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In music or music theory, a 'triad' is a three-note chord (or, more generally, any set of three notes, pitches, or tones). Because the term originated during the "common practice" period in Western European art music (approximately from 1600 to 1900), it is most commonly associated with tertian diatonic chords having a tonal function. When such a chord is voiced in thirds, its members, ascending from lowest pitched tone to highest, are called:

★ the 'Root'

★ the 'Third' (whose interval is a major third or minor third above the root)

★ and the 'Fifth' (whose interval is a major or minor third above the third, and a diminished, perfect, or augmented fifth above the root).
The function of a given triad is determined primarily by its root tone and the degree of the scale it corresponds to, but also by the quality of the chord (the exact third and fifth).
There are four basic tertian triads: 'major', 'minor', 'diminished' and 'augmented'. All but the augmented triad can be derived from the Major (or diatonic) scale. Triads (and all other larger tertian chords) are built by combining or stacking ''every other'' tone the scale above each individual degree (or scale-tone) of the given seven-tone scale. The four triads are built of the following intervals:

★ ''Major'' triads contain a major third and perfect fifth interval, symbolized: R 3 5 (or 0-4-7 as semitones)

★ ''minor'' triads contain a minor third, and perfect fifth, symbolized: R ♭3 5 (or 0-3-7)

★ ''diminished'' triads contain a minor third, and diminished fifth, symbolized: R ♭3 ♭5 (or 0-3-6)

★ ''augmented'' triads contain a major third, and augmented fifth, symbolized: R 3 ♯5 (or 0-4-8)
'Primary triads' of a diatonic 'key' (major or minor) include the tonic, subdominant, and dominant degree chords, otherwise symbolized: I, IV, and V respectively.
In the twentieth century, the term ''triad'' was broadened (by Howard Hanson, for example, in his ''Harmonic Materials of Modern Music: Resources of the Tempered Scale''^[1], by Carleton Gamer in his "Some Combinational Resources of Equal-Tempered Systems"^[2] and by others) to include three-note chords made of intervals other than thirds. We can speak thus of quartal triads, secundal triads, and so on.

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★ Tertian harmony

★ Trichord

References

1. Hanson, H (1960) ''Harmonic Materials of Modern Music'', Irvington, ISBN: 978-0891972075
2. Gamer, C (1967) Some Combinational Resources of Equal-Tempered Systems, ''Journal of Music Theory'', Vol. 11, No. 1 (Spring, 1967), pp. 32-59