The major and minor triads

There are two types of chord which form the fundamental building blocks of harmonic music. These are the major triad and the minor triad.

They are fundamental in that any other type of three note chord is heard as a deviation from one of these two archetypal forms. Furthermore, both the major and the minor triad is heard as a unified entity in itself - it is a sum which is more than its parts. So what is it about the major and minor triads that is so unique, meaningful and pleasing to the ear ?

Mutual consonance

The first unique quality of these two types of triad is that the intervals found between every pair of its tones is a consonant one - both the major and minor triad contain a perfect fifth, a major third and a minor third. They contain none of the dissonant intervals - the minor second, major second, augmented second, diminished fourth, augmented fourth, and their inversions.

There is no other combination of three notes in which all of the intervals are consonant.

The only other triad which appears to have full mutual consonance is the augmented triad (1 - 3 - 5). On a piano keyboard this triad appears to contain two major thirds and a minor sixth - all of which are consonant, but in actuality the interval between the top and bottom tones is not the consonant minor sixth but the dissonant augmented fifth.

The augmented fifth and the minor sixth may be represented by the same number of semitones in 12-tone equal temperament, but this does not mean that the aural effect of these two intervals is the same.

This may seem paradoxical and somewhat pedantic, but it is not - neither in a theoretical nor an empirical sense. The augmented fifth is a disturbing interval, even when expressed in equal temperament.

Harmonic roots

The intervals of the octave, the perfect fifth and the major third are rooted intervals. This means that they have a root tone at the bottom and a tone which is subsidiary to this root at the top.

Of the two tones in these intervals, it is the root tone which most effectively represents the pitch of the interval as a whole.

This can be demonstrated by playing each of these three intervals and hearing how it is the root tone which, even when played in isolation, seems somehow to define the overall pitch of the interval itself and which seems to best represent the interval as a whole.

The subsidiary tone partially loses its own pitch identity, and becomes a heard more as a timbral enhancement of its root.

The two notes in the rooted intervals are partially unified and are stable in quality.

When the rooted intervals are inverted (so that the root is higher in pitch than its subsidiary) they become unstable and tend to seek resolution to their nearest rooted interval neighbour - so a perfect fourth tends to resolve to a major third and a minor sixth tends to resolve to a perfect fifth.

So far I have talked of only two notes played together - an interval is either rooted and unified, or it isn't. When we put together three notes, however, we can unify them in two different ways.

1. One of the tones can be a root and the other two tones subsidiary to that one root - the major triad
2. One of the tones can be a subsidiary and the other two tones roots to that one subsidiary - the minor triad

So we can have either a common root or a common subsidiary.

The major triad

The intervals of the root position major triad from the bass note upwards are a perfect fifth and a major third. The lowest tone of the root position major triad is the root of the other two notes, which are subsidiary to this root.

This unifies the three tones because the lowest tone is the common root and can effectively represent the entire triad, while the two upper tones are subsidiary in that they provide a support, colouration and extension of this root tone.

The major triad represents two ideas:

• the enhancement of the one through the sacrifice and rebirth of the two in the one
• the unification of two, otherwise independent identities through their common sacrifice and rebirth in the one

The minor triad

The intervals of a minor triad from its fifth downwards are a perfect fifth and a major third. The fifth of the minor triad is subsidiary to the other two tones which are roots to this subsidiary.

This unifies the three tones because the fifth is the common subsidiary and so serves both to support and strengthen both the other two tones. It is the nexus of two otherwise independent identities.

The minor triad represents two ideas:

• the enhancement of the two through the sacrifice and rebirth of the one in the two
• the unification of two, otherwise independent identities through their common enhancement

Musical emotion

The psychological effects of the major and minor triads, and their respective tonalities, can be understood as the emotional corollaries of these underlying ideas.

The major triad revolves around the ideas and the concomitant emotions of order, purity, devotion, submission and worship.

The minor triad revolves around the ideas and the concomitant emotions of sacrifice, altruism, complexity and partnership.