12/7: Difference between revisions

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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 = supermajor sixth, septimal major sixth
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-09-29 18:25:05 UTC</tt>.<br>
| Color name = r6, ru 6th
: The original revision id was <tt>259800020</tt>.<br>
| Sound = jid_12_7_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>
{{Wikipedia| Septimal major sixth }}
<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">In [[7-limit]] [[Just Intonation]], 12/7 is the septimal supermajor sixth of about 933.1¢. It represents the interval between the 12th and 7th harmonics and appears in chords such as 4:5:7:9:12. It differs from the 5-limit major sixth of [[5_3|5/3]] by [[36_35|36/25]] -- the septimal quartertone -- a [[superparticular]] interval of about 48.8¢. It differs from the Pythagorean major sixth of [[27_16|27/16]] by [[64_63|64/63]] -- Archytas' comma -- about 27.3¢. And finally, it differs from the harmonic seventh -- [[7_4|7/4]], about 968.8¢ -- by [[49_48|49/48]] -- the large septimal diesis or slendro diesis -- about 35.7¢. 12/7 is the inversion of the septimal subminor third of [[7_6|7/6]].


See: [[Gallery of Just Intervals]]</pre></div>
In [[7-limit]] [[just intonation]], '''12/7''' is the '''septimal (super)major sixth''' of about 933.1¢. It represents the interval between the 12th and 7th harmonics and appears in chords such as 4:5:7:9:12. It differs from the 5-limit major sixth of [[5/3]] by [[36/35]] – the septimal quartertone a [[superparticular]] interval of about 48.8¢. It differs from the Pythagorean major sixth of [[27/16]] by [[64/63]] – Archytas' comma about 27.3¢. And finally, it differs from the harmonic seventh of [[7/4]] by [[49/48]] – the large septimal diesis or slendro diesis about 35.7¢. 12/7 is the inversion of the septimal subminor third of [[7/6]].
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;12_7&lt;/title&gt;&lt;/head&gt;&lt;body&gt;In &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, 12/7 is the septimal supermajor sixth of about 933.1¢. It represents the interval between the 12th and 7th harmonics and appears in chords such as 4:5:7:9:12. It differs from the 5-limit major sixth of &lt;a class="wiki_link" href="/5_3"&gt;5/3&lt;/a&gt; by &lt;a class="wiki_link" href="/36_35"&gt;36/25&lt;/a&gt; -- the septimal quartertone -- a &lt;a class="wiki_link" href="/superparticular"&gt;superparticular&lt;/a&gt; interval of about 48.8¢. It differs from the Pythagorean major sixth of &lt;a class="wiki_link" href="/27_16"&gt;27/16&lt;/a&gt; by &lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt; -- Archytas' comma -- about 27.3¢. And finally, it differs from the harmonic seventh -- &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt;, about 968.8¢ -- by &lt;a class="wiki_link" href="/49_48"&gt;49/48&lt;/a&gt; -- the large septimal diesis or slendro diesis -- about 35.7¢. 12/7 is the inversion of the septimal subminor third of &lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;.&lt;br /&gt;
== See also ==  
&lt;br /&gt;
* [[7/6]] – its [[octave complement]]
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>
* [[7/4]] – its [[twelfth complement]]
* [[Gallery of just intervals]]
* [[:File:Ji-12-7-csound-foscil-220hz.mp3]] – an alternative sound sample
 
[[Category:Sixth]]
[[Category:Major sixth]]
[[Category:Supermajor sixth]]
[[Category:Over-7 intervals]]

Latest revision as of 16:59, 14 April 2025

Interval information
Ratio 12/7
Factorization 22 × 3 × 7-1
Monzo [2 1 0 -1
Size in cents 933.1291¢
Names supermajor sixth,
septimal major sixth
Color name r6, ru 6th
FJS name [math]\displaystyle{ \text{M6}_{7} }[/math]
Special properties reduced
Tenney height (log2 nd) 6.39232
Weil height (log2 max(n, d)) 7.16993
Wilson height (sopfr(nd)) 14

[sound info]
Open this interval in xen-calc
English Wikipedia has an article on:

In 7-limit just intonation, 12/7 is the septimal (super)major sixth of about 933.1¢. It represents the interval between the 12th and 7th harmonics and appears in chords such as 4:5:7:9:12. It differs from the 5-limit major sixth of 5/3 by 36/35 – the septimal quartertone – a superparticular interval of about 48.8¢. It differs from the Pythagorean major sixth of 27/16 by 64/63 – Archytas' comma – about 27.3¢. And finally, it differs from the harmonic seventh of 7/4 by 49/48 – the large septimal diesis or slendro diesis – about 35.7¢. 12/7 is the inversion of the septimal subminor third of 7/6.

See also