15/8: Difference between revisions

: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-09-29 18:37:23 UTC</tt>.<br>

: The original revision id was <tt>259802992</tt>.<br>

<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 [[5-limit]] [[Just Intonation]], 15/8 is a slightly narrow major seventh of about 1088.3¢. It is also the 15th overtone, and appears as a complex consonance in chords such as 8:10:12:15, a just version of a major seventh chord. Since 15 is 3*5, it can be seen as a perfect fifth above a major third or vice versa, and this understanding is compatible with the 1100¢ interval of [[12edo]]. Since 15 it is a [[3_2|3/2]] perfect fifth above 10, [[List of root-3rd-P5 triads in JI|root-3rd-P5 triads]] can be formed with the 10th harmonic as root and 15th harmonic as perfect fifth. The simplest and most familiar example is the classic minor triad 10:12:15 -- a [[6_5|6/5]] with a [[5_4|5/4]] stacked on top of it. Another is the Barbados triad, 10:13:15 -- a [[13_10|13/10]] on bottom and a [[15_13|15/13]] on top. And a particularly uncommon but mentionable example is the [[23-limit]] inframinor triad 20:23:30.

<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;15_8&lt;/title&gt;&lt;/head&gt;&lt;body&gt;In &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, 15/8 is a slightly narrow major seventh of about 1088.3¢. It is also the 15th overtone, and appears as a complex consonance in chords such as 8:10:12:15, a just version of a major seventh chord. Since 15 is 3*5, it can be seen as a perfect fifth above a major third or vice versa, and this understanding is compatible with the 1100¢ interval of &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;. Since 15 it is a &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt; perfect fifth above 10, &lt;a class="wiki_link" href="/List%20of%20root-3rd-P5%20triads%20in%20JI"&gt;root-3rd-P5 triads&lt;/a&gt; can be formed with the 10th harmonic as root and 15th harmonic as perfect fifth. The simplest and most familiar example is the classic minor triad 10:12:15 -- a &lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt; with a &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt; stacked on top of it. Another is the Barbados triad, 10:13:15 -- a &lt;a class="wiki_link" href="/13_10"&gt;13/10&lt;/a&gt; on bottom and a &lt;a class="wiki_link" href="/15_13"&gt;15/13&lt;/a&gt; on top. And a particularly uncommon but mentionable example is the &lt;a class="wiki_link" href="/23-limit"&gt;23-limit&lt;/a&gt; inframinor triad 20:23:30.&lt;br /&gt;