Xenharmonic Wiki

13edt: Difference between revisions

← Older editNewer edit →
VisualWikitext
Wikispaces>spt3125
**Imported revision 615834357 - Original comment: added link (deorphaning)**
Wikispaces>FREEZE
No edit summary
Line 1: Line 1:
<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>
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2017-07-22 22:43:08 UTC</tt>.<br>
: The original revision id was <tt>615834357</tt>.<br>
: The revision comment was: <tt>added link (deorphaning)</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">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.
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.


[[image:13edt.png]]
[[File:13edt.png|alt=13edt.png|13edt.png]]


==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
| |  
|}


==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">&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;
[[Category:tritave]]
&lt;br /&gt;
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:206:&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:206 --&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;
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;Steps&lt;br /&gt;
&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;
&lt;/th&gt;
        &lt;th&gt;Comments&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Generator for...&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;146.3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A1/m2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;27/25~49/45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;292.6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;M2/d3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;25/21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&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;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;438.9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A2/P3/d4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Bohlen-Pierce"&gt;Linear BP&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;585.2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A3/m4/d5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Canopus"&gt;Canopus&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;731.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;M4/m5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;75/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;False 3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;false Father&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;877.8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A4/M5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Arcturus"&gt;Arcturus&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1024.1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A5/m6/d7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Arcturus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&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;49/25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;False 2/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;false Father&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1316.7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A6/M7/d8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Canopus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1463.0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P8/d9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Linear BP&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1609.3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A8/m9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;63/25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Sirius&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1755.7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;M9/d10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;25/9~135/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1902.0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A9/P10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Tritave&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-See also"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;See also&lt;/h2&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Catalog%20of%203.5.7%20subgroup%20rank%20two%20temperaments"&gt;Catalog of 3.5.7 subgroup rank two temperaments&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
Retrieved from "https://en.xen.wiki/w/13edt"