5edo: Difference between revisions
Wikispaces>Cenobyte **Imported revision 370816884 - Original comment: ** |
Wikispaces>spt3125 **Imported revision 480694862 - 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:spt3125|spt3125]] and made on <tt>2014-01-05 11:53:22 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>480694862</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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==="Equal Pentatonic"=== | ==="Equal Pentatonic"=== | ||
5-edo divides the 1200-[[cent]] octave into 5 equal parts, making its smallest interval exactly 240 [[cent|cents]], or the fifth root of | 5-edo divides the 1200-[[cent]] octave into 5 equal parts, making its smallest interval exactly 240 [[cent|cents]], or the fifth root of two. 5-edo is the 3rd [[prime numbers|prime]] edo, after [[2edo]] and [[3edo]]. Most importantly, 5-edo is the smallest [[edo]] containing xenharmonic intervals! (1edo 2edo 3edo 4edo are all subsets of 12edo.) | ||
==Listen to the sound of the 5-edo scale== | ==Listen to the sound of the 5-edo scale== | ||
For any musician, there is no substitute for the experience of a particular xenharmonic sound. The user going by the name Hyacinth on Wikipedia and Wikimedia Commons has many xenharmonic MIDI's and has graciously copylefted them! This is his 5-edo scale MIDI: | For any musician, there is no substitute for the experience of a particular xenharmonic sound. The user going by the name Hyacinth on Wikipedia and Wikimedia Commons has many xenharmonic MIDI's and has graciously copylefted them! This is his 5-edo scale MIDI: | ||
http://commons.wikimedia.org/wiki/File:5-tet_scale_on_C.mid | [[@http://commons.wikimedia.org/wiki/File:5-tet_scale_on_C.mid]] | ||
==Intervals in 5-edo== | ==Intervals in 5-edo== | ||
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-8.826 c from septimal seventh 7/4 || | -8.826 c from septimal seventh 7/4 || | ||
|| 5 || 1200.0 || eighth || exactly 2/1 || | || 5 || 1200.0 || eighth || exactly 2/1 || | ||
[[media type="custom" key="24802268"]] | |||
[[file:5ed2-001.svg]] | |||
==Related scales== | ==Related scales== | ||
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If 5-edo is regarded as a temperament, which is to say as 5-et, then the most salient fact is that 16/15 is tempered out. This means in 5-et the major third and the fourth, and the minor sixth and the fifth, are not distinguished; this is 5-limit [[Trienstonic clan|father temperament]]. | If 5-edo is regarded as a temperament, which is to say as 5-et, then the most salient fact is that 16/15 is tempered out. This means in 5-et the major third and the fourth, and the minor sixth and the fifth, are not distinguished; this is 5-limit [[Trienstonic clan|father temperament]]. | ||
Also tempered out is 27/25, if we temper this out in preference to 16/15 we obtain [[Bug family|bug temperament]], 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 | Also tempered out is 27/25, if we temper this out in preference to 16/15 we obtain [[Bug family|bug temperament]], 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 I-III-V-I and involves triads with common intervals because of fourth-thirds equivalence. | ||
Despite its lack of accuracy, 5EDO is the second [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]], after 2EDO. It also is the smallest equal division representing the [[9-limit]] [[consistent]]ly, giving a distinct value modulo five to 2, 3, 5, 7 and 9. Hence in a way similar to how [[4edo]] 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 [[The Seven Limit Symmetrical Lattices|lattice]] of tetrads/pentads together with the number of scale steps in 5EDO. However, while [[2edo]] represents the [[3-limit]] consistently, [[3edo]] the [[5-limit]], [[4edo]] the [[7-limit]] and [[5edo]] the [[9-limit]], to represent the [[11-limit]] consistently with a [[patent val]] requires going all the way to [[22edo]]. | Despite its lack of accuracy, 5EDO is the second [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]], after 2EDO. It also is the smallest equal division representing the [[9-limit]] [[consistent]]ly, giving a distinct value modulo five to 2, 3, 5, 7 and 9. Hence in a way similar to how [[4edo]] 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 [[The Seven Limit Symmetrical Lattices|lattice]] of tetrads/pentads together with the number of scale steps in 5EDO. However, while [[2edo]] represents the [[3-limit]] consistently, [[3edo]] the [[5-limit]], [[4edo]] the [[7-limit]] and [[5edo]] the [[9-limit]], to represent the [[11-limit]] consistently with a [[patent val]] requires going all the way to [[22edo]]. | ||
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** Bill Sethares: //5-tet funk// (2004), //Pentacle// (2004) | ** Bill Sethares: //5-tet funk// (2004), //Pentacle// (2004) | ||
** "Cenobyte" Ukulele [[http://www.youtube.com/watch?v=UKUCRnEJKKU| http://www.youtube.com/watch?v=UKUCRnEJKKU]] | ** "Cenobyte" Ukulele [[http://www.youtube.com/watch?v=UKUCRnEJKKU| http://www.youtube.com/watch?v=UKUCRnEJKKU]] | ||
** " | ** "[[@http://www.jamendo.com/en/list/a104474/true-island-5-equal-divisions-of-the-octave-ukulele|True Island]]" (album) by Small Scale Revolution (2011) | ||
>> | >> | ||
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==Melody== | ==Melody== | ||
Smallest edo which can be used for melodies in "standard" way. Relatively large step of 240 c can be used as major second for the melody construction. The scale has whole-tone as well as pentatonic character. | |||
==Chord or scale?== | ==Chord or scale?== | ||
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||= 676/675 ||> 2.563 || Parizeksma || || || | 2 -3 -2 0 0 2 > || ||</pre></div> | ||= 676/675 ||> 2.563 || Parizeksma || || || | 2 -3 -2 0 0 2 > || ||</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>5edo</title></head><body><!-- ws:start:WikiTextTocRule: | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>5edo</title></head><body><!-- ws:start:WikiTextTocRule:29:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><a href="#x5 Equal Divisions of the Octave: Theory">5 Equal Divisions of the Octave: Theory</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --> | <a href="#x5-edo in Musicmaking">5-edo in Musicmaking</a><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="x5 Equal Divisions of the Octave: Theory"></a><!-- ws:end:WikiTextHeadingRule:1 -->5 Equal Divisions of the Octave: Theory</h1> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:3:&lt;h3&gt; --><h3 id="toc1"><a name="x5 Equal Divisions of the Octave: Theory--&quot;Equal Pentatonic&quot;"></a><!-- ws:end:WikiTextHeadingRule:3 -->&quot;Equal Pentatonic&quot;</h3> | ||
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5-edo divides the 1200-<a class="wiki_link" href="/cent">cent</a> octave into 5 equal parts, making its smallest interval exactly 240 <a class="wiki_link" href="/cent">cents</a>, or the fifth root of | 5-edo divides the 1200-<a class="wiki_link" href="/cent">cent</a> octave into 5 equal parts, making its smallest interval exactly 240 <a class="wiki_link" href="/cent">cents</a>, or the fifth root of two. 5-edo is the 3rd <a class="wiki_link" href="/prime%20numbers">prime</a> edo, after <a class="wiki_link" href="/2edo">2edo</a> and <a class="wiki_link" href="/3edo">3edo</a>. Most importantly, 5-edo is the smallest <a class="wiki_link" href="/edo">edo</a> containing xenharmonic intervals! (1edo 2edo 3edo 4edo are all subsets of 12edo.)<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc2"><a name="x5 Equal Divisions of the Octave: Theory-Listen to the sound of the 5-edo scale"></a><!-- ws:end:WikiTextHeadingRule:5 -->Listen to the sound of the 5-edo scale</h2> | ||
<br /> | <br /> | ||
For any musician, there is no substitute for the experience of a particular xenharmonic sound. The user going by the name Hyacinth on Wikipedia and Wikimedia Commons has many xenharmonic MIDI's and has graciously copylefted them! This is his 5-edo scale MIDI:<br /> | For any musician, there is no substitute for the experience of a particular xenharmonic sound. The user going by the name Hyacinth on Wikipedia and Wikimedia Commons has many xenharmonic MIDI's and has graciously copylefted them! This is his 5-edo scale MIDI:<br /> | ||
<a class="wiki_link_ext" href="http://commons.wikimedia.org/wiki/File:5-tet_scale_on_C.mid" rel="nofollow" target="_blank">http://commons.wikimedia.org/wiki/File:5-tet_scale_on_C.mid</a><br /> | |||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:7:&lt;h2&gt; --><h2 id="toc3"><a name="x5 Equal Divisions of the Octave: Theory-Intervals in 5-edo"></a><!-- ws:end:WikiTextHeadingRule:7 -->Intervals in 5-edo</h2> | ||
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<!-- ws:start:WikiTextHeadingRule:9:&lt;h2&gt; --><h2 id="toc4"><a name="x5 Equal Divisions of the Octave: Theory-Related scales"></a><!-- ws:end:WikiTextHeadingRule:9 -->Related scales</h2> | |||
<ul><li>By its cardinality, 5-edo is related to other <a class="wiki_link" href="/pentatonic">pentatonic</a> scales, and it is especially close in sound to many Indonesian <a class="wiki_link" href="/slendro">slendros</a>.</li><li>Due to the interest around the &quot;fifth&quot; interval size, there are many <a class="wiki_link" href="/nonoctave">nonoctave</a> &quot;stretch sisters&quot; to 5-edo: square root of 4/3, cube root of 3/2, 8th root of 3, etc.</li><li>For the same reason there are many &quot;circle sisters&quot;:<ul><li>Make a chain of five &quot;bigger fifths&quot; (50/33), which makes three octaves 3.227¢ flat. (50/33)^5=7.985099.</li></ul></li></ul><br /> | <ul><li>By its cardinality, 5-edo is related to other <a class="wiki_link" href="/pentatonic">pentatonic</a> scales, and it is especially close in sound to many Indonesian <a class="wiki_link" href="/slendro">slendros</a>.</li><li>Due to the interest around the &quot;fifth&quot; interval size, there are many <a class="wiki_link" href="/nonoctave">nonoctave</a> &quot;stretch sisters&quot; to 5-edo: square root of 4/3, cube root of 3/2, 8th root of 3, etc.</li><li>For the same reason there are many &quot;circle sisters&quot;:<ul><li>Make a chain of five &quot;bigger fifths&quot; (50/33), which makes three octaves 3.227¢ flat. (50/33)^5=7.985099.</li></ul></li></ul><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:11:&lt;h2&gt; --><h2 id="toc5"><a name="x5 Equal Divisions of the Octave: Theory-As a temperament"></a><!-- ws:end:WikiTextHeadingRule:11 -->As a temperament</h2> | ||
If 5-edo is regarded as a temperament, which is to say as 5-et, then the most salient fact is that 16/15 is tempered out. This means in 5-et the major third and the fourth, and the minor sixth and the fifth, are not distinguished; this is 5-limit <a class="wiki_link" href="/Trienstonic%20clan">father temperament</a>.<br /> | If 5-edo is regarded as a temperament, which is to say as 5-et, then the most salient fact is that 16/15 is tempered out. This means in 5-et the major third and the fourth, and the minor sixth and the fifth, are not distinguished; this is 5-limit <a class="wiki_link" href="/Trienstonic%20clan">father temperament</a>.<br /> | ||
<br /> | <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 | 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 I-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 <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a>, after 2EDO. It also is the smallest equal division representing the <a class="wiki_link" href="/9-limit">9-limit</a> <a class="wiki_link" href="/consistent">consistent</a>ly, 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 <a class="wiki_link" href="/7-limit">7-limit</a> 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 <a class="wiki_link" href="/3-limit">3-limit</a> consistently, <a class="wiki_link" href="/3edo">3edo</a> the <a class="wiki_link" href="/5-limit">5-limit</a>, <a class="wiki_link" href="/4edo">4edo</a> the <a class="wiki_link" href="/7-limit">7-limit</a> and <a class="wiki_link" href="/5edo">5edo</a> the <a class="wiki_link" href="/9-limit">9-limit</a>, to represent the <a class="wiki_link" href="/11-limit">11-limit</a> 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 /> | Despite its lack of accuracy, 5EDO is the second <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a>, after 2EDO. It also is the smallest equal division representing the <a class="wiki_link" href="/9-limit">9-limit</a> <a class="wiki_link" href="/consistent">consistent</a>ly, 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 <a class="wiki_link" href="/7-limit">7-limit</a> 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 <a class="wiki_link" href="/3-limit">3-limit</a> consistently, <a class="wiki_link" href="/3edo">3edo</a> the <a class="wiki_link" href="/5-limit">5-limit</a>, <a class="wiki_link" href="/4edo">4edo</a> the <a class="wiki_link" href="/7-limit">7-limit</a> and <a class="wiki_link" href="/5edo">5edo</a> the <a class="wiki_link" href="/9-limit">9-limit</a>, to represent the <a class="wiki_link" href="/11-limit">11-limit</a> 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 /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:13:&lt;h2&gt; --><h2 id="toc6"><a name="x5 Equal Divisions of the Octave: Theory-Cycles, Divisions"></a><!-- ws:end:WikiTextHeadingRule:13 -->Cycles, Divisions</h2> | ||
5 is a prime number so 5-edo contains no sub-edos. Only simple cycles:<br /> | 5 is a prime number so 5-edo contains no sub-edos. Only simple cycles:<br /> | ||
Cycle of seconds: 0-1-2-3-4-0<br /> | Cycle of seconds: 0-1-2-3-4-0<br /> | ||
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Cycle of sevenths: 0-4-3-2-1-0<br /> | Cycle of sevenths: 0-4-3-2-1-0<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:15:&lt;h1&gt; --><h1 id="toc7"><a name="x5-edo in Musicmaking"></a><!-- ws:end:WikiTextHeadingRule:15 -->5-edo in Musicmaking</h1> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:17:&lt;h2&gt; --><h2 id="toc8"><a name="x5-edo in Musicmaking-Compositions, improvisations"></a><!-- ws:end:WikiTextHeadingRule:17 --><strong>Compositions</strong>, improvisations</h2> | ||
<ul><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><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> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Wong/Slendronica1b.ogg" rel="nofollow">play</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><li>Bill Sethares: <em>5-tet funk</em> (2004), <em>Pentacle</em> (2004)</li><li>&quot;Cenobyte&quot; Ukulele <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=UKUCRnEJKKU" rel="nofollow"> http://www.youtube.com/watch?v=UKUCRnEJKKU</a></li><li>&quot | <ul><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><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> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Wong/Slendronica1b.ogg" rel="nofollow">play</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><li>Bill Sethares: <em>5-tet funk</em> (2004), <em>Pentacle</em> (2004)</li><li>&quot;Cenobyte&quot; Ukulele <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=UKUCRnEJKKU" rel="nofollow"> http://www.youtube.com/watch?v=UKUCRnEJKKU</a></li><li>&quot;<a class="wiki_link_ext" href="http://www.jamendo.com/en/list/a104474/true-island-5-equal-divisions-of-the-octave-ukulele" rel="nofollow" target="_blank">True Island</a>&quot; (album) by Small Scale Revolution (2011)<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:19:&lt;h2&gt; --><h2 id="toc9"><a name="x5-edo in Musicmaking-Notation"></a><!-- ws:end:WikiTextHeadingRule:19 -->Notation</h2> | ||
<ul><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></ul><br /> | <ul><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></ul><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:21:&lt;h2&gt; --><h2 id="toc10"><a name="x5-edo in Musicmaking-Harmony"></a><!-- ws:end:WikiTextHeadingRule:21 -->Harmony</h2> | ||
5edo does not have any strong consonance nor dissonance. The 240 cent interval can serve as either a major second or minor third, and the 960 cent interval as either a major sixth or minor seventh. The fourth is about 18 cents flat of a just fourth, making it rather &quot;dirty&quot; but recognizable. The fifth is likewise about 18 cents sharp of a just fifth, dissonant but still easily recognizable.<br /> | 5edo does not have any strong consonance nor dissonance. The 240 cent interval can serve as either a major second or minor third, and the 960 cent interval as either a major sixth or minor seventh. The fourth is about 18 cents flat of a just fourth, making it rather &quot;dirty&quot; but recognizable. The fifth is likewise about 18 cents sharp of a just fifth, dissonant but still easily recognizable.<br /> | ||
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Important chords:<br /> | Important chords:<br /> | ||
<ul><li>0+1+3</li><li>0+2+3</li><li>0+1+3+4</li><li>0+2+3+4</li></ul><br /> | <ul><li>0+1+3</li><li>0+2+3</li><li>0+1+3+4</li><li>0+2+3+4</li></ul><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:23:&lt;h2&gt; --><h2 id="toc11"><a name="x5-edo in Musicmaking-Melody"></a><!-- ws:end:WikiTextHeadingRule:23 -->Melody</h2> | ||
Smallest edo which can be used for melodies in &quot;standard&quot; way. Relatively large step of 240 c can be used as major second for the melody construction. The scale has whole-tone as well as pentatonic character.<br /> | |||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:25:&lt;h2&gt; --><h2 id="toc12"><a name="x5-edo in Musicmaking-Chord or scale?"></a><!-- ws:end:WikiTextHeadingRule:25 -->Chord or scale?</h2> | ||
Either way, it is hard to wander very far from where you start. However, it has the scale-like feature that there are (barely) enough notes to create melody, in the form of an equal version of pentatonic.<br /> | Either way, it is hard to wander very far from where you start. However, it has the scale-like feature that there are (barely) enough notes to create melody, in the form of an equal version of pentatonic.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:27:&lt;h2&gt; --><h2 id="toc13"><a name="x5-edo in Musicmaking-Commas Tempered"></a><!-- ws:end:WikiTextHeadingRule:27 -->Commas Tempered</h2> | ||
5-EDO tempers out the following commas. (Note: This assumes the val &lt; 5 8 12 14 17 19 |.)<br /> | 5-EDO tempers out the following commas. (Note: This assumes the val &lt; 5 8 12 14 17 19 |.)<br /> | ||
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