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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | 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|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|26edt]], [[39edt|39edt]] and [[52edt|52edt]] come to the fore. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2017-07-22 22:43:08 UTC</tt>.<br>
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| : The original revision id was <tt>615834357</tt>.<br>
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| : The revision comment was: <tt>added link (deorphaning)</tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <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">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.
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| 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. | | Below is a plot of the [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|no-twos Z-function]], in terms of which 13edt is the fourth no-twos zeta peak edt. |
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| [[image:13edt.png]] | | [[File:13edt.png|alt=13edt.png|13edt.png]] |
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| ==Intervals== | | ==Intervals== |
| ||~ Steps ||~ Cents ||~ BP nonatonic degree ||~ Corresponding JI intervals ||~ Comments ||~ Generator for... || | | |
| || 1 || 146.3 || A1/m2 || 27/25~49/45 || || || | | {| class="wikitable" |
| || 2 || 292.6 || M2/d3 || 25/21 || || [[Sirius]] || | | |- |
| || 3 || 438.9 || A2/P3/d4 || 9/7 || || [[Bohlen-Pierce|Linear BP]] || | | ! | Steps |
| || 4 || 585.2 || A3/m4/d5 || 7/5 || || [[Canopus]] || | | ! | Cents |
| || 5 || 731.5 || M4/m5 || 75/49 || False 3/2 || false Father || | | ! | BP nonatonic degree |
| || 6 || 877.8 || A4/M5 || 5/3 || || [[Arcturus]] || | | ! | Corresponding JI intervals |
| || 7 || 1024.1 || A5/m6/d7 || 9/5 || || Arcturus || | | ! | Comments |
| || 8 || 1170.4 || M6/m7 || 49/25 || False 2/1 || false Father || | | ! | Generator for... |
| || 9 || 1316.7 || A6/M7/d8 || 15/7 || || Canopus || | | |- |
| || 10 || 1463.0 || P8/d9 || 7/3 || || Linear BP || | | | | 1 |
| || 11 || 1609.3 || A8/m9 || 63/25 || || Sirius || | | | | 146.3 |
| || 12 || 1755.7 || M9/d10 || 25/9~135/49 || || || | | | | A1/m2 |
| || 13 || 1902.0 || A9/P10 || 3/1 || Tritave || || | | | | 27/25~49/45 |
| | | | |
| | | | |
| | |- |
| | | | 2 |
| | | | 292.6 |
| | | | M2/d3 |
| | | | 25/21 |
| | | | |
| | | | [[Sirius|Sirius]] |
| | |- |
| | | | 3 |
| | | | 438.9 |
| | | | A2/P3/d4 |
| | | | 9/7 |
| | | | |
| | | | [[Bohlen-Pierce|Linear BP]] |
| | |- |
| | | | 4 |
| | | | 585.2 |
| | | | A3/m4/d5 |
| | | | 7/5 |
| | | | |
| | | | [[Canopus|Canopus]] |
| | |- |
| | | | 5 |
| | | | 731.5 |
| | | | M4/m5 |
| | | | 75/49 |
| | | | False 3/2 |
| | | | false Father |
| | |- |
| | | | 6 |
| | | | 877.8 |
| | | | A4/M5 |
| | | | 5/3 |
| | | | |
| | | | [[Arcturus|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 |
| | | | |
| | |} |
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| ==See also== | | ==See also== |
| * [[Catalog of 3.5.7 subgroup rank two temperaments]]</pre></div>
| | <ul><li>[[Catalog_of_3.5.7_subgroup_rank_two_temperaments|Catalog of 3.5.7 subgroup rank two temperaments]]</li></ul> [[Category:3th_harmonic]] |
| <h4>Original HTML content:</h4>
| | [[Category:edt]] |
| <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>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 />
| | [[Category:tritave]] |
| <br />
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| 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 />
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| <!-- ws:start:WikiTextLocalImageRule:206:&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:206 --><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Intervals"></a><!-- ws:end:WikiTextHeadingRule:0 -->Intervals</h2>
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| <table class="wiki_table">
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| <tr>
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| <th>Steps<br />
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| </th>
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| <th>Cents<br />
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| </th>
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| <th>BP nonatonic degree<br />
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| </th>
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| <th>Corresponding JI intervals<br />
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| </th>
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| <th>Comments<br />
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| </th>
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| <th>Generator for...<br />
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| </th>
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| </tr>
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| <tr>
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| <td>1<br />
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| </td>
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| <td>146.3<br />
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| </td>
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| <td>A1/m2<br />
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| </td>
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| <td>27/25~49/45<br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td>2<br />
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| </td>
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| <td>292.6<br />
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| </td>
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| <td>M2/d3<br />
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| </td>
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| <td>25/21<br />
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| </td>
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| <td><br />
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| </td>
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| <td><a class="wiki_link" href="/Sirius">Sirius</a><br />
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| </td>
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| </tr>
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| <tr>
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| <td>3<br />
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| </td>
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| <td>438.9<br />
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| </td>
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| <td>A2/P3/d4<br />
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| </td>
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| <td>9/7<br />
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| </td>
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| <td><br />
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| </td>
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| <td><a class="wiki_link" href="/Bohlen-Pierce">Linear BP</a><br />
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| </td>
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| </tr>
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| <tr>
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| <td>4<br />
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| </td>
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| <td>585.2<br />
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| </td>
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| <td>A3/m4/d5<br />
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| </td>
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| <td>7/5<br />
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| </td>
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| <td><br />
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| </td>
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| <td><a class="wiki_link" href="/Canopus">Canopus</a><br />
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| </td>
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| </tr>
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| <tr>
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| <td>5<br />
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| </td>
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| <td>731.5<br />
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| </td>
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| <td>M4/m5<br />
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| </td>
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| <td>75/49<br />
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| </td>
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| <td>False 3/2<br />
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| </td>
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| <td>false Father<br />
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| </td>
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| </tr>
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| <tr>
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| <td>6<br />
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| </td>
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| <td>877.8<br />
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| </td>
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| <td>A4/M5<br />
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| </td>
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| <td>5/3<br />
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| </td>
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| <td><br />
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| </td>
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| <td><a class="wiki_link" href="/Arcturus">Arcturus</a><br />
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| </td>
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| </tr>
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| <tr>
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| <td>7<br />
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| </td>
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| <td>1024.1<br />
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| </td>
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| <td>A5/m6/d7<br />
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| </td>
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| <td>9/5<br />
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| </td>
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| <td><br />
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| </td>
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| <td>Arcturus<br />
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| </td>
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| </tr>
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| <tr>
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| <td>8<br />
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| </td>
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| <td>1170.4<br />
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| </td>
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| <td>M6/m7<br />
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| </td>
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| <td>49/25<br />
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| </td>
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| <td>False 2/1<br />
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| </td>
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| <td>false Father<br />
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| </td>
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| </tr>
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| <tr>
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| <td>9<br />
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| </td>
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| <td>1316.7<br />
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| </td>
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| <td>A6/M7/d8<br />
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| </td>
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| <td>15/7<br />
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| </td>
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| <td><br />
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| </td>
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| <td>Canopus<br />
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| </td>
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| </tr>
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| <tr>
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| <td>10<br />
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| </td>
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| <td>1463.0<br />
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| </td>
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| <td>P8/d9<br />
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| </td>
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| <td>7/3<br />
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| </td>
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| <td><br />
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| </td>
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| <td>Linear BP<br />
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| </td>
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| </tr>
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| <tr>
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| <td>11<br />
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| </td>
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| <td>1609.3<br />
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| </td>
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| <td>A8/m9<br />
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| </td>
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| <td>63/25<br />
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| </td>
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| <td><br />
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| </td>
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| <td>Sirius<br />
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| </td>
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| </tr>
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| <tr>
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| <td>12<br />
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| </td>
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| <td>1755.7<br />
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| </td>
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| <td>M9/d10<br />
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| </td>
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| <td>25/9~135/49<br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td>13<br />
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| </td>
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| <td>1902.0<br />
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| </td>
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| <td>A9/P10<br />
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| </td>
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| <td>3/1<br />
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| </td>
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| <td>Tritave<br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| </table>
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-See also"></a><!-- ws:end:WikiTextHeadingRule:2 -->See also</h2>
| |
| <ul><li><a class="wiki_link" href="/Catalog%20of%203.5.7%20subgroup%20rank%20two%20temperaments">Catalog of 3.5.7 subgroup rank two temperaments</a></li></ul></body></html></pre></div>
| |
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 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 no-twos Z-function, in terms of which 13edt is the fourth no-twos zeta peak edt.
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
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438.9
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A2/P3/d4
|
9/7
|
|
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
|
|
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| 13
|
1902.0
|
A9/P10
|
3/1
|
Tritave
|
|
See also
