Harmony of 23edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:~~Osmiorisbendi~~|~~Osmiorisbendi~~]] and made on <tt>2012-01-~~21 17~~:18:32 UTC</tt>.<br>

: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2012-01-22 14:51:51 UTC</tt>.<br>

: The original revision id was <tt>~~294146236~~</tt>.<br>

: The original revision id was <tt>294270202</tt>.<br>

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

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I'd also like to set an arbitrary limit on how high up the harmonic series we will go. I'll set my limit at the 23rd harmonic. I'll consider harmonics 1, 9, 17, 21, & 23, excluding (at least for now) 33, 35, 55, 79, & 117. Those sonorities could no doubt prove useful to a thoughful composer, but for this study, I'll leave them out.

Thus we produce ten triads, five tetrads, & one ~~quintad~~, 16 chords, which, with their inversions (given), doubles to 32 chords. I've written then in a closed position (within one octave), & I recommend trying different voicings. Moving chord tones up & down by octaves, you can unmuddy a muddy chord.

Thus we produce ten triads, five tetrads, & one pentad, 16 chords, which, with their inversions (given), doubles to 32 chords. I've written then in a closed position (within one octave), & I recommend trying different voicings. Moving chord tones up & down by octaves, you can unmuddy a muddy chord.

==~~[[Triad]]s~~==

==Triads==

**16:17:18, degrees 0, 2, 4 (inversion 0, 19, 21)**.

17/16 (104.955, error -0.607)

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==~~[[Tetrad]]s~~==

==Tetrads==

**16:17:18:21, degrees 0, 2, 4, 9 (inversion 0, 14, 19, 21)**.

17/16 (104.955, error -0.607)

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==~~[[Quintad]]~~==

==Pentad==

**16:17:18:21:23, degrees 0, 2, 4, 9, 12 (inversion 0, 11, 14, 19, 21)**.

17/16 (104.955, error -0.607)

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I'd also like to set an arbitrary limit on how high up the harmonic series we will go. I'll set my limit at the 23rd harmonic. I'll consider harmonics 1, 9, 17, 21, &amp; 23, excluding (at least for now) 33, 35, 55, 79, &amp; 117. Those sonorities could no doubt prove useful to a thoughful composer, but for this study, I'll leave them out.<br />

<br />

Thus we produce ten triads, five tetrads, &amp; one ~~quintad~~, 16 chords, which, with their inversions (given), doubles to 32 chords. I've written then in a closed position (within one octave), &amp; I recommend trying different voicings. Moving chord tones up &amp; down by octaves, you can unmuddy a muddy chord.<br />

Thus we produce ten triads, five tetrads, &amp; one pentad, 16 chords, which, with their inversions (given), doubles to 32 chords. I've written then in a closed position (within one octave), &amp; I recommend trying different voicings. Moving chord tones up &amp; down by octaves, you can unmuddy a muddy chord.<br />

<br />

<h2 id="toc0"><a name="x-Triads"></a>~~<a class="wiki_link" href="/Triad">Triad</a>s~~</h2>

<h2 id="toc0"><a name="x-Triads"></a>Triads</h2>

<strong>16:17:18, degrees 0, 2, 4 (inversion 0, 19, 21)</strong>.<br />

17/16 (104.955, error -0.607)<br />

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<br />

<h2 id="toc10"><a name="x-Tetrads"></a>~~<a class="wiki_link" href="/Tetrad">Tetrad</a>s~~</h2>

<h2 id="toc10"><a name="x-Tetrads"></a>Tetrads</h2>

<strong>16:17:18:21, degrees 0, 2, 4, 9 (inversion 0, 14, 19, 21)</strong>.<br />

17/16 (104.955, error -0.607)<br />

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<br />

<h2 id="toc15"><a name="x-~~Quintad~~"></a>~~<a class="wiki_link" href="/Quintad">Quintad</a>~~</h2>

<h2 id="toc15"><a name="x-Pentad"></a>Pentad</h2>

<strong>16:17:18:21:23, degrees 0, 2, 4, 9, 12 (inversion 0, 11, 14, 19, 21)</strong>.<br />

17/16 (104.955, error -0.607)<br />

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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:<br>
-: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2012-01-21 17:18:32 UTC</tt>.<br>
+: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2012-01-22 14:51:51 UTC</tt>.<br>
-: The original revision id was <tt>294146236</tt>.<br>
+: The original revision id was <tt>294270202</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 36: / Line 36: @@
 I'd also like to set an arbitrary limit on how high up the harmonic series we will go. I'll set my limit at the 23rd harmonic. I'll consider harmonics 1, 9, 17, 21, &amp; 23, excluding (at least for now) 33, 35, 55, 79, &amp; 117. Those sonorities could no doubt prove useful to a thoughful composer, but for this study, I'll leave them out.
-Thus we produce ten triads, five tetrads, &amp; one quintad, 16 chords, which, with their inversions (given), doubles to 32 chords. I've written then in a closed position (within one octave), &amp; I recommend trying different voicings. Moving chord tones up &amp; down by octaves, you can unmuddy a muddy chord.
+Thus we produce ten triads, five tetrads, &amp; one pentad, 16 chords, which, with their inversions (given), doubles to 32 chords. I've written then in a closed position (within one octave), &amp; I recommend trying different voicings. Moving chord tones up &amp; down by octaves, you can unmuddy a muddy chord.
-==[[Triad]]s==
+==Triads==
 **16:17:18, degrees 0, 2, 4 (inversion 0, 19, 21)**.
 /16 (104.955, error -0.607)
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-==[[Tetrad]]s==
+==Tetrads==
 **16:17:18:21, degrees 0, 2, 4, 9 (inversion 0, 14, 19, 21)**.
 /16 (104.955, error -0.607)
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-==[[Quintad]]==
+==Pentad==
 **16:17:18:21:23, degrees 0, 2, 4, 9, 12 (inversion 0, 11, 14, 19, 21)**.
 /16 (104.955, error -0.607)
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 I'd also like to set an arbitrary limit on how high up the harmonic series we will go. I'll set my limit at the 23rd harmonic. I'll consider harmonics 1, 9, 17, 21, &amp;amp; 23, excluding (at least for now) 33, 35, 55, 79, &amp;amp; 117. Those sonorities could no doubt prove useful to a thoughful composer, but for this study, I'll leave them out.&lt;br /&gt;
 &lt;br /&gt;
-Thus we produce ten triads, five tetrads, &amp;amp; one quintad, 16 chords, which, with their inversions (given), doubles to 32 chords. I've written then in a closed position (within one octave), &amp;amp; I recommend trying different voicings. Moving chord tones up &amp;amp; down by octaves, you can unmuddy a muddy chord.&lt;br /&gt;
+Thus we produce ten triads, five tetrads, &amp;amp; one pentad, 16 chords, which, with their inversions (given), doubles to 32 chords. I've written then in a closed position (within one octave), &amp;amp; I recommend trying different voicings. Moving chord tones up &amp;amp; down by octaves, you can unmuddy a muddy chord.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Triads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;a class="wiki_link" href="/Triad"&gt;Triad&lt;/a&gt;s&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Triads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Triads&lt;/h2&gt;
   &lt;strong&gt;16:17:18, degrees 0, 2, 4 (inversion 0, 19, 21)&lt;/strong&gt;.&lt;br /&gt;
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-&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="x-Tetrads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;&lt;a class="wiki_link" href="/Tetrad"&gt;Tetrad&lt;/a&gt;s&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="x-Tetrads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Tetrads&lt;/h2&gt;
   &lt;strong&gt;16:17:18:21, degrees 0, 2, 4, 9 (inversion 0, 14, 19, 21)&lt;/strong&gt;.&lt;br /&gt;
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-&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="x-Quintad"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;&lt;a class="wiki_link" href="/Quintad"&gt;Quintad&lt;/a&gt;&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="x-Pentad"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Pentad&lt;/h2&gt;
   &lt;strong&gt;16:17:18:21:23, degrees 0, 2, 4, 9, 12 (inversion 0, 11, 14, 19, 21)&lt;/strong&gt;.&lt;br /&gt;
 /16 (104.955, error -0.607)&lt;br /&gt;