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In music theory, the root of a chord (in Italian, basse fondamentale) is the note or pitch upon which a chord may be built by stacking thirds. For example, a three-note triad using C as a root would be C-E-G. Conventionally, the name of the root note denotes the chord. Thus, a major chord built upon C is called a C major chord. The root is often confused with the tonic, which is the reference note of a scale, rather than that of a chord.
While the theory of chordal roots describes bottom-up construction of chords, chords appearing in musical scores or performances will not always use the chordal root as the lowest pitch. When a chord's bass note 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 said to be inverted. Consequently, changing the configuration of pitches above a given bass note will typically result in a new note becoming the root.[clarification needed]
Identifying a chord's root 
It is possible to recognize a chord's root using several different techniques. "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 [if a triad]). 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."
If the chord is an inverted triad in close spacing, then the root will be directly above the interval of a fourth. Similarly, if the chord is an inverted seventh chord in close spacing, then the root will be directly above the interval of a second.
Root progressions in music 
Jean-Philippe Rameau introduced the theory of chord roots in his Traité de l'harmonie (1722). Subsequently, the analysis and theory of tonal music has typically treated chordal roots as the defining feature of harmony. Because inverting a chord simply reshuffles the same pitch material, chords of the same root sound and function similarly. Rameau's insight led him to describe chord-to-chord movements in terms of the interval between the chordal roots, instead of their bass notes. Allowing for octave equivalence, root progressions of a second, third, or fourth are possible in a diatonic context.
By using Roman numeral analysis, musicians describe harmonic progressions in reference to a given key's tonic pitch. "Individual chord progressions can be analyzed in terms of the interval formed between their roots." Such analyses reveal similarities between music which might be in different keys or employ different chordal inversions.
Why is it so important to know the root of the chord? Because the roots of the chords will sound whether we want them to or not, whether or not the alphabetical symbol is correct. The root progression which emerges may not coincide with what we think we have written; it may be better or it may be worse; but art does not permit chance. The root progression supports the work. The total root progression is heard as a substantive element, almost like another melody, and it determines the tonal basis of the music. And the tonal basis of a piece is very important to the construction of themes and to the orchestration.—Russo (1975).
Possible mathematical and scientific basis 
The concept of root has some basis in the physical properties of waves. When two notes of an interval 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) 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.[clarification needed]
The file plays A880, followed by 1026.67 Hz, followed by both tones together, followed by the implied root frequency of 586.67 Hz, a fifth below the A.
|Problems listening to this file? See media help.|
This concept formed the basis for the method by which the composer Paul Hindemith 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 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 commencement 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," 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 chord, of which a note a major third below the chord is often assumed to be the absent root, making it a ninth chord (on ii). 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 below notes present in the chord (D♭ to C).
Fundamental bass 
The fundamental bass (basse fondamentale) is a concept originated 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.
See also 
- 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."
- Wyatt and Schroeder (2002). Hal Leonard Pocket Music Theory, p.80. ISBN 0-634-04771-X.
- 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.
- Benward & Saker (2003). Music in Theory and Practice, p.178. ISBN 978-0-07-294262-0.
- Russo, William (1975). Jazz Composition and Orchestration, p.28. ISBN 0-226-73213-4.
- Hindemith, Paul (1945). The Craft of Musical Composition,[page needed]. Schott & Co.
- Latarski, Don (1999). Ultimate Guitar Chords: First Chords, p.5. ISBN 978-0-7692-8522-1.
- Chapman, Charles (2004). Rhythm Guitar Tutor: An Essential Guide to Becoming the Consumate [sic] Rhythm Guitarist, p.4. ISBN 978-0-7866-2022-7.
- John Curwen (1872). The Standard Course of Lessons and Exercises in the Tonic Sol-Fa Method of Teaching Music, p.27. Londong: Tonic Sol-Fa Agency, 8, Warwick Lane, Paternoster Row, E.C.
- Curwen, John (1881). The new How to observe harmony, p.44. Tonic Sol-Fa Agency.
- Richard Lawn, Jeffrey L. Hellmer (1996). Jazz: Theory and Practice, p.124. ISBN 0-88284-722-8.
- Adela Harriet Sophia Bagot Wodehouse (1890). A Dictionary of Music and Musicians: (A.D. 1450-1889), p.448. Macmillan and Co., Ltd.
- Schoenberg, Arnold (1983). Theory of Harmony, 197. ISBN 978-0-520-04944-4.
- Schoenberg (1983), p.267.