Chord notation

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:

the root note
the chord quality
whether the chord is a triad, seventh chord, or an extended chord
any altered notes
any added tones
the bass note if it is not the root

Triad	Root	Quality	Example	Audio
Major triad	Uppercase		C
Minor triad	Lowercase		c
Augmented triad	Uppercase	⁺	C⁺
Diminished triad	Lowercase	^o	c^o
Dominant seventh	Uppercase	⁷	C⁷

For instance, the name C augmented seventh, and the corresponding symbol C, or C, are both composed of parts 1, 2, and 3. These indicate a chord formed by the notes C–E–G–B. The three parts of the symbol refer to the root C, the augmented interval from C to G, and the 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", 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
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. 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 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 uses the chord symbols to help improvise a bass line that outlines the chords, often by emphasizing the root and other key scale tones.
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 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". In 2003 Benjamin, Horvit, and Nelson describe the use of letters to indicate chord root as, "popular music lead sheet symbols." 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."
Other notation systems for chords include:

Traditional staff notation.
Roman numerals, commonly used in harmonic analysis.
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 or for major
, or for minor
or for augmented
for diminished

In addition,

is used for major seventh, instead of the standard, or
− is sometimes used for minor, instead of the standard or
a lowercase root note is sometimes used for minor, e.g. instead of
is used for augmented
is for diminished
is used for half-diminished
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 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, 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. 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:
In this case, the quality of the additional interval is omitted. Less often, the full name or symbol of the additional interval 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:
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 has been substituted with an augmented fifth. A diminished triad can be viewed as a minor triad in which the perfect fifth has been substituted with a diminished fifth. In this case, the augmented triad can be named major triad sharp five, or major triad augmented fifth. Similarly, the diminished triad can be named minor triad flat five, or minor triad diminished fifth.
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, CM⁷⁵, or Cmaj^7aug5:
In this case, the chord is viewed as a C major seventh chord in which the third note is an augmented fifth from root, rather than a perfect fifth from root. All chord names and symbols including altered fifths, i.e., augmented or diminished fifths can be interpreted in a similar way.

Common types of chords

Triads

As shown in the table below, there are four triads, each made up of the root, the third above the root, and the fifth above the root. The table below shows the names, symbols, and definition for the four triads, using C as the root.

Seventh chords

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, or a diminished seventh above the root. 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.

Extended chords

add further notes to seventh chords. Of the seven notes in the major scale, a seventh chord uses only four. The other three notes 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 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 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 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.