22/15: 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 = undecimal diminished fifth, undecimal acute ultra-diminished fifth
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-12 13:55:39 UTC</tt>.<br>
| Color name = 1og5, logu 5th
: The original revision id was <tt>300957128</tt>.<br>
| Sound = jid_22_15_pluck_adu_dr220.mp3
: 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>
 
<h4>Original Wikitext content:</h4>
The '''undecimal diminished fifth''' of '''22/15''' is flat of [[3/2]] by [[45/44]], and is the interval between [[5/4]] and [[11/6]]. It is wider than [[16/11]] by exactly [[121/120]] and narrower than [[40/27]] by exactly [[100/99]].  Additionally, it is wider than [[352/243]] by exactly [[81/80]], which lends to it being called the '''undecimal acute ultra-diminished fifth'''.
<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 undecimal diminished fifth of 22/15 is flat of [[3_2|3/2]] by [[45_44|45/44]], and is the interval between [[5_4|5/4]] and [[11_6|11/6]].</pre></div>
5 steps of [[9edo]] is a good approximation of this interval.
<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;22_15&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The undecimal diminished fifth of 22/15 is flat of &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt; by &lt;a class="wiki_link" href="/45_44"&gt;45/44&lt;/a&gt;, and is the interval between &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt; and &lt;a class="wiki_link" href="/11_6"&gt;11/6&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
== See also ==
* [[15/11]] – its [[octave complement]]
* [[45/44]] – its [[fifth complement]]
* [[Gallery of just intervals]]
 
[[Category:Fifth]]
[[Category:Subfifth]]

Latest revision as of 01:01, 4 December 2022

Interval information
Ratio 22/15
Factorization 2 × 3-1 × 5-1 × 11
Monzo [1 -1 -1 0 1⟩
Size in cents 663.0492¢
Names undecimal diminished fifth,
undecimal acute ultra-diminished fifth
Color name 1og5, logu 5th
FJS name [math]\displaystyle{ \text{d5}^{11}_{5} }[/math]
Special properties reduced
Tenney height (log2 nd) 8.36632
Weil height (log2 max(n, d)) 8.91886
Wilson height (sopfr(nd)) 21

[sound info]
Open this interval in xen-calc

The undecimal diminished fifth of 22/15 is flat of 3/2 by 45/44, and is the interval between 5/4 and 11/6. It is wider than 16/11 by exactly 121/120 and narrower than 40/27 by exactly 100/99. Additionally, it is wider than 352/243 by exactly 81/80, which lends to it being called the undecimal acute ultra-diminished fifth. 5 steps of 9edo is a good approximation of this interval.

See also

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