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[[File:13edt.png|thumb|alt=13edt.png|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]].]]
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-16 22:21:43 UTC</tt>.<br>
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<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.
'''13 equal divisions of the tritave''' ('''13edt''') is the [[nonoctave]] [[tuning system]] derived by dividing the [[tritave]] (3/1) into 13 equal steps of 146.3 [[cent]]s each, or the thirteenth root of 3. It is best known as the equal-tempered version of the [[Bohlen–Pierce]] scale, and therefore has received by far the most attention among equal divisions of the tritave.
[[image:13edt.png]]
It provides an excellent approximation to the [[3.5.7 subgroup]], especially for its size, being comparable to [[34edo]]'s accuracy in the 5-limit. In this subgroup, it tempers out [[245/243]] and [[3125/3087]], the same commas as [[Sensamagic_clan#Bohpier|bohpier temperament]]. It is less impressive in higher prime 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.
==Intervals==
13edt can be described as approximately 8.202[[edo]]. This implies that each step of 13edt can be approximated by 5 steps of [[41edo]].
||~ Steps ||~ Cents ||~ BP nonatonic degree ||~ Corresponding JI intervals ||~ Comments ||~ Generator for... ||
<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 />
<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 />
In the [[no-2]] [[3/1]]-[[equave]]-[[7-limit]], [[13edt]] maintains the smallest relative error of any EDT until [[258edt]] and [[271edt]], and the smallest absolute error until [[56edt]].
A plot of the no-twos Z-function, in terms of which 13edt is the fourth no-twos zeta peak EDT.
13 equal divisions of the tritave (13edt) is the nonoctavetuning system derived by dividing the tritave (3/1) into 13 equal steps of 146.3 cents each, or the thirteenth root of 3. It is best known as the equal-tempered version of the Bohlen–Pierce scale, and therefore has received by far the most attention among equal divisions of the tritave.
It provides an excellent approximation to the 3.5.7 subgroup, especially for its size, being comparable to 34edo's accuracy in the 5-limit. In this subgroup, it tempers out 245/243 and 3125/3087, the same commas as bohpier temperament. It is less impressive in higher prime 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.
13edt can be described as approximately 8.202edo. This implies that each step of 13edt can be approximated by 5 steps of 41edo.
