Root (chord)
In music theory
Music theory
Music theory is the study of how music works. It examines the language and notation of music. It seeks to identify patterns and structures in composers' techniques across or within genres, styles, or historical periods...

, the root of a chord
Chord (music)
A chord in music is any harmonic set of two–three or more notes that is heard as if sounding simultaneously. These need not actually be played together: arpeggios and broken chords may for many practical and theoretical purposes be understood as chords...

 (in French, basse fondamentale) is the note or pitch
Pitch (music)
Pitch is an auditory perceptual property that allows the ordering of sounds on a frequency-related scale.Pitches are compared as "higher" and "lower" in the sense associated with musical melodies,...

 upon which a triadic
Triad (music)
In music and music theory, a triad is a three-note chord that can be stacked in thirds. Its members, when actually stacked in thirds, from lowest pitched tone to highest, are called:* the Root...

 chord is built. For example, the root of the major triad C-E-G is C.

When a chord's bass note
Bass note
In music theory, the bass note of a chord or sonority is the lowest note played or notated. If there are multiple voices it is the note played or notated in the lowest voice. While the bass note is often the root or fundamental of the chord, it does not have to be, and sometimes one of the other...

 is its root, the chord is said to be in root position or in normal form. When the root is not the lowest pitch played in a chord, it is inverted
Inversion (music)
In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices...


"When an inverted chord is written on the staff in musical notation, the root of the chord may be identified by rearranging the notes of the chord until they are stacked in third intervals (as close together as possible). Once this is done, the lowest note will automatically be the root. Then the inversion can be identified, and a slash chord symbol used, if necessary."

Conventionally, the name of the root note denotes the chord. Thus, a major chord built upon C is a C Major chord
Major chord
In music theory, a major chord is a chord having a root, a major third, and a perfect fifth. When a chord has these three notes alone, it is called a major triad...


Chords in atonal
Atonality in its broadest sense describes music that lacks a tonal center, or key. Atonality in this sense usually describes compositions written from about 1908 to the present day where a hierarchy of pitches focusing on a single, central tone is not used, and the notes of the chromatic scale...

 music are often of indeterminate root, as are equal-interval chords and mixed-interval chord
Mixed-interval chord
In music a mixed-interval chord is a chord not characterized by one consistent interval. Chords characterized by one consistent interval, or primarily but with alterations, are equal-interval chords...

s are often best characterized by their interval content.

Figured bass

Starting with Rameau
Jean-Philippe Rameau
Jean-Philippe Rameau was one of the most important French composers and music theorists of the Baroque era. He replaced Jean-Baptiste Lully as the dominant composer of French opera and is also considered the leading French composer for the harpsichord of his time, alongside François...

, the analysis and theory
Music theory
Music theory is the study of how music works. It examines the language and notation of music. It seeks to identify patterns and structures in composers' techniques across or within genres, styles, or historical periods...

 of tonal music
Tonality is a system of music in which specific hierarchical pitch relationships are based on a key "center", or tonic. The term tonalité originated with Alexandre-Étienne Choron and was borrowed by François-Joseph Fétis in 1840...

 usually treats the roots as the defining feature of chords and much information can be gained from a progression of roots even if chord inversions
Inversion (music)
In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices...

 are unknown. Also, if the key
Key (music)
In music theory, the term key is used in many different and sometimes contradictory ways. A common use is to speak of music as being "in" a specific key, such as in the key of C major or in the key of F-sharp. Sometimes the terms "major" or "minor" are appended, as in the key of A minor or in the...

 is known then the chord qualities are known for each root in simple music.
In a root progression, the most familiar form of labeling chord progression
Chord progression
A chord progression is a series of musical chords, or chord changes that "aims for a definite goal" of establishing a tonality founded on a key, root or tonic chord. In other words, the succession of root relationships...

s, chords are labeled by their root, rather than bass if different, as above. "Individual chord progressions can be analyzed in terms of the interval formed between their roots." This is in contrast to an older pre-tonal conception of chords as sonorities wherein root position or first inversion triads are simply considered alternative and fairly equivalent ways of "filling in" the consonance between octaves, C (E G) C or C (F A) C.

Basis in physics and mathematics

The concept of root has some basis in the physical properties of waves. When two notes of an interval
Interval (music)
In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...

 from the harmonic series are played at the same time, people sometimes perceive the fundamental note of the interval. For example, if notes with frequency ratios of 7:6 (a septimal minor third
Septimal minor third
In music, the septimal minor third , also called the subminor third, is the musical interval exactly or approximately equal to a 7/6 ratio of frequencies. In terms of cents, it is 267 cents, a quartertone of size 36/35 flatter than a just minor third of 6/5...

) were played, people could perceive a note whose frequency was 1/6th of the lower interval. The following sound file demonstrates this phenomenon, using sine waves, pure and simple waves for which this phenomenon is most easily evident.
This concept formed the basis for the method by which the composer Paul Hindemith
Paul Hindemith
Paul Hindemith was a German composer, violist, violinist, teacher, music theorist and conductor.- Biography :Born in Hanau, near Frankfurt, Hindemith was taught the violin as a child...

 used to determine and identify roots of chords in his harmonic system which he used both to write music and to analyze the music of other composers. Hindemith's system has been criticized for being based generically in theory derived rules and not on perception of specific instances.

Assumed root

An assumed root (also absent, or omitted root) is, "when a chord does not contain a root ([which is] not unusual)," in guitar playing, where the root may or may not be supplied by the bass guitar
Bass guitar
The bass guitar is a stringed instrument played primarily with the fingers or thumb , or by using a pick....

 or another instrument. In any context, it is the unperformed root of a performed chord. This 'assumption' may be established by the interaction of physics and perception (per Hindemith, above), or by pure convention. "We only interpret a chord as having its root omitted when the habits of the ear make it absolutely necessary for us to think of the absent root in such a place."[emphasis original] "We do not acknowledge omitted Roots except in cases where the mind is necessarily conscious of them...There are also cases in instrumental accompaniment in which the root having been struck at the commencemnt of a measure, the ear feels it through the rest of the measure."[emphasis original]

In guitar tablature, this may be indicated, "to show you where the root would be,"[emphasis added] and to assist one with, "align[ing] the chord shape at the appropriate fret
A fret is a raised portion on the neck of a stringed instrument, that extends generally across the full width of the neck. On most modern western instruments, frets are metal strips inserted into the fingerboard...

," with an assumed root in grey, other notes in white, and a sounded root in black.
Outside of guitar playing, an example of an assumed root is the diminished seventh
Diminished seventh chord
A diminished seventh chord is a four note chord that comprises a diminished triad plus the interval of a diminished seventh above the root. Thus it is , or enharmonically , of any major scale; for example, C diminished-seventh would be , or enharmonically...

 chord, of which a note a major third below the chord is often assumed to be the absent root, making it a ninth chord
Ninth chord
A ninth chord is a chord that encompasses the interval of a ninth when arranged in close position with the root in the bass.A dominant ninth is a dominant chord with a ninth. A ninth chord, as an extended chord, typically includes the seventh along with the basic triad structure. Thus, a Cmaj9...

 (on ii
In music or music theory, the supertonic is the second degree or note of a diatonic scale, one step above the tonic. In music theory, the supertonic chord is symbolized by the Roman numeral ii in a major scale, indicating that the chord is a minor chord , or ii in a natural minor scale, indicating...

). However, the diminished seventh chord affords, "singular facilities for modulation," as it may be notated four ways, to represent four different assumed roots, each a semitone
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically....

below notes present in the chord (D to C).
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