Root (chord)

Root notes (blue) and bass notes (red, both=purple) from an 18th-century Chorale Play

In music theory, the root of a chord is the note that names and typifies the chord. Tertian chords are named based on (1) their root, (2) their quality (assumed to be major if no quality is named), and (3) their extensions, if any (assumed to be a triad if no extensions are named). For example, a C chord refers to a C major triad, a major triad built on the note C, which is its root.

The root of a tertian chord is the note on which the subsequent thirds are stacked. For instance, the root of the E minor triad is E, independent of the vertical placement of the three notes that compose it (i.e., E, G, and B).

The root of a chord need not be its bass note (i.e., its lowest note). If the root is the bass note, then the chord is said to be in root position ; otherwise, it is an inverted chord . A triad can be in three possible positions: (1) root position, with its root in the bass; (2) first inversion, with its third in the bass; or (3) second inversion, with its fifth in the bass. In the music below, the root of each chord is shown in red.

Seventh chords and chords with higher extensions can similarly be inverted.

Identifying roots

Determining chord root from inversion Play . "Revoicing inverted triads to root position".

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:

• Chord names and symbols (e.g., C major, A minor, G⁷ etc.)
• Roman numeral analysis (e.g., I to indicate the tonic chord and V to indicate the dominant chord)
• Slash chords (e.g., G/B bass, which instructs the chord-playing performer to play a G major triad with a "B" in bass voice/lowest note)

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 A^{sus4(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:

Root position triads from C major scale Play .

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

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 Treatise on Harmony (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).

See also

• Figured bass

References

1. Wyatt and Schroeder (2002). Hal Leonard Pocket Music Theory, p.80. ISBN   0-634-04771-X.
2. Palmer, Manus, and Lethco (1994). The Complete Book of Scales, Chords, Arpeggios and Cadences, p.6. ISBN   0-7390-0368-2. "The root is the note from which the triad gets its name. The root of a C triad is C."
3. Reisberg, Horace (1975). "The Vertical Dimension in Twentieth-Century Music", Aspects of Twentieth-Century Music, p.362-72. Wittlich, Gary (ed.). Englewood Cliffs, New Jersey: Prentice-Hall. ISBN   0-13-049346-5.
4. Joel Lester, "Root-Position and Inverted Triads in Theory around 1600", Journal of the American Musicological Society 27/1 (Spring 1974), pp. 113-116.
5. Joel Lester, op. cit., p. 112.
6. B. Rivera, "The Seventeenth-Century Theory of Triadic Generation and Invertibility and its Application in Contemporaneous Rules of Composition", Music Theory Spectrum, p. 67.