Thirteenth in the context of "Eleventh chord"

An added tone chord, or added note chord, is a non-tertian chord composed of a triad and an extra "added" note. Any tone that is not a seventh factor is commonly categorized as an added tone. It can be outside the tertian sequence of ascending thirds from the root, such as the added sixth or fourth, or it can be in a chord that doesn't consist of a continuous stack of thirds, such as the added thirteenth (six thirds from the root, but the chord doesn't have the previous tertian notes – the seventh, ninth or eleventh). The concept of added tones is convenient in that all notes may be related to familiar chords.

Inversions of added tone chords where the added tone is the bass note are usually simply notated as slash chords instead of added-tone chords. For example, instead of C/D, just C/D is used.

In music, a factor or chord factor is a member or component of a chord. These are named root, third, fifth, sixth, seventh, ninth (compound 2nd), eleventh (compound 4th), thirteenth (compound 6th), and so on, for their generic interval above the root.In harmony, the consonance and dissonance of a chord factor and a nonchord tone are distinguished, respectively.

Chord factors are taken into consideration in voicing and voice leading. A chord contains exactly as many factors as it contains unique pitch names (octaves don't matter), while a voicing can have any number of voices that draw from and represent some or all the factors of a chord in various octaves. Thus, a chord with three unique pitch names always has three factors, even if some of those pitches are doubled or omitted in a particular voicing. For example, the figure to the right shows a four-note voicing of a C Major triad, which has three chord factors. The "root" chord factor (pitch name "C"), is represented twice in the voicing by voices 1 and 4 in different octaves. The chord factor called the "fifth" (pitch name "G") is represented in voice 2 (shown in red).

In music theory, tertian (Latin: tertianus, "of or concerning thirds") describes any piece, chord, counterpoint etc. constructed from the intervals of (major and minor) thirds. An interval such as that between the notes A and C encompasses 3 semitone intervals (A-B♭-B♮-C) and is termed a minor third while one such as that between C and E encompasses 4 semitones (C-D♭-D♮-E♭-E♮) and is called a major third. Tertian harmony (also called tertiary harmony) principally uses chords based on thirds; the term is typically used to contrast with quartal and quintal harmony which uses chords based on fourths or fifths.

A common triad chord can be regarded as consisting of a "stack" of two consecutive thirds. This allows for four permutations, each producing a chord with distinct quality:

Jazz chords are chords, chord voicings and chord symbols that jazz musicians commonly use in composition, improvisation, and harmony. In jazz chords and theory, most triads that appear in lead sheets or fake books can have sevenths added to them, using the performer's discretion and ear. For example, if a tune is in the key of C, if there is a G chord, the chord-playing performer usually voices this chord as G. While the notes of a G chord are G–B–D–F, jazz often omits the fifth of the chord—and even the root if playing in a group. However, not all jazz pianists leave out the root when they play voicings: Bud Powell, one of the best-known of the bebop pianists, and Horace Silver, whose quintet included many of jazz's biggest names from the 1950s to the 1970s, included the root note in their voicings.

Improvising chord-playing musicians who omit the root and fifth are given the option to play other notes. For example, if a seventh chord, such as G, appears in a lead sheet or fake book, many chord-playing performers add the ninth, thirteenth or other notes to the chord, even though the lead sheet does not specify these additional notes. Jazz players can add these additional, upper notes because they can create an important part of the jazz sound. Lead sheets and fake books often do not detail how to voice the chord because a lead sheet or fake book is only intended to provide basic guide to the harmony. An experienced comping performer playing electric guitar or piano may add or remove notes as chosen according to the style and desired sound of that musician, but must do so in a way that still emphasizes the correct musical context for other musicians and listeners.