Major and minor triads

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 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 tendo and arto, corresponding to interseptimal and 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

! majortriad.scl
!
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])
3
!
5/4
3/2
2/1

! minortriad.scl
!
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])
3
!
6/5
3/2

2/1