Four triad qualities
Major (M): major third plus minor third, perfect fifth. Minor (m): minor third plus major third, perfect fifth. Diminished (d or °): two minor thirds, diminished fifth. Augmented (A or +): two major thirds, augmented fifth. Quality is determined by stacking the chord in thirds and measuring the intervals from the root.
Roman numerals and diatonic chords
Every scale degree in a key produces a diatonic chord. Uppercase Roman numerals label major triads, lowercase label minor, lowercase with ° labels diminished, and uppercase with + labels augmented. In C major: I, ii, iii, IV, V, vi, vii°. In natural minor: i, ii°, III, iv, v, VI, VII.
Inversions and figured bass
Root position places the root in the bass (5/3, abbreviated). First inversion places the third in the bass (6). Second inversion places the fifth in the bass (6/4). Seventh chords add a third inversion (4/2) where the seventh is in the bass. Figures attach to Roman numerals: V6, V6/5, V4/3, V4/2.