7edo: Difference between revisions

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<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>~~2014~~-05-~~02 09~~:38:03 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-03-24 01:12:08 UTC</tt>.

: The original revision id was <tt>~~506006792~~</tt>.

: The original revision id was <tt>545084694</tt>.

: The revision comment was: <tt>~~Reverted to Jan 5, 2014 9:15 am: I already did the AAH link. :)~~</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.

<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]]

="neutral diatonic"=

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|| **Interval** || **Interval**

**size**

**in ¢** || **Closest**

**in ¢, DMS** || **Closest**

**diatonic**

**interval name** || **The "neighborhood" of just intervals** ||

|| 0 || 0.0 || unison / prime || exactly 1/1 ||

|| 1 || 171.429 || second || 6.424 c from Ptolemy (neutral) second 11/10

|| 1 || 171.429,

3.215 c from second 54/49

51°25'43" || second || 6.424 c, 1°55'38" from Ptolemy (neutral) second 11/10

-10.~~976~~ c from (Didymus) major second (small whole tone) 10/9 ||

3.215 c, 57'53" from second 54/49

|| 2 || 342.857 || third || -4.551 c from neutral third 11/9 ||

-10.9 c, -3°17'33"76 from (Didymus) major second (small whole tone) 10/9 ||

|| 3 || 514.286 || fourth || 16.241 c from just fourth 4/3 (498.045 c)

|| 2 || 342.857,

-5.265 c from wide fourth 27/20 ||

102°51'26" || third || -4.551 c, -1°21'55" from neutral third 11/9 ||

|| 4 || 685.714 || fifth || 5.265 c from narrow fifth 40/27

|| 3 || 514.286,

-16.241 c from just fifth 3/2 (701.955 c) ||

154°17'9" || fourth || 16.241 c, 4°52'20" from just fourth 4/3 (498.045 c)

|| 5 || 857.143 || sixth || 4.551 c from neutral sixth 18/11 ||

-5.265 c, -1°34'47" from wide fourth 27/20 ||

|| 6 || 1028.571 || seventh || 10.975 c from (Didymus) minor seventh 9/5

|| 4 || 685.714,

-6.425 c from neutral seventh 20/11

205°42'51" || fifth || 5.265 c, 1°34'47" from narrow fifth 40/27

1.006 c from the 29th harmonic 29/16

-16.241 c, -4°52'20" from just fifth 3/2 (701.955 c) ||

-3.216 c from seventh 49/27 ||

|| 5 || 857.143,

|| 7 (0) || 1200.0 || eighth || exactly 2/1 ||

257°8'34" || sixth || 4.551 c, 1°21'55" from neutral sixth 18/11 ||

|| 6 || 1028.571,

308°34'17" || seventh || 10.975 c, 3°17'33" from (Didymus) minor seventh 9/5

-6.425 c, -1°55'38" from neutral seventh 20/11

1.006 c, 18'6" from the 29th harmonic 29/16

-3.216 c, -57'53" from seventh 49/27 ||

|| 7 (0) || 1200.0, 360º || eighth || exactly 2/1 ||

[[media type="custom" key="24802290"]]

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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"><html><head><title>7edo</title></head><body><a href="#x&quot;neutral diatonic&quot;">&quot;neutral diatonic&quot;</a> | <a href="#Intervals in 7-edo">Intervals in 7-edo</a> | <a href="#Related scales">Related scales</a> | <a href="#Music">Music</a> | <a href="#Commas">Commas</a>

~~ ~~

<h1 id="toc0"><a name="x&quot;neutral diatonic&quot;"></a>&quot;neutral diatonic&quot;</h1>

<h1 id="toc0"><a name="x&quot;neutral diatonic&quot;"></a>&quot;neutral diatonic&quot;</h1>

7-edo divides the 1200-cent <a class="wiki_link" href="/octave">octave</a> into 7 equal parts, making its smallest interval <a class="wiki_link" href="/cent">171.428¢</a>, or the seventh root of 2. It is the fourth <a class="wiki_link" href="/prime%20numbers">prime</a> edo, after <a class="wiki_link" href="/2edo">2edo</a>, <a class="wiki_link" href="/3edo">3edo</a> and <a class="wiki_link" href="/5edo">5edo</a>.

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<td>Interval

size

in ¢

in ¢, DMS

</td>

<td>Closest

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<td>1

</td>

<td>171.429

<td>171.429,

51°25'43&quot;

</td>

<td>second

</td>

<td>6.424 c from Ptolemy (neutral) second 11/10

<td>6.424 c, 1°55'38&quot; from Ptolemy (neutral) second 11/10

3.215 c from second 54/49

3.215 c, 57'53&quot; from second 54/49

-10.~~976~~ c from (Didymus) major second (small whole tone) 10/9

-10.9 c, -3°17'33&quot;76 from (Didymus) major second (small whole tone) 10/9

</td>

</tr>

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<td>2

</td>

<td>342.857

<td>342.857,

102°51'26&quot;

</td>

<td>third

</td>

<td>-4.551 c from neutral third 11/9

<td>-4.551 c, -1°21'55&quot; from neutral third 11/9

</td>

</tr>

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<td>3

</td>

<td>514.286

<td>514.286,

154°17'9&quot;

</td>

<td>fourth

</td>

<td>16.241 c from just fourth 4/3 (498.045 c)

<td>16.241 c, 4°52'20&quot; from just fourth 4/3 (498.045 c)

-5.265 c from wide fourth 27/20

-5.265 c, -1°34'47&quot; from wide fourth 27/20

</td>

</tr>

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<td>4

</td>

<td>685.714

<td>685.714,

205°42'51&quot;

</td>

<td>fifth

</td>

<td>5.265 c from narrow fifth 40/27

<td>5.265 c, 1°34'47&quot; from narrow fifth 40/27

-16.241 c from just fifth 3/2 (701.955 c)

-16.241 c, -4°52'20&quot; from just fifth 3/2 (701.955 c)

</td>

</tr>

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<td>5

</td>

<td>857.143

<td>857.143,

257°8'34&quot;

</td>

<td>sixth

</td>

<td>4.551 c from neutral sixth 18/11

<td>4.551 c, 1°21'55&quot; from neutral sixth 18/11

</td>

</tr>

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<td>6

</td>

<td>1028.571

<td>1028.571,

308°34'17&quot;

</td>

<td>seventh

</td>

<td>10.975 c from (Didymus) minor seventh 9/5

<td>10.975 c, 3°17'33&quot; from (Didymus) minor seventh 9/5

-6.425 c from neutral seventh 20/11

-6.425 c, -1°55'38&quot; from neutral seventh 20/11

1.006 c from the 29th harmonic 29/16

1.006 c, 18'6&quot; from the 29th harmonic 29/16

-3.216 c from seventh 49/27

-3.216 c, -57'53&quot; from seventh 49/27

</td>

</tr>

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<td>7 (0)

</td>

<td>1200.0

<td>1200.0, 360º

</td>

<td>eighth

@@ 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>2014-05-02 09:38:03 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-03-24 01:12:08 UTC</tt>.<br>
-: The original revision id was <tt>506006792</tt>.<br>
+: The original revision id was <tt>545084694</tt>.<br>
-: The revision comment was: <tt>Reverted to Jan 5, 2014 9:15 am: I already did the AAH link. :)</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>
 <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]]
 ="neutral diatonic"=
@@ Line 25: / Line 24: @@
 || **Interval** || **Interval**
 **size**
-**in ¢** || **Closest**
+**in ¢, DMS** || **Closest**
 **diatonic**
 **interval name** || **The "neighborhood" of just intervals** ||
 || 0 || 0.0 || unison / prime || exactly 1/1 ||
-|| 1 || 171.429 || second || 6.424 c from Ptolemy (neutral) second 11/10
+|| 1 || 171.429,
-.215 c from second 54/49
+°25'43" || second || 6.424 c, 1°55'38" from Ptolemy (neutral) second 11/10
--10.976 c from (Didymus) major second (small whole tone) 10/9 ||
+.215 c, 57'53" from second 54/49
-|| 2 || 342.857 || third || -4.551 c from neutral third 11/9 ||
+-10.9&lt;span style="line-height: 1.5;"&gt; c, -3°17'33"76 from (Didymus) major second (small whole tone) 10/9&lt;/span&gt; ||
-|| 3 || 514.286 || fourth || 16.241 c from just fourth 4/3 (498.045 c)
+|| 2 || 342.857,
--5.265 c from wide fourth 27/20 ||
+°51'26" || third || -4.551 c, -1°21'55" from neutral third 11/9 ||
-|| 4 || 685.714 || fifth || 5.265 c from narrow fifth 40/27
+|| 3 || 514.286,
--16.241 c from just fifth 3/2 (701.955 c) ||
+°17'9" || fourth || 16.241 c, 4°52'20" from just fourth 4/3 (498.045 c)
-|| 5 || 857.143 || sixth || 4.551 c from neutral sixth 18/11 ||
+-5.265 c, -1°34'47" from wide fourth 27/20 ||
-|| 6 || 1028.571 || seventh || 10.975 c from (Didymus) minor seventh 9/5
+|| 4 || 685.714,
--6.425 c from neutral seventh 20/11
+°42'51" || fifth || 5.265 c, 1°34'47" from narrow fifth 40/27
-.006 c from the 29th harmonic 29/16
+-16.241 c&lt;span style="line-height: 1.5;"&gt;, -4°52'20" from just fifth 3/2 (701.955 c)&lt;/span&gt; ||
--3.216 c from seventh 49/27 ||
+|| 5 || 857.143,
-|| 7 (0) || 1200.0 || eighth || exactly 2/1 ||
+°8'34" || sixth || 4.551 c, 1°21'55" from neutral sixth 18/11 ||
+|| 6 || 1028.571&lt;span style="line-height: 1.5;"&gt;,&lt;/span&gt;
+&lt;span style="line-height: 1.5;"&gt; 308°34'17"&lt;/span&gt; || seventh || 10.975 c, 3°17'33" from (Didymus) minor seventh 9/5
+-6.425 c, -1°55'38" from neutral seventh 20/11
+.006 c, 18'6" from the 29th harmonic 29/16
+-3.216 c, -57'53" from seventh 49/27 ||
+|| 7 (0) || 1200.0, 360º || eighth || exactly 2/1 ||
 [[media type="custom" key="24802290"]]
@@ Line 102: / Line 107: @@
 <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:WikiTextTocRule:22:&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:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;a href="#x&amp;quot;neutral diatonic&amp;quot;"&gt;&amp;quot;neutral diatonic&amp;quot;&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt; | &lt;a href="#Intervals in 7-edo"&gt;Intervals in 7-edo&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt; | &lt;a href="#Related scales"&gt;Related scales&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&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;a href="#Music"&gt;Music&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt; | &lt;a href="#Commas"&gt;Commas&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x&amp;quot;neutral diatonic&amp;quot;"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;&amp;quot;neutral diatonic&amp;quot;&lt;/h1&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x&amp;quot;neutral diatonic&amp;quot;"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;&amp;quot;neutral diatonic&amp;quot;&lt;/h1&gt;
   &lt;br /&gt;
 -edo divides the 1200-cent &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 7 equal parts, making its smallest interval &lt;a class="wiki_link" href="/cent"&gt;171.428¢&lt;/a&gt;, or the seventh root of 2. It is the fourth &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime&lt;/a&gt; edo, after &lt;a class="wiki_link" href="/2edo"&gt;2edo&lt;/a&gt;, &lt;a class="wiki_link" href="/3edo"&gt;3edo&lt;/a&gt; and &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;.&lt;br /&gt;
@@ Line 126: / Line 130: @@
          &lt;td&gt;&lt;strong&gt;Interval&lt;/strong&gt;&lt;br /&gt;
 &lt;strong&gt;size&lt;/strong&gt;&lt;br /&gt;
-&lt;strong&gt;in ¢&lt;/strong&gt;&lt;br /&gt;
+&lt;strong&gt;in ¢, DMS&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;strong&gt;Closest&lt;/strong&gt;&lt;br /&gt;
@@ Line 148: / Line 152: @@
          &lt;td&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;171.429&lt;br /&gt;
+         &lt;td&gt;171.429, &lt;br /&gt;
+°25'43&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;second&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;6.424 c from Ptolemy (neutral) second 11/10&lt;br /&gt;
+         &lt;td&gt;6.424 c, 1°55'38&amp;quot; from Ptolemy (neutral) second 11/10&lt;br /&gt;
-.215 c from second 54/49&lt;br /&gt;
+.215 c, 57'53&amp;quot; from second 54/49&lt;br /&gt;
--10.976 c from (Didymus) major second (small whole tone) 10/9&lt;br /&gt;
+-10.9&lt;span style="line-height: 1.5;"&gt; c, -3°17'33&amp;quot;76 from (Didymus) major second (small whole tone) 10/9&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 160: / Line 165: @@
          &lt;td&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;342.857&lt;br /&gt;
+         &lt;td&gt;342.857, &lt;br /&gt;
+°51'26&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;third&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-4.551 c from neutral third 11/9&lt;br /&gt;
+         &lt;td&gt;-4.551 c, -1°21'55&amp;quot; from neutral third 11/9&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 170: / Line 176: @@
          &lt;td&gt;3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;514.286&lt;br /&gt;
+         &lt;td&gt;514.286, &lt;br /&gt;
+°17'9&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;fourth&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;16.241 c from just fourth 4/3 (498.045 c)&lt;br /&gt;
+         &lt;td&gt;16.241 c, 4°52'20&amp;quot; from just fourth 4/3 (498.045 c)&lt;br /&gt;
--5.265 c from wide fourth 27/20&lt;br /&gt;
+-5.265 c, -1°34'47&amp;quot; from wide fourth 27/20&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 181: / Line 188: @@
          &lt;td&gt;4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;685.714&lt;br /&gt;
+         &lt;td&gt;685.714,&lt;br /&gt;
+°42'51&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;fifth&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;5.265 c from narrow fifth 40/27&lt;br /&gt;
+         &lt;td&gt;5.265 c, 1°34'47&amp;quot; from narrow fifth 40/27&lt;br /&gt;
--16.241 c from just fifth 3/2 (701.955 c)&lt;br /&gt;
+-16.241 c&lt;span style="line-height: 1.5;"&gt;, -4°52'20&amp;quot; from just fifth 3/2 (701.955 c)&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 192: / Line 200: @@
          &lt;td&gt;5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;857.143&lt;br /&gt;
+         &lt;td&gt;857.143,&lt;br /&gt;
+°8'34&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;sixth&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;4.551 c from neutral sixth 18/11&lt;br /&gt;
+         &lt;td&gt;4.551 c, 1°21'55&amp;quot; from neutral sixth 18/11&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 202: / Line 211: @@
          &lt;td&gt;6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1028.571&lt;br /&gt;
+         &lt;td&gt;1028.571&lt;span style="line-height: 1.5;"&gt;,&lt;/span&gt;&lt;br /&gt;
+&lt;span style="line-height: 1.5;"&gt; 308°34'17&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;seventh&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;10.975 c from (Didymus) minor seventh 9/5&lt;br /&gt;
+         &lt;td&gt;10.975 c, 3°17'33&amp;quot; from (Didymus) minor seventh 9/5&lt;br /&gt;
--6.425 c from neutral seventh 20/11&lt;br /&gt;
+-6.425 c, -1°55'38&amp;quot; from neutral seventh 20/11&lt;br /&gt;
-.006 c from the 29th harmonic 29/16&lt;br /&gt;
+.006 c, 18'6&amp;quot; from the 29th harmonic 29/16&lt;br /&gt;
--3.216 c from seventh 49/27&lt;br /&gt;
+-3.216 c, -57'53&amp;quot; from seventh 49/27&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 215: / Line 225: @@
          &lt;td&gt;7 (0)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1200.0&lt;br /&gt;
+         &lt;td&gt;1200.0, 360º&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;eighth&lt;br /&gt;