7edo: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:~~genewardsmith~~|~~genewardsmith~~]] and made on <tt>~~2010~~-05-25 ~~22:45~~:45 UTC</tt>.

: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 17:25:31 UTC</tt>.

: The original revision id was <tt>~~144741553~~</tt>.

: The original revision id was <tt>233285188</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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==Intervals in 7-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** ||

|| 1 || 0.0 || unison / prime || exactly 1/1 ||

|| 2 || 171,429 || second || 6,424 c from Ptolemy (neutral) second 11/10

Line 50:

Neutral feel between whole tone scale and major/minor diatonic scale. The second 171,429 c works well as a basic step for melodic progression.

Step from seventh to octave is too large for the leading tone.

==Relative tuning accuracy==

7-edo is the third Zeta function integral tuning, see http://www.research.att.com/~njas/sequences/A117538

Line 63:

[[http://www.seraph.it/dep/det/7edo%20dance.mp3|7edo Dance]] by Carlo Serafini

[[@http://www.ronsword.com/sounds/7edo2.mp3|7-edo Acoustic drone free-improv I]] by Ron Sword

[[@http://www.ronsword.com/sounds/7edo3.mp3|7-edo Acoustic drone free-improv II]] by Ron Sword</pre></div>

[[@http://www.ronsword.com/sounds/7edo3.mp3|7-edo Acoustic drone free-improv II]] by Ron Sword

==Commas==

7 EDO tempers out the following commas. (Note: This assumes val < 7 11 16 20 24 26 |.)

||~ Comma ||~ Monzo ||~ Cents ||~ Name 1 ||~ Name 2 ||~ Name 3 ||

|| 2187/2048 || | -11 7 > || 113.69 || Apotome || || ||

|| 135/128 || | -7 3 1 > || 92.18 || Major Chroma || Major Limma || Pelogic Comma ||

|| 250/243 || | 1 -5 3 > || 49.17 || Maximal Diesis || Porcupine Comma || ||

|| 20000/19683 || | 5 -9 4 > || 27.66 || Minimal Diesis || Tetracot Comma || ||

|| 81/80 || | -4 4 -1 > || 21.51 || Syntonic Comma || Didymos Comma || Meantone Comma ||

|| 1600000/1594323 || | 9 -13 5 > || 6.15 || Amity Comma || || ||

|| 36/35 || | 2 2 -1 -1 > || 48.77 || Septimal Quarter Tone || || ||

|| 525/512 || | -9 1 2 1 > || 43.41 || Avicennma || Avicenna's Enharmonic Diesis || ||

|| 64/63 || | 6 -2 0 -1 > || 27.26 || Septimal Comma || Archytas' Comma || Leipziger Komma ||

|| 875/864 || | -5 -3 3 1 > || 21.90 || Keema || || ||

|| 5120/5103 || | 10 -6 1 -1 > || 5.76 || Hemifamity || || ||

|| 6144/6125 || | 11 1 -3 -2 > || 5.36 || Porwell || || ||

|| 4375/4374 || | -1 -7 4 1 > || 0.40 || Ragisma || || ||

|| 394839/394762 || | 47 -7 -7 -7 > || 0.34 || Akjaysma || 5\7 Octave Comma || ||

|| 100/99 || | 2 -2 2 -1 > || 17.40 || Ptolemisma || || ||

|| 121/120 || | -3 -1 -1 2 > || 14.37 || Biyatisma || || ||

|| 176/175 || | 4 -2 -1 1 > || 9.86 || Valinorsma || || ||

|| 65536/65219 || | 16 -2 -3 > || 8.39 || Orgonisma || || ||

|| 243/242 || | -1 5 -2 > || 7.14 || Rastma || || ||

|| 385/384 || | -7 -1 1 1 1 > || 4.50 || Keenanisma || || ||

|| 4000/3993 || | 5 -1 3 -3 > || 3.03 || Wizardharry || || ||</pre></div>

<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>7edo</title></head><body><h1 id="toc0"><a name="x7 Equal Divisions of the Octave"></a>7 Equal Divisions of the Octave</h1>

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Similarly, in equi-heptatonic systems the desire for harmonic sound may dictate constant adjustments of intonation away from the theoretical interval of 171 cents. One of the most impressive areas in Africa in which a pen-equidistant heptatonic scale is combined with a distinctively harmonic style based on singing in intervals of thirds plus fifths, or thirds plus fourths, is the eastern Angolan culture area. This music is heptatonic and non-modal; i.e., there is no concept of major or minor thirds as distinctive intervals. In principle all the thirds are neutral, but in practice the thirds rendered by the singers often approximate natural major thirds (386 cents), especially at points of rest. In this manner, the principles of equidistance and harmonic euphony are accommodated within one tonal-harmonic system. For the notation of such music, a seven-line stave is most appropriate, with each horizontal line representing one pitch level.

(&quot;African music.&quot; Encyclopædia Britannica. 2009. Encyclopædia Britannica Online. 05 Jul. 2009 &lt;<a class="wiki_link_ext" href="http://www.britannica.com/EBchecked/topic/719112/African-music" rel="nofollow">http://www.britannica.com/EBchecked/topic/719112/African-music</a>&gt;.)

(&quot;African music.&quot; Encyclopædia Britannica. 2009. Encyclopædia Britannica Online. 05 Jul. 2009 &lt;<a class="wiki_link_ext" href="http://www.britannica.com/EBchecked/topic/719112/African-music" rel="nofollow">http://www.britannica.com/EBchecked/topic/719112/African-music</a>&gt;.)

A Thai xylophone measured by Morton (1974) &quot;varied only plus or minus 5 cents,&quot; from 7-TET. A Ugandan Chopi xylophone measured by Haddon (1952) was also tuned to this system.

Line 83:

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<tr>

<td>Interval,

<td>Interval,

in fifths of

in fifths of

an octave

an octave

</td>

<td>Interval

<td>Interval

in ¢

in ¢

</td>

<td>Closest

<td>Closest

diatonic

diatonic

interval name

interval name

</td>

<td>The &quot;neighborhood&quot; of just intervals

Line 194:

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Step from seventh to octave is too large for the leading tone.

<h2 id="toc7"><a name="x7 Equal Divisions of the Octave-Relative tuning accuracy"></a>Relative tuning accuracy</h2>

7-edo is the third Zeta function integral tuning, see <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>

7-edo is the third Zeta function integral tuning, see <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>

<h3 id="toc8"> </h3>

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<a class="wiki_link_ext" href="http://www.seraph.it/dep/det/7edo%20dance.mp3" rel="nofollow">7edo Dance</a> by Carlo Serafini

<a class="wiki_link_ext" href="http://www.ronsword.com/sounds/7edo2.mp3" rel="nofollow" target="_blank">7-edo Acoustic drone free-improv I</a> by Ron Sword

<a class="wiki_link_ext" href="http://www.ronsword.com/sounds/7edo3.mp3" rel="nofollow" target="_blank">7-edo Acoustic drone free-improv II</a> by Ron Sword</body></html></pre></div>

<a class="wiki_link_ext" href="http://www.ronsword.com/sounds/7edo3.mp3" rel="nofollow" target="_blank">7-edo Acoustic drone free-improv II</a> by Ron Sword

<h2 id="toc10"><a name="x7 Equal Divisions of the Octave-Commas"></a>Commas</h2>

7 EDO tempers out the following commas. (Note: This assumes val &lt; 7 11 16 20 24 26 |.)

<tr>

<th>Comma

</th>

<th>Monzo

</th>

<th>Cents

</th>

<th>Name 1

</th>

<th>Name 2

</th>

<th>Name 3

</th>

</tr>

<tr>

<td>2187/2048

</td>

<td>| -11 7 &gt;

</td>

<td>113.69

</td>

<td>Apotome

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>135/128

</td>

<td>| -7 3 1 &gt;

</td>

<td>92.18

</td>

<td>Major Chroma

</td>

<td>Major Limma

</td>

<td>Pelogic Comma

</td>

</tr>

<tr>

<td>250/243

</td>

<td>| 1 -5 3 &gt;

</td>

<td>49.17

</td>

<td>Maximal Diesis

</td>

<td>Porcupine Comma

</td>

<td>

</td>

</tr>

<tr>

<td>20000/19683

</td>

<td>| 5 -9 4 &gt;

</td>

<td>27.66

</td>

<td>Minimal Diesis

</td>

<td>Tetracot Comma

</td>

<td>

</td>

</tr>

<tr>

<td>81/80

</td>

<td>| -4 4 -1 &gt;

</td>

<td>21.51

</td>

<td>Syntonic Comma

</td>

<td>Didymos Comma

</td>

<td>Meantone Comma

</td>

</tr>

<tr>

<td>1600000/1594323

</td>

<td>| 9 -13 5 &gt;

</td>

<td>6.15

</td>

<td>Amity Comma

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>36/35

</td>

<td>| 2 2 -1 -1 &gt;

</td>

<td>48.77

</td>

<td>Septimal Quarter Tone

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>525/512

</td>

<td>| -9 1 2 1 &gt;

</td>

<td>43.41

</td>

<td>Avicennma

</td>

<td>Avicenna's Enharmonic Diesis

</td>

<td>

</td>

</tr>

<tr>

<td>64/63

</td>

<td>| 6 -2 0 -1 &gt;

</td>

<td>27.26

</td>

<td>Septimal Comma

</td>

<td>Archytas' Comma

</td>

<td>Leipziger Komma

</td>

</tr>

<tr>

<td>875/864

</td>

<td>| -5 -3 3 1 &gt;

</td>

<td>21.90

</td>

<td>Keema

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>5120/5103

</td>

<td>| 10 -6 1 -1 &gt;

</td>

<td>5.76

</td>

<td>Hemifamity

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>6144/6125

</td>

<td>| 11 1 -3 -2 &gt;

</td>

<td>5.36

</td>

<td>Porwell

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>4375/4374

</td>

<td>| -1 -7 4 1 &gt;

</td>

<td>0.40

</td>

<td>Ragisma

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>394839/394762

</td>

<td>| 47 -7 -7 -7 &gt;

</td>

<td>0.34

</td>

<td>Akjaysma

</td>

<td>5\7 Octave Comma

</td>

<td>

</td>

</tr>

<tr>

<td>100/99

</td>

<td>| 2 -2 2 -1 &gt;

</td>

<td>17.40

</td>

<td>Ptolemisma

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>121/120

</td>

<td>| -3 -1 -1 2 &gt;

</td>

<td>14.37

</td>

<td>Biyatisma

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>176/175

</td>

<td>| 4 -2 -1 1 &gt;

</td>

<td>9.86

</td>

<td>Valinorsma

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>65536/65219

</td>

<td>| 16 -2 -3 &gt;

</td>

<td>8.39

</td>

<td>Orgonisma

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>243/242

</td>

<td>| -1 5 -2 &gt;

</td>

<td>7.14

</td>

<td>Rastma

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>385/384

</td>

<td>| -7 -1 1 1 1 &gt;

</td>

<td>4.50

</td>

<td>Keenanisma

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>4000/3993

</td>

<td>| 5 -1 3 -3 &gt;

</td>

<td>3.03

</td>

<td>Wizardharry

</td>

<td>

</td>

<td>

</td>

</tr>

</table>

</body></html></pre></div>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2010-05-25 22:45:45 UTC</tt>.<br>
+: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 17:25:31 UTC</tt>.<br>
-: The original revision id was <tt>144741553</tt>.<br>
+: The original revision id was <tt>233285188</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>
@@ Line 20: / Line 20: @@
 ==Intervals in 7-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** ||
 || 1 || 0.0 || unison / prime || exactly 1/1 ||
 || 2 || 171,429 || second || 6,424 c from Ptolemy (neutral) second 11/10
@@ Line 50: / Line 50: @@
 Neutral feel between whole tone scale and major/minor diatonic scale. The second 171,429 c works well as a basic step for melodic progression.
 Step from seventh to octave is too large for the leading tone.
 ==Relative tuning accuracy==
 -edo is the third Zeta function integral tuning, see http://www.research.att.com/~njas/sequences/A117538
@@ Line 63: / Line 63: @@
 [[http://www.seraph.it/dep/det/7edo%20dance.mp3|7edo Dance]] by Carlo Serafini
 [[@http://www.ronsword.com/sounds/7edo2.mp3|7-edo Acoustic drone free-improv I]] by Ron Sword
-[[@http://www.ronsword.com/sounds/7edo3.mp3|7-edo Acoustic drone free-improv II]] by Ron Sword</pre></div>
+[[@http://www.ronsword.com/sounds/7edo3.mp3|7-edo Acoustic drone free-improv II]] by Ron Sword
+==Commas==
+EDO tempers out the following commas. (Note: This assumes val &lt; 7 11 16 20 24 26 |.)
+||~ Comma ||~ Monzo ||~ Cents ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
+|| 2187/2048 || | -11 7 &gt; || 113.69 || Apotome ||   ||   ||
+|| 135/128 || | -7 3 1 &gt; || 92.18 || Major Chroma || Major Limma || Pelogic Comma ||
+|| 250/243 || | 1 -5 3 &gt; || 49.17 || Maximal Diesis || Porcupine Comma ||   ||
+|| 20000/19683 || | 5 -9 4 &gt; || 27.66 || Minimal Diesis || Tetracot Comma ||   ||
+|| 81/80 || | -4 4 -1 &gt; || 21.51 || Syntonic Comma || Didymos Comma || Meantone Comma ||
+|| 1600000/1594323 || | 9 -13 5 &gt; || 6.15 || Amity Comma ||   ||   ||
+|| 36/35 || | 2 2 -1 -1 &gt; || 48.77 || Septimal Quarter Tone ||   ||   ||
+|| 525/512 || | -9 1 2 1 &gt; || 43.41 || Avicennma || Avicenna's Enharmonic Diesis ||   ||
+|| 64/63 || | 6 -2 0 -1 &gt; || 27.26 || Septimal Comma || Archytas' Comma || Leipziger Komma ||
+|| 875/864 || | -5 -3 3 1 &gt; || 21.90 || Keema ||   ||   ||
+|| 5120/5103 || | 10 -6 1 -1 &gt; || 5.76 || Hemifamity ||   ||   ||
+|| 6144/6125 || | 11 1 -3 -2 &gt; || 5.36 || Porwell ||   ||   ||
+|| 4375/4374 || | -1 -7 4 1 &gt; || 0.40 || Ragisma ||   ||   ||
+|| 394839/394762 || | 47 -7 -7 -7 &gt; || 0.34 || Akjaysma || 5\7 Octave Comma ||   ||
+|| 100/99 || | 2 -2 2 -1 &gt; || 17.40 || Ptolemisma ||   ||   ||
+|| 121/120 || | -3 -1 -1 2 &gt; || 14.37 || Biyatisma ||   ||   ||
+|| 176/175 || | 4 -2 -1 1 &gt; || 9.86 || Valinorsma ||   ||   ||
+|| 65536/65219 || | 16 -2 -3 &gt; || 8.39 || Orgonisma ||   ||   ||
+|| 243/242 || | -1 5 -2 &gt; || 7.14 || Rastma ||   ||   ||
+|| 385/384 || | -7 -1 1 1 1 &gt; || 4.50 || Keenanisma ||   ||   ||
+|| 4000/3993 || | 5 -1 3 -3 &gt; || 3.03 || Wizardharry ||   ||   ||</pre></div>
 <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;7edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x7 Equal Divisions of the Octave"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;7 Equal Divisions of the Octave&lt;/h1&gt;
@@ Line 74: / Line 100: @@
 &lt;br /&gt;
 Similarly, in equi-heptatonic systems the desire for harmonic sound may dictate constant adjustments of intonation away from the theoretical interval of 171 cents. One of the most impressive areas in Africa in which a pen-equidistant heptatonic scale is combined with a distinctively harmonic style based on singing in intervals of thirds plus fifths, or thirds plus fourths, is the eastern Angolan culture area. This music is heptatonic and non-modal; i.e., there is no concept of major or minor thirds as distinctive intervals. In principle all the thirds are neutral, but in practice the thirds rendered by the singers often approximate natural major thirds (386 cents), especially at points of rest. In this manner, the principles of equidistance and harmonic euphony are accommodated within one tonal-harmonic system. For the notation of such music, a seven-line stave is most appropriate, with each horizontal line representing one pitch level.&lt;br /&gt;
-&lt;u&gt;&lt;em&gt;(&amp;quot;African music.&amp;quot; Encyclopædia Britannica. 2009. Encyclopædia Britannica Online. 05 Jul. 2009 &amp;lt;&lt;!-- ws:start:WikiTextUrlRule:203:http://www.britannica.com/EBchecked/topic/719112/African-music --&gt;&lt;a class="wiki_link_ext" href="http://www.britannica.com/EBchecked/topic/719112/African-music" rel="nofollow"&gt;http://www.britannica.com/EBchecked/topic/719112/African-music&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:203 --&gt;&amp;gt;.&lt;/em&gt;&lt;/u&gt;)&lt;br /&gt;
+&lt;u&gt;&lt;em&gt;(&amp;quot;African music.&amp;quot; Encyclopædia Britannica. 2009. Encyclopædia Britannica Online. 05 Jul. 2009 &amp;lt;&lt;!-- ws:start:WikiTextUrlRule:651:http://www.britannica.com/EBchecked/topic/719112/African-music --&gt;&lt;a class="wiki_link_ext" href="http://www.britannica.com/EBchecked/topic/719112/African-music" rel="nofollow"&gt;http://www.britannica.com/EBchecked/topic/719112/African-music&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:651 --&gt;&amp;gt;.&lt;/em&gt;&lt;/u&gt;)&lt;br /&gt;
 &lt;br /&gt;
 A Thai xylophone measured by Morton (1974) &amp;quot;varied only plus or minus 5 cents,&amp;quot; from 7-TET. A Ugandan Chopi xylophone measured by Haddon (1952) was also tuned to this system.&lt;br /&gt;
@@ Line 83: / Line 109: @@
 &lt;table class="wiki_table"&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;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;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;strong&gt;The &amp;quot;neighborhood&amp;quot; of just intervals&lt;/strong&gt;&lt;br /&gt;
@@ Line 194: / Line 220: @@
 Step from seventh to octave is too large for the leading tone.&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="x7 Equal Divisions of the Octave-Relative tuning accuracy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Relative tuning accuracy&lt;/h2&gt;
--edo is the third Zeta function integral tuning, see &lt;!-- ws:start:WikiTextUrlRule:204: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:204 --&gt;&lt;br /&gt;
+-edo is the third Zeta function integral tuning, see &lt;!-- ws:start:WikiTextUrlRule:652: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:652 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt; &lt;/h3&gt;
@@ Line 206: / Line 232: @@
 &lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/7edo%20dance.mp3" rel="nofollow"&gt;7edo Dance&lt;/a&gt; by Carlo Serafini&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://www.ronsword.com/sounds/7edo2.mp3" rel="nofollow" target="_blank"&gt;7-edo Acoustic drone free-improv I&lt;/a&gt; by Ron Sword&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://www.ronsword.com/sounds/7edo3.mp3" rel="nofollow" target="_blank"&gt;7-edo Acoustic drone free-improv II&lt;/a&gt; by Ron Sword&lt;/body&gt;&lt;/html&gt;</pre></div>
+&lt;a class="wiki_link_ext" href="http://www.ronsword.com/sounds/7edo3.mp3" rel="nofollow" target="_blank"&gt;7-edo Acoustic drone free-improv II&lt;/a&gt; by Ron Sword&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="x7 Equal Divisions of the Octave-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Commas&lt;/h2&gt;
+EDO tempers out the following commas. (Note: This assumes val &amp;lt; 7 11 16 20 24 26 |.)&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;Monzo&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Cents&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Name 1&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Name 2&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Name 3&lt;br /&gt;
+&lt;/th&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;2187/2048&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -11 7 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;113.69&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Apotome&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;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;135/128&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -7 3 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;92.18&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Major Chroma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Major Limma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Pelogic Comma&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;250/243&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 1 -5 3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;49.17&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Maximal Diesis&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Porcupine Comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;20000/19683&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 5 -9 4 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;27.66&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Minimal Diesis&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Tetracot Comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;81/80&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -4 4 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;21.51&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;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1600000/1594323&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 9 -13 5 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;6.15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Amity Comma&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;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;36/35&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 2 2 -1 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;48.77&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;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;525/512&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -9 1 2 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;43.41&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Avicennma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Avicenna's Enharmonic Diesis&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;64/63&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 6 -2 0 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;27.26&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;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;875/864&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -5 -3 3 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;21.90&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Keema&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;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;5120/5103&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 10 -6 1 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5.76&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;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;6144/6125&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 11 1 -3 -2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5.36&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Porwell&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;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;4375/4374&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -1 -7 4 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0.40&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Ragisma&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;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;394839/394762&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 47 -7 -7 -7 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0.34&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Akjaysma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5\7 Octave Comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;100/99&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 2 -2 2 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;17.40&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Ptolemisma&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;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;121/120&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -3 -1 -1 2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;14.37&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Biyatisma&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;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;176/175&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 4 -2 -1 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9.86&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Valinorsma&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;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;65536/65219&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 16 -2 -3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8.39&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Orgonisma&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;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;243/242&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -1 5 -2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7.14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Rastma&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;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;385/384&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -7 -1 1 1 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4.50&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;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;4000/3993&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 5 -1 3 -3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3.03&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Wizardharry&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;/tr&gt;
+&lt;/table&gt;
+&lt;/body&gt;&lt;/html&gt;</pre></div>