13edt
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author JosephRuhf and made on 2016-10-14 01:17:06 UTC.
- The original revision id was 595310942.
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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 || || [[Siirius]] || || 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:<img src="/file/view/13edt.png/250612880/13edt.png" alt="" title="" /> --><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:<h2> --><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><a class="wiki_link" href="/Siirius">Siirius</a><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>