4edo: Difference between revisions
Wikispaces>hstraub **Imported revision 479441308 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 514125680 - 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:genewardsmith|genewardsmith]] and made on <tt>2014-06-16 17:32:22 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>514125680</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> | ||
<h4>Original Wikitext content:</h4> | <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. | <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. | ||
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"Nothing of any importance" by [[Rozencrantz|Rozencrantz the Sane]] (his contribution to the [[MMMday06|MMM day 2006]])</pre></div> | "Nothing of any importance" by [[Rozencrantz|Rozencrantz the Sane]] (his contribution to the [[MMMday06|MMM day 2006]])</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. | <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 /> | ||
<br /> | <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 /> | 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 /> | ||