4edo: Difference between revisions
Wikispaces>hstraub **Imported revision 239086831 - Original comment: ** |
Wikispaces>spt3125 **Imported revision 479398476 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2013-12-25 20:34:07 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>479398476</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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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 | 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)</pre></div> | |||
<h4>Original HTML content:</h4> | <h4>Original HTML 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;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. Sometimes confusingly, 9/8 is mapped to the unison also.<br /> | <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. Sometimes confusingly, 9/8 is mapped to the unison also.<br /> | ||
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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 /> | 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 /> | ||
<br /> | <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 | 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 /> | ||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Music"></a><!-- ws:end:WikiTextHeadingRule:0 -->Music</h2> | |||
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<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)</body></html></pre></div> | |||