19/12: Difference between revisions

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
	https://en.xen.wiki/w/File:Jid_19_12_pluck_adu_dr220.mp3; [sound info]
	Open this interval in xen-calc

VisualWikitext

Latest revision as of 13:05, 3 November 2025

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

@@ 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 = large undevicesimal minor sixth, Boethius' minor sixth
-: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2013-05-19 18:18:18 UTC</tt>.<br>
+| Color name = 19o6, ino 6th
-: The original revision id was <tt>432734570</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>
+'''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]].
-<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** is a [[19-limit]] interval, 795.56 [[Cent|cents]] in size, that is very close to the minor sixth of [[12edo]]. Interestingly, this interval - together with [[19_15|19/15]] - adds up close to an octave.</pre></div>
+== Approximation ==
-<h4>Original HTML content:</h4>
+{{Interval edo approximation|19/12}}
-<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; is a &lt;a class="wiki_link" href="/19-limit"&gt;19-limit&lt;/a&gt; interval, 795.56 &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;. Interestingly, this interval - together with &lt;a class="wiki_link" href="/19_15"&gt;19/15&lt;/a&gt; - adds up close to an octave.&lt;/body&gt;&lt;/html&gt;</pre></div>
+== See also ==
+* [[24/19]] – its [[octave complement]]
+* [[30/19]] – the small undevicesimal minor sixth
+* [[Gallery of just intervals]]
+[[Category:Minor sixth]]
+[[Category:Sixth]]
+[[Category:Boethius]]

19/12: Difference between revisions

Latest revision as of 13:05, 3 November 2025

Approximation

See also

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