44/37: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox Interval
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| Name = 37-limit quasi-tempered minor third, beryl minor third, tricesimoseptimal minor third, tricesimoseptimal quarter-octave
: This revision was by author [[User:bootmii|bootmii]] and made on <tt>2016-12-11 20:49:29 UTC</tt>.<br>
| Color name = 37u1o2, thisulo 2nd
: The original revision id was <tt>601938462</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>
44/37, the 37-limit quasi-tempered minor third, is the continued fraction convergent to 3\[[12edo|12]] after [[25/21]] and [[19/16]]. It is followed by a 40 in the expansion, so it's a great approximation for its odd limit (compare 355/113 for π).
<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">Very close to [[12edo|3\12]].</pre></div>
Equating it to the quarter-octave leads to the [[berylic]] temperament, tempering out the [[berylisma]].
<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;44_37&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Very close to &lt;a class="wiki_link" href="/12edo"&gt;3\12&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
== See also ==
* [[37/22]] &ndash; its octave complement
* [[Gallery of just intervals]]
 
[[category:Third]]
[[Category:Minor third]]

Latest revision as of 01:09, 29 November 2024

Interval information
Ratio 44/37
Subgroup monzo 2.11.37 [2 1 -1⟩
Size in cents 299.9739¢
Names 37-limit quasi-tempered minor third,
beryl minor third,
tricesimoseptimal minor third,
tricesimoseptimal quarter-octave
Color name 37u1o2, thisulo 2nd
FJS name [math]\displaystyle{ \text{m3}^{11}_{37} }[/math]
Special properties reduced
Tenney norm (log2 nd) 10.6689
Weil norm (log2 max(n, d)) 10.9189
Wilson norm (sopfr(nd)) 52
Open this interval in xen-calc

44/37, the 37-limit quasi-tempered minor third, is the continued fraction convergent to 3\12 after 25/21 and 19/16. It is followed by a 40 in the expansion, so it's a great approximation for its odd limit (compare 355/113 for π).

Equating it to the quarter-octave leads to the berylic temperament, tempering out the berylisma.

See also

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