Major and minor triads: Difference between revisions

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

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

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* 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.

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.

== SCL files ==

@@ Line 1: / Line 1: @@
-Major and minor triads refer to triads containing a fifth alongside a major and minor third respectively.
+Major and minor triads refer to [[triad]]s containing a [[fifth]] alongside a [[major third|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 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.
@@ Line 11: / Line 11: @@
 * 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.
+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.
 == SCL files ==