21/17: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Wikispaces>spt3125
**Imported revision 513546852 - Original comment: **
 
m Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"
 
(11 intermediate revisions by 10 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 submajor third
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-10 21:49:05 UTC</tt>.<br>
| Color name = 17uz3, suzo 3rd
: The original revision id was <tt>513546852</tt>.<br>
| Sound = jid_21_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>
'''21/17''' is the '''septendecimal submajor third'''. It is well represented in [[23edo]] and [[36edo]].
<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">**21/17**
== Approximation ==
|0 1 0 1 0 0 -1&gt;
{{Interval edo approximation|21/17}}
365.8255 cents
== See also ==
[[media type="file" key="jid_21_17_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_21_17_pluck_adu_dr220.mp3|sound sample]]
* [[34/21]] – its [[octave complement]]
</pre></div>
* [[17/14]] – its [[fifth complement]]
<h4>Original HTML content:</h4>
* [[Gallery of just intervals]]
<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;21_17&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;21/17&lt;/strong&gt;&lt;br /&gt;
 
|0 1 0 1 0 0 -1&amp;gt;&lt;br /&gt;
[[Category:Third]]
365.8255 cents&lt;br /&gt;
[[Category:Submajor third]]
&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_21_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_21_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_21_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_21_17_pluck_adu_dr220.mp3/513545342/jid_21_17_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_21_17_pluck_adu_dr220.mp3/513545342/jid_21_17_pluck_adu_dr220.mp3');"&gt;sound sample&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 13:17, 3 November 2025

Interval information
Ratio 21/17
Factorization 3 × 7 × 17-1
Monzo [0 1 0 1 0 0 -1
Size in cents 365.8255¢
Name septendecimal submajor third
Color name 17uz3, suzo 3rd
FJS name [math]\displaystyle{ \text{M3}^{7}_{17} }[/math]
Special properties reduced
Tenney norm (log2 nd) 8.47978
Weil norm (log2 max(n, d)) 8.78463
Wilson norm (sopfr(nd)) 27

[sound info]
Open this interval in xen-calc

21/17 is the septendecimal submajor third. It is well represented in 23edo and 36edo.

Approximation

Edo approximations for 21/17 (365.83 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
3 1\3 400.00 +34.17 +8.54
10 3\10 360.00 -5.83 -4.85
13 4\13 369.23 +3.41 +3.69
20 6\20 360.00 -5.83 -9.71
23 7\23 365.22 -0.61 -1.17
26 8\26 369.23 +3.41 +7.38
33 10\33 363.64 -2.19 -6.02
36 11\36 366.67 +0.84 +2.52
46 14\46 365.22 -0.61 -2.33
49 15\49 367.35 +1.52 +6.21
56 17\56 364.29 -1.54 -7.19
59 18\59 366.10 +0.28 +1.36
62 19\62 367.74 +1.92 +9.90
69 21\69 365.22 -0.61 -3.50
72 22\72 366.67 +0.84 +5.05
79 24\79 364.56 -1.27 -8.35

See also