Root (chord)

This article is about chord roots. For interval roots, see interval root.

Root, in red, of a C major chord ( Play (help·info)). Note that the root is doubled at the octave.

Root position triads from C major scale^[1]  Play (help·info).

Root position, first inversion, and second inversion C major chords  Play root position C major chord (help·info),  Play first inversion C major chord (help·info), or  Play second inversion C major chord (help·info). Chord roots (all the same) in red.

Root position, first inversion, and second inversion chords over C bass  Play root position C major chord (help·info),  Play first inversion A minor chord (help·info), or  Play second inversion F major chord (help·info). Chord roots in red.

In music theory, the root of a chord (in French, basse fondamentale) is the note or pitch upon which a triadic chord is built. For example, the root of the major triad C-E-G is C.

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 inverted.

"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."^[2]

Conventionally, the name of the root note denotes the chord. Thus, a major chord built upon C is a C Major chord.

Chords in atonal music are often of indeterminate root, as are equal-interval chords and mixed-interval chords are often best characterized by their interval content.^[3]

Figured bass

Starting with Rameau, the analysis and theory of tonal music 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 are unknown. Also, if the key is known then the chord qualities are known for each root in simple music.

Determining chord root from inversion  Play (help·info). "Revoicing inverted triads to root position".^[2]

In a root progression, the most familiar form of labeling chord progressions, 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."^[4] 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.

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).^[5]

Basis in physics and mathematics

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]}

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.^[6] Hindemith's system has been criticized for being based generically in theory derived rules and not on perception of specific instances.^[3]

Assumed root

Assumed root, Am7/B: A minor ninth chord without root and with B in the bass.^[7]  Play (help·info) Am9/B, Am7, then full Am9.

An assumed root (also absent, or omitted root) is, "when a chord does not contain a root ([which is] not unusual)," in guitar playing,^[8] 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]^[9] "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]^[10]

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.^[7]

A comparison of the diminished 7th  Play (help·info) and dominant 7th^[11] (♭9)  Play (help·info) chords.

Diminished seventh chord's use in modulation: each assumed root, in parenthesis, may be used as a dominant, tonic, or supertonic.^[12]  Play ninth chords (help·info) Thus C, taken as dominant, would modulate to F.

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).^[13] However, the diminished seventh chord affords, "singular facilities for modulation," as it may be notated four ways, to represent four different assumed roots,^[12] each a semitone below notes present in the chord (D♭ to C).^[14]

See also

• Figured bass

References

1. ^ Palmer, Manus, and Lethco (1994). The Complete Book of Scales, Chords, Arpeggios and Cadences, p.6. ISBN 0739003682. "The root is the note from which the triad gets its name. The root of a C triad is C."
2. ^ ^{a b} Wyatt and Schroeder (2002). Hal Leonard Pocket Music Theory, p.80. ISBN 063404771X.
3. ^ ^{a b} 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. ^ Benward & Saker (2003). Music in Theory and Practice, p.178. ISBN 978-0-07-294262-0.
5. ^ Russo, William (1975). Jazz Composition and Orchestration, p.28. ISBN 0226732134.
6. ^ Hindemith, Paul (1945). The Craft of Musical Composition,^{[page needed]}. Schott & Co.
7. ^ ^{a b} Latarski, Don (1999). Ultimate Guitar Chords: First Chords, p.5. ISBN 9780769285221.
8. ^ Chapman, Charles (2004). Rhythm Guitar Tutor: An Essential Guide to Becoming the Consumate Rhythm Guitarist, p.4. ISBN 9780786620227.
9. ^ 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.
10. ^ Curwen, John (1881). The new How to observe harmony, p.44. Tonic Sol-Fa Agency.
11. ^ Richard Lawn, Jeffrey L. Hellmer (1996). Jazz: Theory and Practice, p.124. ISBN 0882847228.
12. ^ ^{a b} Adela Harriet Sophia Bagot Wodehouse (1890). A Dictionary of Music and Musicians: (A.D. 1450-1889), p.448. Macmillan and Co., Ltd.
13. ^ Schoenberg, Arnold (1983). Theory of Harmony, 197. ISBN 9780520049444.
14. ^ Schoenberg (1983), p.267.