23edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-25 20:35:21 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-25 20:44:40 UTC</tt>.

: The original revision id was <tt>~~602809014~~</tt>.

: The original revision id was <tt>602809034</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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[[image:Ciclo Icositrifonía.png width="491" height="490" link="Harmony of 23edo"]]

Like 16edo, 23edo can be notated with conventional notation, including the staff, note names, chord names, relative notation, etc. in two ways. The first is with major wider than minor, and sharp higher than flat, to preserve melodic contour. The second way is with major narrower than minor, and sharp lower than flat, to preserve interval arithmetic and chord names.

23edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first preserves the __melodic__ meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.

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The second approach preserves the __harmonic__ meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 23edo "on the fly".

||= [[Degree]] ||= [[Cent]]s ||= Approximate

Armodue notation is a nonatonic notation that uses the numbers 1-9 as note names.

Ratios* ||||= Major wider

||= [[Degree]]* ||= [[Cent]]s ||= Approximate

Ratios** ||||= Major wider

than minor ||||= Major narrower

than minor ||= Armodue

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||= 21 ||= 1095.652 ||= 15/8, 17/9, 32/17 ||= A7 ||= C# ||= d7 ||= Cb ||= 8# || ||

||= 22 ||= 1147.826 ||= 33/17, 64/33 ||= d8 ||= Db ||= A8 ||= D# ||= 9 || ||

||= 23 ||= 1200 ||= 2/1 ||= P8 ||= D ||= P8 ||= D ||= 1 || ||

||= 23·· ||= 1200 ||= 2/1 ||= P8 ||= D ||= P8 ||= D ||= 1 || ||

*based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible.

*The dots indicate which frets on a 23-edo guitar would have dots.

**based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible.

The chart below shows some of the [[MOSScales|Moment of Symmetry (MOS)]] modes of [[Mavila]] available in 23edo, mainly Pentatonic(5-note), anti-diatonic(7-note), 9- and 16-note MOSs. Here the outer ring represents individual step of 23edo itself, while the rings moving inward represent 16, 9, 7 and 5 note MOSs:

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<a href="/Harmony%20of%2023edo"><img src="/file/view/Ciclo%20Icositrifon%C3%ADa.png/390051610/491x490/Ciclo%20Icositrifon%C3%ADa.png" alt="Ciclo Icositrifonía.png" title="Ciclo Icositrifonía.png" style="height: 490px; width: 491px;" /></a>

Like 16edo, 23edo can be notated with conventional notation, including the staff, note names, chord names, relative notation, etc. in two ways. The first is with major wider than minor, and sharp higher than flat, to preserve melodic contour. The second way is with major narrower than minor, and sharp lower than flat, to preserve interval arithmetic and chord names.

23edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first preserves the melodic meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.

The second approach preserves the harmonic meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 23edo &quot;on the fly&quot;.

Armodue notation is a nonatonic notation that uses the numbers 1-9 as note names.

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<tr>

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

<td style="text-align: center;"><a class="wiki_link" href="/Degree">Degree</a>*

</td>

<td style="text-align: center;"><a class="wiki_link" href="/Cent">Cent</a>s

</td>

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

Ratios*

Ratios

</td>

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

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</tr>

<tr>

<td style="text-align: center;">23

<td style="text-align: center;">23··

</td>

<td style="text-align: center;">1200

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</table>

*based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible.

*The dots indicate which frets on a 23-edo guitar would have dots.

based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible.

The chart below shows some of the <a class="wiki_link" href="/MOSScales">Moment of Symmetry (MOS)</a> modes of <a class="wiki_link" href="/Mavila">Mavila</a> available in 23edo, mainly Pentatonic(5-note), anti-diatonic(7-note), 9- and 16-note MOSs. Here the outer ring represents individual step of 23edo itself, while the rings moving inward represent 16, 9, 7 and 5 note MOSs:

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-25 20:35:21 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-25 20:44:40 UTC</tt>.<br>
-: The original revision id was <tt>602809014</tt>.<br>
+: The original revision id was <tt>602809034</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 20: / Line 20: @@
 [[image:Ciclo Icositrifonía.png width="491" height="490" link="Harmony of 23edo"]]
-Like 16edo, 23edo can be notated with conventional notation, including the staff, note names, chord names, relative notation, etc. in two ways. The first is with major wider than minor, and sharp higher than flat, to preserve melodic contour. The second way is with major narrower than minor, and sharp lower than flat, to preserve interval arithmetic and chord names.
 edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first preserves the __melodic__ meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.
@@ Line 26: / Line 25: @@
 The second approach preserves the __harmonic__ meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 23edo "on the fly".
-||= &lt;span style="color: #660000;"&gt;[[Degree]]&lt;/span&gt; ||= [[Cent]]s ||= Approximate
+Armodue notation is a nonatonic notation that uses the numbers 1-9 as note names.
-Ratios* ||||= Major wider
+||= &lt;span style="color: #660000;"&gt;[[Degree]]*&lt;/span&gt; ||= [[Cent]]s ||= Approximate
+Ratios** ||||= Major wider
 than minor ||||= Major narrower
 than minor ||= Armodue
@@ Line 54: / Line 55: @@
 ||= 21 ||= 1095.652 ||= 15/8, 17/9, 32/17 ||= A7 ||= C# ||= d7 ||= Cb ||= 8# ||   ||
 ||= 22 ||= 1147.826 ||= 33/17, 64/33 ||= d8 ||= Db ||= A8 ||= D# ||= 9 ||   ||
-||= 23 ||= 1200 ||= 2/1 ||= P8 ||= D ||= P8 ||= D ||= 1 ||   ||
+||= 23·· ||= 1200 ||= 2/1 ||= P8 ||= D ||= P8 ||= D ||= 1 ||   ||
-*based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible.
+*The dots indicate which frets on a 23-edo guitar would have dots.
+**based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible.
 The chart below shows some of the [[MOSScales|Moment of Symmetry (MOS)]] modes of [[Mavila]] available in 23edo, mainly Pentatonic(5-note), anti-diatonic(7-note), 9- and 16-note MOSs. Here the outer ring represents individual step of 23edo itself, while the rings moving inward represent 16, 9, 7 and 5 note MOSs:
@@ Line 224: / Line 226: @@
 &lt;!-- ws:start:WikiTextLocalImageRule:1012:&amp;lt;a href=&amp;quot;/Harmony%20of%2023edo&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/Ciclo%20Icositrifon%C3%ADa.png/390051610/491x490/Ciclo%20Icositrifon%C3%ADa.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 490px; width: 491px;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/Harmony%20of%2023edo"&gt;&lt;img src="/file/view/Ciclo%20Icositrifon%C3%ADa.png/390051610/491x490/Ciclo%20Icositrifon%C3%ADa.png" alt="Ciclo Icositrifonía.png" title="Ciclo Icositrifonía.png" style="height: 490px; width: 491px;" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1012 --&gt;&lt;br /&gt;
 &lt;br /&gt;
-Like 16edo, 23edo can be notated with conventional notation, including the staff, note names, chord names, relative notation, etc. in two ways. The first is with major wider than minor, and sharp higher than flat, to preserve melodic contour. The second way is with major narrower than minor, and sharp lower than flat, to preserve interval arithmetic and chord names.&lt;br /&gt;
 &lt;br /&gt;
 edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first preserves the &lt;u&gt;melodic&lt;/u&gt; meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.&lt;br /&gt;
 &lt;br /&gt;
 The second approach preserves the &lt;u&gt;harmonic&lt;/u&gt; meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 23edo &amp;quot;on the fly&amp;quot;.&lt;br /&gt;
+&lt;br /&gt;
+Armodue notation is a nonatonic notation that uses the numbers 1-9 as note names.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 234: / Line 237: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;&lt;span style="color: #660000;"&gt;&lt;a class="wiki_link" href="/Degree"&gt;Degree&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="color: #660000;"&gt;&lt;a class="wiki_link" href="/Degree"&gt;Degree&lt;/a&gt;*&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/Cent"&gt;Cent&lt;/a&gt;s&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Approximate&lt;br /&gt;
-Ratios*&lt;br /&gt;
+Ratios&lt;strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td colspan="2" style="text-align: center;"&gt;Major wider&lt;br /&gt;
@@ Line 714: / Line 717: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;23&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;23··&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;1200&lt;br /&gt;
@@ Line 735: / Line 738: @@
 &lt;/table&gt;
-*based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible.&lt;br /&gt;
+*The dots indicate which frets on a 23-edo guitar would have dots.&lt;br /&gt;
+&lt;/strong&gt;based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible.&lt;br /&gt;
 &lt;br /&gt;
 The chart below shows some of the &lt;a class="wiki_link" href="/MOSScales"&gt;Moment of Symmetry (MOS)&lt;/a&gt; modes of &lt;a class="wiki_link" href="/Mavila"&gt;Mavila&lt;/a&gt; available in 23edo, mainly Pentatonic(5-note), anti-diatonic(7-note), 9- and 16-note MOSs. Here the outer ring represents individual step of 23edo itself, while the rings moving inward represent 16, 9, 7 and 5 note MOSs:&lt;br /&gt;