Inmusic, atriad is a set of three notes (or "pitch classes") that can be stacked vertically in thirds.^[1] Triads are the most commonchords in Western music.

When stacked in thirds, notes produce triads. The triad's members, from lowest-pitched tone to highest, are called:^[1]

• theroot
  • Note:Inversion does not change the root. (The third or fifth can be the lowest note.)
• thethird – itsinterval above the root being aminor third (threesemitones) or amajor third (four semitones)
• thefifth – its interval above the third being a minor third or a major third, hence its interval above the root being adiminished fifth (six semitones),perfect fifth (seven semitones), oraugmented fifth (eight semitones). Perfect fifths are the most commonly used interval above the root in Westernclassical,popular andtraditional music.

Some 20th-century theorists, notablyHoward Hanson,^[2]Carlton Gamer,^[3] andJoseph Schillinger^[4] expand the term to refer to any combination of three different pitches, regardless of the intervals. Schillinger defined triads as "A structure in harmony of but three parts; conventionally, but not necessarily, the familiar triad of ordinary diatonic harmony." The word used by other theorists for this more general concept is "trichord".^[5] Others use the term to refer to combinations apparently stacked by other intervals, as in "quartal triad"; a combination stacked in thirds is then called a "tertian triad".

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 oraugmented. Major and minor triads are the most commonly used triad qualities in Westernclassical,popular andtraditional music. In standardtonal music, only major and minor triads can be used as atonic 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 atemporary, 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 consideredconsonant and stable, and diminished and augmented triads are considereddissonant and unstable.^{[citation needed]}

When we consider musical works we find that the triad is ever-present and that the interpolateddissonances have no other purpose than to effect the continuous variation of the triad.

— Lorenz Mizler (1739)^[6]

In the lateRenaissance music era, and especially during theBaroque music era (1600–1750), Western art music shifted from a more "horizontal"contrapuntal approach (in whichmultiple, independent melody lines were interwoven) towardprogressions, which are sequences of triads. The progression approach, which was the foundation of the Baroque-erabasso continuo accompaniment, required a more "vertical" approach, thus relying more heavily on the triad as the basic building block offunctional harmony.

The primacy of the triad in Western music was first theorized byGioseffo Zarlino (1500s), and the term "harmonic triad" was coined byJohannes Lippius in hisSynopsis musicae novae (1612).

Triads (or any othertertian chords) are built by superimposingevery other note of adiatonic scale (e.g., standard major or minor scale). For example, a C major triad uses the notes C–E–G. This spells a triad byskipping 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^ⓘ
• minor triads contain a minor third, and perfect fifth, symbolized: R♭3 5 (or 0–3–7)play^ⓘ
• diminished triads contain a minor third, and diminished fifth, symbolized: R♭3♭5 (or 0–3–6)play^ⓘ
• augmented triads contain a major third, and augmented fifth, symbolized: R 3♯5 (or 0–4–8)play^ⓘ

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).

Triads appear in close or open positions. "When the three upper voices are as close together as possible, the spacing is described as close position or close harmony. [...] The other arrangements [...] are called open position or open harmony."^[7]

Each triad found in a diatonic (single-scale-based) key corresponds to a particulardiatonic function. Functional harmony tends to rely heavily on theprimary triads: triads built on thetonic,subdominant, anddominant degrees.^[8] The roots of these triads are the first, fourth, and fifth degrees (respectively) of the diatonic scale, and the triads are accordingly symbolized I, IV, and V. Primary triads "expressfunction clearly and unambiguously."^[8] The other triads in diatonic keys include thesupertonic,mediant,submediant, andleading-tone, whose roots are the second, third, sixth, and seventh degrees (respectively) of the diatonic scale, symbolized ii, iii, vi, and vii^o. They function as auxiliary or supportive triads to the primary triads.

• Upper structure triad