- the root
- Note: Inversion does not change the root. (The third or fifth can be the lowest note.)
- the third – its interval above the root being a minor third (three semitones) or a major third (four semitones)
- the fifth – its interval above the third being a minor third or a major third, hence its interval above the root being a diminished fifth (six semitones), perfect fifth (seven semitones), or augmented fifth (eight semitones). Perfect fifths are the most commonly used interval above the root in Western classical, popular and traditional music.
Some 20th-century theorists, notably Howard Hanson and Carlton Gamer, expand the term to refer to any combination of three different pitches, regardless of the intervals. The word used by other theorists for this more general concept is "trichord". Others use the term to refer to combinations apparently stacked by other intervals, as in "quartal triad".
In the late Renaissance music era, and especially during the Baroque music era (1600–1750), Western art music shifted from a more "horizontal" contrapuntal approach (in which multiple, independent melody lines were interwoven) toward progressions, which are sequences of triads. The progression approach, which was the foundation of the Baroque-era basso continuo accompaniment, required a more "vertical" approach, thus relying more heavily on the triad as the basic building block of functional harmony.
The root of a triad, together with the degree of the scale to which it corresponds, primarily determine its function. Secondarily, a triad's function is determined by its quality: major, minor, diminished or augmented. Major and minor triads are the most commonly used triad qualities in Western classical, popular and traditional music. In standard tonal music, only major and minor triads can be used as a tonic in a song or some other piece of music. That is, a song or other vocal or instrumental piece can be in the key of C major or A minor, but a song or some other piece cannot be in the key of B diminished or F augmented (although songs or other pieces might include these triads within the triad progression, typically in a temporary, passing role). Three of these four kinds of triads are found in the major (or diatonic) scale. In popular music and 18th-century classical music, major and minor triads are considered consonant and stable, and diminished and augmented triads are considered dissonant and unstable.
When we consider musical works we find that the triad is ever-present and that the interpolated dissonances have no other purpose than to effect the continuous variation of the triad.— Lorenz Mizler (1739)
Triads (or any other tertian chords) are built by superimposing every other note of a diatonic scale (e.g., standard major or minor scale). For example, a C major triad uses the notes C–E–G. This spells a triad by skipping over D and F. While the interval from each note to the one above it is a third, the quality of those thirds varies depending on the quality of the triad:
- major triads contain a major third and perfect fifth interval, symbolized: R 3 5 (or 0–4–7 as semitones) play (help·info)
- minor triads contain a minor third, and perfect fifth, symbolized: R ♭3 5 (or 0–3–7) play (help·info)
- diminished triads contain a minor third, and diminished fifth, symbolized: R ♭3 ♭5 (or 0–3–6) play (help·info)
- augmented triads contain a major third, and augmented fifth, symbolized: R 3 ♯5 (or 0–4–8) play (help·info)
The above definitions spell out the interval of each note above the root. Since triads are constructed of stacked thirds, they can be alternatively defined as follows:
- major triads contain a major third with a minor third stacked above it, e.g., in the major triad C–E–G (C major), the interval C–E is major third and E–G is a minor third.
- minor triads contain a minor third with a major third stacked above it, e.g., in the minor triad A–C–E (A minor), A–C is a minor third and C–E is a major third.
- diminished triads contain two minor thirds stacked, e.g., B–D–F (B diminished)
- augmented triads contain two major thirds stacked, e.g., D–F♯–A♯ (D augmented).
Each triad found in a diatonic (single-scale-based) key corresponds to a particular diatonic function. Functional harmony tends to rely heavily on the primary triads: triads built on the tonic, subdominant (typically the ii or IV triad), and dominant (typically the V triad) degrees. The roots of these triads are the first, fourth, and fifth degrees (respectively) of the diatonic scale, otherwise symbolized I, IV, and V. Primary triads "express function clearly and unambiguously." The other triads in diatonic keys include the supertonic, mediant, submediant, and subtonic, whose roots are the second, third, sixth, and seventh degrees (respectively) of the diatonic scale, otherwise symbolized ii, iii, vi, and viio. They function as auxiliary or supportive triads to the primary triads.
- Ronald Pen, Introduction to Music (New York: McGraw-Hill, 1992): 81. ISBN 0-07-038068-6. "A triad is a set of notes consisting of three notes built on successive intervals of a third. A triad can be constructed upon any note by adding alternating notes drawn from the scale. ... In each case the note that forms the foundation pitch is called the root, the middle tone of the triad is designated the third (because it is separated by the interval of a third from the root), and the top tone is referred to as the fifth (because it is a fifth away from the root)."
- Howard Hanson, Harmonic Materials of Modern Music: Resources of the Tempered Scale (New York: Appleton-Century-Crofts, 1960).
- Carlton Gamer, "Some Combinational Resources of Equal-Tempered Systems", Journal of Music Theory 11, no. 1 (1967): 37, 46, 50–52.
- Julien Rushton, "Triad", The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell (London: Macmillan Publishers, 2001).
- Allen Forte, Tonal Harmony in Concept and Practice, third edition (New York: Holt, Rinehart and Winston, 1979): 136. ISBN 0-03-020756-8.
- Daniel Harrison, Harmonic Function in Chromatic Music: A Renewed Dualist Theory and an Account of its Precedents (Chicago: University of Chicago Press, 1994): 45. ISBN 0-226-31808-7. Cited on p. 274 of Deborah Rifkin, "A Theory of Motives for Prokofiev's Music", Music Theory Spectrum 26, no. 2 (2004): 265–289.