Root (chord)
In the music theory of harmony, the root is a specific note that names and typifies a given chord. Chords are often spoken about in terms of their root, their quality, and their extensions. When a chord is named without reference to quality, it is assumed to be major—for example, a "C chord" refers to a C major triad, containing the notes C, E, and G. In a given harmonic context, the root of a chord need not be in the bass position, as chords may be inverted while retaining the same name, and therefore the same root.
In tertian harmonic theory, wherein 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)).
The idea of chord root links to that of a chord's root position, as opposed to its inversion. When speaking of a "C triad" (C E G), the name of the chord (C) also is its root. When the root is the lowest note in the chord, it is in root position. When the root is a higher note (E G C or G C E), the chord is inverted but retains the same root. Classified chords in tonal music usually can be described as stacks of thirds (even although some notes may be missing, particularly in chords containing more that three or four notes, i.e. 7ths, 9ths, and above). The safest way to recognize a chord's root, in these cases, is to rearrange the possibly inverted chord as a stack of thirds: the root then is the lowest note.
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(add♭7) 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:
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]
History[edit]
The first mentions of the relation of inversion between triads appears in Otto Sigfried Harnish's Artis musicae (1608), which describes perfect triads in which the lower note of the fifth is expressed in its own position, and imperfect ones, in which the base (i.e., root) of the chord appears only higher. Johannes Lippius, in his Disputatio musica tertia (1610) and Synopsis musicae novae (1612), is the first to use the term "triad" (trias harmonica); he also uses the term "root" (radix), but in a slightly different meaning.[4] Thomas Campion, A New Way of Making Fowre Parts in Conterpoint, London, c. 1618, notes that when chords are in first inversions (sixths), the bass is not "a true base", which is implicitly a third lower. Campion's "true base" is the root of the chord.[5]
Full recognition of the relationship between the triad and its inversions is generally credited to Jean-Philippe Rameau and his Traité d’harmonie (1722). Rameau was not the first to discover triadic inversion,[6] but his main achievement is to have recognized the importance of the succession of roots (or of chords identified by their roots) for the construction of tonality (see below, Root progressions).
Root vs fundamental[edit]
The concept of chord root is not the same as that of the fundamental of a complex vibration. When a harmonic sound, i. e. a sound with harmonic partials, lacks a component at the fundamental frequency itself, the pitch of this fundamental frequency may nevertheless be heard: this is the missing fundamental. The effect is increased by the fact that the missing fundamental also is the difference tone of the harmonic partials.
Chord notes, however, do not necessarily form a harmonic series. In addition, each of these notes has its own fundamental. The only case where the chord notes may seem to form a harmonic series is that of the major triad. However, the major triad may be formed of the intervals of a third and a fifth, while the corresponding harmonic partials are distant by the intervals of a 12th and a 17th. For instance, C3 E3 G3 is a major triad, but the corresponding harmonic partials would be C3, G4 and E5. The root of the triad is an abstract C, while the (missing) fundamental of C3 E3 G3 is C1 – which would usually not be heard.