5edo: Difference between revisions

Wikispaces>xenwolf
**Imported revision 215469498 - Original comment: **
Wikispaces>jdfreivald
**Imported revision 233282612 - Original comment: Added commas tempered out.**
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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:xenwolf|xenwolf]] and made on <tt>2011-03-30 11:29:43 UTC</tt>.<br>
: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 17:16:39 UTC</tt>.<br>
: The original revision id was <tt>215469498</tt>.<br>
: The original revision id was <tt>233282612</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt>Added commas tempered out.</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>
<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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]]
<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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]]
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==Intervals in 5-edo==  
==Intervals in 5-edo==  
|| **Interval,
|| **Interval,**
in fifths of
**in fifths of**
an octave** || **Interval
**an octave** || **Interval**
in ¢** || **Closest
**in ¢** || **Closest**
diatonic
**diatonic**
interval name** || **The "neighborhood" of just intervals** ||
**interval name** || **The "neighborhood" of just intervals** ||
|| 0 || 0.0 || unison / prime || exactly 1/1 ||
|| 0 || 0.0 || unison / prime || exactly 1/1 ||
|| 1 || 240.0 || second / third || +8.826 c from septimal second 8/7
|| 1 || 240.0 || second / third || +8.826 c from septimal second 8/7
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==**Compositions**, improvisations==  
==**Compositions**, improvisations==  
* Brian McLaren: various and sundry
* Brian McLaren: various and sundry
* [[http://www.io.com/~hmiller/|Herman Miller]]: //[[http://micro.soonlabel.com/herman_miller/Daybreak.mp3|Daybreak on Slendro Mountain]]// (2000)
* [[http://www.io.com/%7Ehmiller/|Herman Miller]]: //[[http://micro.soonlabel.com/herman_miller/Daybreak.mp3|Daybreak on Slendro Mountain]]// (2000)
* Paul Rubenstein: various, with electric guitars in 10- and 15-edo
* Paul Rubenstein: various, with electric guitars in 10- and 15-edo
* Aaron K. Johnson: //[[http://www.akjmusic.com/audio/5tet_funk.mp3|5tet funk]]// (2004)
* Aaron K. Johnson: //[[http://www.akjmusic.com/audio/5tet_funk.mp3|5tet funk]]// (2004)
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==Chord or scale?==  
==Chord or scale?==  
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.</pre></div>
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.
 
==Commas Tempered==
5-EDO tempers out the following commas. (Note: This assumes the val &lt; 5 8 12 14 17 19 |.)
 
||~ Comma ||~ Value (cents) ||~ Name ||~ Second Name ||~ Third Name ||~ Val ||
||= 256/243 ||&gt; 90.225 || Limma || Pythagorean Minor 2nd ||  || | 8 -5 &gt; ||
||= 81/80 ||&gt; 21.506 || Syntonic Comma || Didymos Comma || Meantone Comma || | -4 4 -1 &gt; ||
||= 2889416/2882415 ||&gt; 4.200 || Vulture ||  ||  || | 24 -21 4 &gt; ||
||= 36/35 ||&gt; 48.770 || Septimal Quarter Tone ||  ||  || | 2 2 -1 -1 &gt; ||
||= 49/48 ||&gt; 35.697 || Slendro Diesis ||  ||  || | -4 -1 2 &gt; ||
||= 64/63 ||&gt; 27.264 || Septimal Comma || Archytas' Comma || Leipziger Komma || | 6 -2 0 -1 &gt; ||
||= 245/243 ||&gt; 14.191 || Sensamagic ||  ||  || | -5 1 2 &gt; ||
||= 1728/1715 ||&gt; 13.074 || Orwellisma || Orwell Comma ||  || | 6 3 -1 -3 &gt; ||
||= 1029/1024 ||&gt; 8.433 || Gamelisma ||  ||  || | -10 1 0 3 &gt; ||
||= 19683/19600 ||&gt; 7.316 || Cataharry ||  ||  || | -4 9 -2 -2 &gt; ||
||= 5120/5103 ||&gt; 5.758 || Hemifamity ||  ||  || | 10 -6 1 -1 &gt; ||
||= 1065875/1063543 ||&gt; 3.792 || Wadisma ||  ||  || | -26 -1 1 9 &gt; ||
||= 420175/419904 ||&gt; 1.117 || Wizma ||  ||  || | -6 -8 2 5 &gt; ||
||= 99/98 ||&gt; 17.576 || Mothwellsma ||  ||  || | -1 2 -2 1 &gt; ||
||= 896/891 ||&gt; 9.688 || Pentacircle ||  ||  || | 7 -4 0 1 -1 &gt; ||
||= 385/384 ||&gt; 4.503 || Keenanisma ||  ||  || | -7 -1 1 1 1 &gt; ||
||= 441/440 ||&gt; 3.930 || Werckisma ||  ||  || | -3 2 -1 2 -1 &gt; ||
||= 3025/3024 ||&gt; 0.572 || Lehmerisma ||  ||  || | -4 -3 2 -1 2 &gt; ||
||= 91/90 ||&gt; 19.130 || Superleap ||  ||  || | -1 -2 -1 1 1 &gt; ||
||= 676/675 ||&gt; 2.563 || Parizeksma ||  ||  || | 2 -3 -2 2 &gt; ||
 
&lt;span style="display: block; height: 1px; left: -10000px; overflow: hidden; position: absolute; top: 1730px; width: 1px;"&gt;
|| &lt; 5 8 12 14 17 19 | ||
&lt;/span&gt;</pre></div>
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<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;5edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:26:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;a href="#x5 Equal Divisions of the Octave: Theory"&gt;5 Equal Divisions of the Octave: Theory&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt; | &lt;a href="#x5-edo in Musicmaking"&gt;5-edo in Musicmaking&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt;&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt;&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&gt;&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt;&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;5edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:28:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt;&lt;a href="#x5 Equal Divisions of the Octave: Theory"&gt;5 Equal Divisions of the Octave: Theory&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt;&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt; | &lt;a href="#x5-edo in Musicmaking"&gt;5-edo in Musicmaking&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt;&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&gt;&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt;&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&gt;&lt;!-- ws:end:WikiTextTocRule:40 --&gt;&lt;!-- ws:start:WikiTextTocRule:41: --&gt;&lt;!-- ws:end:WikiTextTocRule:41 --&gt;&lt;!-- ws:start:WikiTextTocRule:42: --&gt;&lt;!-- ws:end:WikiTextTocRule:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&gt;
&lt;!-- ws:end:WikiTextTocRule:40 --&gt;&lt;br /&gt;
&lt;!-- ws:end:WikiTextTocRule:43 --&gt;&lt;hr /&gt;
&lt;br /&gt;
&lt;hr /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x5 Equal Divisions of the Octave: Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;5 Equal Divisions of the Octave: Theory&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x5 Equal Divisions of the Octave: Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;5 Equal Divisions of the Octave: Theory&lt;/h1&gt;
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&lt;table class="wiki_table"&gt;
&lt;table class="wiki_table"&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;Interval,&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;Interval,&lt;/strong&gt;&lt;br /&gt;
in fifths of&lt;br /&gt;
&lt;strong&gt;in fifths of&lt;/strong&gt;&lt;br /&gt;
an octave&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;an octave&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;strong&gt;Interval&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;Interval&lt;/strong&gt;&lt;br /&gt;
in ¢&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;in ¢&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;strong&gt;Closest&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;Closest&lt;/strong&gt;&lt;br /&gt;
diatonic&lt;br /&gt;
&lt;strong&gt;diatonic&lt;/strong&gt;&lt;br /&gt;
interval name&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;interval name&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;strong&gt;The &amp;quot;neighborhood&amp;quot; of just intervals&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;The &amp;quot;neighborhood&amp;quot; of just intervals&lt;/strong&gt;&lt;br /&gt;
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Also tempered out is 27/25, if we temper this out in preference to 16/15 we obtain &lt;a class="wiki_link" href="/Bug%20family"&gt;bug temperament&lt;/a&gt;, 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.&lt;br /&gt;
Also tempered out is 27/25, if we temper this out in preference to 16/15 we obtain &lt;a class="wiki_link" href="/Bug%20family"&gt;bug temperament&lt;/a&gt;, 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.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Despite its lack of accuracy, 5EDO is the second Zeta function integral tuning, after 2EDO. See &lt;!-- ws:start:WikiTextUrlRule:248:http://www.research.att.com/~njas/sequences/A117538 --&gt;&lt;a class="wiki_link_ext" href="http://www.research.att.com/~njas/sequences/A117538" rel="nofollow"&gt;http://www.research.att.com/~njas/sequences/A117538&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:248 --&gt;&lt;br /&gt;
Despite its lack of accuracy, 5EDO is the second Zeta function integral tuning, after 2EDO. See &lt;!-- ws:start:WikiTextUrlRule:686:http://www.research.att.com/~njas/sequences/A117538 --&gt;&lt;a class="wiki_link_ext" href="http://www.research.att.com/~njas/sequences/A117538" rel="nofollow"&gt;http://www.research.att.com/~njas/sequences/A117538&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:686 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x5 Equal Divisions of the Octave: Theory-Cycles, Divisions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Cycles, Divisions&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x5 Equal Divisions of the Octave: Theory-Cycles, Divisions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Cycles, Divisions&lt;/h2&gt;
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  &lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt; &lt;/h2&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt; &lt;/h2&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x5-edo in Musicmaking-Compositions, improvisations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;&lt;strong&gt;Compositions&lt;/strong&gt;, improvisations&lt;/h2&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x5-edo in Musicmaking-Compositions, improvisations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;&lt;strong&gt;Compositions&lt;/strong&gt;, improvisations&lt;/h2&gt;
  &lt;ul&gt;&lt;li&gt;Brian McLaren: various and sundry&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.io.com/~hmiller/" rel="nofollow"&gt;Herman Miller&lt;/a&gt;: &lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/herman_miller/Daybreak.mp3" rel="nofollow"&gt;Daybreak on Slendro Mountain&lt;/a&gt;&lt;/em&gt; (2000)&lt;/li&gt;&lt;li&gt;Paul Rubenstein: various, with electric guitars in 10- and 15-edo&lt;/li&gt;&lt;li&gt;Aaron K. Johnson: &lt;em&gt;&lt;a class="wiki_link_ext" href="http://www.akjmusic.com/audio/5tet_funk.mp3" rel="nofollow"&gt;5tet funk&lt;/a&gt;&lt;/em&gt; (2004)&lt;/li&gt;&lt;li&gt;Bill Sethares: &lt;em&gt;5-tet funk&lt;/em&gt; (2004), &lt;em&gt;Pentacle&lt;/em&gt; (2004)&lt;/li&gt;&lt;li&gt;X.J.Scott: &lt;em&gt;Sleeping Through It All&lt;/em&gt; (2004)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&amp;amp;songID=1519939" rel="nofollow"&gt;Andrew Heathwaite: //Pinta Penta// (2004)&lt;/a&gt; (rendered in 6 alternative pentatonics as well)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Hans%20Straub"&gt;Hans Straub&lt;/a&gt;: &lt;a class="wiki_link_ext" href="http://home.datacomm.ch/straub/mamuth/5tet_e.html#asimchomsaia" rel="nofollow"&gt;Asîmchômsaia&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Brian%20Wong"&gt;Brian Wong&lt;/a&gt;: &lt;a class="wiki_link_ext" href="http://bwong.ca/template1.php?sub=3" rel="nofollow"&gt;Slendronica#1b&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
  &lt;ul&gt;&lt;li&gt;Brian McLaren: various and sundry&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/" rel="nofollow"&gt;Herman Miller&lt;/a&gt;: &lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/herman_miller/Daybreak.mp3" rel="nofollow"&gt;Daybreak on Slendro Mountain&lt;/a&gt;&lt;/em&gt; (2000)&lt;/li&gt;&lt;li&gt;Paul Rubenstein: various, with electric guitars in 10- and 15-edo&lt;/li&gt;&lt;li&gt;Aaron K. Johnson: &lt;em&gt;&lt;a class="wiki_link_ext" href="http://www.akjmusic.com/audio/5tet_funk.mp3" rel="nofollow"&gt;5tet funk&lt;/a&gt;&lt;/em&gt; (2004)&lt;/li&gt;&lt;li&gt;Bill Sethares: &lt;em&gt;5-tet funk&lt;/em&gt; (2004), &lt;em&gt;Pentacle&lt;/em&gt; (2004)&lt;/li&gt;&lt;li&gt;X.J.Scott: &lt;em&gt;Sleeping Through It All&lt;/em&gt; (2004)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&amp;amp;songID=1519939" rel="nofollow"&gt;Andrew Heathwaite: //Pinta Penta// (2004)&lt;/a&gt; (rendered in 6 alternative pentatonics as well)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Hans%20Straub"&gt;Hans Straub&lt;/a&gt;: &lt;a class="wiki_link_ext" href="http://home.datacomm.ch/straub/mamuth/5tet_e.html#asimchomsaia" rel="nofollow"&gt;Asîmchômsaia&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Brian%20Wong"&gt;Brian Wong&lt;/a&gt;: &lt;a class="wiki_link_ext" href="http://bwong.ca/template1.php?sub=3" rel="nofollow"&gt;Slendronica#1b&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="x5-edo in Musicmaking-Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Notation&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="x5-edo in Musicmaking-Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Notation&lt;/h2&gt;
  &lt;ul&gt;&lt;li&gt;via Reinhard's cents notation&lt;/li&gt;&lt;li&gt;Sagittal: naturals on a five-line staff, with enharmonics (used interchangably) E=F and B=C&lt;/li&gt;&lt;li&gt;a four-line hybrid treble/bass staff.&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
  &lt;ul&gt;&lt;li&gt;via Reinhard's cents notation&lt;/li&gt;&lt;li&gt;Sagittal: naturals on a five-line staff, with enharmonics (used interchangably) E=F and B=C&lt;/li&gt;&lt;li&gt;a four-line hybrid treble/bass staff.&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="x5-edo in Musicmaking-Chord or scale?"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Chord or scale?&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="x5-edo in Musicmaking-Chord or scale?"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Chord or scale?&lt;/h2&gt;
  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.&lt;/body&gt;&lt;/html&gt;</pre></div>
  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.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="x5-edo in Musicmaking-Commas Tempered"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Commas Tempered&lt;/h2&gt;
5-EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 5 8 12 14 17 19 |.)&lt;br /&gt;
&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;Comma&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Value (cents)&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Name&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Second Name&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Third Name&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Val&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;256/243&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;90.225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Limma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Pythagorean Minor 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 8 -5 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;81/80&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;21.506&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Syntonic Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Didymos Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Meantone Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -4 4 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;2889416/2882415&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;4.200&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Vulture&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 24 -21 4 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;36/35&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;48.770&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Septimal Quarter Tone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 2 2 -1 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;49/48&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;35.697&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Slendro Diesis&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -4 -1 2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;64/63&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;27.264&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Septimal Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Archytas' Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Leipziger Komma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 6 -2 0 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;245/243&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;14.191&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Sensamagic&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -5 1 2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;1728/1715&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;13.074&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Orwellisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Orwell Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 6 3 -1 -3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;1029/1024&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;8.433&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gamelisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -10 1 0 3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;19683/19600&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;7.316&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Cataharry&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -4 9 -2 -2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;5120/5103&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;5.758&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Hemifamity&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 10 -6 1 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;1065875/1063543&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;3.792&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Wadisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -26 -1 1 9 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;420175/419904&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1.117&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Wizma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -6 -8 2 5 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;99/98&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;17.576&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Mothwellsma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -1 2 -2 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;896/891&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;9.688&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Pentacircle&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 7 -4 0 1 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;385/384&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;4.503&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Keenanisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -7 -1 1 1 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;441/440&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;3.930&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Werckisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -3 2 -1 2 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3025/3024&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;0.572&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Lehmerisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -4 -3 2 -1 2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;91/90&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;19.130&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Superleap&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -1 -2 -1 1 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;676/675&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;2.563&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Parizeksma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 2 -3 -2 2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;span style="display: block; height: 1px; left: -10000px; overflow: hidden; position: absolute; top: 1730px; width: 1px;"&gt;&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&amp;lt; 5 8 12 14 17 19 |&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/span&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>