385/384: Difference between revisions
Wikispaces>phylingual **Imported revision 354809076 - Original comment: ** |
Wikispaces>phylingual **Imported revision 354810156 - 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:phylingual|phylingual]] and made on <tt>2012-07-25 17: | : This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-07-25 17:50:56 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>354810156</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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The keenanisma equates 48/35 with 11/8 and 35/24 with 16/11; these are 7-limit intervals of low complexity, lying across from 1/1 in the hexanies 8/7-6/5-48/35-8/5-12/7-2 and 7/6-5/4-35/24-5/3-7/4-2. Hence keenanismic tempering allows the hexany to be viewed as containing some 11-limit harmony. The hexany is a fundamental construct in the 3D lattice of [[The Seven Limit Symmetrical Lattices|7-limit pitch classes]], the "deep holes" of the lattice as opposed to the "holes" represented by major and minor tetrads, and in terms of the [[The Seven Limit Symmetrical Lattices|cubic lattice of 7-limit tetrads]], the otonal tetrad with root 11 (or 11/8) is represented by [-2 0 0]: 1-6/5-48/35-12/7-2. In terms of 7-limit chord relationships, this complexity is as low as possible for an 11-limit projection comma, equaling the [0 1 -1] of 56/55 and less than the other alternatives. Since keenanismic temperament is also quite accurate, this singles it out as being of special interest. | The keenanisma equates 48/35 with 11/8 and 35/24 with 16/11; these are 7-limit intervals of low complexity, lying across from 1/1 in the hexanies 8/7-6/5-48/35-8/5-12/7-2 and 7/6-5/4-35/24-5/3-7/4-2. Hence keenanismic tempering allows the hexany to be viewed as containing some 11-limit harmony. The hexany is a fundamental construct in the 3D lattice of [[The Seven Limit Symmetrical Lattices|7-limit pitch classes]], the "deep holes" of the lattice as opposed to the "holes" represented by major and minor tetrads, and in terms of the [[The Seven Limit Symmetrical Lattices|cubic lattice of 7-limit tetrads]], the otonal tetrad with root 11 (or 11/8) is represented by [-2 0 0]: 1-6/5-48/35-12/7-2. In terms of 7-limit chord relationships, this complexity is as low as possible for an 11-limit projection comma, equaling the [0 1 -1] of 56/55 and less than the other alternatives. Since keenanismic temperament is also quite accurate, this singles it out as being of special interest. | ||
EDOs with [[patent val]]s tempering out the keenansima include [[19edo|19]], [[22edo|22]], [[31edo|31]], [[41edo|41]], [[53edo|53]], [[68edo|68]], [[72edo|72]], [[118edo|118]], [[159edo|159]], [[190edo|190]], [[212edo|212]] and [[284edo|284]]. | EDOs with [[patent val]]s tempering out the keenansima include [[15edo|15]], [[19edo|19]], [[22edo|22]], [[31edo|31]], [[34edo|34]], [[37edo|37]], [[41edo|41]], [[53edo|53]], [[68edo|68]], [[72edo|72]], [[118edo|118]], [[159edo|159]], [[190edo|190]], [[212edo|212]] and [[284edo|284]]. | ||
Characteristic of keenanismic tempering are the [[keenanismic tetrads]], 385/384-tempered versions of 1-5/4-3/2-12/7, 1-5/4-10/7-12/7, 1-6/5-3/2-7/4, 1-5/4-16/11-7/4, and 1-14/11-16/11-7/4. These are essentially tempered [[dyadic chord]]s, where every dyad of the chord is a keenanismic tempered version of an interval of the 11-limit [[tonality diamond]], and hence regarded as an 11-limit consonance. | Characteristic of keenanismic tempering are the [[keenanismic tetrads]], 385/384-tempered versions of 1-5/4-3/2-12/7, 1-5/4-10/7-12/7, 1-6/5-3/2-7/4, 1-5/4-16/11-7/4, and 1-14/11-16/11-7/4. These are essentially tempered [[dyadic chord]]s, where every dyad of the chord is a keenanismic tempered version of an interval of the 11-limit [[tonality diamond]], and hence regarded as an 11-limit consonance. | ||
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The keenanisma equates 48/35 with 11/8 and 35/24 with 16/11; these are 7-limit intervals of low complexity, lying across from 1/1 in the hexanies 8/7-6/5-48/35-8/5-12/7-2 and 7/6-5/4-35/24-5/3-7/4-2. Hence keenanismic tempering allows the hexany to be viewed as containing some 11-limit harmony. The hexany is a fundamental construct in the 3D lattice of <a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices">7-limit pitch classes</a>, the &quot;deep holes&quot; of the lattice as opposed to the &quot;holes&quot; represented by major and minor tetrads, and in terms of the <a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices">cubic lattice of 7-limit tetrads</a>, the otonal tetrad with root 11 (or 11/8) is represented by [-2 0 0]: 1-6/5-48/35-12/7-2. In terms of 7-limit chord relationships, this complexity is as low as possible for an 11-limit projection comma, equaling the [0 1 -1] of 56/55 and less than the other alternatives. Since keenanismic temperament is also quite accurate, this singles it out as being of special interest.<br /> | The keenanisma equates 48/35 with 11/8 and 35/24 with 16/11; these are 7-limit intervals of low complexity, lying across from 1/1 in the hexanies 8/7-6/5-48/35-8/5-12/7-2 and 7/6-5/4-35/24-5/3-7/4-2. Hence keenanismic tempering allows the hexany to be viewed as containing some 11-limit harmony. The hexany is a fundamental construct in the 3D lattice of <a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices">7-limit pitch classes</a>, the &quot;deep holes&quot; of the lattice as opposed to the &quot;holes&quot; represented by major and minor tetrads, and in terms of the <a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices">cubic lattice of 7-limit tetrads</a>, the otonal tetrad with root 11 (or 11/8) is represented by [-2 0 0]: 1-6/5-48/35-12/7-2. In terms of 7-limit chord relationships, this complexity is as low as possible for an 11-limit projection comma, equaling the [0 1 -1] of 56/55 and less than the other alternatives. Since keenanismic temperament is also quite accurate, this singles it out as being of special interest.<br /> | ||
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EDOs with <a class="wiki_link" href="/patent%20val">patent val</a>s tempering out the keenansima include <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/41edo">41</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/118edo">118</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/190edo">190</a>, <a class="wiki_link" href="/212edo">212</a> and <a class="wiki_link" href="/284edo">284</a>.<br /> | EDOs with <a class="wiki_link" href="/patent%20val">patent val</a>s tempering out the keenansima include <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/37edo">37</a>, <a class="wiki_link" href="/41edo">41</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/118edo">118</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/190edo">190</a>, <a class="wiki_link" href="/212edo">212</a> and <a class="wiki_link" href="/284edo">284</a>.<br /> | ||
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Characteristic of keenanismic tempering are the <a class="wiki_link" href="/keenanismic%20tetrads">keenanismic tetrads</a>, 385/384-tempered versions of 1-5/4-3/2-12/7, 1-5/4-10/7-12/7, 1-6/5-3/2-7/4, 1-5/4-16/11-7/4, and 1-14/11-16/11-7/4. These are essentially tempered <a class="wiki_link" href="/dyadic%20chord">dyadic chord</a>s, where every dyad of the chord is a keenanismic tempered version of an interval of the 11-limit <a class="wiki_link" href="/tonality%20diamond">tonality diamond</a>, and hence regarded as an 11-limit consonance.<br /> | Characteristic of keenanismic tempering are the <a class="wiki_link" href="/keenanismic%20tetrads">keenanismic tetrads</a>, 385/384-tempered versions of 1-5/4-3/2-12/7, 1-5/4-10/7-12/7, 1-6/5-3/2-7/4, 1-5/4-16/11-7/4, and 1-14/11-16/11-7/4. These are essentially tempered <a class="wiki_link" href="/dyadic%20chord">dyadic chord</a>s, where every dyad of the chord is a keenanismic tempered version of an interval of the 11-limit <a class="wiki_link" href="/tonality%20diamond">tonality diamond</a>, and hence regarded as an 11-limit consonance.<br /> | ||
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