5edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 235619756 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 235621164 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-06-09 20: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-09 20:22:45 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>235621164</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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* Bill Sethares: //5-tet funk// (2004), //Pentacle// (2004) | * Bill Sethares: //5-tet funk// (2004), //Pentacle// (2004) | ||
* [[http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&songID=1519939|Andrew Heathwaite: //Pinta Penta// (2004)]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+pintapentain5tet.mp3|play]] (rendered in 6 alternative pentatonics as well) | * [[http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&songID=1519939|Andrew Heathwaite: //Pinta Penta// (2004)]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+pintapentain5tet.mp3|play]] (rendered in 6 alternative pentatonics as well) | ||
* [[Hans Straub]]: [[http://home.datacomm.ch/straub/mamuth/5tet_e.html#asimchomsaia|Asîmchômsaia]] | * [[Hans Straub]]: [[http://home.datacomm.ch/straub/mamuth/5tet_e.html#asimchomsaia|Asîmchômsaia]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Straub/asimchomsaia.mp3|play]] | ||
* [[Brian Wong]]: [[http://bwong.ca/template1.php?sub=3|Slendronica#1b]] | * [[Brian Wong]]: [[http://bwong.ca/template1.php?sub=3|Slendronica#1b]] | ||
* Brian McLaren: various and sundry | * Brian McLaren: various and sundry | ||
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Also tempered out is 27/25, if we temper this out in preference to 16/15 we obtain <a class="wiki_link" href="/Bug%20family">bug temperament</a>, which equates 10/9 with 6/5: it is a little more perverse even than father. 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, if we temper this out in preference to 16/15 we obtain <a class="wiki_link" href="/Bug%20family">bug temperament</a>, which equates 10/9 with 6/5: it is a little more perverse even than father. 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 /> | ||
<br /> | <br /> | ||
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:692: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:692 -->. It also is the smallest equal division representing the 9-limit consistently, giving a distinct value modulo five to 2, 3, 5, 7 and 9. Hence in a way similar to how <a class="wiki_link" href="/4edo">4edo</a> can be used, and which is discussed in that article, it can be used to represent 7-limit intervals in terms of their position in a pentad, by giving a triple of integers representing a pentad in the <a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices">lattice</a> of tetrads/pentads together with the number of scale steps in 5EDO. However, while <a class="wiki_link" href="/2edo">2edo</a> represents the 3-limit consistently, <a class="wiki_link" href="/3edo">3edo</a> the 5-limit, <a class="wiki_link" href="/4edo">4edo</a> the 7-limit and <a class="wiki_link" href="/5edo">5edo</a> the 9-limit, to represent the 11-limit consistently with a <a class="wiki_link" href="/patent%20val">patent val</a> requires going all the way to <a class="wiki_link" href="/22edo">22edo</a>.<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><a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/" rel="nofollow">Herman Miller</a>: <em><a class="wiki_link_ext" href="http://micro.soonlabel.com/herman_miller/Daybreak.mp3" rel="nofollow">Daybreak on Slendro Mountain</a></em> (2000)</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><a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&amp;songID=1519939" rel="nofollow">Andrew Heathwaite: //Pinta Penta// (2004)</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+pintapentain5tet.mp3" rel="nofollow">play</a> (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><li>Brian McLaren: various and sundry</li><li>Paul Rubenstein: various, with electric guitars in 10- and 15-edo</li><li>X.J.Scott: <em>Sleeping Through It All</em> (2004)</li></ul><!-- 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><a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/" rel="nofollow">Herman Miller</a>: <em><a class="wiki_link_ext" href="http://micro.soonlabel.com/herman_miller/Daybreak.mp3" rel="nofollow">Daybreak on Slendro Mountain</a></em> (2000)</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><a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&amp;songID=1519939" rel="nofollow">Andrew Heathwaite: //Pinta Penta// (2004)</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+pintapentain5tet.mp3" rel="nofollow">play</a> (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> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Straub/asimchomsaia.mp3" rel="nofollow">play</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><li>Brian McLaren: various and sundry</li><li>Paul Rubenstein: various, with electric guitars in 10- and 15-edo</li><li>X.J.Scott: <em>Sleeping Through It All</em> (2004)</li></ul><!-- 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 /> | ||
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="x5-edo in Musicmaking-Harmony"></a><!-- ws:end:WikiTextHeadingRule:20 -->Harmony</h2> | <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="x5-edo in Musicmaking-Harmony"></a><!-- ws:end:WikiTextHeadingRule:20 -->Harmony</h2> | ||