19/12: Difference between revisions

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**Imported revision 513277854 - 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 = large undevicesimal minor sixth, Boethius' minor sixth
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-08 21:18:23 UTC</tt>.<br>
| Color name = 19o6, ino 6th
: The original revision id was <tt>513277854</tt>.<br>
| Sound = jid_19_12_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">**19/12**
|-2 -1 0 0 0 0 0 1&gt;
795.558 cents
[[media type="file" key="jid_19_12_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_19_12_pluck_adu_dr220.mp3|sound sample]]


**19/12** is a [[19-limit]] interval, about 795.6 [[Cent|cents]] in size, that is very close to the minor sixth of [[12edo]] (800 cents). Interestingly, 19/12 * [[19_15|19/15]] = 361/180 (1204.8 cents), which is very close to an octave.</pre></div>
'''19/12''', the '''large undevicesimal minor sixth''' or '''Boethius' minor sixth''', is a [[19-limit]] interval that is very close to the minor sixth of [[12edo]] (800 cents). It is an undevicesimal comma aka Boethius' comma (513/512) above the [[128/81|Pythagorean minor sixth]].  
<h4>Original HTML content:</h4>
== Approximation ==
<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;19_12&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;19/12&lt;/strong&gt;&lt;br /&gt;
{{Interval edo approximation|19/12}}
|-2 -1 0 0 0 0 0 1&amp;gt;&lt;br /&gt;
== See also ==
795.558 cents&lt;br /&gt;
* [[24/19]] – its [[octave complement]]
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* [[30/19]] – the small undevicesimal minor sixth
&lt;br /&gt;
* [[Gallery of just intervals]]
&lt;strong&gt;19/12&lt;/strong&gt; is a &lt;a class="wiki_link" href="/19-limit"&gt;19-limit&lt;/a&gt; interval, about 795.6 &lt;a class="wiki_link" href="/Cent"&gt;cents&lt;/a&gt; in size, that is very close to the minor sixth of &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; (800 cents). Interestingly, 19/12 * &lt;a class="wiki_link" href="/19_15"&gt;19/15&lt;/a&gt; = 361/180 (1204.8 cents), which is very close to an octave.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
[[Category:Minor sixth]]
[[Category:Sixth]]
[[Category:Boethius]]

Latest revision as of 13:05, 3 November 2025

Interval information
Ratio 19/12
Subgroup monzo 2.3.19 [-2 -1 1⟩
Size in cents 795.558¢
Names large undevicesimal minor sixth,
Boethius' minor sixth
Color name 19o6, ino 6th
FJS name [math]\displaystyle{ \text{m6}^{19} }[/math]
Special properties reduced
Tenney norm (log2 nd) 7.83289
Weil norm (log2 max(n, d)) 8.49586
Wilson norm (sopfr(nd)) 26

[sound info]
Open this interval in xen-calc

19/12, the large undevicesimal minor sixth or Boethius' minor sixth, is a 19-limit interval that is very close to the minor sixth of 12edo (800 cents). It is an undevicesimal comma aka Boethius' comma (513/512) above the Pythagorean minor sixth.

Approximation

Edo approximations for 19/12 (795.56 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
3 2\3 800.00 +4.44 +1.11
6 4\6 800.00 +4.44 +2.22
9 6\9 800.00 +4.44 +3.33
12 8\12 800.00 +4.44 +4.44
15 10\15 800.00 +4.44 +5.55
18 12\18 800.00 +4.44 +6.66
21 14\21 800.00 +4.44 +7.77
24 16\24 800.00 +4.44 +8.88
27 18\27 800.00 +4.44 +9.99
65 43\65 793.85 -1.71 -9.27
68 45\68 794.12 -1.44 -8.16
71 47\71 794.37 -1.19 -7.05
74 49\74 794.59 -0.96 -5.94
77 51\77 794.81 -0.75 -4.83
80 53\80 795.00 -0.56 -3.72

See also

Retrieved from "https://en.xen.wiki/index.php?title=19/12&oldid=215999"