21/19: Difference between revisions

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**Imported revision 602876398 - 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 = hendrix major second, undevicesimal submajor second, undevicesimal supraneutral second
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-28 13:51:56 UTC</tt>.<br>
| Color name = 19uz2, nuzo 2nd
: The original revision id was <tt>602876398</tt>.<br>
| Sound = ji-21-19-csound-foscil-220hz.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">**21/19**
|0 1 0 1 0 0 0 -1&gt;
173.26789 cents


[[media type="file" key="ji-21-19-csound-foscil-220hz.mp3"]] [[file:xenharmonic/ji-21-19-csound-foscil-220hz.mp3|sound sample]]
In [[19-limit]] [[just intonation]], '''21/19''' is the '''hendrix major second''', also known as the '''undevicesimal submajor second''' or '''undevicesimal supraneutral second''', named for falling short of the [[9/8|Pythagorean major second (9/8)]] by a [[57/56|hendrix comma (57/56)]]. In [[counterpyth]] systems, it is equated to the diminished third (the interval formed by two [[256/243|limmas (256/243)]]). It can also be considered to approximate the [[tetracot]] generator.
== Approximation ==
{{Interval edo approximation|21/19}}
== See also ==
* [[38/21]] – its [[octave complement]]
* [[19/14]] – its [[fifth complement]]
* [[Gallery of just intervals]]


The **large neutral undevicesimal second**, its inverse is the minor neutral undevicesimal seventh [[38_21|38/21]].
[[Category:Second]]
 
[[Category:Neutral second]]
See also: [[Gallery of Just Intervals]]</pre></div>
[[Category:Equable heptatonic]]
<h4>Original HTML content:</h4>
[[Category:Tetracot]]
<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_19&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;21/19&lt;/strong&gt;&lt;br /&gt;
[[Category:Hendrix]]
|0 1 0 1 0 0 0 -1&amp;gt;&lt;br /&gt;
173.26789 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/ji-21-19-csound-foscil-220hz.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;ji-21-19-csound-foscil-220hz.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%252Fji-21-19-csound-foscil-220hz.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/ji-21-19-csound-foscil-220hz.mp3/602875936/ji-21-19-csound-foscil-220hz.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/ji-21-19-csound-foscil-220hz.mp3/602875936/ji-21-19-csound-foscil-220hz.mp3');"&gt;sound sample&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
The &lt;strong&gt;large neutral undevicesimal second&lt;/strong&gt;, its inverse is the minor neutral undevicesimal seventh &lt;a class="wiki_link" href="/38_21"&gt;38/21&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
See also: &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 13:07, 3 November 2025

Interval information
Ratio 21/19
Factorization 3 × 7 × 19-1
Monzo [0 1 0 1 0 0 0 -1
Size in cents 173.2679¢
Names hendrix major second,
undevicesimal submajor second,
undevicesimal supraneutral second
Color name 19uz2, nuzo 2nd
FJS name [math]\displaystyle{ \text{M2}^{7}_{19} }[/math]
Special properties reduced
Tenney norm (log2 nd) 8.64024
Weil norm (log2 max(n, d)) 8.78463
Wilson norm (sopfr(nd)) 29

[sound info]
Open this interval in xen-calc

In 19-limit just intonation, 21/19 is the hendrix major second, also known as the undevicesimal submajor second or undevicesimal supraneutral second, named for falling short of the Pythagorean major second (9/8) by a hendrix comma (57/56). In counterpyth systems, it is equated to the diminished third (the interval formed by two limmas (256/243)). It can also be considered to approximate the tetracot generator.

Approximation

Edo approximations for 21/19 (173.27 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
7 1\7 171.43 -1.84 -1.07
14 2\14 171.43 -1.84 -2.15
21 3\21 171.43 -1.84 -3.22
28 4\28 171.43 -1.84 -4.29
34 5\34 176.47 +3.20 +9.07
35 5\35 171.43 -1.84 -5.36
41 6\41 175.61 +2.34 +8.00
42 6\42 171.43 -1.84 -6.44
48 7\48 175.00 +1.73 +6.93
49 7\49 171.43 -1.84 -7.51
55 8\55 174.55 +1.28 +5.86
56 8\56 171.43 -1.84 -8.58
62 9\62 174.19 +0.93 +4.78
63 9\63 171.43 -1.84 -9.66
69 10\69 173.91 +0.65 +3.71
76 11\76 173.68 +0.42 +2.64

See also