22/17: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>spt3125
**Imported revision 513255176 - Original comment: **
m Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"
 
(10 intermediate revisions by 9 users not shown)
Line 1: Line 1:
<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 = septendecimal ultramajor third
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-08 15:29:22 UTC</tt>.<br>
| Color name = 17u1o3, sulo 3rd
: The original revision id was <tt>513255176</tt>.<br>
| Sound = jid_22_17_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">**22/17**
|1 0 0 0 1 0 -1&gt;
446.3625 cents
[[media type="file" key="jid_22_17_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_22_17_pluck_adu_dr220.mp3|sound sample]]


In [[17-limit]] [[Just Intonation]], 22/17 is the "septendecimal supermajor third," measuring about 446.4¢. It is the [[mediant]] between [[9_7|9/7]] and [[13_10|13/10]], as it is (9+13)/(7+10).
In [[17-limit]] [[just intonation]], '''22/17''' is the '''septendecimal ultramajor third''', measuring about 446.4{{cent}}. It is the [[mediant]] between [[9/7]] and [[13/10]], as it is (9+13)/(7+10).


Intervals around this size or a few cents smaller make good generators for [[sensi]] temperament.
Intervals around this size or a few cents smaller make good generators for [[sensi]] temperament.
== Approximation ==
{{Interval edo approximation|22/17}}
== See also ==
* [[Gallery of just intervals]]
* [[17/11]] -- its [[octave complement]]


See: [[Gallery of Just Intervals]]</pre></div>
[[Category:Third]]
<h4>Original HTML content:</h4>
[[Category:Supermajor third]]
<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_17&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;22/17&lt;/strong&gt;&lt;br /&gt;
[[Category:Interseptimal intervals]]
|1 0 0 0 1 0 -1&amp;gt;&lt;br /&gt;
[[Category:Naiadic]]
446.3625 cents&lt;br /&gt;
&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_22_17_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_17_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_17_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_17_pluck_adu_dr220.mp3/513250080/jid_22_17_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_22_17_pluck_adu_dr220.mp3/513250080/jid_22_17_pluck_adu_dr220.mp3');"&gt;sound sample&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
In &lt;a class="wiki_link" href="/17-limit"&gt;17-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, 22/17 is the &amp;quot;septendecimal supermajor third,&amp;quot; measuring about 446.4¢. It is the &lt;a class="wiki_link" href="/mediant"&gt;mediant&lt;/a&gt; between &lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt; and &lt;a class="wiki_link" href="/13_10"&gt;13/10&lt;/a&gt;, as it is (9+13)/(7+10).&lt;br /&gt;
&lt;br /&gt;
Intervals around this size or a few cents smaller make good generators for &lt;a class="wiki_link" href="/sensi"&gt;sensi&lt;/a&gt; temperament.&lt;br /&gt;
&lt;br /&gt;
See: &lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;Gallery of Just Intervals&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 13:03, 3 November 2025

Interval information
Ratio 22/17
Factorization 2 × 11 × 17-1
Monzo [1 0 0 0 1 0 -1⟩
Size in cents 446.3625¢
Name septendecimal ultramajor third
Color name 17u1o3, sulo 3rd
FJS name [math]\displaystyle{ \text{M3}^{11}_{17} }[/math]
Special properties reduced
Tenney norm (log2 nd) 8.54689
Weil norm (log2 max(n, d)) 8.91886
Wilson norm (sopfr(nd)) 30

[sound info]
Open this interval in xen-calc

In 17-limit just intonation, 22/17 is the septendecimal ultramajor third, measuring about 446.4 ¢. It is the mediant between 9/7 and 13/10, as it is (9+13)/(7+10).

Intervals around this size or a few cents smaller make good generators for sensi temperament.

Approximation

Edo approximations for 22/17 (446.36 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
8 3\8 450.00 +3.64 +2.42
11 4\11 436.36 -10.00 -9.17
16 6\16 450.00 +3.64 +4.85
19 7\19 442.11 -4.26 -6.74
24 9\24 450.00 +3.64 +7.27
27 10\27 444.44 -1.92 -4.32
32 12\32 450.00 +3.64 +9.70
35 13\35 445.71 -0.65 -1.89
43 16\43 446.51 +0.15 +0.53
51 19\51 447.06 +0.70 +2.96
54 20\54 444.44 -1.92 -8.63
59 22\59 447.46 +1.10 +5.38
62 23\62 445.16 -1.20 -6.21
67 25\67 447.76 +1.40 +7.81
70 26\70 445.71 -0.65 -3.78
78 29\78 446.15 -0.21 -1.36

See also

Retrieved from "https://en.xen.wiki/index.php?title=22/17&oldid=215982"