15/8: Difference between revisions

Wikispaces>spt3125
**Imported revision 513214416 - Original comment: **
Wikispaces>spt3125
**Imported revision 513256132 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-07 22:54:06 UTC</tt>.<br>
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-08 15:45:34 UTC</tt>.<br>
: The original revision id was <tt>513214416</tt>.<br>
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In [[5-limit]] [[Just Intonation]], 15/8 is a major seventh of about 1088.3¢. It is also the 15th overtone (octave-reduced), 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]].
In [[5-limit]] [[Just Intonation]], 15/8 is a major seventh of about 1088.3¢. It is also the 15th overtone (octave-reduced), 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 is a perfect fifth above 10 (15/10 = [[3_2|3/2]]), [[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.//
//&lt;range type="comment" id="513214416_1"&gt;Since 15 is a perfect fifth above 10 (15/10 = [[3_2|3/2]]), [[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.&lt;/range id="513214416_1"&gt;//  


See: [[Gallery of Just Intervals]]</pre></div>
See: [[Gallery of Just Intervals]]</pre></div>
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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 major seventh of about 1088.3¢. It is also the 15th overtone (octave-reduced), 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;.&lt;br /&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 major seventh of about 1088.3¢. It is also the 15th overtone (octave-reduced), 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;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;em&gt;Since 15 is a perfect fifth above 10 (15/10 = &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;), &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;/em&gt;&lt;br /&gt;
&lt;em&gt;&lt;a name="comment-513214416_1-open" class="range"&gt;&lt;/a&gt;Since 15 is a perfect fifth above 10 (15/10 = &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;), &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;a name="comment-513214416_1-close" class="range"&gt;&lt;/a&gt;&lt;/em&gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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>
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>