22/15: Difference between revisions

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**Imported revision 513277222 - Original comment: **
m Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"
 
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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:spt3125|spt3125]] and made on <tt>2014-06-08 21:09:47 UTC</tt>.<br>
| Color name = 1og5, logu 5th
: The original revision id was <tt>513277222</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>
<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">**22/15**
|1 -1 -1 0 1&gt;
663.0492 cents
[[media type="file" key="jid_22_15_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_22_15_pluck_adu_dr220.mp3|sound sample]]


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>
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'''.
<h4>Original HTML content:</h4>
5 steps of [[9edo]] is a good approximation of this interval.
<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;&lt;strong&gt;22/15&lt;/strong&gt;&lt;br /&gt;
== Approximation ==
|1 -1 -1 0 1&amp;gt;&lt;br /&gt;
{{Interval edo approximation|22/15}}
663.0492 cents&lt;br /&gt;
== See also ==
&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_22_15_pluck_adu_dr220.mp3?h=20&amp;amp;w=240&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;jid_22_15_pluck_adu_dr220.mp3&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;20&amp;quot; width=&amp;quot;240&amp;quot;/&amp;gt; --&gt;&lt;embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Fjid_22_15_pluck_adu_dr220.mp3?file_extension=mp3&amp;autostart=false&amp;repeat=false&amp;showdigits=true&amp;showfsbutton=false&amp;width=240&amp;height=20"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt; &lt;a href="http://xenharmonic.wikispaces.com/file/view/jid_22_15_pluck_adu_dr220.mp3/513250070/jid_22_15_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_22_15_pluck_adu_dr220.mp3/513250070/jid_22_15_pluck_adu_dr220.mp3');"&gt;sound sample&lt;/a&gt;&lt;br /&gt;
* [[15/11]] – its [[octave complement]]
&lt;br /&gt;
* [[45/44]] – its [[fifth complement]]
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>
* [[Gallery of just intervals]]
 
[[Category:Fifth]]
[[Category:Subfifth]]

Latest revision as of 13:13, 3 November 2025

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 norm (log2 nd) 8.36632
Weil norm (log2 max(n, d)) 8.91886
Wilson norm (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.

Approximation

Edo approximations for 22/15 (663.05 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
9 5\9 666.67 +3.62 +2.71
11 6\11 654.55 -8.50 -7.80
18 10\18 666.67 +3.62 +5.43
20 11\20 660.00 -3.05 -5.08
27 15\27 666.67 +3.62 +8.14
29 16\29 662.07 -0.98 -2.37
38 21\38 663.16 +0.11 +0.34
47 26\47 663.83 +0.78 +3.06
49 27\49 661.22 -1.82 -7.45
56 31\56 664.29 +1.24 +5.77
58 32\58 662.07 -0.98 -4.74
65 36\65 664.62 +1.57 +8.48
67 37\67 662.69 -0.36 -2.02
76 42\76 663.16 +0.11 +0.69
78 43\78 661.54 -1.51 -9.82

See also

Retrieved from "https://en.xen.wiki/index.php?title=22/15&oldid=216085"