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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 Classical music generally refers to the art music of the Western world, considered to be distinct from Western folk music or popular music traditions. It is sometimes distinguished as Western classical music, as the term "classical music" al ...
or
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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 music theory, an inversion is a type of change to intervals, chords, voices (in counterpoint), and melodies. In each of these cases, "inversion" has a distinct but related meaning. The concept of inversion also plays an important role in mus ...
. In this concept, chords can be inverted while still retaining their root. In tertian harmonic theory, wherein chords can be considered stacks of third intervals (e.g. in common practice
tonality Tonality is the arrangement of pitches and/or chords of a musical work in a hierarchy of perceived relations, stabilities, attractions and directionality. In this hierarchy, the single pitch or triadic chord with the greatest stability is ca ...
), the root of a chord is the note on which the subsequent thirds are stacked. For instance, the root of a
triad Triad or triade may refer to: * a group of three Businesses and organisations * Triad (American fraternities), certain historic groupings of seminal college fraternities in North America * Triad (organized crime), a Chinese transnational orga ...
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)).


Identifying a chord's root

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.Wyatt and Schroeder (2002). ''Hal Leonard Pocket Music Theory'', p.80. . 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: * Chord names and symbols (e.g., C major, A minor, G7 etc.) * Roman numeral analysis (e.g., I to indicate the tonic chord and V to indicate the dominant chord) * Slash chords (e.g., G/B bass, which instructs the chord-playing performer to play a G major triad with a "B" in bass voice/lowest note) 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 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 The major scale (or Ionian mode) is one of the most commonly used musical scales, especially in Western music. It is one of the diatonic scales. Like many musical scales, it is made up of seven notes: the eighth duplicates the first at doub ...
contains seven unique pitch classes, each of which might serve as the root of a chord: Chords in
atonal Atonality in its broadest sense is music that lacks a tonal center, or key. ''Atonality'', in this sense, usually describes compositions written from about the early 20th-century to the present day, where a hierarchy of harmonies focusing on a s ...
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.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. .


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. 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. 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, 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).


Root ''vs'' fundamental

The concept of chord root is not the same as that of the fundamental of a complex vibration. When a
harmonic A harmonic is a wave with a frequency that is a positive integer multiple of the ''fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', t ...
sound In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by ...
, i. e. a sound with harmonic partials, lacks a component at the fundamental frequency itself, the pitch of this fundamental frequency may nevertheless be heard: this is the missing fundamental. The effect is increased by the fact that the missing fundamental also is the difference tone of the harmonic partials. Chord notes, however, do not necessarily form a harmonic series. In addition, each of these notes has its own fundamental. The only case where the chord notes may seem to form a harmonic series is that of the major triad. However, the major triad may be formed of the intervals of a third and a fifth, while the corresponding harmonic partials are distant by the intervals of a 12th and a 17th. For instance, C3 E3 G3 is a major triad, but the corresponding harmonic partials would be C3, G4 and E5. The root of the triad is an abstract C, while the (missing) fundamental of C3 E3 G3 is C1 – which would usually not be heard.


Assumed root

An assumed root (also absent, or omitted root) is "when a chord does not contain a root (
hich is Ij ( fa, ايج, also Romanized as Īj; also known as Hich and Īch) is a village in Golabar Rural District, in the Central District of Ijrud County, Zanjan Province, Iran Iran, officially the Islamic Republic of Iran, and also ...
not unusual)". 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." mphasis 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 in original). In
guitar tablature Tablature (or tabulature, or tab for short) is a form of musical notation indicating instrument fingering rather than musical pitches. Tablature is common for fretted stringed instruments such as the guitar, lute or vihuela, as well as many fre ...
, this may be indicated, "to show you where the root would be", and to assist one with, "align ngthe chord shape at the appropriate fret", with an assumed root in grey, other notes in white, and a sounded root in black. 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. The diminished seventh chord affords, "singular facilities for modulation", as it may be notated four ways, to represent four different assumed roots.Adela Harriet Sophia Bagot Wodehouse (1890). ''A Dictionary of Music and Musicians: (A.D. 1450–1889)'', p.448. Macmillan and Co., Ltd.


In jazz

In
jazz Jazz is a music genre that originated in the African-American communities of New Orleans, Louisiana in the late 19th and early 20th centuries, with its roots in blues and ragtime. Since the 1920s Jazz Age, it has been recognized as a m ...
and
jazz fusion Jazz fusion (also known as fusion and progressive jazz) is a music genre that developed in the late 1960s when musicians combined jazz harmony and improvisation with rock music, funk, and rhythm and blues. Electric guitars, amplifiers, and ke ...
, roots are often omitted from chords when chord-playing musicians (e.g.,
electric guitar An electric guitar is a guitar that requires external amplification in order to be heard at typical performance volumes, unlike a standard acoustic guitar (however combinations of the two - a semi-acoustic guitar and an electric acoustic gu ...
,
piano The piano is a stringed keyboard instrument in which the strings are struck by wooden hammers that are coated with a softer material (modern hammers are covered with dense wool felt; some early pianos used leather). It is played using a keyboa ...
, Hammond organ) are improvising chords in an ensemble that includes a bass player (either
double bass The double bass (), also known simply as the bass () (or #Terminology, by other names), is the largest and lowest-pitched Bow (music), bowed (or plucked) string instrument in the modern orchestra, symphony orchestra (excluding unorthodox addit ...
, 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. 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.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


See also

* Figured bass


References

{{DEFAULTSORT:Root (Chord) Chord factors Diatonic functions Voicing (music) eo:Toniko (muziko)