15/8: Difference between revisions

Wikispaces>Andrew_Heathwaite
**Imported revision 259802992 - Original comment: **
 
Overthink (talk | contribs)
m more readable wording
 
(27 intermediate revisions by 14 users not shown)
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 = just major seventh, classic(al) major seventh, ptolemaic major seventh
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-09-29 18:37:23 UTC</tt>.<br>
| Color name = y7, yo 7th
: The original revision id was <tt>259802992</tt>.<br>
| Sound = jid_15_8_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|Major seventh}}
<h4>Original Wikitext content:</h4>
In [[5-limit]] [[just intonation]], '''15/8''' is the '''just major seventh''', '''classic(al) major seventh''', or '''ptolemaic major seventh'''<ref>For reference, see [[5-limit]]. </ref> of about 1088.3¢. It is also the [[octave-reduced]] 15th [[harmonic]], and appears as a complex consonance in chords such as [[8:10:12:15]], a just version of a major seventh chord. Since 15/8 = [[3/2]] × [[5/4]], it can be seen as a perfect fifth above a major third or vice versa, and this understanding works in [[12edo]], as the sum of [[~]]3/2 and ~5/4 is 700{{c}} + 400{{c}} = 1100{{c}}, which 15/8 is mapped to.
<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.


See: [[Gallery of Just Intervals]]</pre></div>
Since 15 is a perfect fifth above 10 (15/10 = [[3/2]]), seventh chords can be formed with the 10th harmonic as major third and 15th harmonic as major seventh. The simplest and most familiar example is the classical major seventh chord 8:10:12:15 with steps 5/4, 6/5 and 5/4. Another example replaces the 12 with 13, which leads to [[8:10:13:15]] with steps 5/4, 13/10 and 15/13, and contains the [[10:13:15]] barbados triad. A particularly uncommon but mentionable example is the [[23-limit]] seventh chord [[16:20:23:30]].
<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;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;
{{Interval edo approximation|15/8}}
&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 also ==
* [[16/15]] – its [[octave complement]]
* [[8/5]] – its [[twelfth complement]]
* [[Ed15/8]]
* [[Gallery of just intervals]]
 
== Notes ==
<references/>
 
[[Category:Seventh]]
[[Category:Major seventh]]