- the root
- 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.
(Note: The notes of a triad do not have to use the root as the lowest note of the triad, due to the principle of inversion. A triad can also use the third or fifth as the lowest note of the triad. Inverting a triad does not change the root note.)
Some twentieth-century theorists, notably Howard Hanson and Carlton Gamer, expand the term to refer to any combination of three different pitches, regardless of the intervals amongst them. The word used by other theorists for this more general concept is "trichord". Others, notably Allen Forte, use the term to refer to combinations apparently stacked of 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 tone of a triad, together with the degree of the scale to which it corresponds, primarily determine a given triad's 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 to be consonant and stable, and diminished and augmented triads are considered to be 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)
- 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)
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 begin on the first, fourth, and fifth degrees (respectively) of the diatonic scale, otherwise symbolized: I, IV, and V (respectively). Primary triads, "express function clearly and unambiguously." The other triads of the diatonic key include the supertonic, mediant, submediant, and subtonic, whose roots begin on the second, third, sixth, and seventh degrees (respectively) of the diatonic scale, otherwise symbolized: ii, iii, vi, and viio (respectively). They function as auxiliary or supportive triads to the primary triads.
Number of unique triads
Each triad can be transposed a number of times, given by the number of tones in the scale used. Typically there are 12 tones in the western scale. Computing the number of unique triads is a mathematical problem, which is most easily solved using a computer program. A computer can quickly iterate all the triads and remove those that are transpositions of each other. For 12 scale music, the following is the complete list of triads possible, which cannot be transposed into another triad in the list.
- C Db D – this combination has no name (half step cluster, with doubly diminished third and quintuply diminished fifth, spelled enharmonically)
- C Db Eb – this combination has no name
- C Db E – Eaug with sus6
- C Db F – Faug with sus5
- C Db Gb – Gbsus#4
- C D Eb – this combination has no name
- C D E – Eaug with sus#6
- C D F – Fsus6
- C D Gb – Gbaug with sus#4
- C D G – Csus2
- C Eb E – Eaug with sus7
- C Eb F – Fsus#6
- C Eb Gb – Cdim
- C Eb G – Cminor
- C E F – Fsus7
- C E Gb – Eaug with sus2
- C E G – Cmajor
- C E Ab – Caug
- C F Gb – Fsus#1
Total number of triads inside a single octave is 220 and 19 are unique. This number can be computed as the Binomial_coefficient of picking 3 keys out of 12.
- Upper structure triad – triads superimposed on another harmony
- 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, The Structure of Atonal Music (New Haven and London: Yale University Press, 1973): ISBN 0-300-02120-8.
- 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.
- fretjam Guitar Theory – Triads on Guitar