13edt: Difference between revisions

Revision as of 10:52, 13 October 2016

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author JosephRuhf and made on 2016-10-13 10:52:28 UTC.

The original revision id was 595253804.

The revision comment was:

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

Original Wikitext content:

The 13 equal division of 3, the tritave, divides it into 13 equal parts of 146.304 cents each, corresponding to 8.202 edo. An alternative name for it is the [[Bohlen-Pierce]] scale. In the 7-limit, it tempers out 245/243 and 3125/3087, the same commas as [[Sensamagic clan#Bohpier|bohpier temperament]]. It is less impressive in higher p-limits, but makes for excellent no-twos 7-limit harmony. For higher limits, the multiples of 13 [[26edt]], [[39edt]] and [[52edt]] come to the fore.

Below is a plot of the [[The Riemann Zeta Function and Tuning#Removing%20primes|no-twos Z-function]], in terms of which 13edt is the fourth no-twos zeta peak edt.

[[image:13edt.png]]

==Intervals== 
||~ Steps ||~ Cents ||~ BP nonatonic degree ||~ Corresponding JI intervals ||~ Comments ||~ Generator for... ||
|| 1 || 146.3 || P1 || 27/25~49/45 ||   ||   ||
|| 2 || 292.6 || m2 || 25/21 ||   || Sirius ||
|| 3 || 438.9 || M2 || 9/7 ||   || [[Bohlen-Pierce|Linear BP]] ||
|| 4 || 585.2 || m3 || 7/5 ||   || [[Canopus]] ||
|| 5 || 731.5 || M3/m4 ||   || False 3/2 ||   ||
|| 6 || 877.8 || M5 || 5/3 ||   || [[Arcturus]] ||
|| 7 || 1024.1 || m6 || 9/5 ||   || Arcturus ||
|| 8 || 1170.4 || M6/m7 ||   || False 2/1 ||   ||
|| 9 || 1316.7 || M7 || 15/7 ||   || Canopus ||
|| 10 || 1463.0 || m8 || 7/3 ||   || Linear BP ||
|| 11 || 1609.3 || M8/m9 || 63/25 ||   || Sirius ||
|| 12 || 1755.7 || M9 || 25/9~135/49 ||   ||   ||
|| 13 || 1902.0 || P10 || 3/1 || Tritave ||   ||

Original HTML content:

<html><head><title>13edt</title></head><body>The 13 equal division of 3, the tritave, divides it into 13 equal parts of 146.304 cents each, corresponding to 8.202 edo. An alternative name for it is the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale. In the 7-limit, it tempers out 245/243 and 3125/3087, the same commas as <a class="wiki_link" href="/Sensamagic%20clan#Bohpier">bohpier temperament</a>. It is less impressive in higher p-limits, but makes for excellent no-twos 7-limit harmony. For higher limits, the multiples of 13 <a class="wiki_link" href="/26edt">26edt</a>, <a class="wiki_link" href="/39edt">39edt</a> and <a class="wiki_link" href="/52edt">52edt</a> come to the fore.<br />
<br />
Below is a plot of the <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Removing%20primes">no-twos Z-function</a>, in terms of which 13edt is the fourth no-twos zeta peak edt.<br />
<br />
<!-- ws:start:WikiTextLocalImageRule:200:&lt;img src=&quot;/file/view/13edt.png/250612880/13edt.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/13edt.png/250612880/13edt.png" alt="13edt.png" title="13edt.png" /><!-- ws:end:WikiTextLocalImageRule:200 --><br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Intervals"></a><!-- ws:end:WikiTextHeadingRule:0 -->Intervals</h2>
 

<table class="wiki_table">
    <tr>
        <th>Steps<br />
</th>
        <th>Cents<br />
</th>
        <th>BP nonatonic degree<br />
</th>
        <th>Corresponding JI intervals<br />
</th>
        <th>Comments<br />
</th>
        <th>Generator for...<br />
</th>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>146.3<br />
</td>
        <td>P1<br />
</td>
        <td>27/25~49/45<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>292.6<br />
</td>
        <td>m2<br />
</td>
        <td>25/21<br />
</td>
        <td><br />
</td>
        <td>Sirius<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>438.9<br />
</td>
        <td>M2<br />
</td>
        <td>9/7<br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="/Bohlen-Pierce">Linear BP</a><br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>585.2<br />
</td>
        <td>m3<br />
</td>
        <td>7/5<br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="/Canopus">Canopus</a><br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>731.5<br />
</td>
        <td>M3/m4<br />
</td>
        <td><br />
</td>
        <td>False 3/2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>877.8<br />
</td>
        <td>M5<br />
</td>
        <td>5/3<br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="/Arcturus">Arcturus</a><br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>1024.1<br />
</td>
        <td>m6<br />
</td>
        <td>9/5<br />
</td>
        <td><br />
</td>
        <td>Arcturus<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>1170.4<br />
</td>
        <td>M6/m7<br />
</td>
        <td><br />
</td>
        <td>False 2/1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>1316.7<br />
</td>
        <td>M7<br />
</td>
        <td>15/7<br />
</td>
        <td><br />
</td>
        <td>Canopus<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>1463.0<br />
</td>
        <td>m8<br />
</td>
        <td>7/3<br />
</td>
        <td><br />
</td>
        <td>Linear BP<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>1609.3<br />
</td>
        <td>M8/m9<br />
</td>
        <td>63/25<br />
</td>
        <td><br />
</td>
        <td>Sirius<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>1755.7<br />
</td>
        <td>M9<br />
</td>
        <td>25/9~135/49<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>1902.0<br />
</td>
        <td>P10<br />
</td>
        <td>3/1<br />
</td>
        <td>Tritave<br />
</td>
        <td><br />
</td>
    </tr>
</table>

</body></html>

@@ 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:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-02 23:48:08 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-13 10:52:28 UTC</tt>.<br>
-: The original revision id was <tt>593844192</tt>.<br>
+: The original revision id was <tt>595253804</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 13: / Line 13: @@
 ==Intervals==
-||~ Steps ||~ Cents ||~ Corresponding JI intervals ||~ Comments ||~ Generator for... ||
+||~ Steps ||~ Cents ||~ BP nonatonic degree ||~ Corresponding JI intervals ||~ Comments ||~ Generator for... ||
-|| 1 || 146.3 || 27/25~49/45 ||   ||   ||
+|| 1 || 146.3 || P1 || 27/25~49/45 ||   ||   ||
-|| 2 || 292.6 || 25/21 ||   || Sirius ||
+|| 2 || 292.6 || m2 || 25/21 ||   || Sirius ||
-|| 3 || 438.9 || 9/7 ||   || [[Bohlen-Pierce|Linear BP]] ||
+|| 3 || 438.9 || M2 || 9/7 ||   || [[Bohlen-Pierce|Linear BP]] ||
-|| 4 || 585.2 || 7/5 ||   || [[Canopus]] ||
+|| 4 || 585.2 || m3 || 7/5 ||   || [[Canopus]] ||
-|| 5 || 731.5 ||   || False 3/2 ||   ||
+|| 5 || 731.5 || M3/m4 ||   || False 3/2 ||   ||
-|| 6 || 877.8 || 5/3 ||   || [[Arcturus]] ||
+|| 6 || 877.8 || M5 || 5/3 ||   || [[Arcturus]] ||
-|| 7 || 1024.1 || 9/5 ||   || Arcturus ||
+|| 7 || 1024.1 || m6 || 9/5 ||   || Arcturus ||
-|| 8 || 1170.4 ||   || False 2/1 ||   ||
+|| 8 || 1170.4 || M6/m7 ||   || False 2/1 ||   ||
-|| 9 || 1316.7 || 15/7 ||   || Canopus ||
+|| 9 || 1316.7 || M7 || 15/7 ||   || Canopus ||
-|| 10 || 1463.0 || 7/3 ||   || Linear BP ||
+|| 10 || 1463.0 || m8 || 7/3 ||   || Linear BP ||
-|| 11 || 1609.3 || 63/25 ||   || Sirius ||
+|| 11 || 1609.3 || M8/m9 || 63/25 ||   || Sirius ||
-|| 12 || 1755.7 || 25/9~135/49 ||   ||   ||
+|| 12 || 1755.7 || M9 || 25/9~135/49 ||   ||   ||
-|| 13 || 1902.0 || 3/1 || Tritave ||   ||</pre></div>
+|| 13 || 1902.0 || P10 || 3/1 || Tritave ||   ||</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;13edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 13 equal division of 3, the tritave, divides it into 13 equal parts of 146.304 cents each, corresponding to 8.202 edo. An alternative name for it is the &lt;a class="wiki_link" href="/Bohlen-Pierce"&gt;Bohlen-Pierce&lt;/a&gt; scale. In the 7-limit, it tempers out 245/243 and 3125/3087, the same commas as &lt;a class="wiki_link" href="/Sensamagic%20clan#Bohpier"&gt;bohpier temperament&lt;/a&gt;. It is less impressive in higher p-limits, but makes for excellent no-twos 7-limit harmony. For higher limits, the multiples of 13 &lt;a class="wiki_link" href="/26edt"&gt;26edt&lt;/a&gt;, &lt;a class="wiki_link" href="/39edt"&gt;39edt&lt;/a&gt; and &lt;a class="wiki_link" href="/52edt"&gt;52edt&lt;/a&gt; come to the fore.&lt;br /&gt;
@@ Line 32: / Line 32: @@
 Below is a plot of the &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Removing%20primes"&gt;no-twos Z-function&lt;/a&gt;, in terms of which 13edt is the fourth no-twos zeta peak edt.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:172:&amp;lt;img src=&amp;quot;/file/view/13edt.png/250612880/13edt.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/13edt.png/250612880/13edt.png" alt="13edt.png" title="13edt.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:172 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:200:&amp;lt;img src=&amp;quot;/file/view/13edt.png/250612880/13edt.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/13edt.png/250612880/13edt.png" alt="13edt.png" title="13edt.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:200 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Intervals&lt;/h2&gt;
@@ Line 42: / Line 42: @@
 &lt;/th&gt;
          &lt;th&gt;Cents&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;BP nonatonic degree&lt;br /&gt;
 &lt;/th&gt;
          &lt;th&gt;Corresponding JI intervals&lt;br /&gt;
@@ Line 54: / Line 56: @@
 &lt;/td&gt;
          &lt;td&gt;146.3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;P1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;27/25~49/45&lt;br /&gt;
@@ Line 66: / Line 70: @@
 &lt;/td&gt;
          &lt;td&gt;292.6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;m2&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;25/21&lt;br /&gt;
@@ Line 78: / Line 84: @@
 &lt;/td&gt;
          &lt;td&gt;438.9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;M2&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;9/7&lt;br /&gt;
@@ Line 90: / Line 98: @@
 &lt;/td&gt;
          &lt;td&gt;585.2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;m3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;7/5&lt;br /&gt;
@@ Line 102: / Line 112: @@
 &lt;/td&gt;
          &lt;td&gt;731.5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;M3/m4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 114: / Line 126: @@
 &lt;/td&gt;
          &lt;td&gt;877.8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;M5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;5/3&lt;br /&gt;
@@ Line 126: / Line 140: @@
 &lt;/td&gt;
          &lt;td&gt;1024.1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;m6&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;9/5&lt;br /&gt;
@@ Line 138: / Line 154: @@
 &lt;/td&gt;
          &lt;td&gt;1170.4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;M6/m7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 150: / Line 168: @@
 &lt;/td&gt;
          &lt;td&gt;1316.7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;M7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;15/7&lt;br /&gt;
@@ Line 162: / Line 182: @@
 &lt;/td&gt;
          &lt;td&gt;1463.0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;m8&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;7/3&lt;br /&gt;
@@ Line 174: / Line 196: @@
 &lt;/td&gt;
          &lt;td&gt;1609.3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;M8/m9&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;63/25&lt;br /&gt;
@@ Line 186: / Line 210: @@
 &lt;/td&gt;
          &lt;td&gt;1755.7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;M9&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;25/9~135/49&lt;br /&gt;
@@ Line 198: / Line 224: @@
 &lt;/td&gt;
          &lt;td&gt;1902.0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;P10&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;3/1&lt;br /&gt;

13edt: Difference between revisions

Revision as of 10:52, 13 October 2016

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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