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.