3rds and triads
In most classical and modern music the interval of a 3rd is considered critical to establishing the quality of a chord or key center (i.e. major or minor). In terms of scale steps, a triad is two diatonic scale steps, thus one b2 bracket. In chromatic scale steps though one must distinguish major from minor 3rds. I introduced chromatic pitch brackets previously. A major 3rd has two c2 brackets and the minor 3rd has one c2 plus one c1 bracket. When forming a triad on each of the scale steps in any given diatonic scale you will form several major and minor chords and a diminished chord. Below I have written the triads on each major scale step. The initial scale step of each melody line is written preceding the line. Major triads have a major 3rd followed by a minor 3rd. Minor triads have a minor 3rd followed by a major 3rd. The triad on the 7th scale step has two minor 3rds which forms a diminished chord.