Root (chord)

Root, in red, of a C major chord (About this soundPlay ). Note that the root is doubled at the octave.
Root notes (blue) and bass notes (red, both=purple) from an 18th century Chorale About this soundPlay 

In music theory, the concept of root is the idea that a chord can be represented and named by one of its notes. It is linked to harmonic thinking— the idea that vertical aggregates of notes can form a single unit, a chord. It is in this sense that one speaks of a "C chord" or a "chord on C"—a chord built from "C" and of which the note (or pitch) "C" is the root. When a chord is referred to in Classical music or popular music without a reference to what type of chord it is (either major or minor, in most cases), it is assumed a major triad, which for C contains the notes C, E and G. The root need not be the bass note, the lowest note of the chord: the concept of root is linked to that of the inversion of chords, which is derived from the notion of invertible counterpoint. In this concept, chords can be inverted while still retaining their root.

In tertian harmonic theory, that is in a theory where chords can be considered stacks of third intervals (e.g. in common practice tonality), the root of a chord is the note on which the subsequent thirds are stacked. For instance, the root of a triad such as C Major is C, independently of the vertical order in which the three notes (C, E and G) are presented. A triad can be in three possible positions, a "root position" with the root in the bass (i.e., with the root as the lowest note, thus C, E, G or C, G, E, from lowest to highest notes), a first inversion, e.g. E, C, G or E, G, C (i.e., with the note which is a third interval above the root, E, as the lowest note) and a second inversion, e.g. G, C, E or G, E, C, in which the note that is a fifth interval above the root (G ) is the lowest note.

Regardless of whether a chord is in root position or in an inversion, the root remains the same in all three cases. Four-note seventh chords have four possible positions. That is, the chord can be played with the root as the bass note, the note a third above the root as the bass note (first inversion), the note a fifth above the root as the bass note (second inversion), or the note a seventh above the root as the bass note (third inversion). Five-note ninth chords know five positions, etc., but the root position always is that of the stack of thirds, and the root is the lowest note of this stack (see also Factor (chord)).

Root position, first inversion, and second inversion C major chords About this soundPlay root position C major chord , About this soundPlay first inversion C major chord , or About this soundPlay second inversion C major chord . Chord roots (all the same) in red.
Root position, first inversion, and second inversion chords over C bass About this soundPlay root position C major chord , About this soundPlay first inversion A minor chord , or About this soundPlay second inversion F major chord . Chord roots in red.

Identifying a chord's root

Determining chord root from inversion About this soundPlay . "Revoicing inverted triads to root position".[1]

Although the safest way to recognize a chord’s root is, after having reduced the chord to close spacing, to rearrange it as a stack of thirds, there are shortcuts to this: in inverted triads, the root is directly above the interval of a fourth, in inverted sevenths, it is directly above the interval of a second.[1] With chord types, such as chords with added sixths or chords over pedal points, more than one possible chordal analysis may be possible. For example, in a tonal piece of music, the notes C, E, G, A, sounded as a chord, could be analyzed as a C major sixth chord in root position (a major triad – C, E, G – with an added sixth – A – above the root) or as a first inversion A minor seventh chord (the A minor seventh chord contains the notes A, C, E and G, but in this example, the C note, the third of the A minor chord, is in the bass). Deciding which note is the root of this chord could be determined by considering context. If the chord spelled C, E, G, A occurs immediately before a D7 chord (spelled D, F, A, C), most theorists and musicians would consider the first chord a minor seventh chord in first inversion, because the progression ii7–V7 is a standard chord movement.

Various devices have been imagined to notate inverted chords and their roots:

The concept of root has been extended for the description of intervals of two notes: the interval can either be analyzed as formed from stacked thirds (with the inner notes missing): third, fifth, seventh, etc., (i.e., intervals corresponding to odd numerals), and its low note considered as the root; or as an inversion of the same: second (inversion of a seventh), fourth (inversion of a fifth), sixth (inversion of a third), etc., (intervals corresponding to even numerals) in which cases the upper note is the root. See Interval.

Some theories of common-practice tonal music admit the sixth as a possible interval above the root and consider in some cases that 6
5
chords nevertheless are in root position – this is the case particularly in Riemannian theory. Chords that cannot be reduced to stacked thirds (e.g. chords of stacked fourths) may not be amenable to the concept of root, although in practice, in a lead sheet, the composer may specify that a quartal chord has a certain root (e.g., a fake book chart that indicates that a song uses an Asus4(add7) chord, which would use the notes A, D, G. Even though this is a quartal chord, the composer has indicated that it has a root of A.)

A major scale contains seven unique pitch classes, each of which might serve as the root of a chord:

Root position triads from C major scale[2] About this soundPlay .

Chords in atonal music are often of indeterminate root, as are equal-interval chords and mixed-interval chords; such chords are often best characterized by their interval content.[3]

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