In music

Music

Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...

 or music theory

Music theory

Music theory is the study of how music works. It examines the language and notation of music. It seeks to identify patterns and structures in composers' techniques across or within genres, styles, or historical periods...

, a thirteenth is the interval

Interval (music)

In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...

 between the sixth and first scale degrees when the sixth is transposed up an octave, creating a compound sixth

Sixth chord

A sixth chord may be any of several kinds of chord depending on the use of the term in classical music and popular music. The original meaning of the term is a chord in first inversion, in other words with its third in the bass and its root a sixth above it...

, or thirteenth. The thirteenth (an octave

Octave

In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...

 plus a sixth) is most commonly major or minor .
A thirteenth chord is the stacking of six thirds

Third (music)

In music and music theory third may refer to:*major third*minor third*augmented third/perfect fourth*diminished third/major second*Third , chord member a third above the root*Mediant, third degree of the diatonic scale...

, the last being above the 11th of an eleventh chord

Eleventh chord

In music, an eleventh chord is a chord which contains the tertian extension of the eleventh. Typically found in jazz, an eleventh chord will also usually include the seventh and ninth along with elements of the basic triad structure. Variants include the dominant eleventh, minor eleventh, and the...

. Thus a thirteenth chord is a tertian

Tertian

In music theory, tertian describes any piece, chord, counterpoint etc. constructed from the interval of a third...

 (built from thirds) chord containing the interval of a thirteenth, and is an extended chord

Extended chord

In music, extended chords are tertian chords or triads with notes extended, or added, beyond the seventh. Ninth, eleventh, and thirteenth chords are extended chords...

 if it includes the ninth

Ninth

In music, a ninth is a compound interval consisting of an octave plus a second.Like the second, the interval of a ninth is classified as a dissonance in common practice tonality. Since a ninth is a larger than a second, its sonority level is considered less dense.-Major ninth:A major ninth is a...

 and/or the eleventh

Eleventh

In music or music theory an eleventh is the note eleven scale degrees from the root of a chord and also the interval between the root and the eleventh....

. "The jazzy thirteenth is a very versatile chord and is used in many genres." Since 13th chords tend to become unclear or confused with other chords when inverted

Inversion (music)

In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices...

 they are generally found in root position

Root (chord)

In music theory, the root of a chord is the note or pitch upon which a triadic chord is built. For example, the root of the major triad C-E-G is C....

. For example, depending on voicing

Voicing (music)

In music composition and arranging, a voicing is the instrumentation and vertical spacing and ordering of the pitches in a chord...

, a major triad with an added major sixth is usually called a sixth chord

Sixth chord

A sixth chord may be any of several kinds of chord depending on the use of the term in classical music and popular music. The original meaning of the term is a chord in first inversion, in other words with its third in the bass and its root a sixth above it...

 , because the sixth serves as a substitution for the major seventh, thus considered a chord tone in such context. However, Walter Piston, writing in 1952, considered that, "a true thirteenth chord, arrived at by superposition of thirds, is a rare phenomenon even in 20th-century music." This may be due to four part writing, instrument limitations, and voice leading and stylistic considerations. For example, "to make the chord more playable [on guitar], thirteenth chords often omit the fifth and the ninth."

Dominant thirteenth

Most commonly 13th chords serve a dominant

Dominant (music)

In music, the dominant is the fifth scale degree of the diatonic scale, called "dominant" because it is next in importance to the tonic,and a dominant chord is any chord built upon that pitch, using the notes of the same diatonic scale...

 function

Diatonic function

In tonal music theory, a diatonic function is the specific, recognized role of each of the 7 notes and their chords in relation to the diatonic key...

 (V13), whether they have the exact intervals of a dominant thirteenth or not. Typically, a dominant chord anticipating a major resolution will feature a natural 13, while a dominant chord anticipating a minor resolution will feature a flat 13. Since thirteenth chords contain more than four notes, in four-voice writing the root, third, seventh, and thirteenth are most often included, excluding the fifth, ninth, and eleventh . The third indicates the quality of the chord as major or minor, the seventh is important for the quality as a dominant chord, while the thirteenth is necessary in a thirteenth chord.

In modern pop/jazz harmony, after the dominant thirteenth, a thirteenth chord (usually notated as X13, e.g. C13) contains an implied flatted seventh interval. Thus, a C13 consists of C E G B♭ and A. The underlying harmony during a thirteenth chord is usually Mixolydian

Mixolydian mode

Mixolydian mode may refer to one of three things: the name applied to one of the ancient Greek harmoniai or tonoi, based on a particular octave species or scale; one of the medieval church modes; a modern musical mode or diatonic scale, related to the medieval mode.-Greek Mixolydian:The idea of a...

 or Lydian dominant (see chord-scale system

Chord-scale system

The chord-scale system is a method of matching, from a list of possible chords, a list of possible scales. The system has been widely used since the 1970s and is "generally accepted in the jazz world today"...

). A thirteenth chord does not imply the quality of the ninth or eleventh scale degrees. In general, what gives a thirteenth chord its characteristic sound is the dissonance between the flat seventh and the thirteenth, a major seventh

Major seventh

In classical music from Western culture, a seventh is a musical interval encompassing seven staff positions , and the major seventh is one of two commonly occurring sevenths. It is qualified as major because it is the larger of the two...

.

In the common practice period

Common practice period

The common practice period, in the history of Western art music , spanning the Baroque, Classical, and Romantic periods, lasted from c. 1600 to c. 1900.-General characteristics:...

 the "most common" pitches present in V¹³ chord are the root, 3rd, 7th, and 13th; with the 5th, 9th, and 11th "typically omitted". The 13th is most often in the soprano, or highest voice, and usually resolves down by a 3rd to the tonic I or i. If the V¹³ is followed by a I⁹ the 13th may resolve to the 9th.

Other thirteenth chords

These voice leading guidelines may not be followed after the common practice period in techniques such as parallel harmony and in the following example:

13th chords may less often be built on degrees other than the dominant, such as the tonic

Tonic (music)

In music, the tonic is the first scale degree of the diatonic scale and the tonal center or final resolution tone. The triad formed on the tonic note, the tonic chord, is thus the most significant chord...

 or subdominant.

While the dominant thirteenth is the most common thirteenth chord, the major thirteenth is also fairly common. A major thirteenth chord (containing a major seventh) will nearly always feature a chromatically raised eleventh (C E G B D F A) (see lydian mode

Lydian mode

The Lydian musical scale is a rising pattern of pitches comprising three whole tones, a semitone, two more whole tones, and a final semitone. This sequence of pitches roughly describes the fifth of the eight Gregorian modes, known as Mode V or the authentic mode on F, theoretically using B but in...

), except for cases when the eleventh is omitted altogether. "It is customary to omit the eleventh on dominant or major thirteenth chords because the eleventh conflicts with the third," in these chords by a semitone.

Inversions

Generally found in root position, the inversion

Inversion (music)

In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices...

 of a complete thirteenth chord including all seven notes, itself, "a rare phenomenon", is a theoretic impossible since a new thirteenth chord with a different root along the is produced, for example C major 13 (C-E-G-B-D-F-A) becomes e13 (E-G-B-D-F-A-C) then G13 (G-B-D-F-A-C-E), and so on, when inverted.

Gallery

Given the number of notes that may be included there are a great variety of thirteenth chords. The following chords are notated below lead sheet

Lead sheet

A lead sheet is a form of music notation that specifies the essential elements of a popular song: the melody, lyrics and harmony. The melody is written in modern Western music notation, the lyric is written as text below the staff and the harmony is specified with chord symbols above the...

symbols: