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Major seventh chord on C, notated as C^Δ7

Letters for triads built on C

Musicians use various kinds of chord names and symbols in different contexts to represent musical chords. In most genres of popular music, including jazz, pop, and rock, a chord name and its corresponding symbol typically indicate one or more of the following:

1. the root note (e.g. C♯),
2. the chord quality (e.g. minor or lowercase m, or the symbols ^o or + for diminished and augmented chords, respectively; chord quality is usually omitted for major chords),
3. whether the chord is a triad, seventh chord, or an extended chord (e.g. ^Δ7),
4. any altered notes (e.g. sharp five, or ♯5),
5. any added tones (e.g. ^add2), and
6. the bass note if it is not the root (e.g. a slash chord).

For instance, the name C augmented seventh, and the corresponding symbol C^aug7, or C⁺⁷, are both composed of parts 1 (letter 'C'), 2 ('aug' or '+'), and 3 (digit '7'). These indicate a chord formed by the notes C–E–G^♯–B^♭. The three parts of the symbol (C, aug, and ⁷) refer to the root C, the augmented (fifth) interval from C to G♯, and the (minor) seventh interval from C to B♭.

Although they are used occasionally in classical music, typically in an educational setting for harmonic analysis, these names and symbols are "universally used in jazz and popular music",^[1] in lead sheets, fake books, and chord charts, to specify the chords that make up the chord progression of a song or other piece of music. A typical sequence of a jazz or rock song in the key of C major might indicate a chord progression such as

C – Am – Dm – G⁷.

This chord progression instructs the performer to play, in sequence, a C major triad, an A minor chord, a D minor chord, and a G dominant seventh chord. In a jazz context, players have the freedom to add sevenths, ninths, and higher extensions to the chord. In some pop, rock and folk genres, triads are generally performed unless specified in the chord chart.

Purpose

These chord symbols are used by musicians for a number of purposes. Chord-playing instrumentalists in the rhythm section, such as pianists, use these symbols to guide their improvised performance of chord voicings and fills. A rock or pop guitarist or keyboardist might literally play the chords as indicated (e.g., the C major chord would be played by playing the notes C, E and G at the same time). In jazz, particularly for music from the 1940s bebop era or later, players typically have latitude to add in the sixth, seventh, and/or ninth of the chord. Jazz chord voicings often omit the root (leaving it to the bass player) and fifth. As such, a jazz guitarist might voice the C major chord with the notes E, A and D—which are the third, sixth, and ninth of the chord. The bassist (electric bass or double bass) uses the chord symbols to help improvise a bass line that outlines the chords, often by emphasizing the root and other key scale tones (third, fifth, and in a jazz context, the seventh).

The lead instruments, such as a saxophonist or lead guitarist, use the chord chart to guide their improvised solos. The instrumentalist improvising a solo may use scales that work well with certain chords or chord progressions, according to the chord-scale system. For example, in rock and blues soloing, the pentatonic scale built on the root note is widely used to solo over straightforward chord progressions that use I, IV, and V chords (in the key of C major, these would be the chords C, F, and G⁷).

In a journal of the American Composers Forum the use of letters to indicate chords is defined as, "a reductive analytical system that views music via harmonic motion to and from a target chord or tonic".^[2] In 2003 Benjamin, Horvit, and Nelson describe the use of letters to indicate chord root as, "popular music ( jazz) lead sheet symbols."^[3] The use of letters, "is an analytical technique that may be employed along with, or instead of, more conventional methods of analysis such as Roman numeral analysis. The system employs letter names to indicate the roots of chords, accompanied by specific symbols to depict chord quality."^[4]

Other notation systems for chords include:^[5]

• Traditional staff notation.
• Roman numerals, commonly used in harmonic analysis.^[6]
• figured bass, widely used in the Baroque era.
• numbered musical notation, a musical notation that use numbers characters instance of graphical symbols, widely used in China.
• Nashville Number System, a variant of modern chord symbols, that use Arabic numerals for scale degrees.

Chord quality

Chord qualities are related to the qualities of the component intervals that define the chord. The main chord qualities are:

• Major and minor
• Augmented, diminished, and half-diminished
• Dominant

Some of the symbols used for chord quality are similar to those used for interval quality:

• No symbol, or sometimes M or Maj for major
• m, or min for minor
• aug for augmented
• dim for diminished

In addition,

• Δ is used for major seventh,^[a] instead of the standard M, or maj
• − is sometimes used for minor, instead of the standard m or min
• a lowercase root note is sometimes used for minor, e.g. c instead of Cm
• ⁺ is used for augmented (A is not used)
• ^o is for diminished (d is not used)
• ^ø is used for half-diminished
• dom may occasionally be used for dominant

Chord qualities are sometimes omitted. When specified, they appear immediately after the root note or, if the root is omitted, at the beginning of the chord name or symbol. For instance, in the symbol Cm⁷ (C minor seventh chord) C is the root and m is the chord quality. When the terms minor, major, augmented, diminished, or the corresponding symbols do not appear immediately after the root note, or at the beginning of the name or symbol, they should be considered interval qualities, rather than chord qualities. For instance, in Cm^M7 (minor major seventh chord), m is the chord quality and M refers to the interval.

Major, minor, augmented, and diminished chords

Three-note chords are called triads. There are four basic triads (major, minor, augmented, diminished). They are all tertian—which means defined by the root, a third, and a fifth. Since most other chords are made by adding one or more notes to these triads, the name and symbol of a chord is often built by just adding an interval number to the name and symbol of a triad. For instance, a C augmented seventh chord is a C augmented triad with an extra note defined by a minor seventh interval:

C+ 7	=	C+	+	♭
augmented seventh chord		augmented triad		minor seventh

In this case, the quality of the additional interval is omitted. Less often, the full name or symbol of the additional interval (minor, in the example) is provided. For instance, a C augmented major seventh chord is a C augmented triad with an extra note defined by a major seventh interval:

C+Δ 7	=	C+	+
augmented major seventh chord		augmented triad		major seventh

In both cases, the quality of the chord is the same as the quality of the basic triad it contains. This is not true for all chord qualities: the chord qualities half-diminished and dominant refer not only to the quality of the basic triad but also the quality of the additional intervals.

Altered fifths

A more complex approach is sometimes used to name and denote augmented and diminished chords. An augmented triad can be viewed as a major triad in which the perfect fifth interval (spanning 7 semitones) has been substituted with an augmented fifth (8 semitones). A diminished triad can be viewed as a minor triad in which the perfect fifth has been substituted with a diminished fifth (6 semitones). In this case, the augmented triad can be named major triad sharp five, or major triad augmented fifth (M^♯5, M⁺⁵, maj^aug5). Similarly, the diminished triad can be named minor triad flat five, or minor triad diminished fifth (m^♭5, m^o5, min^dim5).

Again, the terminology and notation used for triads affects the terminology and notation used for larger chords, formed by four or more notes. For instance, the above-mentioned C augmented major seventh chord, is sometimes called C major seventh sharp five, or C major seventh augmented fifth. The corresponding symbol is CM⁷⁺⁵, CM^7♯5, or Cmaj^7aug5:

(In chord symbols, the symbol A, used for augmented intervals, is typically replaced by + or ♯)

In this case, the chord is viewed as a C major seventh chord (CM⁷) in which the third note is an augmented fifth from root (G♯), rather than a perfect fifth from root (G). All chord names and symbols including altered fifths, i.e., augmented (♯5, +5, aug5) or diminished (♭5, ^o5, dim5) fifths can be interpreted in a similar way.

Common types of chords

Triads

The four triads, all built on C: major (C), minor (C–), augmented (C+), and diminished (C^o)

As shown in the table below, there are four triads, each made up of the root, the third (either major or minor ) above the root, and the fifth (perfect , augmented , or diminished ) above the root. The table below shows the names, symbols, and definition for the four triads, using C as the root.

Seventh chords

Five of the most common seventh chord, all built on C: major (C^Δ7), dominant (C⁷), minor (C–⁷), half-diminished (C^ø7), and diminished (C^o7)

A seventh chord is a triad with a seventh. The seventh is either a major seventh above the root, a minor seventh above the root (flatted 7th), or a diminished seventh above the root (double flatted 7th). Note that the diminished seventh note is enharmonically equivalent to the major sixth above the root of the chord.

The table below shows the names, symbols, and definitions for the various kinds of seventh chords, using C as the root.

Name	semi- tones	Symbol(s) (on C)			Definitions
		Short	Long	Altered fifth	Component intervals			Notes (on C)
					Third	Fifth	Seventh
Dominant seventh	047X	C7			M3	P5	m7	C–E–G–B♭
Major seventh	047N	CM7 CMa7 Cmaj7 CΔ7 CΔ[a]	Cmaj7		M3	P5	M7	C–E–G–B
Minor-major seventh	037N	CmM7 Cm♯7 C−M7 C−Δ7 C−Δ	Cminmaj7		m3	P5	M7	C–E♭–G–B
Minor seventh	037X	Cm7 C–7	Cmin7		m3	P5	m7	C–E♭–G–B♭
Augmented-major seventh (major seventh sharp five)	048N	C+M7 C+Δ	Caugmaj7	CM7♯5 CM7+5 CΔ♯5 CΔ+5	M3	A5	M7	C–E–G♯–B
Augmented seventh (dominant seventh sharp five)	048X	C+7	Caug7	C7♯5 C7+5	M3	A5	m7	C–E–G♯–B♭
Half-diminished seventh (minor seventh flat five)	036X	Cø Cø7	Cmin7dim5	Cm7♭5 Cm7o5 C−7♭5 C−7o5	m3	d5	m7	C–E♭–G♭–B♭
Diminished seventh	0369	Co7	Cdim7		m3	d5	d7	C–E♭–G♭–B
Dominant seventh flat five (dominant seventh flat five)	046X	C7♭5	C7dim5		M3	d5	m7	C–E–G♭–B♭

Extended chords

Extended chords add further notes to seventh chords. Of the seven notes in the major scale, a seventh chord uses only four (the root, third, fifth, and seventh). The other three notes (the second, fourth, and sixth) can be added in any combination; however, just as with the triads and seventh chords, notes are most commonly stacked – a seventh implies that there is a fifth and a third and a root. In practice, especially in jazz, certain notes can be omitted without changing the quality of the chord. In a jazz ensemble with a bass player, the chord-playing instrumentalists (guitar, organ, piano, etc.) can omit the root, as the bass player typically plays it.

Ninth, eleventh, and thirteenth chords are known as extended tertian chords. These notes are enharmonically equivalent to the second, fourth, and sixth, respectively, except they are more than an octave above the root. However, this does not mean that they must be played in the higher octave. Although changing the octave of certain notes in a chord (within reason) does change the way the chord sounds, it does not change the essential characteristics or tendency of it. Accordingly, using the ninth, eleventh, or thirteenth in chord notation implies that the chord is an extended tertian chord rather than an added chord.

The convention is that using an odd number (7, 9, 11, or 13) implies that all the other lower odd numbers are also included. Thus C¹³ implies that 3, 5, 7, 9, and 11 are also there. Using an even number such as 6, implies that only that one extra note has been added to the base triad e.g. 1, 3, 5, 6. Remember that this is theory, so in practice they do not have to be played in that ascending order e.g. 5, 1, 6, 3. Also, to resolve the clash between the third and eleventh, one of them may be deleted or separated by an octave. Another way to resolve might be to convert the chord to minor by lowering the third, which generates a clash between the ♭3 and the 9.

Ninth chords

Four of the most common ninth chords, all built on C: major (C^Δ9), dominant (C⁹), dominant minor ninth (C^7♭9), and minor (C–⁹)

Ninth chords are built by adding a ninth to a seventh chord, either a major ninth or a minor ninth . A ninth chord includes the seventh; without the seventh, the chord is not an extended chord but an added tone chord—in this case, an add 9. Ninths can be added to any chord but are most commonly seen with major, minor, and dominant seventh chords. The most commonly omitted note for a voicing is the perfect fifth.

The table below shows the names, symbols, and definitions for the various kinds of ninth chords, using C as the root.

Name	semi- tones	Symbol(s) (on C)		Quality of added 9th	Notes (on C)
		Short	Long
Major ninth	047N2	CM9 CΔ9	Cmaj9	M9	C–E–G–B–D
Dominant ninth	047X2	C9		M9	C–E–G–B♭–D
Dominant minor ninth	047X1	C7♭9		m9	C–E–G–B♭–D♭
Minor-major ninth	037N2	CmM9 C−M9	Cminmaj9	M9	C–E♭–G–B–D
Minor ninth	037X2	Cm9 C−9	Cmin9	M9	C–E♭–G–B♭–D
Augmented major ninth	048N2	C+M9	Caugmaj9	M9	C–E–G♯–B–D
Augmented dominant ninth	048X2	C+9 C9♯5	Caug9	M9	C–E–G♯–B♭–D
Half-diminished ninth	036X2	Cø9		M9	C–E♭–G♭–B♭–D
Half-diminished minor ninth	036X1	Cø♭9		m9	C–E♭–G♭–B♭–D♭
Diminished ninth	03692	Co9	Cdim9	M9	C–E♭–G♭–B–D
Diminished minor ninth	03691	Co♭9	Cdim♭9	m9	C–E♭–G♭–B–D♭

Eleventh chords

Three eleventh chords, all built on C: an eleventh chord (C¹¹), a major eleventh chord (CM¹¹), and a minor eleventh chord (C–¹¹)

Eleventh chords are theoretically ninth chords with the 11th (or fourth) added. However, it is common to leave certain notes out. The major third is often omitted because of a strong dissonance with the 11th, making the third an avoid note.^{[citation needed]} Omission of the third reduces an 11th chord to the corresponding 9sus4 chord (suspended 9th chord^[7]). Similarly, omission of the third as well as fifth in C¹¹ results in a major chord with alternate base B♭/C, which is characteristic in soul and gospel music. For instance:

C¹¹ without 3rd = C–(E)–G–B♭–D–F ➡ C–F–G–B♭–D = C^9sus4

C¹¹ without 3rd and 5th = C–(E)–(G)–B♭–D–F ➡ C–F–B♭–D = B♭/C

If the ninth is omitted, the chord is no longer an extended chord but an added tone chord. Without the third, this added tone chord becomes a 7sus4 (suspended 7th chord). For instance:

C¹¹ without 9th = C^7add11 = C–E–G–B♭–(D)–F

C^7add11 without 3rd = C–(E)–G–B♭–(D)–F ➡ C–F–G–B♭ = C^7sus4

The table below shows the names, symbols, and definitions for the various kinds of eleventh chords, using C as the root.

Name	semi- tones	Symbol(s) (on C)		Quality of added 11th	Notes (on C)
		Short	Long
Eleventh	047X25	C11		P11	C–E–G–B♭–D–F
Major eleventh	047N25	CM11	Cmaj11	P11	C–E–G–B–D–F
Minor major eleventh	037N25	CmM11 C−M11	Cminmaj11	P11	C–E♭–G–B–D–F
Minor eleventh	037X25	Cm11 C−11	Cmin11	P11	C–E♭–G–B♭–D–F
Augmented major eleventh	048N25	C+M11	Caugmaj11	P11	C–E–G♯–B–D–F
Augmented eleventh	048X25	C+11 C11♯5	Caug11	P11	C–E–G♯–B♭–D–F
Half-diminished eleventh	036X25	Cø11		P11	C–E♭–G♭–B♭–D–F
Diminished eleventh	036925	Co11	Cdim11	P11	C–E♭–G♭–B–D–F

Alterations from the natural diatonic chords can be specified as C^9♯11 ... etc. Omission of the fifth in a raised 11th chord reduces its sound to a ♭5 chord.^[8]

C^9♯11 = C–E–(G)–B♭–D–F♯ ➡ C–E–G♭–B♭–D = C^9♭5.

Thirteenth chords

Three thirteenth chords, all built on C: an thirteenth chord (C¹³), a major thirteenth chord (CM¹³), and a minor thirteenth chord (C–¹³)

Thirteenth chords are theoretically eleventh chords with the 13th (or sixth) added. In other words, theoretically they are formed by all the seven notes of a diatonic scale at once. Again, it is common to leave certain notes out. After the fifth, the most commonly omitted note is the 11th (fourth). The ninth (second) may also be omitted. A very common voicing on guitar for a 13th chord is just the root, third, seventh and 13th (or sixth). For example: C–E–(G)–B♭–(D)–(F)–A, or C–E–(G)–A–B♭–(D)–(F). On the piano, this is usually voiced C–B♭–E–A.

The table below shows the names, symbols, and definitions for some thirteenth chords, using C as the root.