7-limit symmetrical lattices: Difference between revisions
Wikispaces>guest **Imported revision 142266299 - Original comment: ** |
Wikispaces>guest **Imported revision 142266305 - 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:guest|guest]] and made on <tt>2010-05-16 01: | : This revision was by author [[User:guest|guest]] and made on <tt>2010-05-16 01:29:11 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>142266305</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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where we may remove the sqrt(2) factor without changing anything substantial. We may also remove the two term, and write elements of symmetrical interval class space by |* x y z>. | where we may remove the sqrt(2) factor without changing anything substantial. We may also remove the two term, and write elements of symmetrical interval class space by |* x y z>. | ||
The thirteen intervals of the 7-limit [[Tonality Diamond|tonality diamond]] are represented by the unison |* 0 0 0> and twelve twelve lattice points at a distance of one from the unison, given by +-|* 1 0 0>, +-|* 0 1 0>, +-|* 0 0 1>, +-|* 1 -1 0>, +-|* 1 0 -1> and +-|* 0 1 -1>. These lie on the verticies of a [[http://en.wikipedia.org/wiki/Cuboctahedron|cubeoctahedron]], a semiregular solid. The lattice has two types of holes--the shallow holes, which are [[http://en.wikipedia.org/wiki/Tetrahedron|tetrahera]] and which correspond to the major and minor [[http://tonalsoft.com/enc/tetrad.htm|tetrads]] 4:5:6:7 and 1/4:1/5:1/6:1/7, and the deep holes which are [[http://en.wikipedia.org/wiki/Octahedron|octaheda]] and | The thirteen intervals of the 7-limit [[Tonality Diamond|tonality diamond]] are represented by the unison |* 0 0 0> and twelve twelve lattice points at a distance of one from the unison, given by +-|* 1 0 0>, +-|* 0 1 0>, +-|* 0 0 1>, +-|* 1 -1 0>, +-|* 1 0 -1> and +-|* 0 1 -1>. These lie on the verticies of a [[http://en.wikipedia.org/wiki/Cuboctahedron|cubeoctahedron]], a semiregular solid. The lattice has two types of holes--the shallow holes, which are [[http://en.wikipedia.org/wiki/Tetrahedron|tetrahera]] and which correspond to the major and minor [[http://tonalsoft.com/enc/tetrad.htm|tetrads]] 4:5:6:7 and 1/4:1/5:1/6:1/7, and the deep holes which are [[http://en.wikipedia.org/wiki/Octahedron|octaheda]] and | ||
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where we may remove the sqrt(2) factor without changing anything substantial. We may also remove the two term, and write elements of symmetrical interval class space by |* x y z&gt;.<br /> | where we may remove the sqrt(2) factor without changing anything substantial. We may also remove the two term, and write elements of symmetrical interval class space by |* x y z&gt;.<br /> | ||
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The thirteen intervals of the 7-limit <a class="wiki_link" href="/Tonality%20Diamond">tonality diamond</a> are represented by the unison |* 0 0 0&gt; and twelve twelve lattice points at a distance of one from the unison, given by +-|* 1 0 0&gt;, +-|* 0 1 0&gt;, +-|* 0 0 1&gt;, +-|* 1 -1 0&gt;, +-|* 1 0 -1&gt; and +-|* 0 1 -1&gt;. These lie on the verticies of a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Cuboctahedron" rel="nofollow">cubeoctahedron</a>, a semiregular solid. The lattice has two types of holes--the shallow holes, which are <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Tetrahedron" rel="nofollow">tetrahera</a> and which correspond to the major and minor <a class="wiki_link_ext" href="http://tonalsoft.com/enc/tetrad.htm" rel="nofollow">tetrads</a> 4:5:6:7 and 1/4:1/5:1/6:1/7, and the deep holes which are <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Octahedron" rel="nofollow">octaheda</a> and<br /> | The thirteen intervals of the 7-limit <a class="wiki_link" href="/Tonality%20Diamond">tonality diamond</a> are represented by the unison |* 0 0 0&gt; and twelve twelve lattice points at a distance of one from the unison, given by +-|* 1 0 0&gt;, +-|* 0 1 0&gt;, +-|* 0 0 1&gt;, +-|* 1 -1 0&gt;, +-|* 1 0 -1&gt; and +-|* 0 1 -1&gt;. These lie on the verticies of a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Cuboctahedron" rel="nofollow">cubeoctahedron</a>, a semiregular solid. The lattice has two types of holes--the shallow holes, which are <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Tetrahedron" rel="nofollow">tetrahera</a> and which correspond to the major and minor <a class="wiki_link_ext" href="http://tonalsoft.com/enc/tetrad.htm" rel="nofollow">tetrads</a> 4:5:6:7 and 1/4:1/5:1/6:1/7, and the deep holes which are <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Octahedron" rel="nofollow">octaheda</a> and<br /> | ||