Chord
A chord is a set of multiple pitch classes. The use of the term 'chord' generally implies that the notes are sounded together, creating harmonic intervals, although chords can also be broken chords, with the notes played separately in some sequence. An arpeggio is a broken chord wherein the notes are played in ascending or descending order. Therefore, the distinction between chords and scales is somewhat vague.
In Western musical tradition, chords conventionally accompany melodies, in that there is an instrument playing the melody separately from the chords being played, although melodies tend to match the notes played in the current chord to some extent. The main variety of chord in Western music is the triad, a series of three notes separated by thirds, also called a tertian triad (though see #Cardinality for further information on this definition.) The two most common triads are the major triad (with a major third and perfect fifth over the root) and minor triad (with a minor third and perfect fifth over the root). Note that the ordering of the sequence of intervals in a chord matters for determining its identity; the step pattern m3-M3-P4 is different from M3-m3-P4.
Characteristics of chords
Quality
A chord's quality is the combination of the qualities of the intervals it contains. A major chord generally contains major intervals, and a minor chord generally contains minor intervals. The qualities of the chords found in a scale determine the quality of the scale itself. A minor scale has a minor triad on the tonic note, meanwhile a major scale has a major triad on the tonic note.
Other qualities, such as dominant, exist exclusively for certain kinds of chords and are discussed below.
Inversion
Inversions are the rotations of a chord. If a chord were a scale, inversions would be its modes. An inversion is still usually considered to be rooted on the original tonic of the chord, so that even if a C major triad is voiced such that the lowest note of the chord is G, the chord is still identified with the note C. A related concept is chord homonyms, which is when inversions of a chord are considered chords with distinct identities, much like the modes of a scale are. An example in Western music is sixth chords, which may alternatively be viewed as seventh chords rooted on a different note, but are their own things regardless.
Extension
Extension refers to continuing the structure of a chord by continuing to stack intervals in a manner suggested by the chord's pattern. Note that this is a different sense of the term than temperament extension. Extended chords in Western music consist of chords made of stacked thirds with more than four notes (while a stack of three thirds, producing a four-note chord, can be considered an extension of a tertian triad, called a seventh chord or tertian tetrad, it is not considered an extended chord in Western theory as it is instead the largest kind of 'normal' tertian chord). You could similarly continue to stack chthonics, naiadics, or whatever other interval the chord is composed of.
Cardinality
Note: There is no correlation between opinions on the various definitions of 'triad' and opinions on the concept of music.
The cardinality of a chord is the number of pitch classes it contains. Chords are categorized based on cardinality, using terms derived from Greek: dyad for 2, triad for 3, tetrad for 4, pentad for 5, etc. Note that this introduces a broader, conflicting definition of "triad" compared to the one given on the top of the page. This is the one generally used in xenharmony and on this page, though some theorists do prefer to reserve 'triad' for tertian triads as in conventional theory.
Types of chords
Tertian chords
Major chords
A major triad consists of the root, a major third, and a perfect fifth. In the conventional Ionian major scale, major triads are found on the first, fourth, and fifth degrees, and contribute to the mode's "happy" sound. In xenharmonic systems, there may be multiple types of major triads, such as nearmajor (with a third flat of 12edo major) and supermajor (with a third sharp of 12edo major); of these nearmajor is the more resolved or relaxed of the two qualities.
A major seventh chord, notated M7 or Δ7, is one of two conventional major tetrads, consisting of a major triad alongside a major seventh over the root (forming a perfect fifth with the major third). The major seventh on its own is a somewhat tense sound, though due to functional reasons the major seventh chord itself is considered consonant, especially if voiced in root position, due to the tertian and fifth-based structure.
Meanwhile, a dominant seventh chord, often notated simply 7, is the other major tetrad, consisting of a major triad and minor seventh. The dominant seventh is found on the fifth degree of a major scale, and provides a point of tension due to the tritone between its third and seventh, which resolves to the major chord on the tonic. The harmonic tetrad 4:5:6:7 may be considered a kind of dominant seventh chord, and is notated as such in barbershop music, although in most tunings it does not produce the same kind of tension, due to having a mildly consonant 7/5 instead of a dissonant semioctave.
Minor chords
A minor triad consists of the root, a minor third, and a perfect fifth. In the major scale, minor triads are found on the second, third, and sixth degrees. In the minor scale, they are found on the first, fourth, and fifth degrees. Minor chords can give a sad, tense, and/or angry sound depending on compositional style; in xenharmonic systems, there may be multiple types of minor triads. 12edo minor triads are farminor, and are uniquely "rooted" among reasonably simple minor chords, having a 19/16 minor third. Meanwhile, minor triads with a flatter third are subminor, and inherit more of the sad/depressed sound of minor, while nearminor triads have a sharper third and more of the "angry/tense" sound.
The minor seventh chord, notated m7, is the primary minor tetrad, consisting of a minor triad with a minor seventh over the root.
Other tertian chords
Augmented chords
The augmented triad consists of a major third or diminished fourth and an augmented fifth or minor sixth over the root (inversions are not distinguished in 12edo theory due to the relevant intervals being tempered together). In 12edo, the 5-limit version of this chord is equated to 3edo, which is the fittingly named augmented temperament. It produces a dissonant, tense sound, notably rather unlike the major third or minor sixth individually. "Augmented triad" does not refer to a triad with an augmented third; instead the fifth is augmented.
Diminished chords
The diminished triad consists of a minor third and diminished fifth, and is found on the seventh degree of major. However, the diminished tetrad is not found in diatonic at all, being composed of a minor third, diminished fifth, and diminished seventh (or enharmonic equivalents, see the section on the augmented triad). In 12edo, the 5-limit version of this chord is equated to 4edo, which is similarly diminished temperament. The diminished chord is also tense, but in a more 'minor' way.
The chord 5:6:7 can be seen as a consonant diminished triad, and contributes to the stability of 4:5:6:7 as opposed to the tension of the 12edo dominant.
Arto and tendo chords
Tendo refers to a chord quality with a third wider than a major third, and similarly arto refers to a chord quality with a third narrower than a minor third. The rough boundary for an arto third is from 8/7 to 7/6 (making it a chthonic), and for a tendo third it is between 9/7 and 21/16 (making it a naiadic). Arto and tendo chords have the same kinds of feels that minor and major chords do, with the added property that you can play an arto and tendo interval at the same time without excessive crowding. Slendric temperament represents the simplest, equalized arto/tendo structure, dividing the perfect fifth into three equal parts.
Neutral chords
Neutral chords have an unstable quality "in between" major and minor, with thirds that roughly evenly divide the fifth. They are commonly associated with the 11-limit (specifically, the 2.3.11 "Alpharabian" subgroup) and with 24edo, and as such they are the most well-known microtonal chord quality. Systems that do not distinguish between major and minor (such as 7edo) also have neutral chords. The "perfect" neutral chord equally divides the perfect fifth in pitch, resulting in two stacked thirds of sqrt(3/2); temperaments (supported by 7 and 10edo) that equate a JI triad to this perfect neutral chord are called neutral temperaments; rastmatic (11/9 ~ 27/22) is one example.
Suspended chords
A suspended chord consists of a major second or perfect fourth, and a perfect fifth. This makes it particularly simple on the chain of fifths, and therefore the primary kind of triad found in 3-limit harmony, and the only kind of triad available in 5edo, where they overlap with arto and tendo triads. Historically, suspended chords were used for tension, with the second or fourth being a note "suspended" from a previous chord. In oneirotonic systems, suspended chords become the primary counterpart of major and minor, called taphric and simic respectively. A suspended chord is a MOS, specifically monocot[3].
Suspended chords may be defined more loosely, especially in a functional harmony / "suspension" context, to refer to a chord with any note that resolves down to a major third, or up to a minor third, such as 8:11:12 (the "otonal suspended chord" found in 22edo that resolves to 14:18:21).
Chthonic chords
Chthonic chords are a type of chord constructed by stacking intervals between a major second and a minor third, typically spanning a perfect fourth or some other form of fourth. They may be functionally analyzed in the 5- or 10-form, wherein all chthonics fall on the same scale degree, and the fourth is divisible into two. Chthonic chords can also be major or minor, like tertian chords can, although in this case "major" refers to a subminor third (1-m3-P4), and "minor" refers to a supermajor second (1-M2-P4). The chthonic analog to 4:5:6 in tertian harmony is 6:7:8. Stacking a chthonic chord on a tertian chord of the same quality produces a harmonic tetrad, generalizing the characteristics of the harmonic seventh chord 4:5:6:7. This is especially significant in jubilismic temperaments, wherein the diesis between 5/4 and 6/5 is equated to the diesis between 7/4 and 12/7.
Naiadic chords
Naiadic chords are chords constructed by stacking intervals between and including a perfect fourth and major third, usually stacking to the interval 5/3, which is a "perfect" sixth in this system. The "major" naiadic chord is 3:4:5, analogous to 4:5:6 for tertian harmony.
Dyads
A dyad is two notes, separated by a single interval, played together. "Dyad" is largely equivalent to "interval", although dyads have additional voicing and inversion characteristics in some analyses. A dyad, when used as a chord, often implies the quality of a more "complete" chord, for example a major third dyad could be played on its own to imply a major triad.
Trine
A trine is a voicing of a dyad, typically from 450-750 cents, in which the lower note is doubled at the octave; equivalently it is a set of three notes spanning an octave, and may be considered equivalent to a 2-note scale. The basic otonal trine is 2:3:4, serving as a basis for 3-limit harmony much as the triad 4:5:6 serves as a basis for 5-limit harmony.
