Tertian

The most common chords are tertian, constructed using a sequence of major thirds (spanning 4 semitones) and/or minor thirds (3 semitones). Since there are 3 third intervals in a seventh chord (4 notes) and each can be major or minor, there are 7 possible permutations (the 8th one, consisted of four major thirds, results in a non-seventh augmented chord, since a major third equally divides the octave^[2]). The five commonly found in western music are the major seventh, the minor (or minor/minor) seventh, the dominant (or major/minor) seventh, the half-diminished seventh, and the diminished seventh. The less commonly found tertians are the minor major seventh and the augmented major seventh.

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Tertian seventh chords used in Western music

Common name	Chord on C	Common symbols on C	Intervals from root			Quality of consecutive thirds
			Third	Fifth	Seventh	1st	2nd	3rd
Major seventh		Cmaj7 CM7 CΔ7 CΔ	major	perfect	major	major	minor	major
Minor seventh		Cmin7 Cm7 C−7	minor	perfect	minor	minor	major	minor
Dominant seventh		C7	major	perfect	minor	major	minor	minor
Half-diminished seventh		Cm7♭5 C−7♭5 Cø7	minor	diminished	minor	minor	minor	major
Diminished seventh		Co7 Cdim7 Cm(♭7)♭5 C−(♭7)♭5	minor	diminished	diminished	minor	minor	minor
Minor major seventh		Cmmaj7 CmM7 CmΔ7 C−Δ7	minor	perfect	major	minor	major	major
Augmented major seventh		Caugmaj7 C+maj7 C+M7 C+Δ7	major	augmented	major	major	major	minor

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Non-tertian

Seventh chords can also be constructed using augmented or diminished thirds. These chords are not tertian and can be used in non-tertian harmony. There are many (mathematically, 64) chords that can be built, however, only a few of them are used in Western music.

More information Common name, Chord on C ...

Commonly used non-tertian seventh chords

Common name	Chord on C	Common symbols on C	Intervals from root			Quality of consecutive thirds
			Third	Fifth	Seventh	1st	2nd	3rd
Augmented seventh		Caug7 C+7	major	augmented	minor	major	major	diminished (equiv. major second)
Diminished major seventh		CmM7♭5 C−Δ7♭5	minor	diminished	major	minor	minor	augmented (equiv. perfect fourth)
Dominant seventh flat five		C7♭5	major	diminished	minor	major	diminished	major
Major seventh flat five		CM7♭5	major	diminished	major	major	diminished	augmented

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In tuning systems other than equal temperament there are further possible seventh chords. In just intonation, for example, there is the harmonic seventh.

Dominant seventh chord

A dominant seventh chord, or major-minor seventh chord is a chord composed of a root, major third, perfect fifth, and minor seventh. It can be also viewed as a major triad with an additional minor seventh. It is denoted using popular music symbols by adding a superscript "7" after the letter designating the chord root.^[3]: 77 The dominant seventh is found almost as often as the dominant triad.^[3]: 199 The chord can be represented by the integer notation (0, 4, 7, 10).

Of all the seventh chords, perhaps the most important is the dominant seventh. It was the first seventh chord to appear regularly in classical music. The name comes from the fact that the flat seventh occurs naturally in the scale built upon the root when it functions as the dominant (i.e., the fifth degree) of some major diatonic scale.

Take for example the C major scale (C, D, E, F, G, A, B, C):

The note G is the dominant degree of C major—its fifth note. When we arrange the notes of the C major scale in ascending pitch and use only these notes to build a seventh chord, and we start with G (not C), then the resulting chord contains the four notes G–B–D–F and is called G dominant seventh (G⁷). The note F is a minor seventh from G, and is also called the dominant seventh with respect to G.

Harmonic seventh chord

The harmonic seventh chord is a dominant seventh chord formed by a major triad plus a harmonic seventh interval.

The harmonic seventh interval is a minor seventh tuned in the 7:4 pitch ratio, one of the possible "just ratios" defined for this interval in just intonation (slightly below the width of a minor seventh as tuned in equal temperament). With just intonation on all notes of the harmonic seventh chord, the ratio between the frequencies of the pitches in the chord is 4:5:6:7. For example, a justly intuned A harmonic seventh chord in root position starting at A440 consists of the pitches 440 Hz, 550 Hz, 660 Hz, and 770 Hz.

Sometimes called a "blue note", the harmonic seventh is used by singers, through note bending on guitars, and on other instruments not restricted to equal temperament. An often heard example of the harmonic seventh chord is the last word of the modern addition to the song "Happy Birthday to You", with the lyrics, "and many more!" The harmony on the word "more" is typically sung as a harmonic seventh chord.^[4]

Frequent use of the harmonic seventh chord is one of the defining characteristics of blues and barbershop harmony; barbershoppers refer to it as "the barbershop seventh". Since barbershop music tends to be sung in just intonation, the barbershop seventh chord may be accurately termed a harmonic seventh chord. The harmonic seventh chord is also widely used in blues-flavored music. As pianos, and other equal-temperament instruments cannot play this chord, it is frequently approximated by a dominant seventh. As a result, it is often called a dominant seventh chord and written with the same symbols (such as the blues progression I⁷–V⁷–IV⁷).

Major and minor seventh chords

While the dominant seventh chord is typically built on the fifth (or dominant) degree of a major scale, the minor seventh chord is built on the second, third, or sixth degree. A minor seventh chord contains the same notes as an added sixth chord. For example, C–E♭–G–B♭ can function as both a C minor seventh and an E♭ added sixth (Id chord).

Major seventh chords are usually constructed on the first or fourth degree of a scale, (in C or G major: C–E–G–B). Due to the major seventh interval between the root and seventh (C–B, an inverted minor second), this chord can sometimes sound dissonant, depending on the voicing used. For example, Bacharach and David's "Raindrops Keep Fallin' on My Head" opens with a major chord followed by a major seventh in the next measure.

The major seventh is sometimes notated as Δ7 (a delta chord) or just a Δ (which has the same meaning).

Half-diminished seventh chord

A half-diminished seventh chord is a seventh chord built from the seventh degree of a major scale. It is considered "half-diminished" because a fully diminished seventh has a double-flatted (diminished) seventh, making it enharmonically the same as a major sixth. The half-diminished seventh chord uses a minor seventh over the root of a diminished triad.

Example: (in the key of C major) B–D–F–A.

Diminished seventh chord

A diminished seventh chord is made of three superimposed minor thirds (e.g., B–D–F–A♭), which is two tritones a minor third apart (e.g., B–F, D–A♭). The diminished seventh chord has been used by composers and musicians for a variety of reasons over time. Some reasons include: as a symbol of Sturm und Drang; modulation; and for characterisation. The diminished seventh chord is seen more frequently in late classical and romantic period works but is also found in Baroque and Renaissance period works, though not as frequently.

All of the elements of the diminished seventh chord can be found in the dominant seventh flat nine (7♭9) chord as seen in a comparison of the two chords.