Root (chord)

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Root, in red, of a C major chord (
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). Note that the root is doubled at the octave. Root of a major chord on C.png
Root, in red, of a C major chord ( Loudspeaker.svg Play  ). Note that the root is doubled at the octave.
Root notes (blue) and bass notes (red, both=purple) from an 18th century Chorale
Play (help*info) Leading-tone triad and secondary leading-tone triad in Chorale Gotte der Vater, wohn' uns bei colored roots and bass.png
Root notes (blue) and bass notes (red, both=purple) from an 18th century Chorale Loudspeaker.svg Play  

In music theory, the concept of root is the idea that a chord can be represented and named by one of its notes. It is linked to harmonic thinking— the idea that vertical aggregates of notes can form a single unit, a chord. It is in this sense that one speaks of a "C chord" or a "chord on C"—a chord built from C and of which the note (or pitch) C is the root. When a chord is referred to in Classical music or popular music without a reference to what type of chord it is (either major or minor, in most cases), it is assumed a major triad, which for C contains the notes C, E and G. The root need not be the bass note, the lowest note of the chord: the concept of root is linked to that of the inversion of chords, which is derived from the notion of invertible counterpoint. In this concept, chords can be inverted while still retaining their root.

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In tertian harmonic theory, that is in a theory where 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)).

Root position, first inversion, and second inversion C major chords
Play root position C major chord (help*info)
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Play first inversion C major chord (help*info)
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Play second inversion C major chord (help*info)
. Chord roots (all the same) in red. Root position, first inversion, and second inversion C major chords.png
Root position, first inversion, and second inversion C major chords Loudspeaker.svg Play root position C major chord  , Loudspeaker.svg Play first inversion C major chord  , or Loudspeaker.svg Play second inversion C major chord  . 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)
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Play first inversion A minor chord (help*info)
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Play second inversion F major chord (help*info)
. Chord roots in red. Root position, first inversion, and second inversion chords over C bass.png
Root position, first inversion, and second inversion chords over C bass Loudspeaker.svg Play root position C major chord  , Loudspeaker.svg Play first inversion A minor chord  , or Loudspeaker.svg Play second inversion F major chord  . Chord roots in red.

Identifying a chord's root

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

Although the safest way to recognize a chord’s root is, after having reduced the chord to close spacing, to rearrange it as a stack of thirds, 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:

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 Asus4(add7) 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
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. Root position triads from C major scale.svg
Root position triads from C major scale Loudspeaker.svg 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, ca. 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 Traité d’harmonie (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).

Possible mathematical and scientific basis

The concept of root has some basis in the physical properties of harmonic sounds. When two notes or more notes from the harmonic series are played at the same time, people sometimes perceive the fundamental note of the series, even if that note is not present (see Missing fundamental). This property has been used in organ building for the production of low notes by resultant tones. Andreas Werckmeister’s Harmonologia (1702) describes the major triad in root position and in first inversion in terms of the harmonic series, but this description cannot be extended to the minor triad. [7]

Hindemith, who described the chromatic scale as resulting from "the juxtaposition of vibrating units in the proportions of the simple numbers from 1 to 6", i.e. from the intervals corresponding to harmonic partials 1 to 6, called the fundamental of this harmonic series the "root" of the scale. [8] From this root, he then derived a series of notes in diminishing degree of relationship, which he called Series 1 and on which he built a system of composition. This system however has been criticized for being based generically in theory derived rules and not on perception of specific instances. [3]

Assumed root

Assumed root, Am /B: A minor ninth chord without root and with B in the bass.
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Am /B, Am , then full Am9. Assumed root A minor ninth chord.png
Assumed root, Am /B: A minor ninth chord without root and with B in the bass. Loudspeaker.svg Play   Am /B, Am , then full Am9.

An assumed root (also absent, or omitted root) is "when a chord does not contain a root ([which is] not unusual)". [10] In any context, it is the unperformed root of a performed chord. This 'assumption' may be established by the interaction of physics and perception, 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]. [11] "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 in original). [12]

In guitar tablature, this may be indicated, "to show you where the root would be", 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. [9]

A comparison of the diminished 7th
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and dominant 7th (9)
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chords. Diminished7thandMinor9thComparison.png
A comparison of the diminished 7th Loudspeaker.svg Play   and dominant 7th (9) Loudspeaker.svg Play   chords.
Diminished seventh chord's use in modulation: each assumed root, in parenthesis, may be used as a dominant, tonic, or supertonic.
Play ninth chords (help*info)
Thus C, taken as dominant, would modulate to F. Diminished seventh modulation.png
Diminished seventh chord's use in modulation: each assumed root, in parenthesis, may be used as a dominant, tonic, or supertonic. Loudspeaker.svg Play ninth chords   Thus C, taken as dominant, would modulate to F.

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. [15] The diminished seventh chord affords, "singular facilities for modulation", as it may be notated four ways, to represent four different assumed roots. [14]

In jazz

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.)

Root progressions in music

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. [16]

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. [17]

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, [18] Yizhak Sadaï [19] and Nicolas Meeùs. [20]

See also

Related Research Articles

Harmony aspect of music

In music, harmony is the process by which the composition of individual sounds, or superpositions of sounds, is analysed by hearing. Usually, this means simultaneously occurring frequencies, pitches, or chords.

A seventh chord is a chord consisting of a triad plus a note forming an interval of a seventh above the chord's root. When not otherwise specified, a "seventh chord" usually means a dominant seventh chord: a major triad together with a minor seventh. However, a variety of sevenths may be added to a variety of triads, resulting in many different types of seventh chords.

Chord (music) harmonic set of three or more notes

A chord, in music, is any harmonic set of pitches consisting of multiple notes that are heard as if sounding simultaneously. For many practical and theoretical purposes, arpeggios and broken chords, or sequences of chord tones, may also be considered as chords.

Major chord chord having a root, a major third, and a perfect fifth; e.g. C–E–G or F–A–C

In music theory, a major chord is a chord that has a root, major third, and perfect fifth. When a chord has these three notes alone, it is called a major triad. For example, the major triad built on C, called a C major triad, has pitches C–E–G:

In music theory, an augmented sixth chord contains the interval of an augmented sixth, usually above its bass tone. This chord has its origins in the Renaissance, was further developed in the Baroque, and became a distinctive part of the musical style of the Classical and Romantic periods.

Tertian

In music theory, tertian describes any piece, chord, counterpoint etc. constructed from the intervals of thirds. An interval such as that between the notes A and C encompasses 3 semitone intervals and is termed a minor third while one such as that between C and E encompasses 4 semitones and is called a major third. Tertian harmony principally uses chords based on thirds; the term is typically used to contrast with quartal and quintal harmony which uses chords based on fourths or fifths.

The term sixth chord refers to two different kinds of chord, the first in classical music and the second in modern popular music.

Thirteenth musical interval

In music or music theory, a thirteenth is the interval between the sixth and first scale degrees when the sixth is transposed up an octave, creating a compound sixth, or thirteenth. The thirteenth is most commonly major Play  or minor Play .

Eleventh chord chord that contains the tertian extension of the eleventh, typically found in jazz

In music theory, an eleventh chord is a chord that contains the tertian extension of the eleventh. Typically found in jazz, an eleventh chord also usually includes the seventh and ninth, and elements of the basic triad structure. Variants include the dominant eleventh, minor eleventh, and the major eleventh chord. Symbols include: Caug11, C9aug11, C9+11, C9alt11, Cm9(11), C−9(11). The eleventh in an eleventh chord is, "almost always sharpened, especially in jazz," at least in reference to the third, with CM11 (major eleventh): C–E–G–B–D–F, Cm11 (minor eleventh): C-E-G-B-D-F, and C11 (dominant eleventh): C–E–G–B–D–F.

In music theory, a ninth chord is a chord that encompasses the interval of a ninth when arranged in close position with the root in the bass.

The ninth chord and its inversions exist today, or at least they can exist. The pupil will easily find examples in the literature [such as Schoenberg's Verklärte Nacht and Strauss's opera Salome]. It is not necessary to set up special laws for its treatment. If one wants to be careful, one will be able to use the laws that pertain to the seventh chords: that is, dissonances resolve by step downward, the root leaps a fourth upward.

In music, a triad is a set of three notes that can be stacked vertically in thirds. The term "harmonic triad" was coined by Johannes Lippius in his Synopsis musicae novae (1612).

Root position

The root position of a chord is the voicing of a triad, seventh chord, or ninth chord in which the root of the chord is the bass note and the other chord factors are above it. In the root position, uninverted, of a C-major triad, the bass is C — the root of the triad — with the third and the fifth stacked above it, forming the intervals of a third and a fifth above the root of C, respectively.

Guitar chord set of notes played on a guitar

In music, a guitar chord is a set of notes played on a guitar. A chord's notes are often played simultaneously, but they can be played sequentially in an arpeggio. The implementation of guitar chords depends on the guitar tuning. Most guitars used in popular music have six strings with the "standard" tuning of the Spanish classical guitar, namely E-A-D-G-B-E' ; in standard tuning, the intervals present among adjacent strings are perfect fourths except for the major third (G,B). Standard tuning requires four chord-shapes for the major triads.

Second inversion the voicing of a triad, seventh chord, or ninth chord with the fifth of the chord in the bass and the root a third above it

The second inversion of a chord is the voicing of a triad, seventh chord, or ninth chord in which the fifth of the chord is the bass note. In this inversion, the bass note and the root of the chord are a fourth apart which traditionally qualifies as a dissonance. There is therefore a tendency for movement and resolution. In notation form, it is referred to with a c following the chord position or as a 6
4
chord.

Inversions are not restricted to the same number of tones as the original chord, nor to any fixed order of tones except with regard to the interval between the root, or its octave, and the bass note, hence, great variety results.

First inversion the voicing of a triad, seventh chord, or ninth chord with the third of the chord in the bass and the root a sixth above it

The first inversion of a chord is the voicing of a triad, seventh chord, or ninth chord in which the third of the chord is the bass note and the root a sixth above it. In the first inversion of a C-major triad, the bass is E — the third of the triad — with the fifth and the root stacked above it, forming the intervals of a third and a sixth above the inverted bass of E, respectively.

In music theory, the word inversion has distinct, but related, meanings when applied to intervals, chords, voices, and melodies. The concept of inversion also plays an important role in musical set theory.

Roman numeral analysis Use of Roman numeral symbols in the musical analysis of chords

Roman numeral analysis is a type of musical analysis in which chords are represented by Roman numerals. In some cases, Roman numerals denote scale degrees themselves. More commonly, however, they represent the chord whose root note is that scale degree. For instance, III denotes either the third scale degree or, more commonly, the chord built on it. Typically, uppercase Roman numerals are used to represent major chords, while lowercase Roman numerals are used to represent minor chords. However, some music theorists use upper-case Roman numerals for all chords, regardless of chord quality.

Seventh (chord)

In music, the seventh factor of a chord is the note or pitch seven scale degrees above the root or tonal center. When the seventh is the bass note, or lowest note, of the expressed chord, the chord is in third inversion Play .

Musicians use various kinds of chord names and symbols in different contexts to represent musical chords. In most genres of popular music, including jazz, pop, and rock, a chord name and its corresponding symbol typically indicate one or more of the following:

  1. the root note,
  2. the chord quality,
  3. whether the chord is a triad, seventh chord, or an extended chord,
  4. any altered notes,
  5. any added tones, and
  6. the bass note if it is not the root.
Inversions higher than third

The fourth inversion of a ninth chord is the voicing in which the ninth of the chord is the bass note and the root a minor seventh above it. In the fourth inversion of a G-dominant ninth with ninth, the bass is A — the ninth of the chord — with the root, third, fifth, and seven stacked above it, forming the intervals of a second, a fourth, a sixth, and a seventh above the inverted bass of F, respectively. Inversions higher than the third require extended chords; the fourth inversion requires a ninth chord, the fifth an eleventh chord, etc.

The chord of the ninth, having four intervals like the flat seventh, of course admits of four inversions in both major and minor... The...fourth inversion, ["marked"]: 642...is seldom used.

If...the Ninth is in the bass: 4th inversion of a Ninth-chord.

References

  1. 1 2 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. 1 2 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.
  7. B. Rivera, op. cit., p. 66-67.
  8. P. Hindemith, Craft of Musical Composition, A. Mendel transl., New York, 1942, p. 53. (Ein einziger Ton die Wurzel der zu ihm gehörenden Tonleiter, Unterweisung im Tonsatz, new edition, Mainz, 1940, p. 73.)
  9. 1 2 Latarski, Don (1999). Ultimate Guitar Chords: First Chords, p.5. ISBN   978-0-7692-8522-1.
  10. Chapman, Charles (2004). Rhythm Guitar Tutor: An Essential Guide to Becoming the Consumate[ sic ] Rhythm Guitarist, p.4. ISBN   978-0-7866-2022-7.
  11. 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.
  12. Curwen, John (1881). The new How to observe harmony, p.44. Tonic Sol-Fa Agency.
  13. Richard Lawn, Jeffrey L. Hellmer (1996). Jazz: Theory and Practice, p.124. ISBN   0-88284-722-8.
  14. 1 2 Adela Harriet Sophia Bagot Wodehouse (1890). A Dictionary of Music and Musicians: (A.D. 1450–1889), p.448. Macmillan and Co., Ltd.
  15. Schoenberg, Arnold (1983). Theory of Harmony, 197. ISBN   978-0-520-04944-4.
  16. Simon Sechter, Die Grundsätze der musikalischen Komposition, vol. I, Leipzig, 1853.
  17. Russo, William (1975). Jazz Composition and Orchestration, p.28. ISBN   0-226-73213-4.
  18. A. Schoenberg, Theory of Harmony, op. cit., and Structural Functions of Harmony, ²1969, pp. 6-9 and passim.
  19. Y. Sadaï, Harmony in its Systemic and Phenomenological Aspects, Jerusalem, pp. 87-88.
  20. N. Meeùs, “Toward a Post-Schoenbergian Grammar of Tonal and Pre-tonal Harmonic Progressions”, Music Theory Online 6/1 (2000), http://www.mtosmt.org/issues/mto.00.6.1/mto.00.6.1.meeus.html. See also http://nicolas.meeus.free.fr/NMVecteurs.html