Major and minor triads: Difference between revisions

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<pre>! majortriad.scl

Major and minor triads refer to triads containing a fifth alongside a major and minor third respectively.

== Approaches ==

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 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 400c and minor is 300c.

* 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 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.

== SCL files ==

.SCL files for the classical major and minor triads are provided below<pre>! majortriad.scl

!

The major triad as a wakalix

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-<pre>! majortriad.scl
+Major and minor triads refer to triads containing a fifth alongside a major and minor third respectively.
+== Approaches ==
+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 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 400c and minor is 300c.
+* 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 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.
+== SCL files ==
+.SCL files for the classical major and minor triads are provided below<pre>! majortriad.scl
 !
 The major triad as a wakalix