5-limit: Difference between revisions
Wikispaces>Omegatron **Imported revision 519425308 - Original comment: ** |
Wikispaces>PiotrGrochowski **Imported revision 589203844 - 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:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-08-11 03:40:03 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>589203844</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 octave equivalence classes of 5-limit intervals can usefully be depicted on a lattice diagram, either as a [[http://en.wikipedia.org/wiki/Hexagonal_lattice|hexagonal lattice]] or as a [[http://en.wikipedia.org/wiki/Square_lattice|square lattice]]; this can be done automatically by [[http://www.huygens-fokker.org/scala/|Scala]]. If the intervals are depicted with maximum symmetry as a hexagonal lattice, then the corresponding 5-limit triads define a [[http://en.wikipedia.org/wiki/Hexagonal_tiling|hexagonal tiling]]. | The octave equivalence classes of 5-limit intervals can usefully be depicted on a lattice diagram, either as a [[http://en.wikipedia.org/wiki/Hexagonal_lattice|hexagonal lattice]] or as a [[http://en.wikipedia.org/wiki/Square_lattice|square lattice]]; this can be done automatically by [[http://www.huygens-fokker.org/scala/|Scala]]. If the intervals are depicted with maximum symmetry as a hexagonal lattice, then the corresponding 5-limit triads define a [[http://en.wikipedia.org/wiki/Hexagonal_tiling|hexagonal tiling]]. | ||
[[EDO]]s which do relatively well in approximating the 5-limit are [[ | [[EDO]]s which do relatively well in approximating the 5-limit are [[2edo]], [[3edo]], [[7edo]], [[9edo]], [[10edo]], [[12edo]], [[19edo]], [[22edo]], [[31edo]], [[34edo]], [[53edo]], [[65edo]], [[118edo]] and [[171edo]]. | ||
==Syntonic Comma Pairs== | ==Syntonic Comma Pairs== | ||
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The octave equivalence classes of 5-limit intervals can usefully be depicted on a lattice diagram, either as a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Hexagonal_lattice" rel="nofollow">hexagonal lattice</a> or as a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Square_lattice" rel="nofollow">square lattice</a>; this can be done automatically by <a class="wiki_link_ext" href="http://www.huygens-fokker.org/scala/" rel="nofollow">Scala</a>. If the intervals are depicted with maximum symmetry as a hexagonal lattice, then the corresponding 5-limit triads define a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Hexagonal_tiling" rel="nofollow">hexagonal tiling</a>.<br /> | The octave equivalence classes of 5-limit intervals can usefully be depicted on a lattice diagram, either as a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Hexagonal_lattice" rel="nofollow">hexagonal lattice</a> or as a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Square_lattice" rel="nofollow">square lattice</a>; this can be done automatically by <a class="wiki_link_ext" href="http://www.huygens-fokker.org/scala/" rel="nofollow">Scala</a>. If the intervals are depicted with maximum symmetry as a hexagonal lattice, then the corresponding 5-limit triads define a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Hexagonal_tiling" rel="nofollow">hexagonal tiling</a>.<br /> | ||
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<a class="wiki_link" href="/EDO">EDO</a>s which do relatively well in approximating the 5-limit are <a class="wiki_link" href="/ | <a class="wiki_link" href="/EDO">EDO</a>s which do relatively well in approximating the 5-limit are <a class="wiki_link" href="/2edo">2edo</a>, <a class="wiki_link" href="/3edo">3edo</a>, <a class="wiki_link" href="/7edo">7edo</a>, <a class="wiki_link" href="/9edo">9edo</a>, <a class="wiki_link" href="/10edo">10edo</a>, <a class="wiki_link" href="/12edo">12edo</a>, <a class="wiki_link" href="/19edo">19edo</a>, <a class="wiki_link" href="/22edo">22edo</a>, <a class="wiki_link" href="/31edo">31edo</a>, <a class="wiki_link" href="/34edo">34edo</a>, <a class="wiki_link" href="/53edo">53edo</a>, <a class="wiki_link" href="/65edo">65edo</a>, <a class="wiki_link" href="/118edo">118edo</a> and <a class="wiki_link" href="/171edo">171edo</a>.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Syntonic Comma Pairs"></a><!-- ws:end:WikiTextHeadingRule:0 -->Syntonic Comma Pairs</h2> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Syntonic Comma Pairs"></a><!-- ws:end:WikiTextHeadingRule:0 -->Syntonic Comma Pairs</h2> | ||