Factor (chord)

This article is about music. For Geodesics, see Geodesic dome#Chord factors.

Fifth (G), in red, of a C major chord (

Play ).

Seventh (F) of a third inversion dominant seventh chord in C (G7) (

Play ).

Dominant thirteenth extended chord: C E G B♭ D F A

play . The upper structure or extensions, i.e. notes beyond the seventh, in red (ninth, eleventh, thirteenth).

In music, a factor or chord factor is a member or component of a chord. These are named root, third, fifth, sixth, seventh, ninth, eleventh, thirteenth, and so on, for their generic interval above the root.^[1] In harmony, the consonance and dissonance of a chord factor and a nonchord tone are distinguished, respectively.^[2]

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).

The chord factor that is in the bass determines the inversion of the chord. For example, if the third is in the bass it is a first inversion chord ( ${}_{3}^{6}$ ) while if the seventh is in the bass the chord is in third inversion ( ${}_{2}^{4}$ ). The illustration shows one possible four-note voicing of a G7 third-inversion chord (written G7/F in lead-sheet chord-symbol notation), with every chord factor being represented once by a voice in the voicing.

In Tertian harmony, chords are made more complex, or "extended" by introducing additional chord factors stacked in thirds. The illustration shows the theoretical construction of a C13 chord having seven chord factors, with the "extended" chord factors shown in red. In real applications, it is common practice to omit the eleventh from voicings of a dominant 13 chord, because though being necessary to theoretically derive the thirteenth by stacking on it, the unaltered perfect eleventh clashes with the major third.

Sources

↑ O'Toole, Patricia (2003). Shaping Sound Musicians, p.368. ISBN 1-57999-211-0.
↑ Ostransky, Leroy (1977). Understanding Jazz, p.91. ISBN 0-13-936542-7.

Chord factors

Root Third Fifth Seventh Ninth Eleventh Thirteenth Fifteenth (Bass note)

Chords

By form

Triad	Major Minor Augmented Diminished Suspended

Seventh	Major Minor Dominant Dominant seventh flat five Diminished Half-diminished Diminished major Minor-major Augmented major Augmented minor Altered seventh Nondominant Harmonic seventh

Extended	Ninth Eleventh Thirteenth Upper structure Dominant 7♯9 Polychord Tone cluster

Added / omitted	Sixth Augmented sixth Lydian Seven six

Specific	Alpha Bridge Complexe sonore Dream Elektra Farben Grandmother Magic µ Mystic Northern lights Petrushka Psalms So What Tristan Viennese trichord

General	Mixed interval Secundal Tertian Quartal Synthetic chord

By function

Diatonic	Tonic Dominant Subdominant Supertonic Mediant Submediant Leading / Subtonic

Altered	Approach Borrowed Chromatic mediant Neapolitan Passing

Secondary	Secondary dominant Secondary leading-tone Secondary supertonic

Other	Common Contrast Primary triad Subsidiary

Techniques

Other

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Factor (chord)

See also

Sources