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Major and minor triads: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
Major and minor triads refer to [[triad]]s containing a [[perfect fifth|fifth]] alongside a [[major third|major]] and [[minor third]] respectively.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
 
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-03-29 01:01:51 UTC</tt>.<br>
== In tempered scales ==
: The original revision id was <tt>499164858</tt>.<br>
In [[5L 2s|diatonic (5L&nbsp;2s) scales]], "[[Major third (diatonic interval category)|major third]]" and "[[Minor third (diatonic interval category)|minor third]]" are precisely defined intervals corresponding to [[81/64]] and [[32/27]] in [[Pythagorean tuning]], but generated by a tempered fifth.
: 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>
* In [[12edo]], major is 400{{cent}} and minor is 300{{cent}}.
<h4>Original Wikitext content:</h4>
* In [[19edo]], major is 379{{c}} and minor is 316{{c}}.
<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">! majortriad.scl
* In [[22edo]], major is 436{{c}} and minor is 273{{c}}.
* If we pretend that [[16edo]]'s fifth generates a diatonic scale, this places major at 300{{c}} and minor at 375{{c}}, leading to the controversial "harmonic notation" of 16edo.
** A more conventional interpretation labels the 300{{c}} third as "minor" and 375{{c}} as major, which is more sensible in terms of interval size and sound, despite technically not following Pythagorean notation.
 
The triads closer to the middle of the respective ranges correspond to simple [[5-limit|classical]] or [[7-limit|septimal]] intervals. More extreme than major and minor are [[Extraclassical tonality|tendo and arto]], corresponding to [[interseptimal]] and [[13-limit|tridecimal]] intervals, and ultimately suspended, corresponding to simple [[3-limit]] intervals; less extreme than major and minor are neutral triads.
 
As interval regions, [[Minor third (interval region)|minor thirds]] and [[Major third (interval region)|major thirds]] range from, at the widest, 240-340c and 360-460c, although people tend to restrict this further, such as to roughly 260-330c and 370-440c. And as an interval region, [[Perfect fifth]]s range from around 660 to 740 cents at the widest, often being restricted to 680-720 cents.
 
== In just intonation ==
In [[just intonation]], [[4:5:6]] and [[10:12:15]] are the canonical tunings for the major and minor triads. Major and minor triads may also be tuned to simple [[7-limit|septimal]] intervals, for example, to [[14:18:21]] and [[6:7:9]]. Further details lie below.
 
=== Simple major triads ===
{{Wikipedia|Major chord}}
 
A '''major triad''' is a [[triad]] comprising a root, [[major]] third, and [[perfect]] fifth.
 
In the 3-limit:
 
* [[64:81:96]] is found on the I, IV, and V of the Pythagorean [[5L 2s|diatonic scale]].
 
In the 5-limit:
 
* [[4:5:6]] is found on the I ({{Frac|1|1}}), IV ({{Frac|4|3}}), and V ({{Frac|3|2}}) of Ptolemy's intense diatonic scale ([[Zarlino]]).
 
In the 7-limit:
 
* [[14:18:21]], a ''supermajor triad'',  is a [[9-odd-limit]] chord that tunes the third sharper than the 5-limit major.
 
=== Simple minor triads ===
{{Wikipedia|Minor chord}}
 
A '''minor triad''' is a [[triad]] comprising a root, [[minor]] third, and fifth.
 
In the [[3-limit]]:
* [[54:64:81]] is found on the ii ({{Frac|9|8}}), iii ({{Frac|81|64}}), and vi ({{Frac|27|16}}) of the Pythagorean diatonic scale.
 
In the [[5-limit]]:
* [[10:12:15]] is found on the iii ({{Frac|5|4}}) and vi ({{Frac|5|3}}) of Ptolemy's intense diatonic scale ([[Zarlino]]), perhaps the most common 5-limit diatonic.
* [[27:32:40]] is found on the ii ({{Frac|9|8}}) of Ptolemy's intense diatonic scale.
 
In the [[7-limit]]:
* [[6:7:9]], a ''subminor triad'', is a [[9-odd-limit]] chord that tunes the third flatter than the 5-limit minor.
 
== SCL files ==
.SCL files for the classical major and minor triads are provided below:
 
<pre>
! majortriad.scl
!
!
The major triad as a wakalix
The major triad as a wakalix
! Fokblock([25/24, 16/15], [1, 0]) = Fokblock([25/24, 10/9], [2, 0]) = Fokblock([16/15, 10/9], [0, 1])
! Fokblock([25/24, 16/15], [1, 0]) = Fokblock([25/24, 10/9], [2, 0]) = Fokblock([16/15, 10/9], [0, 1])
3
3
!
!
5/4
5/4
3/2
3/2
2/1
2/1
 
</pre>
<pre>
! minortriad.scl
! minortriad.scl
!
!
The minor triad as a wakalix
The minor triad as a wakalix
! Fokblock([25/24, 16/15], [0, 0]) = Fokblock([25/24, 10/9], [1, 0]) = Fokblock([16/15, 10/9], [1, 0])
! Fokblock([25/24, 16/15], [0, 0]) = Fokblock([25/24, 10/9], [1, 0]) = Fokblock([16/15, 10/9], [1, 0])
3
3
!
!
6/5
6/5
3/2
3/2
2/1
2/1</pre>


</pre></div>
[[Category:Wakalixes]]
<h4>Original HTML content:</h4>
[[Category:Triad]]
<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;major and minor triads&lt;/title&gt;&lt;/head&gt;&lt;body&gt;! majortriad.scl&lt;br /&gt;
[[Category:Chords]]
!&lt;br /&gt;
[[Category:Pages with Scala files]]
The major triad as a wakalix&lt;br /&gt;
! Fokblock([25/24, 16/15], [1, 0]) = Fokblock([25/24, 10/9], [2, 0]) = Fokblock([16/15, 10/9], [0, 1])&lt;br /&gt;
3&lt;br /&gt;
!&lt;br /&gt;
5/4&lt;br /&gt;
3/2&lt;br /&gt;
2/1&lt;br /&gt;
&lt;br /&gt;
! minortriad.scl&lt;br /&gt;
!&lt;br /&gt;
The minor triad as a wakalix&lt;br /&gt;
! Fokblock([25/24, 16/15], [0, 0]) = Fokblock([25/24, 10/9], [1, 0]) = Fokblock([16/15, 10/9], [1, 0])&lt;br /&gt;
3&lt;br /&gt;
!&lt;br /&gt;
6/5&lt;br /&gt;
3/2&lt;br /&gt;
2/1&lt;/body&gt;&lt;/html&gt;</pre></div>
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