Kite's ups and downs notation: 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>2015-09-03 17:42:02 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2015-09-03 18:26:04 UTC</tt>.

: The original revision id was <tt>~~558211375~~</tt>.

: The original revision id was <tt>558214783</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.

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=__**Summary of EDO notation**__=

~~There~~ are five EDO categories, based on the size of the fifth:

Besides the trivial EDOs, 1, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO, there are five EDO categories, based on the size of the fifth:

"Fifth-less" EDOs (8, 11, 13 and 18)

Fourthward EDOs (9, 16 and 23)

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Pentatonic EDOs (5, 10, 15, 20, 25 and 30)

"Sweet" EDOs (all others)

The first two categories never use ups and downs, the next two always do (except for 5edo and 7edo). The ~~last~~ may or may not.

The first two categories never use ups and downs, the next two always do (except for 5edo and 7edo). The sweet EDOs may or may not.

To summarize an EDO, a scale fragment from C to D is shown, including C# and Db. The C-C# interval is the augmented unison, and if they are not adjacent, ups and downs are required.The C-Db interval is the minor 2nd

The C-D interval is the major 2nd (P2 for perfect EDOs, m2 for fourthward EDOs).

===__**"Fifth-less" EDOs (8, 11, 13 and 18)**__===

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F# - C# - G# - D# - A# - E# - B# - F - C - G - D - A - E - B - Fb - Cb - Gb - Db - Ab - Eb - Bb - Fbb etc.

**__9edo__:** C/Db C#/D

D E * F G A B * C D

D - E - E#/Fb - F - G - A - B - B#/Cb - C - D

P1 - m2 - M2/m3 - M3 - P4 - P5 - m6 - M6/m7 - M7 - P8

**__16edo__:** C C#/Db D

D * E * * F * G * A * B * * C * D

D - D#/Eb - E - E# - Fb - F F#/Gb - G - G#/Ab - A - A#/Bb - B - B# - Cb - C - C#/Db - D

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Because everything is perfect, the quality can be omitted: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8

**__14edo__:** 2 keys per sharp/flat: C/C# * Db/D

D * E * F * G * A * B * C * D

D - D^/Ev - E - E/ Fv - F - F^/Gv - G - G^/Av - A - A^/Bv - B - B^/Cv - C - C^/Dv - D

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D - D^ - D^^ - Evv - Ev - E/F - F^ - F^^ - Gvv - Gv - G - G^ - G^^ - Avv - Av - A - A^ - A^^ - Bvv - Bv - B/C - C^ - C^^ - Dvv - Dv - D

P1/m2 - ^m2 - ^^m2 - vvM2 - vM2 - M2/m3 - ^m3 - ^^m3 - vvM3 - vM3 - M3/P4 - ^P4 - ^^P4 - vvP5 - vP5 - P5/m6 - ^m6 - ^^m6 - vvM6 - vM6 - M6/m7 - ^m7 - ^^m7 - vvM7 - vM7 - P8

===__Alternative pentatonic notation for pentatonic EDOs:__===

All intervals are perfect, so quality can be omitted.

__**5edo**__**:** zero keys per sharp/flat: C/C# Db/D

D E G A C D

1 - s3 - 4d - 5d - s7 - 8d

__**10edo**__**:** zero keys per sharp/flat: C/C# * Db/D

D * E * G * A * C * D

D - D^/Ev - E - E^/Gv - G - G^/Av - A - A^/Cv - C - C^/Dv - D

1 - ^1/vs3 - s3 - ^s3/v4d - 4d - ^4d/v5d - 5d - ^5d/vs7 - s7 - ^s7/v8d - 8d

__**15edo**__**:** zero keys per sharp/flat: C/C# * * Db/D

D * * E * * G * * A * * C * * D

D - D^ - Ev - E - E^ - Gv - G - G^ - Av - A - A^ - Cv - C - C^ - Dv - D

1 - ^1 - vs3 - s3 - ^s3 - v4d - 4d - ^4d - v5d - 5d - ^5d - vs7 - s7 - ^s7 - v8d - 8d

etc.

===__"Sweet" EDOs (12, 17, 19, 22, 24, 26, 27, 29, 31, ~~etc.~~)__===

===__"Sweet" EDOs (12, 17, 19, 22, 24, 26, 27, 29, 31, 32, 33, 34, 36 and all higher ones)__===

All sweet EDOs use the usual chain of fifths: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 etc.

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Not counting the trivial edos 2, 3, 4 and 6, there are only seven such edos. As seen in this diagram, they are the ones to the left of the central line in the light blue region, plus the ones to the right of the central line in the orange region. The ones on the left edge of the blue region are the fourthward ones like 16edo, and have been dealt with already. 23edo can be notated similarly to 16edo by using a fifth of 13\23 instead of 14\23. That leaves only four edos: 8, 11, 13, and 18.

<img src="/file/view/The%205th%20of%20EDOs%205-53.png/558356515/640x802/The%205th%20of%20EDOs%205-53.png" alt="The 5th of EDOs 5-53.png" title="The 5th of EDOs 5-53.png" style="height: 802px; width: 640px;" />

<img src="/file/view/The%205th%20of%20EDOs%205-53.png/558356515/640x802/The%205th%20of%20EDOs%205-53.png" alt="The 5th of EDOs 5-53.png" title="The 5th of EDOs 5-53.png" style="height: 802px; width: 640px;" />

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<h1 id="toc6"><a name="Summary of EDO notation"></a>Summary of EDO notation</h1>

~~There~~ are five EDO categories, based on the size of the fifth:

Besides the trivial EDOs, 1, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO, there are five EDO categories, based on the size of the fifth:

&quot;Fifth-less&quot; EDOs (8, 11, 13 and 18)

Fourthward EDOs (9, 16 and 23)

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Pentatonic EDOs (5, 10, 15, 20, 25 and 30)

&quot;Sweet&quot; EDOs (all others)

The first two categories never use ups and downs, the next two always do (except for 5edo and 7edo). The ~~last~~ may or may not.

The first two categories never use ups and downs, the next two always do (except for 5edo and 7edo). The sweet EDOs may or may not.

To summarize an EDO, a scale fragment from C to D is shown, including C# and Db. The C-C# interval is the augmented unison, and if they are not adjacent, ups and downs are required.The C-Db interval is the minor 2nd

The C-D interval is the major 2nd (P2 for perfect EDOs, m2 for fourthward EDOs).

~~ ~~

<h3 id="toc7"><a name="Summary of EDO notation--&quot;Fifth-less&quot; EDOs (8, 11, 13 and 18)"></a>&quot;Fifth-less&quot; EDOs (8, 11, 13 and 18)</h3>

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F# - C# - G# - D# - A# - E# - B# - F - C - G - D - A - E - B - Fb - Cb - Gb - Db - Ab - Eb - Bb - Fbb etc.

9edo: C/Db C#/D

9edo: C/Db C#/D

D E * F G A B * C D

D - E - E#/Fb - F - G - A - B - B#/Cb - C - D

P1 - m2 - M2/m3 - M3 - P4 - P5 - m6 - M6/m7 - M7 - P8

16edo: C C#/Db D

16edo: C C#/Db D

D * E * * F * G * A * B * * C * D

D - D#/Eb - E - E# - Fb - F F#/Gb - G - G#/Ab - A - A#/Bb - B - B# - Cb - C - C#/Db - D

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Because everything is perfect, the quality can be omitted: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8

14edo: 2 keys per sharp/flat: C/C# * Db/D

14edo: 2 keys per sharp/flat: C/C# * Db/D

D * E * F * G * A * B * C * D

D - D^/Ev - E - E/ Fv - F - F^/Gv - G - G^/Av - A - A^/Bv - B - B^/Cv - C - C^/Dv - D

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D - D^ - D^^ - Evv - Ev - E/F - F^ - F^^ - Gvv - Gv - G - G^ - G^^ - Avv - Av - A - A^ - A^^ - Bvv - Bv - B/C - C^ - C^^ - Dvv - Dv - D

P1/m2 - ^m2 - ^^m2 - vvM2 - vM2 - M2/m3 - ^m3 - ^^m3 - vvM3 - vM3 - M3/P4 - ^P4 - ^^P4 - vvP5 - vP5 - P5/m6 - ^m6 - ^^m6 - vvM6 - vM6 - M6/m7 - ^m7 - ^^m7 - vvM7 - vM7 - P8

<h3 id="toc12"><a name="Summary of EDO notation--Alternative pentatonic notation for pentatonic EDOs:"></a>Alternative pentatonic notation for pentatonic EDOs:</h3>

All intervals are perfect, so quality can be omitted.

5edo: zero keys per sharp/flat: C/C# Db/D

D E G A C D

1 - s3 - 4d - 5d - s7 - 8d

10edo: zero keys per sharp/flat: C/C# * Db/D

D * E * G * A * C * D

D - D^/Ev - E - E^/Gv - G - G^/Av - A - A^/Cv - C - C^/Dv - D

1 - ^1/vs3 - s3 - ^s3/v4d - 4d - ^4d/v5d - 5d - ^5d/vs7 - s7 - ^s7/v8d - 8d

15edo: zero keys per sharp/flat: C/C# * * Db/D

D * * E * * G * * A * * C * * D

D - D^ - Ev - E - E^ - Gv - G - G^ - Av - A - A^ - Cv - C - C^ - Dv - D

1 - ^1 - vs3 - s3 - ^s3 - v4d - 4d - ^4d - v5d - 5d - ^5d - vs7 - s7 - ^s7 - v8d - 8d

etc.

<h3 id="~~toc12~~"><a name="Summary of EDO notation--&quot;Sweet&quot; EDOs (12, 17, 19, 22, 24, 26, 27, 29, 31, ~~etc.~~)"></a>&quot;Sweet&quot; EDOs (12, 17, 19, 22, 24, 26, 27, 29, 31, ~~etc.~~)</h3>

<h3 id="toc13"><a name="Summary of EDO notation--&quot;Sweet&quot; EDOs (12, 17, 19, 22, 24, 26, 27, 29, 31, 32, 33, 34, 36 and all higher ones)"></a>&quot;Sweet&quot; EDOs (12, 17, 19, 22, 24, 26, 27, 29, 31, 32, 33, 34, 36 and all higher ones)</h3>

All sweet EDOs use the usual chain of fifths: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 etc.

@@ 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>2015-09-03 17:42:02 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2015-09-03 18:26:04 UTC</tt>.<br>
-: The original revision id was <tt>558211375</tt>.<br>
+: The original revision id was <tt>558214783</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 401: / Line 401: @@
 =__**Summary of EDO notation**__=
-There are five EDO categories, based on the size of the fifth:
+Besides the trivial EDOs, 1, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO, there are five EDO categories, based on the size of the fifth:
 "Fifth-less" EDOs (8, 11, 13 and 18)
 Fourthward EDOs (9, 16 and 23)
@@ Line 407: / Line 407: @@
 Pentatonic EDOs (5, 10, 15, 20, 25 and 30)
 "Sweet" EDOs (all others)
-The first two categories never use ups and downs, the next two always do (except for 5edo and 7edo). The last may or may not.
+The first two categories never use ups and downs, the next two always do (except for 5edo and 7edo). The sweet EDOs may or may not.
 To summarize an EDO, a scale fragment from C to D is shown, including C# and Db. The C-C# interval is the augmented unison, and if they are not adjacent, ups and downs are required.The C-Db interval is the minor 2nd
 The C-D interval is the major 2nd (P2 for perfect EDOs, m2 for fourthward EDOs).
 ===__**"Fifth-less" EDOs (8, 11, 13 and 18)**__===
@@ Line 470: / Line 468: @@
 F# - C# - G# - D# - A# - E# - B# - F - C - G - D - A - E - B - Fb - Cb - Gb - Db - Ab - Eb - Bb - Fbb etc.
 **__9edo__:** C/Db C#/D
 D E * F G A B * C D
 D - E - E#/Fb - F - G - A - B - B#/Cb - C - D
 P1 - m2 - M2/m3 - M3 - P4 - P5 - m6 - M6/m7 - M7 - P8
 **__16edo__:** C C#/Db D
 D * E * * F * G * A * B * * C * D
 D - D#/Eb - E - E# - Fb - F F#/Gb - G - G#/Ab - A - A#/Bb - B - B# - Cb - C - C#/Db - D
@@ Line 496: / Line 494: @@
 Because everything is perfect, the quality can be omitted: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8
 **__14edo__:** 2 keys per sharp/flat: C/C# * Db/D
 D * E * F * G * A * B * C * D
 D - D^/Ev - E - E/ Fv - F - F^/Gv - G - G^/Av - A - A^/Bv - B - B^/Cv - C - C^/Dv - D
@@ Line 551: / Line 549: @@
 D - D^ - D^^ - Evv - Ev - E/F - F^ - F^^ - Gvv - Gv - G - G^ - G^^ - Avv - Av - A - A^ - A^^ - Bvv - Bv - B/C - C^ - C^^ - Dvv - Dv - D
 P1/m2 - ^m2 - ^^m2 - vvM2 - vM2 - M2/m3 - ^m3 - ^^m3 - vvM3 - vM3 - M3/P4 - ^P4 - ^^P4 - vvP5 - vP5 - P5/m6 - ^m6 - ^^m6 - vvM6 - vM6 - M6/m7 - ^m7 - ^^m7 - vvM7 - vM7 - P8
+===__Alternative pentatonic notation for pentatonic EDOs:__===
+All intervals are perfect, so quality can be omitted.
+__**5edo**__**:** zero keys per sharp/flat: C/C# Db/D
+D E G A C D
+- s3 - 4d - 5d - s7 - 8d
+__**10edo**__**:** zero keys per sharp/flat: C/C# * Db/D
+D * E * G * A * C * D
+D - D^/Ev - E - E^/Gv - G - G^/Av - A - A^/Cv - C - C^/Dv - D
+- ^1/vs3 - s3 - ^s3/v4d - 4d - ^4d/v5d - 5d - ^5d/vs7 - s7 - ^s7/v8d - 8d
+__**15edo**__**:** zero keys per sharp/flat: C/C# * * Db/D
+D * * E * * G * * A * * C * * D
+D - D^ - Ev - E - E^ - Gv - G - G^ - Av - A - A^ - Cv - C - C^ - Dv - D
+- ^1 - vs3 - s3 - ^s3 - v4d - 4d - ^4d - v5d - 5d - ^5d - vs7 - s7 - ^s7 - v8d - 8d
+etc.
-===__"Sweet" EDOs (12, 17, 19, 22, 24, 26, 27, 29, 31, etc.)__===
+===__"Sweet" EDOs (12, 17, 19, 22, 24, 26, 27, 29, 31, 32, 33, 34, 36 and all higher ones)__===
 All sweet EDOs use the usual chain of fifths: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 etc.
@@ Line 925: / Line 943: @@
 Not counting the trivial edos 2, 3, 4 and 6, there are only seven such edos. As seen in this diagram, they are the ones to the left of the central line in the light blue region, plus the ones to the right of the central line in the orange region. The ones on the left edge of the blue region are the fourthward ones like 16edo, and have been dealt with already. 23edo can be notated similarly to 16edo by using a fifth of 13\23 instead of 14\23. That leaves only four edos: 8, 11, 13, and 18.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:26:&amp;lt;img src=&amp;quot;/file/view/The%205th%20of%20EDOs%205-53.png/558356515/640x802/The%205th%20of%20EDOs%205-53.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 802px; width: 640px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/The%205th%20of%20EDOs%205-53.png/558356515/640x802/The%205th%20of%20EDOs%205-53.png" alt="The 5th of EDOs 5-53.png" title="The 5th of EDOs 5-53.png" style="height: 802px; width: 640px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:26 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:28:&amp;lt;img src=&amp;quot;/file/view/The%205th%20of%20EDOs%205-53.png/558356515/640x802/The%205th%20of%20EDOs%205-53.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 802px; width: 640px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/The%205th%20of%20EDOs%205-53.png/558356515/640x802/The%205th%20of%20EDOs%205-53.png" alt="The 5th of EDOs 5-53.png" title="The 5th of EDOs 5-53.png" style="height: 802px; width: 640px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:28 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;br /&gt;
@@ Line 978: / Line 996: @@
 &lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Summary of EDO notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;&lt;u&gt;&lt;strong&gt;Summary of EDO notation&lt;/strong&gt;&lt;/u&gt;&lt;/h1&gt;
   &lt;br /&gt;
-There are five EDO categories, based on the size of the fifth:&lt;br /&gt;
+Besides the trivial EDOs, 1, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO, there are five EDO categories, based on the size of the fifth:&lt;br /&gt;
 &amp;quot;Fifth-less&amp;quot; EDOs (8, 11, 13 and 18)&lt;br /&gt;
 Fourthward EDOs (9, 16 and 23)&lt;br /&gt;
@@ Line 984: / Line 1,002: @@
 Pentatonic EDOs (5, 10, 15, 20, 25 and 30)&lt;br /&gt;
 &amp;quot;Sweet&amp;quot; EDOs (all others)&lt;br /&gt;
-The first two categories never use ups and downs, the next two always do (except for 5edo and 7edo). The last may or may not. &lt;br /&gt;
+The first two categories never use ups and downs, the next two always do (except for 5edo and 7edo). The sweet EDOs may or may not.&lt;br /&gt;
 &lt;br /&gt;
 To summarize an EDO, a scale fragment from C to D is shown, including C# and Db. The C-C# interval is the augmented unison, and if they are not adjacent, ups and downs are required.The C-Db interval is the minor 2nd&lt;br /&gt;
 The C-D interval is the major 2nd (P2 for perfect EDOs, m2 for fourthward EDOs).&lt;br /&gt;
-&lt;br /&gt;
-&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="Summary of EDO notation--&amp;quot;Fifth-less&amp;quot; EDOs (8, 11, 13 and 18)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;&lt;u&gt;&lt;strong&gt;&amp;quot;Fifth-less&amp;quot; EDOs (8, 11, 13 and 18)&lt;/strong&gt;&lt;/u&gt;&lt;/h3&gt;
@@ Line 1,047: / Line 1,063: @@
 F# - C# - G# - D# - A# - E# - B# - F - C - G - D - A - E - B - Fb - Cb - Gb - Db - Ab - Eb - Bb - Fbb etc.&lt;br /&gt;
 &lt;br /&gt;
-&lt;strong&gt;&lt;u&gt;9edo&lt;/u&gt;:&lt;/strong&gt; C/Db C#/D &lt;br /&gt;
+&lt;strong&gt;&lt;u&gt;9edo&lt;/u&gt;:&lt;/strong&gt; C/Db C#/D&lt;br /&gt;
 D E * F G A B * C D&lt;br /&gt;
 D - E - E#/Fb - F - G - A - B - B#/Cb - C - D&lt;br /&gt;
 P1 - m2 - M2/m3 - M3 - P4 - P5 - m6 - M6/m7 - M7 - P8&lt;br /&gt;
 &lt;br /&gt;
-&lt;strong&gt;&lt;u&gt;16edo&lt;/u&gt;:&lt;/strong&gt; C C#/Db D &lt;br /&gt;
+&lt;strong&gt;&lt;u&gt;16edo&lt;/u&gt;:&lt;/strong&gt; C C#/Db D&lt;br /&gt;
 D * E * * F * G * A * B * * C * D&lt;br /&gt;
 D - D#/Eb - E - E# - Fb - F F#/Gb - G - G#/Ab - A - A#/Bb - B - B# - Cb - C - C#/Db - D&lt;br /&gt;
@@ Line 1,073: / Line 1,089: @@
 Because everything is perfect, the quality can be omitted: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8&lt;br /&gt;
 &lt;br /&gt;
-&lt;strong&gt;&lt;u&gt;14edo&lt;/u&gt;:&lt;/strong&gt; 2 keys per sharp/flat: C/C# * Db/D &lt;br /&gt;
+&lt;strong&gt;&lt;u&gt;14edo&lt;/u&gt;:&lt;/strong&gt; 2 keys per sharp/flat: C/C# * Db/D&lt;br /&gt;
 D * E * F * G * A * B * C * D&lt;br /&gt;
 D - D^/Ev - E - E/ Fv - F - F^/Gv - G - G^/Av - A - A^/Bv - B - B^/Cv - C - C^/Dv - D&lt;br /&gt;
@@ Line 1,128: / Line 1,144: @@
 D - D^ - D^^ - Evv - Ev - E/F - F^ - F^^ - Gvv - Gv - G - G^ - G^^ - Avv - Av - A - A^ - A^^ - Bvv - Bv - B/C - C^ - C^^ - Dvv - Dv - D&lt;br /&gt;
 P1/m2 - ^m2 - ^^m2 - vvM2 - vM2 - M2/m3 - ^m3 - ^^m3 - vvM3 - vM3 - M3/P4 - ^P4 - ^^P4 - vvP5 - vP5 - P5/m6 - ^m6 - ^^m6 - vvM6 - vM6 - M6/m7 - ^m7 - ^^m7 - vvM7 - vM7 - P8&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="Summary of EDO notation--Alternative pentatonic notation for pentatonic EDOs:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;&lt;u&gt;Alternative pentatonic notation for pentatonic EDOs:&lt;/u&gt;&lt;/h3&gt;
+ &lt;br /&gt;
+All intervals are perfect, so quality can be omitted.&lt;br /&gt;
+&lt;br /&gt;
+&lt;u&gt;&lt;strong&gt;5edo&lt;/strong&gt;&lt;/u&gt;&lt;strong&gt;:&lt;/strong&gt; zero keys per sharp/flat: C/C# Db/D&lt;br /&gt;
+D E G A C D&lt;br /&gt;
+- s3 - 4d - 5d - s7 - 8d&lt;br /&gt;
+&lt;br /&gt;
+&lt;u&gt;&lt;strong&gt;10edo&lt;/strong&gt;&lt;/u&gt;&lt;strong&gt;:&lt;/strong&gt; zero keys per sharp/flat: C/C# * Db/D&lt;br /&gt;
+D * E * G * A * C * D&lt;br /&gt;
+D - D^/Ev - E - E^/Gv - G - G^/Av - A - A^/Cv - C - C^/Dv - D&lt;br /&gt;
+- ^1/vs3 - s3 - ^s3/v4d - 4d - ^4d/v5d - 5d - ^5d/vs7 - s7 - ^s7/v8d - 8d&lt;br /&gt;
+&lt;br /&gt;
+&lt;u&gt;&lt;strong&gt;15edo&lt;/strong&gt;&lt;/u&gt;&lt;strong&gt;:&lt;/strong&gt; zero keys per sharp/flat: C/C# * * Db/D&lt;br /&gt;
+D * * E * * G * * A * * C * * D&lt;br /&gt;
+D - D^ - Ev - E - E^ - Gv - G - G^ - Av - A - A^ - Cv - C - C^ - Dv - D&lt;br /&gt;
+- ^1 - vs3 - s3 - ^s3 - v4d - 4d - ^4d - v5d - 5d - ^5d - vs7 - s7 - ^s7 - v8d - 8d&lt;br /&gt;
+&lt;br /&gt;
+etc.&lt;br /&gt;
 &lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="Summary of EDO notation--&amp;quot;Sweet&amp;quot; EDOs (12, 17, 19, 22, 24, 26, 27, 29, 31, etc.)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;&lt;u&gt;&amp;quot;Sweet&amp;quot; EDOs (12, 17, 19, 22, 24, 26, 27, 29, 31, etc.)&lt;/u&gt;&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc13"&gt;&lt;a name="Summary of EDO notation--&amp;quot;Sweet&amp;quot; EDOs (12, 17, 19, 22, 24, 26, 27, 29, 31, 32, 33, 34, 36 and all higher ones)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;&lt;u&gt;&amp;quot;Sweet&amp;quot; EDOs (12, 17, 19, 22, 24, 26, 27, 29, 31, 32, 33, 34, 36 and all higher ones)&lt;/u&gt;&lt;/h3&gt;
   &lt;br /&gt;
 All sweet EDOs use the usual chain of fifths: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 etc.&lt;br /&gt;