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Musical note characterizing a 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)).

[[Image:Diminished seventh modulation. png|thumb|Diminished seventh chord's use in modulation: each assumed root, in parentheses, may be used as a dominant, tonic, or supertonic. The diminished seventh chord affords, "singular facilities for modulation", as it may be notated four ways, to represent four different assumed roots.

In jazz and jazz fusion, roots are often omitted from chords when chord playing musicians (e. g., electric guitar, piano, Hammond organ) are improvising chords in an ensemble that includes a bass player (either double bass, electric bass, or other bass instruments), because the bass player plays the root. For example, if a band is playing a tune in the key of C major, if there is a dominant seventh chord played on the dominant chord (i. e., G7), the chord playing musicians typically do not play the G note in their voicing of the chord, as they expect the bass player to play the root. The chord playing musicians usually play a voicing that includes the third, seventh, and additional extensions (often the ninth and thirteenth, even if they are not specified in the chord chart). Thus a typical voicing by a chord playing musician for a G7 chord would be the notes B and F (the third and flat seventh of the chord), along with the notes A and E (the ninth and thirteenth of the G7 chord). One possible voicing for this G7 chord would be the notes B, E, F, A (the third, thirteenth, seventh and ninth of the G7 chord). (Note: the thirteenth interval is the same "pitch class" as the sixth, except that it is one octave higher; the ninth is the same "pitch class" as the second interval, except that it is one octave higher.)

The fundamental bass (basse fondamentale) is a concept proposed by Jean Philippe Rameau, derived from the thoroughbass, to notate what would today be called the progression of chord roots rather than the actual lowest note found in the music, the bassline. From this Rameau formed rules for the progression of chords based on the intervals between their roots. Subsequently, music theory has typically treated chordal roots as the defining feature of harmony. Roman numeral analysis may be said to derive from the theory of the fundamental bass, although it does not particularly theorize the succession of roots. The theory of the fundamental bass properly speaking has been revived in the 20th century by Arnold Schoenberg, Yizhak Sadaï and Nicolas Meeùs.