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Major and minor triads: Difference between revisions

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Major and minor triads refer to [[triad]]s containing a [[fifth]] alongside a [[major third|major]] and [[minor third]] respectively.  
Major and minor triads refer to [[triad]]s containing a [[perfect fifth|fifth]] alongside a [[major third|major]] and [[minor third]] respectively.  


== Approaches ==
== In tempered scales ==
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]].
In [[5L 2s|diatonic (5L 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.


In diatonic scales, "major third" and "minor third" are precisely defined intervals corresponding to 81/64 and 32/27 in Pythagorean tuning, but generated by a tempered fifth.
* In [[12edo]], major is 400{{cent}} and minor is 300{{cent}}.
* In [[19edo]], major is 379{{c}} and minor is 316{{c}}.
* 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.  


* In [[12edo]], major is 400c and minor is 300c.
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.
* In [[19edo]], major is 379c and minor is 316c.
* In [[22edo]], major is 436c and minor is 273c.
* If we pretend that [[16edo]]'s fifth generates a diatonic scale, this places major at 300c and minor at 375c, leading to the controversial "harmonic notation" of 16edo.


In terms of mediants, minor triads tend to range between a [[mediant (tonality)|mediant]] of 37% and 47%, and major triads tend to range between 53% and 63%, corresponding to simple [[5-limit]] or 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 ==
.SCL files for the classical major and minor triads are provided below<pre>! majortriad.scl
.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
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3/2
3/2
2/1
2/1
</pre><pre>
</pre>
<pre>
! minortriad.scl
! minortriad.scl
!
!
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3/2
3/2
2/1</pre>
2/1</pre>
[[Category:Wakalixes]]
[[Category:Wakalixes]]
[[Category:Triad]]
[[Category:Triad]]
[[Category:Chords]]
[[Category:Chords]]
[[Category:Pages with Scala files]]
[[Category:Pages with Scala files]]
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