13edt: Difference between revisions

Revision as of 23:56, 19 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 2016-10-19 23:56:31 UTC.

The original revision id was 596189816.

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 || A1/m2 || 27/25~49/45 ||   ||   ||
|| 2 || 292.6 || M2/d3 || 25/21 ||   || [[Sirius]] ||
|| 3 || 438.9 || A2/P3/d4 || 9/7 ||   || [[Bohlen-Pierce|Linear BP]] ||
|| 4 || 585.2 || A3/m4/d5 || 7/5 ||   || [[Canopus]] ||
|| 5 || 731.5 || M4/m5 || 75/49 || False 3/2 || false Father ||
|| 6 || 877.8 || A4/M5 || 5/3 ||   || [[Arcturus]] ||
|| 7 || 1024.1 || A5/m6/d7 || 9/5 ||   || Arcturus ||
|| 8 || 1170.4 || M6/m7 || 49/25 || False 2/1 || false Father ||
|| 9 || 1316.7 || A6/M7/d8 || 15/7 ||   || Canopus ||
|| 10 || 1463.0 || P8/d9 || 7/3 ||   || Linear BP ||
|| 11 || 1609.3 || A8/m9 || 63/25 ||   || Sirius ||
|| 12 || 1755.7 || M9/d10 || 25/9~135/49 ||   ||   ||
|| 13 || 1902.0 || A9/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>A1/m2<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/d3<br />
</td>
        <td>25/21<br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="/Sirius">Sirius</a><br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>438.9<br />
</td>
        <td>A2/P3/d4<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>A3/m4/d5<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>M4/m5<br />
</td>
        <td>75/49<br />
</td>
        <td>False 3/2<br />
</td>
        <td>false Father<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>877.8<br />
</td>
        <td>A4/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>A5/m6/d7<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>49/25<br />
</td>
        <td>False 2/1<br />
</td>
        <td>false Father<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>1316.7<br />
</td>
        <td>A6/M7/d8<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>P8/d9<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>A8/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/d10<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>A9/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>2016-10-19 15:53:33 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-19 23:56:31 UTC</tt>.<br>
-: The original revision id was <tt>596162028</tt>.<br>
+: The original revision id was <tt>596189816</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 14: / Line 14: @@
 ==Intervals==
 ||~ Steps ||~ Cents ||~ BP nonatonic degree ||~ Corresponding JI intervals ||~ Comments ||~ Generator for... ||
-|| 1 || 146.3 || P1/m2 || 27/25~49/45 ||   ||   ||
+|| 1 || 146.3 || A1/m2 || 27/25~49/45 ||   ||   ||
-|| 2 || 292.6 || M2/m3 || 25/21 ||   || [[Siirius]] ||
+|| 2 || 292.6 || M2/d3 || 25/21 ||   || [[Sirius]] ||
-|| 3 || 438.9 || M3 || 9/7 ||   || [[Bohlen-Pierce|Linear BP]] ||
+|| 3 || 438.9 || A2/P3/d4 || 9/7 ||   || [[Bohlen-Pierce|Linear BP]] ||
-|| 4 || 585.2 || m4 || 7/5 ||   || [[Canopus]] ||
+|| 4 || 585.2 || A3/m4/d5 || 7/5 ||   || [[Canopus]] ||
 || 5 || 731.5 || M4/m5 || 75/49 || False 3/2 || false Father ||
-|| 6 || 877.8 || M5 || 5/3 ||   || [[Arcturus]] ||
+|| 6 || 877.8 || A4/M5 || 5/3 ||   || [[Arcturus]] ||
-|| 7 || 1024.1 || m6 || 9/5 ||   || Arcturus ||
+|| 7 || 1024.1 || A5/m6/d7 || 9/5 ||   || Arcturus ||
 || 8 || 1170.4 || M6/m7 || 49/25 || False 2/1 || false Father ||
-|| 9 || 1316.7 || M7 || 15/7 ||   || Canopus ||
+|| 9 || 1316.7 || A6/M7/d8 || 15/7 ||   || Canopus ||
-|| 10 || 1463.0 || m8 || 7/3 ||   || Linear BP ||
+|| 10 || 1463.0 || P8/d9 || 7/3 ||   || Linear BP ||
-|| 11 || 1609.3 || M8/m9 || 63/25 ||   || Sirius ||
+|| 11 || 1609.3 || A8/m9 || 63/25 ||   || Sirius ||
-|| 12 || 1755.7 || M9 || 25/9~135/49 ||   ||   ||
+|| 12 || 1755.7 || M9/d10 || 25/9~135/49 ||   ||   ||
-|| 13 || 1902.0 || P10 || 3/1 || Tritave ||   ||</pre></div>
+|| 13 || 1902.0 || A9/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 57: / Line 57: @@
          &lt;td&gt;146.3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;P1/m2&lt;br /&gt;
+         &lt;td&gt;A1/m2&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;27/25~49/45&lt;br /&gt;
@@ Line 71: / Line 71: @@
          &lt;td&gt;292.6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;M2/m3&lt;br /&gt;
+         &lt;td&gt;M2/d3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;25/21&lt;br /&gt;
@@ Line 77: / Line 77: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;a class="wiki_link" href="/Siirius"&gt;Siirius&lt;/a&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/Sirius"&gt;Sirius&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 85: / Line 85: @@
          &lt;td&gt;438.9&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;M3&lt;br /&gt;
+         &lt;td&gt;A2/P3/d4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;9/7&lt;br /&gt;
@@ Line 99: / Line 99: @@
          &lt;td&gt;585.2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;m4&lt;br /&gt;
+         &lt;td&gt;A3/m4/d5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;7/5&lt;br /&gt;
@@ Line 127: / Line 127: @@
          &lt;td&gt;877.8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;M5&lt;br /&gt;
+         &lt;td&gt;A4/M5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;5/3&lt;br /&gt;
@@ Line 141: / Line 141: @@
          &lt;td&gt;1024.1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;m6&lt;br /&gt;
+         &lt;td&gt;A5/m6/d7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;9/5&lt;br /&gt;
@@ Line 169: / Line 169: @@
          &lt;td&gt;1316.7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;M7&lt;br /&gt;
+         &lt;td&gt;A6/M7/d8&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;15/7&lt;br /&gt;
@@ Line 183: / Line 183: @@
          &lt;td&gt;1463.0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;m8&lt;br /&gt;
+         &lt;td&gt;P8/d9&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;7/3&lt;br /&gt;
@@ Line 197: / Line 197: @@
          &lt;td&gt;1609.3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;M8/m9&lt;br /&gt;
+         &lt;td&gt;A8/m9&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;63/25&lt;br /&gt;
@@ Line 211: / Line 211: @@
          &lt;td&gt;1755.7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;M9&lt;br /&gt;
+         &lt;td&gt;M9/d10&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;25/9~135/49&lt;br /&gt;
@@ Line 225: / Line 225: @@
          &lt;td&gt;1902.0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;P10&lt;br /&gt;
+         &lt;td&gt;A9/P10&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;3/1&lt;br /&gt;

13edt: Difference between revisions

Revision as of 23:56, 19 October 2016

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

Navigation menu

Search