

<td>545.45

~~163°38'11&quot; ~~

</td>

<td style="text-align: center;">11/8, 15/11

Line 537:

Line 505:

</td>

<td>600

~~180° ~~

</td>

<td style="text-align: center;">7/5, 10/7, 17/12, 24/17

Line 549:

Line 516:

</td>

<td>654.55

~~196°21'49&quot; ~~

</td>

<td style="text-align: center;">16/11, 22/15

Line 560:

Line 526:

</td>

<td>709.09

~~212°43'38&quot; ~~

</td>

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

Line 571:

Line 536:

</td>

<td>763.64

~~229°5'27&quot; ~~

</td>

<td style="text-align: center;">11/7, 14/9, 17/11

Line 582:

Line 546:

</td>

<td>818.18

~~245°16'22&quot; ~~

</td>

<td style="text-align: center;">8/5

Line 593:

Line 556:

</td>

<td>872.73

~~261°49'5&quot; ~~

</td>

<td style="text-align: center;">5/3, 18/11, 28/17

Line 604:

Line 566:

</td>

<td>927.27

~~278°10'55&quot; ~~

</td>

Line 615:

Line 576:

</td>

<td>981.82

~~294°31'44&quot; ~~

</td>

<td style="text-align: center;">7/4, 16/9, 30/17

Line 626:

Line 586:

</td>

<td>1036.36

~~310°54'33&quot; ~~

</td>

<td style="text-align: center;">20/11, 9/5, 29/16

Line 637:

Line 596:

</td>

<td>1090.91

~~327°16'22&quot; ~~

</td>

<td style="text-align: center;">15/8, 32/17, 17/9, 28/15

Line 648:

Line 606:

</td>

<td>1145.45

~~343°38'11&quot; ~~

</td>

<td style="text-align: center;">33/17, 64/33, 31/16

Line 659:

Line 616:

</td>

<td>1200

~~360° ~~

</td>

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

Line 2,285:

Line 2,241:

<h1 id="toc12"><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 bases music into a 10 tone scale rather than 7.

The decatonic system is an approach of notation based on Paul Erlich's decatonic scales. Unlike typical notation, the decatonic system bases music into a 10 tone scale rather than 7.

This approach requires an entire re-learning of chords, intervals, and notation but the advantage is that it allows 22 EDO to be notated using only one pair of accidentals, as well asgives the opportunity to escape a heptatonic thinking pattern.

This approach requires an entire re-learning of chords, intervals, and notation but the advantage is that it allows 22 EDO to be notated using only one pair of accidentals, as well asgives the opportunity to escape a heptatonic thinking pattern.

<h2 id="toc13"><a name="The Decatonic System-Decatonic Alphabet"></a><a name="TOC-Decatonic-Alphabet"></a>Decatonic Alphabet</h2>

The system is based on two chains of fifths. One represented by latin letters, the other greek. The two chains can be looked at as two juxtaposed pentatonic scales.

The system is based on two chains of fifths. One represented by latin letters, the other greek. The two chains can be looked at as two juxtaposed pentatonic scales.

Chain 1: C G D A EChain 2: γ δ α ε β

Chain 1: C G D A EChain 2: γ δ α ε β

The alphabet is ascending order: C δ D ε E γ G α A β C

The alphabet is ascending order: C δ D ε E γ G α A β C

In this alphabet, a chain of fifths is preserved because equivalent greek letters also represent fifths if they are the same as their latin counter parts. For example G D is a fifth as well as γ δ.

In this alphabet, a chain of fifths is preserved because equivalent greek letters also represent fifths if they are the same as their latin counter parts. For example G D is a fifth as well as γ δ.

<h1 id="toc14"> </h1>

Line 2,390:

Line 2,346:

</table>

<h2 id="toc15"><a name="The Decatonic System-External links"></a>External links</h2>

@@ 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:vaisvil|vaisvil]] and made on <tt>2016-09-02 23:03:30 UTC</tt>.<br>
+: This revision was by author [[User:hearneg|hearneg]] and made on <tt>2016-09-08 11:42:40 UTC</tt>.<br>
-: The original revision id was <tt>590991010</tt>.<br>
+: The original revision id was <tt>591425126</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 29: / Line 29: @@
 Ratios* ||
 || 0 || Natural Unison, 1 || 0 ||= 1/1 ||
-|| 1 || s-minor second, sm2 || 54.55
+|| 1 || s-minor second, sm2 || 54.55 ||= 33/32, 34/33, 32/31 ||
-°&lt;span style="background-color: #ffffff;"&gt;21'49"&lt;/span&gt; ||= 33/32, 34/33, 32/31 ||
+|| 2 || p-diminished second, pd2 || 109.09 ||= 18/17, 17/16, 16/15, 15/14 ||
-|| 2 || p-diminished second, pd2 || 109.09
+|| 3 || p-minor second, pm2 || 163.64 ||= 11/10, 10/9, 32/29 ||
-&lt;span style="background-color: #ffffff;"&gt;32°43'38"&lt;/span&gt; ||= 18/17, 17/16, 16/15, 15/14 ||
+|| 4 || (s/p) Major second, M2 || 218.18 ||= 9/8, 8/7, 17/15 ||
-|| 3 || p-minor second, pm2 || 163.64
+|| 5 || s-minor third, sm3 || 272.73 ||= [[7_6|7/6]], [[20_17|20/17]] ||
-°5'27" ||= 11/10, 10/9, 32/29 ||
+|| 6 || p-minor third, pm3 || 327.27 ||= 6/5, 17/14, 11/9, 29/24 ||
-|| 4 || (s/p) Major second, M2 || 218.18
+|| 7 || p-Major third, pM3 || 381.82 ||= 5/4 ||
-&lt;span style="background-color: #ffffff;"&gt;65°27'16"&lt;/span&gt; ||= 9/8, 8/7, 17/15 ||
+|| 8 || s-Major third, sM3 || 436.36 ||= 9/7, 14/11, 22/17 ||
-|| 5 || s-minor third, sm3 || 272.73
+|| 9 || Natural Fourth, 4, N4 || 490.91 ||= 4/3 ||
-°&lt;span style="background-color: #ffffff;"&gt;49'5"&lt;/span&gt; ||= [[7_6|7/6]], [[20_17|20/17]] ||
-|| 6 || p-minor third, pm3 || 327.27
-&lt;span style="background-color: #ffffff;"&gt;98°10'55"&lt;/span&gt; ||= 6/5, 17/14, 11/9, 29/24 ||
-|| 7 || p-Major third, pM3 || 381.82
-°&lt;span style="background-color: #ffffff;"&gt;31'44"&lt;/span&gt; ||= 5/4 ||
-|| 8 || s-Major third, sM3 || 436.36
-&lt;span style="background-color: #ffffff;"&gt;130°54'33"&lt;/span&gt; ||= 9/7, 14/11, 22/17 ||
-|| 9 || Natural Fourth, 4, N4 || 490.91
-°&lt;span style="background-color: #ffffff;"&gt;16'22"&lt;/span&gt; ||= 4/3 ||
 || 10 || p-Major Fourth, pM4
-s-dim fifth || 545.45
+s-dim fifth || 545.45 ||= 11/8, 15/11 ||
-&lt;span style="background-color: #ffffff;"&gt;163°38'11"&lt;/span&gt; ||= 11/8, 15/11 ||
 || 11 || Augmented Fourth, A4,
-Half-Octave, HO || 600
+Half-Octave, HO || 600 ||= 7/5, 10/7, 17/12, 24/17 ||
-° ||= 7/5, 10/7, 17/12, 24/17 ||
 || 12 || p-minor Fifth, pm5
-s-aug fourth || 654.55
+s-aug fourth || 654.55 ||= 16/11, 22/15 ||
-&lt;span style="background-color: #ffffff;"&gt;196°21'49"&lt;/span&gt; ||= 16/11, 22/15 ||
+|| 13 || Natural Fifth, 5, N5 || 709.09 ||= 3/2 ||
-|| 13 || Natural Fifth, 5, N5 || 709.09
+|| 14 || s-minor sixth, sm6 || 763.64 ||= 11/7, 14/9, 17/11 ||
-°&lt;span style="background-color: #ffffff;"&gt;43'38"&lt;/span&gt; ||= 3/2 ||
+|| 15 || p-minor sixth, pm6 || 818.18 ||= 8/5 ||
-|| 14 || s-minor sixth, sm6 || 763.64
+|| 16 || p-Major sixth, pM6 || 872.73 ||= 5/3, 18/11, 28/17 ||
-&lt;span style="background-color: #ffffff;"&gt;229°5'27"&lt;/span&gt; ||= 11/7, 14/9, 17/11 ||
+|| 17 || s-Major sixth, sM6 || 927.27 ||= [[12_7|12/7]], [[17_10|17/10]] ||
-|| 15 || p-minor sixth, pm6 || 818.18
+|| 18 || (s/p) minor seventh, m7 || 981.82 ||= 7/4, 16/9, 30/17 ||
-°&lt;span style="background-color: #ffffff;"&gt;16'22"&lt;/span&gt; ||= 8/5 ||
+|| 19 || p-Major seventh, pM7 || 1036.36 ||= 20/11, 9/5, 29/16 ||
-|| 16 || p-Major sixth, pM6 || 872.73
+|| 20 || p-Augmented Seventh || 1090.91 ||= 15/8, 32/17, 17/9, 28/15 ||
-&lt;span style="background-color: #ffffff;"&gt;261°49'5"&lt;/span&gt; ||= 5/3, 18/11, 28/17 ||
+|| 21 || s-Major Seventh, sM7 || 1145.45 ||= 33/17, 64/33, 31/16 ||
-|| 17 || s-Major sixth, sM6 || 927.27
+|| 22 || Octave, 8 || 1200 ||= 2/1 ||
-°&lt;span style="background-color: #ffffff;"&gt;10'55"&lt;/span&gt; ||= [[12_7|12/7]], [[17_10|17/10]] ||
-|| 18 || (s/p) minor seventh, m7 || 981.82
-&lt;span style="background-color: #ffffff;"&gt;294°31'44"&lt;/span&gt; ||= 7/4, 16/9, 30/17 ||
-|| 19 || p-Major seventh, pM7 || 1036.36
-°&lt;span style="background-color: #ffffff;"&gt;54'33"&lt;/span&gt; ||= 20/11, 9/5, 29/16 ||
-|| 20 || p-Augmented Seventh || 1090.91
-&lt;span style="background-color: #ffffff;"&gt;327°16'22"&lt;/span&gt; ||= 15/8, 32/17, 17/9, 28/15 ||
-|| 21 || s-Major Seventh, sM7 || 1145.45
-°&lt;span style="background-color: #ffffff;"&gt;38'11"&lt;/span&gt; ||= 33/17, 64/33, 31/16 ||
-|| 22 || Octave, 8 || 1200
-° ||= 2/1 ||
 edo intervals can also be notated using [[Ups and Downs Notation|ups and downs]]: The keyboard runs C * * * D * * * E F * * * G * * * A * * * B C.
@@ Line 274: / Line 252: @@
 =The Decatonic System=
-&lt;span style="background-color: #ffffff; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;The decatonic system is an approach of notation based on Paul Erlich's decatonic scales. Unlike typical notation, the decatonic system bases music into a 10 tone scale rather than 7. &lt;/span&gt;
+&lt;span style="background-color: #ffffff; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;The decatonic system is an approach of notation based on Paul Erlich's decatonic scales. Unlike typical notation, the decatonic system bases music into a 10 tone scale rather than 7. &lt;/span&gt;
-&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;This approach requires an entire re-learning of chords, intervals, and notation but the advantage is that it allows 22 EDO to be notated using only one pair of accidentals, as well as&lt;/span&gt;&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;gives the opportunity to escape a heptatonic thinking pattern.&lt;/span&gt;
+&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;This approach requires an entire re-learning of chords, intervals, and notation but the advantage is that it allows 22 EDO to be notated using only one pair of accidentals, as well as&lt;/span&gt;&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;gives the opportunity to escape a heptatonic thinking pattern.&lt;/span&gt;
-&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;
+&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;
 ==[[#TOC-Decatonic-Alphabet]]Decatonic Alphabet==
-&lt;/span&gt;&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;The system is based on two chains of fifths. One represented by latin letters, the other greek. The two chains can be looked at as two juxtaposed pentatonic scales.&lt;/span&gt;
+&lt;/span&gt;&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;The system is based on two chains of fifths. One represented by latin letters, the other greek. The two chains can be looked at as two juxtaposed pentatonic scales.&lt;/span&gt;
-&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;Chain 1: C G D A E&lt;/span&gt;&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;Chain 2: &lt;span style="background-color: transparent; color: #141823; font-family: helvetica,arial,sans-serif; font-size: 14px;"&gt;γ δ α ε β &lt;/span&gt;&lt;/span&gt;
+&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;Chain 1: C G D A E&lt;/span&gt;&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;Chain 2: &lt;span style="background-color: transparent; color: #141823; font-family: helvetica,arial,sans-serif; font-size: 14px;"&gt;γ δ α ε β &lt;/span&gt;&lt;/span&gt;
-&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;The alphabet is ascending order: C&lt;span style="font-family: helvetica,arial,sans-serif; font-size: 12px;"&gt; δ D ε E γ G α A β C &lt;/span&gt;&lt;/span&gt;&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;
+&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;The alphabet is ascending order: C&lt;span style="font-family: helvetica,arial,sans-serif; font-size: 12px;"&gt; δ D ε E γ G α A β C &lt;/span&gt;&lt;/span&gt;&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;
-&lt;/span&gt;&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;&lt;span style="font-family: helvetica,arial,sans-serif; font-size: 12px;"&gt;In this alphabet, a chain of fifths is preserved because equivalent greek letters also represent fifths if they are the same as their latin counter parts. For example G D is a fifth as well as &lt;/span&gt;&lt;span style="color: #141823; font-family: helvetica,arial,sans-serif; font-size: 14px;"&gt;γ δ. &lt;/span&gt;&lt;/span&gt;
+&lt;/span&gt;&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;&lt;span style="font-family: helvetica,arial,sans-serif; font-size: 12px;"&gt;In this alphabet, a chain of fifths is preserved because equivalent greek letters also represent fifths if they are the same as their latin counter parts. For example G D is a fifth as well as &lt;/span&gt;&lt;span style="color: #141823; font-family: helvetica,arial,sans-serif; font-size: 14px;"&gt;γ δ. &lt;/span&gt;&lt;/span&gt;
 = =
 || **Mode Name** || Notes || Step Structure ||
@@ Line 297: / Line 275: @@
 || &lt;span style="background-color: #ffffff; color: #141823; font-family: helvetica,arial,sans-serif; font-size: 14px;"&gt;Yesod&lt;/span&gt; ||   ||   ||
 || &lt;span style="background-color: #ffffff; color: #141823; font-family: helvetica,arial,sans-serif; font-size: 14px;"&gt;Malkuth&lt;/span&gt; ||   ||   ||
-&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;
+&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;
 &lt;/span&gt;
 ==External links==
@@ Line 425: / Line 403: @@
 &lt;/td&gt;
          &lt;td&gt;54.55&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;21'49&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;33/32, 34/33, 32/31&lt;br /&gt;
@@ Line 436: / Line 413: @@
 &lt;/td&gt;
          &lt;td&gt;109.09&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;32°43'38&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;18/17, 17/16, 16/15, 15/14&lt;br /&gt;
@@ Line 447: / Line 423: @@
 &lt;/td&gt;
          &lt;td&gt;163.64&lt;br /&gt;
-°5'27&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/10, 10/9, 32/29&lt;br /&gt;
@@ Line 458: / Line 433: @@
 &lt;/td&gt;
          &lt;td&gt;218.18&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;65°27'16&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;9/8, 8/7, 17/15&lt;br /&gt;
@@ Line 469: / Line 443: @@
 &lt;/td&gt;
          &lt;td&gt;272.73&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;49'5&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;, &lt;a class="wiki_link" href="/20_17"&gt;20/17&lt;/a&gt;&lt;br /&gt;
@@ Line 480: / Line 453: @@
 &lt;/td&gt;
          &lt;td&gt;327.27&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;98°10'55&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;6/5, 17/14, 11/9, 29/24&lt;br /&gt;
@@ Line 491: / Line 463: @@
 &lt;/td&gt;
          &lt;td&gt;381.82&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;31'44&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;5/4&lt;br /&gt;
@@ Line 502: / Line 473: @@
 &lt;/td&gt;
          &lt;td&gt;436.36&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;130°54'33&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;9/7, 14/11, 22/17&lt;br /&gt;
@@ Line 513: / Line 483: @@
 &lt;/td&gt;
          &lt;td&gt;490.91&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;16'22&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;4/3&lt;br /&gt;
@@ Line 525: / Line 494: @@
 &lt;/td&gt;
          &lt;td&gt;545.45&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;163°38'11&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/8, 15/11&lt;br /&gt;
@@ Line 537: / Line 505: @@
 &lt;/td&gt;
          &lt;td&gt;600&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7/5, 10/7, 17/12, 24/17&lt;br /&gt;
@@ Line 549: / Line 516: @@
 &lt;/td&gt;
          &lt;td&gt;654.55&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;196°21'49&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;16/11, 22/15&lt;br /&gt;
@@ Line 560: / Line 526: @@
 &lt;/td&gt;
          &lt;td&gt;709.09&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;43'38&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;3/2&lt;br /&gt;
@@ Line 571: / Line 536: @@
 &lt;/td&gt;
          &lt;td&gt;763.64&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;229°5'27&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/7, 14/9, 17/11&lt;br /&gt;
@@ Line 582: / Line 546: @@
 &lt;/td&gt;
          &lt;td&gt;818.18&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;16'22&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;8/5&lt;br /&gt;
@@ Line 593: / Line 556: @@
 &lt;/td&gt;
          &lt;td&gt;872.73&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;261°49'5&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;5/3, 18/11, 28/17&lt;br /&gt;
@@ Line 604: / Line 566: @@
 &lt;/td&gt;
          &lt;td&gt;927.27&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;10'55&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/12_7"&gt;12/7&lt;/a&gt;, &lt;a class="wiki_link" href="/17_10"&gt;17/10&lt;/a&gt;&lt;br /&gt;
@@ Line 615: / Line 576: @@
 &lt;/td&gt;
          &lt;td&gt;981.82&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;294°31'44&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7/4, 16/9, 30/17&lt;br /&gt;
@@ Line 626: / Line 586: @@
 &lt;/td&gt;
          &lt;td&gt;1036.36&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;54'33&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;20/11, 9/5, 29/16&lt;br /&gt;
@@ Line 637: / Line 596: @@
 &lt;/td&gt;
          &lt;td&gt;1090.91&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;327°16'22&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;15/8, 32/17, 17/9, 28/15&lt;br /&gt;
@@ Line 648: / Line 606: @@
 &lt;/td&gt;
          &lt;td&gt;1145.45&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;38'11&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;33/17, 64/33, 31/16&lt;br /&gt;
@@ Line 659: / Line 616: @@
 &lt;/td&gt;
          &lt;td&gt;1200&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;2/1&lt;br /&gt;
@@ Line 2,285: / Line 2,241: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="The Decatonic System"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;The Decatonic System&lt;/h1&gt;
-  &lt;span style="background-color: #ffffff; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;The decatonic system is an approach of notation based on Paul Erlich's decatonic scales. Unlike typical notation, the decatonic system bases music into a 10 tone scale rather than 7. &lt;/span&gt;&lt;br /&gt;
+  &lt;span style="background-color: #ffffff; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;The decatonic system is an approach of notation based on Paul Erlich's decatonic scales. Unlike typical notation, the decatonic system bases music into a 10 tone scale rather than 7. &lt;/span&gt;&lt;br /&gt;
-&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;This approach requires an entire re-learning of chords, intervals, and notation but the advantage is that it allows 22 EDO to be notated using only one pair of accidentals, as well as&lt;/span&gt;&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;gives the opportunity to escape a heptatonic thinking pattern.&lt;/span&gt;&lt;br /&gt;
+&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;This approach requires an entire re-learning of chords, intervals, and notation but the advantage is that it allows 22 EDO to be notated using only one pair of accidentals, as well as&lt;/span&gt;&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;gives the opportunity to escape a heptatonic thinking pattern.&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;&lt;br /&gt;
+&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="The Decatonic System-Decatonic Alphabet"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:58:&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:58 --&gt;Decatonic Alphabet&lt;/h2&gt;
-  &lt;/span&gt;&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;The system is based on two chains of fifths. One represented by latin letters, the other greek. The two chains can be looked at as two juxtaposed pentatonic scales.&lt;/span&gt;&lt;br /&gt;
+  &lt;/span&gt;&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;The system is based on two chains of fifths. One represented by latin letters, the other greek. The two chains can be looked at as two juxtaposed pentatonic scales.&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;Chain 1: C G D A E&lt;/span&gt;&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;Chain 2: &lt;span style="background-color: transparent; color: #141823; font-family: helvetica,arial,sans-serif; font-size: 14px;"&gt;γ δ α ε β &lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;Chain 1: C G D A E&lt;/span&gt;&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;Chain 2: &lt;span style="background-color: transparent; color: #141823; font-family: helvetica,arial,sans-serif; font-size: 14px;"&gt;γ δ α ε β &lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;The alphabet is ascending order: C&lt;span style="font-family: helvetica,arial,sans-serif; font-size: 12px;"&gt; δ D ε E γ G α A β C &lt;/span&gt;&lt;/span&gt;&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;&lt;br /&gt;
+&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;The alphabet is ascending order: C&lt;span style="font-family: helvetica,arial,sans-serif; font-size: 12px;"&gt; δ D ε E γ G α A β C &lt;/span&gt;&lt;/span&gt;&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;&lt;br /&gt;
-&lt;/span&gt;&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;&lt;span style="font-family: helvetica,arial,sans-serif; font-size: 12px;"&gt;In this alphabet, a chain of fifths is preserved because equivalent greek letters also represent fifths if they are the same as their latin counter parts. For example G D is a fifth as well as &lt;/span&gt;&lt;span style="color: #141823; font-family: helvetica,arial,sans-serif; font-size: 14px;"&gt;γ δ. &lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;/span&gt;&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;&lt;span style="font-family: helvetica,arial,sans-serif; font-size: 12px;"&gt;In this alphabet, a chain of fifths is preserved because equivalent greek letters also represent fifths if they are the same as their latin counter parts. For example G D is a fifth as well as &lt;/span&gt;&lt;span style="color: #141823; font-family: helvetica,arial,sans-serif; font-size: 14px;"&gt;γ δ. &lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt; &lt;/h1&gt;
@@ Line 2,390: / Line 2,346: @@
 &lt;/table&gt;
-&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.3333px;"&gt;&lt;br /&gt;
+&lt;span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"&gt;&lt;br /&gt;
 &lt;/span&gt;&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="The Decatonic System-External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;External links&lt;/h2&gt;