4edo: Difference between revisions

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~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

Like [[3edo|3EDO]], 4EDO is already familiar as a chord of 12EDO. Again, however, it has a theoretical interest in that it preserves a kind of outline, or skeleton, of melodic movement while erasing key distinctions concerning harmony. The 7-limit tuning map, or [[Vals_and_Tuning_Space|val]], for 4EDO goes <4 6 9 11|, all of which are distinct modulo 4. It therefore goes with tetradic harmony in much the same way that 3EDO goes with triadic harmony, mapping the [[7-limit|7-limit]] [[consistent|consistent]]ly, and sending 15/14, 21/20, 25/24, and 36/35 to the unison. Somewhat confusingly, 9/8 is mapped to the unison also.

~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~

~~: This revision was by author~~ [[~~User:genewardsmith~~|~~genewardsmith]] and made on <tt>2014-06-16 17:32:22 UTC</tt>.<br>~~

~~: The original revision id was <tt>514125680</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>~~

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Like [[3EDO]], 4EDO is already familiar as a chord of 12EDO. Again, however, it has a theoretical interest in that it preserves a kind of outline, or skeleton, of melodic movement while erasing key distinctions concerning harmony. The 7-limit tuning map, or [[~~Vals and Tuning Space~~|val]], for 4EDO goes <4 6 9 11|, all of which are distinct modulo 4. It therefore goes with tetradic harmony in much the same way that 3EDO goes with triadic harmony, mapping the [[7-limit]] [[consistent]]ly, and sending 15/14, 21/20, 25/24, and 36/35 to the unison. Somewhat confusingly, 9/8 is mapped to the unison also.

By putting together the triples of integers which uniquely represent 7-limit tetrads in the [[~~The Seven Limit Symmetrical Lattices~~|7-limit cubic lattice of tetrads]] with the number of 4EDO steps returned by the val <4 6 9 11| we obtain a representation of the 7-limit in terms of four integers, which differs from the usual (monzo) representation in that the triple representing the chord can be swapped for another such triple, resulting in a similar note tuned to a different chord. It is even possible under some circumstances to create a sort of recombinant merging of two pieces of music by using the chords of one with the 4EDO skeletons of another.

By putting together the triples of integers which uniquely represent 7-limit tetrads in the [[The_Seven_Limit_Symmetrical_Lattices|7-limit cubic lattice of tetrads]] with the number of 4EDO steps returned by the val <4 6 9 11| we obtain a representation of the 7-limit in terms of four integers, which differs from the usual (monzo) representation in that the triple representing the chord can be swapped for another such triple, resulting in a similar note tuned to a different chord. It is even possible under some circumstances to create a sort of recombinant merging of two pieces of music by using the chords of one with the 4EDO skeletons of another.

We can also add more kinds of chords, for instance the subminor (1-7/6-3/2-5/3) and supermajor (1-9/7-3/2-9/5) to the mix, and by encoding which kind of tetrad a note reconstitute a version of 9-odd-limit tetradic harmony, again changing the harmonic content of a note without changing its 4EDO skeletal position.

==Music==

[[@http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/fouredo.mp3|A simple 4edo piece]] by [[Gene Ward Smith]] (see [[Composing with tablets]] for explanation)

[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/fouredo.mp3 A simple 4edo piece] by [[Gene_Ward_Smith|Gene Ward Smith]] (see [[Composing_with_tablets|Composing with tablets]] for explanation)

"Nothing of any importance" by [[Rozencrantz|Rozencrantz the Sane]] (his contribution to the [[MMMday06|MMM day 2006]])~~</pre></div>~~

~~<h4>Original HTML content:</h4>~~

"Nothing of any importance" by [[Rozencrantz|Rozencrantz the Sane]] (his contribution to the [[MMMday06|MMM day 2006]])

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>4edo</title></head><body>Like <a class="wiki_link" href="/3EDO">3EDO</a>, 4EDO is already familiar as a chord of 12EDO. Again, however, it has a theoretical interest in that it preserves a kind of outline, or skeleton, of melodic movement while erasing key distinctions concerning harmony. The 7-limit tuning map, or <a class="wiki_link" href="/Vals%20and%20Tuning%20Space">val</a>, for 4EDO goes &lt;4 6 9 11|, all of which are distinct modulo 4. It therefore goes with tetradic harmony in much the same way that 3EDO goes with triadic harmony, mapping the <a class="wiki_link" href="/7-limit">7-limit</a> <a class="wiki_link" href="/consistent">consistent</a>ly, and sending 15/14, 21/20, 25/24, and 36/35 to the unison. Somewhat confusingly, 9/8 is mapped to the unison also.<br />

[[Category:7-limit]]

~~<br />~~

[[Category:edo]]

By putting together the triples of integers which uniquely represent 7-limit tetrads in the <a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices">7-limit cubic lattice of tetrads</a> with the number of 4EDO steps returned by the val &lt;4 6 9 11| we obtain a representation of the 7-limit in terms of four integers, which differs from the usual (monzo) representation in that the triple representing the chord can be swapped for another such triple, resulting in a similar note tuned to a different chord. It is even possible under some circumstances to create a sort of recombinant merging of two pieces of music by using the chords of one with the 4EDO skeletons of another.<br />

[[Category:macrotonal]]

~~<br />~~

We can also add more kinds of chords, for instance the subminor (1-7/6-3/2-5/3) and supermajor (1-9/7-3/2-9/5) to the mix, and by encoding which kind of tetrad a note reconstitute a version of 9-odd-limit tetradic harmony, again changing the harmonic content of a note without changing its 4EDO skeletal position.<br />

~~<br />~~

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

~~<br />~~

~~<a class="wiki_link_ext" href="http~~://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/fouredo.mp3" rel="nofollow" target="_blank">A simple 4edo piece</a> by <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a> (see <a class="wiki_link" href="/Composing%20with%20tablets">Composing with tablets</a> for explanation)<br />

&quot;Nothing of any importance&quot; by <a class="wiki_link" href="/Rozencrantz">Rozencrantz the Sane</a> (his contribution to the <a class="wiki_link" href="/MMMday06">MMM day 2006</a>)</body></html></pre></div>

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+Like [[3edo|3EDO]], 4EDO is already familiar as a chord of 12EDO. Again, however, it has a theoretical interest in that it preserves a kind of outline, or skeleton, of melodic movement while erasing key distinctions concerning harmony. The 7-limit tuning map, or [[Vals_and_Tuning_Space|val]], for 4EDO goes &lt;4 6 9 11|, all of which are distinct modulo 4. It therefore goes with tetradic harmony in much the same way that 3EDO goes with triadic harmony, mapping the [[7-limit|7-limit]] [[consistent|consistent]]ly, and sending 15/14, 21/20, 25/24, and 36/35 to the unison. Somewhat confusingly, 9/8 is mapped to the unison also.
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-06-16 17:32:22 UTC</tt>.<br>
-: The original revision id was <tt>514125680</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>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Like [[3EDO]], 4EDO is already familiar as a chord of 12EDO. Again, however, it has a theoretical interest in that it preserves a kind of outline, or skeleton, of melodic movement while erasing key distinctions concerning harmony. The 7-limit tuning map, or [[Vals and Tuning Space|val]], for 4EDO goes &lt;4 6 9 11|, all of which are distinct modulo 4. It therefore goes with tetradic harmony in much the same way that 3EDO goes with triadic harmony, mapping the [[7-limit]] [[consistent]]ly, and sending 15/14, 21/20, 25/24, and 36/35 to the unison. Somewhat confusingly, 9/8 is mapped to the unison also.
-By putting together the triples of integers which uniquely represent 7-limit tetrads in the [[The Seven Limit Symmetrical Lattices|7-limit cubic lattice of tetrads]] with the number of 4EDO steps returned by the val &lt;4 6 9 11| we obtain a representation of the 7-limit in terms of four integers, which differs from the usual (monzo) representation in that the triple representing the chord can be swapped for another such triple, resulting in a similar note tuned to a different chord. It is even possible under some circumstances to create a sort of recombinant merging of two pieces of music by using the chords of one with the 4EDO skeletons of another.
+By putting together the triples of integers which uniquely represent 7-limit tetrads in the [[The_Seven_Limit_Symmetrical_Lattices|7-limit cubic lattice of tetrads]] with the number of 4EDO steps returned by the val &lt;4 6 9 11| we obtain a representation of the 7-limit in terms of four integers, which differs from the usual (monzo) representation in that the triple representing the chord can be swapped for another such triple, resulting in a similar note tuned to a different chord. It is even possible under some circumstances to create a sort of recombinant merging of two pieces of music by using the chords of one with the 4EDO skeletons of another.
 We can also add more kinds of chords, for instance the subminor (1-7/6-3/2-5/3) and supermajor (1-9/7-3/2-9/5) to the mix, and by encoding which kind of tetrad a note reconstitute a version of 9-odd-limit tetradic harmony, again changing the harmonic content of a note without changing its 4EDO skeletal position.
 ==Music==
-[[@http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/fouredo.mp3|A simple 4edo piece]] by [[Gene Ward Smith]] (see [[Composing with tablets]] for explanation)
+[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/fouredo.mp3 A simple 4edo piece] by [[Gene_Ward_Smith|Gene Ward Smith]] (see [[Composing_with_tablets|Composing with tablets]] for explanation)
-"Nothing of any importance" by [[Rozencrantz|Rozencrantz the Sane]] (his contribution to the [[MMMday06|MMM day 2006]])</pre></div>
-<h4>Original HTML content:</h4>
+"Nothing of any importance" by [[Rozencrantz|Rozencrantz the Sane]] (his contribution to the [[MMMday06|MMM day 2006]])
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;4edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Like &lt;a class="wiki_link" href="/3EDO"&gt;3EDO&lt;/a&gt;, 4EDO is already familiar as a chord of 12EDO. Again, however, it has a theoretical interest in that it preserves a kind of outline, or skeleton, of melodic movement while erasing key distinctions concerning harmony. The 7-limit tuning map, or &lt;a class="wiki_link" href="/Vals%20and%20Tuning%20Space"&gt;val&lt;/a&gt;, for 4EDO goes &amp;lt;4 6 9 11|, all of which are distinct modulo 4. It therefore goes with tetradic harmony in much the same way that 3EDO goes with triadic harmony, mapping the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; &lt;a class="wiki_link" href="/consistent"&gt;consistent&lt;/a&gt;ly, and sending 15/14, 21/20, 25/24, and 36/35 to the unison. Somewhat confusingly, 9/8 is mapped to the unison also.&lt;br /&gt;
+[[Category:7-limit]]
-&lt;br /&gt;
+[[Category:edo]]
-By putting together the triples of integers which uniquely represent 7-limit tetrads in the &lt;a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices"&gt;7-limit cubic lattice of tetrads&lt;/a&gt; with the number of 4EDO steps returned by the val &amp;lt;4 6 9 11| we obtain a representation of the 7-limit in terms of four integers, which differs from the usual (monzo) representation in that the triple representing the chord can be swapped for another such triple, resulting in a similar note tuned to a different chord. It is even possible under some circumstances to create a sort of recombinant merging of two pieces of music by using the chords of one with the 4EDO skeletons of another.&lt;br /&gt;
+[[Category:macrotonal]]
-&lt;br /&gt;
-We can also add more kinds of chords, for instance the subminor (1-7/6-3/2-5/3) and supermajor (1-9/7-3/2-9/5) to the mix, and by encoding which kind of tetrad a note reconstitute a version of 9-odd-limit tetradic harmony, again changing the harmonic content of a note without changing its 4EDO skeletal position.&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-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Music&lt;/h2&gt;
- &lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/fouredo.mp3" rel="nofollow" target="_blank"&gt;A simple 4edo piece&lt;/a&gt; by &lt;a class="wiki_link" href="/Gene%20Ward%20Smith"&gt;Gene Ward Smith&lt;/a&gt; (see &lt;a class="wiki_link" href="/Composing%20with%20tablets"&gt;Composing with tablets&lt;/a&gt; for explanation)&lt;br /&gt;
-&amp;quot;Nothing of any importance&amp;quot; by &lt;a class="wiki_link" href="/Rozencrantz"&gt;Rozencrantz the Sane&lt;/a&gt; (his contribution to the &lt;a class="wiki_link" href="/MMMday06"&gt;MMM day 2006&lt;/a&gt;)&lt;/body&gt;&lt;/html&gt;</pre></div>