5edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 144739479 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 151099181 - Original comment: 1 piece added, 1 link fixed** |
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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:xenwolf|xenwolf]] and made on <tt>2010-06-30 10:54:52 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>151099181</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>1 piece added, 1 link fixed</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> | ||
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* X.J.Scott: //Sleeping Through It All// (2004) | * X.J.Scott: //Sleeping Through It All// (2004) | ||
* Andrew Heathwaite: //Pinta Penta// (2004) (rendered in 6 alternative pentatonics as well) | * Andrew Heathwaite: //Pinta Penta// (2004) (rendered in 6 alternative pentatonics as well) | ||
* Hans Straub: | * [[Hans Straub]]: [[http://home.datacomm.ch/straub/mamuth/5tet_e.html#asimchomsaia|Asîmchômsaia]] | ||
* [[ | * [[Brian Wong]]: [[http://bwong.ca/template1.php?sub=3|Slendronica#1b]] | ||
==Notation== | ==Notation== | ||
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Also tempered out is 27/25, leading to <a class="wiki_link" href="/beep%20temperament">beep temperament</a>, which equates 10/9 with 6/5: it is a little more perverse even than <a class="wiki_link" href="/father%20temperament">father</a>. Because these intervals are so large, this sort of analysis is less significant with 5 than it becomes with larger and more accurate divisions, but it still plays a role. For example, I-IV-V-I is the same as 1-III-V-I and involves triads with common intervals because of fourth-thirds equivalence.<br /> | Also tempered out is 27/25, leading to <a class="wiki_link" href="/beep%20temperament">beep temperament</a>, which equates 10/9 with 6/5: it is a little more perverse even than <a class="wiki_link" href="/father%20temperament">father</a>. Because these intervals are so large, this sort of analysis is less significant with 5 than it becomes with larger and more accurate divisions, but it still plays a role. For example, I-IV-V-I is the same as 1-III-V-I and involves triads with common intervals because of fourth-thirds equivalence.<br /> | ||
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Despite its lack of accuracy, 5EDO is the second Zeta function integral tuning, after 2EDO. See <!-- ws:start:WikiTextUrlRule: | Despite its lack of accuracy, 5EDO is the second Zeta function integral tuning, after 2EDO. See <!-- ws:start:WikiTextUrlRule:247:http://www.research.att.com/~njas/sequences/A117538 --><a class="wiki_link_ext" href="http://www.research.att.com/~njas/sequences/A117538" rel="nofollow">http://www.research.att.com/~njas/sequences/A117538</a><!-- ws:end:WikiTextUrlRule:247 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x5 Equal Divisions of the Octave: Theory-Cycles, Divisions"></a><!-- ws:end:WikiTextHeadingRule:10 -->Cycles, Divisions</h2> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x5 Equal Divisions of the Octave: Theory-Cycles, Divisions"></a><!-- ws:end:WikiTextHeadingRule:10 -->Cycles, Divisions</h2> | ||
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<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><!-- ws:end:WikiTextHeadingRule:14 --> </h2> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><!-- ws:end:WikiTextHeadingRule:14 --> </h2> | ||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x5-edo in Musicmaking-Compositions, improvisations"></a><!-- ws:end:WikiTextHeadingRule:16 --><strong>Compositions</strong>, improvisations</h2> | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x5-edo in Musicmaking-Compositions, improvisations"></a><!-- ws:end:WikiTextHeadingRule:16 --><strong>Compositions</strong>, improvisations</h2> | ||
<ul><li>Brian McLaren: various and sundry</li><li><a class="wiki_link_ext" href="http://home.comcast.net/%7Eteamouse/daybreak-vsc.mp3" rel="nofollow">Herman Miller</a>: <em><a class="wiki_link_ext" href="http://home.comcast.net/%7Eteamouse/daybreak-vsc.mp3" rel="nofollow">Daybreak on Slendro Mountain</a></em> (2000)</li><li>Paul Rubenstein: various, with electric guitars in 10- and 15-edo</li><li>Aaron K. Johnson: <em><a class="wiki_link_ext" href="http://www.akjmusic.com/audio/5tet_funk.mp3" rel="nofollow">5tet funk</a></em> (2004)</li><li>Bill Sethares: <em>5-tet funk</em> (2004), <em>Pentacle</em> (2004)</li><li>X.J.Scott: <em>Sleeping Through It All</em> (2004)</li><li>Andrew Heathwaite: <em>Pinta Penta</em> (2004) (rendered in 6 alternative pentatonics as well)</li><li>Hans Straub | <ul><li>Brian McLaren: various and sundry</li><li><a class="wiki_link_ext" href="http://home.comcast.net/%7Eteamouse/daybreak-vsc.mp3" rel="nofollow">Herman Miller</a>: <em><a class="wiki_link_ext" href="http://home.comcast.net/%7Eteamouse/daybreak-vsc.mp3" rel="nofollow">Daybreak on Slendro Mountain</a></em> (2000)</li><li>Paul Rubenstein: various, with electric guitars in 10- and 15-edo</li><li>Aaron K. Johnson: <em><a class="wiki_link_ext" href="http://www.akjmusic.com/audio/5tet_funk.mp3" rel="nofollow">5tet funk</a></em> (2004)</li><li>Bill Sethares: <em>5-tet funk</em> (2004), <em>Pentacle</em> (2004)</li><li>X.J.Scott: <em>Sleeping Through It All</em> (2004)</li><li>Andrew Heathwaite: <em>Pinta Penta</em> (2004) (rendered in 6 alternative pentatonics as well)</li><li><a class="wiki_link" href="/Hans%20Straub">Hans Straub</a>: <a class="wiki_link_ext" href="http://home.datacomm.ch/straub/mamuth/5tet_e.html#asimchomsaia" rel="nofollow">Asîmchômsaia</a></li><li><a class="wiki_link" href="/Brian%20Wong">Brian Wong</a>: <a class="wiki_link_ext" href="http://bwong.ca/template1.php?sub=3" rel="nofollow">Slendronica#1b</a></li></ul><br /> | ||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="x5-edo in Musicmaking-Notation"></a><!-- ws:end:WikiTextHeadingRule:18 -->Notation</h2> | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="x5-edo in Musicmaking-Notation"></a><!-- ws:end:WikiTextHeadingRule:18 -->Notation</h2> | ||
<ul><li>via Reinhard's cents notation</li><li>Sagittal: naturals on a five-line staff, with enharmonics (used interchangably) E=F and B=C</li><li>a four-line hybrid treble/bass staff.</li></ul><br /> | <ul><li>via Reinhard's cents notation</li><li>Sagittal: naturals on a five-line staff, with enharmonics (used interchangably) E=F and B=C</li><li>a four-line hybrid treble/bass staff.</li></ul><br /> | ||