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[[File:Classical spectacular07.jpg|thumb|right|300px|[[Musical instrument|Instruments]] playing different [[note]]s create chords.]]
:''This article describes pitch simultaneity and harmony in traditional [[Western music|Western]] styles. For information on non-Western styles, consult the articles specific to those styles.''
{{refimprove|date=March 2009}}
[[File:Frets, guitar neck, C-major chord.jpg|thumb|right|200px|Typical fingering for a [[second inversion]] C major chord on a [[guitar]].]]


:''This article describes pitch simultaneity and harmony in music. For other meanings of the word, see [[Chord]].''
In [[music]] and [[music theory]] a '''chord''' is a set of three or more different [[note (music)|notes]] from a specific key that sound simultaneously. Chords constructed of three notes are described as triads and consist of two intervals. The technical name for triad chords is [[tertian]] [[Sonority|sonorities]] and is understood to be chords constructed from stacks of [[third]]s relative to some underlying [[musical scale|scale]]. Two-note combinations are commonly referred to as ''[[Interval (music)|intervals]]''. The technical name for an interval is ''[[dyad (music)|dyads]]''. A succession of chords is called a [[chord progression]].
{{TOCleft}}
[[Image:Ives quarter tone fundamental chord.png|thumb|right|250px|Composer Charles Ives chose the chord above as good possibility for a "fundamental" chord in the quarter tone scale, akin not to the tonic but to the major chord of traditional tonality.<ref name="Boatwright">Boatwright, Howard (1971). "Ives' Quarter-Tone Impressions", p.8-9. ''Perspectives on American Composers'', p.3-12, Boretz & Cone, eds.</ref> {{Audio|Ives fundamental chord (quarter tones).ogg|Play}}]]


A '''chord''' in [[music]] is any set of [[Harmony|harmonically-related]] [[note (music)|notes]] that is heard as if sounding simultaneously (a "harmonic simultaneity", ''see [[Simultaneity (music)]])''. The most [[common chord]]s are the [[major chord|major]] and [[minor chord|minor]], and then the [[augmented triad|augmented]] and [[diminished chord|diminished]] [[Triad (music)|triads]], types of chord that are sometimes referred to generically as the chord's "quality". Triads are so called because they consist of three distinct notes: further notes may be added to give '''[[extended chord]]s''' and '''[[added tone chords]]'''. Chords are also commonly classed by their [[Root (music)|root]] note so, for instance, the chord C Major is a three-note chord of major quality built upon the note C. However, since the structural meaning of a chord depends exclusively upon the '''[[Scale (music)|degree of the scale]]''' upon which it is built,<ref name="Schoenberg">Arnold Schoenberg, ''Structural Functions of Harmony'', Faber and Faber, 1983, p.1-2.</ref> chords are usually analysed by numbering them, using [[Roman numerals]], upwards from the key-note. A chord may also be classified by its '''[[Inversion (music)|inversion]]''', the order in which its notes are stacked from lowest to highest.
Four ways of [[Chord notation|notating or representing chords]] are often used: [[roman numerals]], [[figured bass]], [[macro analysis|macro symbols]], and [[chord notation|popular music symbols]] (Benward & Saker 2003, p.&nbsp;77).


A chord, then, is the harmonic or "vertical" function of any group of notes. These need not actually be played together: [[arpeggio]]s and broken chord figures may for many practical and theoretical purposes be understood as chords. '''[[Polychord]]s''' are formed by two or more chords superimposed. Often these may be analysed as extended chords but some examples lack the [[tertian]] [[sonority]] of triads ''(See: [[altered chord]], [[secundal|secundal chord]], [[quartal and quintal harmony]] and [[Tristan chord]])''. A '''[[nonchord tone]]''' is a [[Consonance and dissonance|dissonant]] or unstable tone that lies outside the chord currently heard, though often [[resolution (music)|resolving]] to a chord tone.
== History ==

A succession of chords is called a '''[[chord progression]]'''. There are four common ways of [[Chord notation|notating or representing chords]] as such (Benward & Saker 2003, p.&nbsp;77):- '''Roman numerals''' are commonly used in harmonic analysis to denote the step of the scale upon which the chord is built and its quality. '''[[Figured bass]]''', much used in the [[Baroque era]], added numbers to a written bass line to enable keyboard players to [[Improvised music|improvise]] chords with the right hand while playing the bass with their left. '''[[Macro analysis|Macro symbols]]''' are a technique of modern musicology while various '''[[chord notation|popular music symbols]]''', such as [[chord chart]]s for guitarists, can quickly lay out the harmonic groundplan of a piece so that the musician may improvise, [[Jam (music)|"jam"]], [[Vamp (music)|"vamp"]], [[Busking|"busk"]] or [[Head arrangement|"head arrange"]] a part.

[[Image:C triad.png|thumb|right|350px|C Major triad {{Audio|Just major triad on C.mid|Play in just intonation}} {{Audio|C major triad.mid|Play in equal temperament}} {{Audio|Lucy Tuning major chord on C.mid|Play in Lucy tuning}} {{Audio|Quarter-comma meantone major chord on C.mid|Play in Quarter-comma meantone tuning}} {{Audio|Young temperament major chord on C.mid|Play in Young temperament}} {{Audio|Pythagorean major chord on C.mid|Play in Pythagorean tuning}}]]

==Definition and history==
{{main|Harmony}}
{{main|Harmony}}
[[File:Mussorgsky Pictures at an Exhibition, chords.PNG|300px|right|Mussorgsky's ''Pictures at an Exhibition'' "Promenade", a piece showing an explicit chord progression|thumb]]
[[Image:BP chord 357 just.png|thumb|right|250px|Bohlen-Pierce chord tuned to harmonics 3, 5, and 7. "BP" above the clefs indicate Bohlen-Pierce notation in which the notes indicated are C, G, and A. {{Audio|BP chord 357 just.mid|Play}}]]


The English word "chord" derives from "cord", a Middle English shortening of "accord" in the sense of "in tune with one another".
The word chord comes from cord which is a Middle English shortening of accord. In the Middle Ages, Western harmony featured the perfect intervals of a fourth, a fifth, and an octave. In the 15th and 16th centuries, the major and minor triads (see below) became increasingly common, and were soon established as the default sonority for Western music. Four-note "seventh chords" were then widely adopted from the 17th century. The harmony of many contemporary popular Western genres continues to be founded in the use of triads and seventh chords, though far from universally. Notable exceptions include: modern jazz (especially circa 1960), in which chords often include at least five notes, with seven (and occasionally more) being quite common; and atonal or post-tonal contemporary classical music (including the music of some film scores), whose chords can be far more complex, rooted in such disparate harmonic philosophies that traditional terms such as triad are rarely useful.


Since a chord may be understood as such even when all its notes are not simultaneously audible there has been some academic discussion regarding the point at which a group of notes can be called a ''chord''. [[Jean-Jacques Nattiez]] (1990, p.&nbsp;218) explains that "we can encounter 'pure chords' in a musical work," such as in the "Promenade" of [[Modest Mussorgsky]]'s ''[[Pictures at an Exhibition]]'' but "often, we must go from a textual given to a more ''abstract'' representation of the chords being used" - as in Claude Debussy's ''[[Arabesques (Debussy)|Première Arabesque]]''. [[File:Debussy Premiere Arabesque melody and chords.PNG|300px|left|Upper stave: [[Claude Debussy]]'s ''[[Arabesques (Debussy)|Première Arabesque.'']] Lower stave: implied chord progression.|thumb]]The chords on the lower stave on the left are constructed from the notes in the actual piece, shown above. For a sound configuration to be recognized as a chord it must have a certain duration.
[[Image:C triad.png|thumb|right|350px|Major triad {{Audio|Just major triad on C.mid|Play in just intonation}} {{Audio|C major triad.mid|Play in equal temperament}} {{Audio|Lucy Tuning major chord on C.mid|Play in Lucy tuning}} {{Audio|Quarter-comma meantone major chord on C.mid|Play in Quarter-comma meantone tuning}} {{Audio|Young temperament major chord on C.mid|Play in Young temperament}} {{Audio|Pythagorean major chord on C.mid|Play in Pythagorean tuning}}]]


In the Middle Ages, Western harmony featured the perfect intervals of a fourth, a fifth, and an octave. In the 15th and 16th centuries, the major and minor triads became increasingly common, and were soon established as the default sonority for Western music. Such triads can be described as a series of three notes; the [[root note]], the "third", and the "fifth" of the chord. As an example, the C [[major scale]] consists of the notes C D E F G A B C. The major triad formed using the C note as the root consists of C itself (the root note of the scale), E (the third note of the scale) and G (the fifth note of the scale). This triad is major because the interval from C to E, of four semitones, is a [[major third]]. Using the same scale a chord may be constructed using the D as the root note; D (root), F (third), A (fifth). While there were four [[semitone]]s between the root and third of the chord on C there are here only 3 semitones between the root and third (the outer notes are still a [[perfect fifth]] apart). Thus, while the C triad is major, the D triad is minor. A triad can be constructed on any note of the C major scale and all will be minor or major, with the exception of the triad on the [[leading-tone]] which is diminished. Taking any other major scale ([[Ionian mode]]), the first, fourth and fifth intervals, when used as roots, form major triads. Similarly, as any major scale can also yield a [[relative minor]], in any natural minor scale ([[Aeolian mode]]) minor triads are found on the tonic, fourth and fifth degrees of the scale. Each seven-note diatonic scale can provide three major and three minor chords, both sets of three standing in the same '''I-IV-V''' relationship to one another. The seventh degree of the major (degree two of the relative minor) will result in a diminished chord. ''See [[Music and mathematics#Mathematics of musical scales]]''.
Chords are so well-established in Western music that sonorities of two pitches, or even monophonic melodies, are often interpreted by listeners (musicians and non-musicians alike) as "implying" chords. This [[psychoacoustic]] phenomenon occurs as a result of a lifetime of exposure to the conventional harmonies of music, with the result that the brain "supplies" the complete expected chord in its absence.<ref> {{Cite journal | last = Schellenberg
| first = E. Glenn | last2 = Bigand | first2 = Emmanuel | last3 = Poulin-Charronnat | first3 = Benedicte | last4 = Garnier | first4 = Cecilia | last5 = Stevens | first5 = Catherine | title = Children's implicit knowledge of harmony in Western music | journal = Developmental Science | volume = 8 | issue = 8 | pages = 551–566 | date = Nov. | year = 2005 | doi = 10.1111/j.1467-7687.2005.00447.x | pmid = 16246247}}</ref>


Four-note "seventh chords" were widely adopted from the 17th century. The harmony of many contemporary popular Western genres continues to be founded in the use of triads and seventh chords, though far from universally. Notable exceptions include: modern jazz (especially circa 1960), in which chords often include at least five notes, with seven (and occasionally more) being quite common; and atonal or post-tonal contemporary classical music (including the music of some film scores), whose chords can be far more complex, rooted in such disparate harmonic philosophies that traditional terms such as triad are rarely useful.
Composers can and do take advantage of this tendency to surprise the listener, by deliberately avoiding certain defining tones. For instance, a composition may be predominantly composed in the [[pentatonic minor scale]], implying common [[Aeolian mode]] to the listener, before deliberately including a more uncommon tone in a melodic progression or chord, such as a major VI (signalling [[Dorian mode]]) or a flattened II (signalling [[Phrygian mode]]).


== Chord characteristics ==
== Constructing and naming chords ==
[[File:Classical spectacular07.jpg|thumb|right|300px|[[Musical instrument|Instruments]] playing different [[note]]s create chords.]]


Every chord has certain characteristics, which include:
Every chord has certain characteristics, which include:


* the number of [[Pitch class|chromas]] used in constructing the chord (or the number of distinct [[pitch class]]es from which the chord takes its notes)
* the number of [[pitch class]]es or chromas (distinct notes without respect to octave) that constitute the chord.
* the general type of [[interval (music)|intervals]] it contains: for example seconds, thirds, or fourths
* its precise intervallic construction, sometimes called "chord quality": for example, if the chord is a triad, is the triad a [[major chord|major]], [[minor chord|minor]], [[augmented triad|augmented]] or [[diminished chord|diminished]]?
* the [[Degree (music)|scale degree]] of the [[root note]]
* the [[Degree (music)|scale degree]] of the [[root note]]
* whether the chord is [[Inversion (music)|inverted]] in register
* The position or [[Inversion (music)|inversion]] of the chord
* the general type of [[interval (music)|intervals]] it contains: for example seconds, thirds, or fourths
*
===Number of distinct notes===


Chords may be classified according to the number of notes they contain. More precisely, since instances of any given note in different octaves may be taken as the same note for the purposes of analysis, it is better to speak of the number of distinct '''[[pitch class]]es''' or "chromas" used in their construction. Three such pitch classes are needed to define any [[Common chord (music)|common chord]], therefore two notes sounded simultaneously is sometimes classed as an '''[[Interval (music)|interval]]''' rather than a chord. Hence Andrew Surmani (2004, p.&nbsp;72) states; "when three or more notes are sounded together, the combination is called a chord" and George T. Jones (1994, p.&nbsp;43) explains; "two tones sounding together are usually termed an ''interval'', while three or mores tones are called a ''chord''" while, according to Monath (1984, p.&nbsp;37); "A chord is a combination of three or more tones sounded simultaneously for which the distances (called intervals) between the tones are based on a particular formula."
=== Number of notes ===
One way of classifying chords is according to the number of distinct '''pitch classes''' used in their construction, a pitch class being identified by a degree of the scale (that is, a certain musical note, such as A, B, C, D, etc.) without regard to which octave it occurs in. Chords using three pitch classes are called '''[[Triad (music)|triads]]'''. Chords using four notes are known as [[tetrad]]s. Those using five are called [[pentad]]s, and those using six are [[hexad]]s. They are sometimes called [[trichord]]s, [[tetrachord]]s, [[pentachord]]s and [[hexachord]]s, however these terms more usually refer to contiguous pitch classes in some scale, usually spanning a [[perfect fourth]], and not generally played simultaneously.


Chords, however, are so well-established in Western music that sonorities of two pitches, or even single-note melodies, are commonly heard as "implying" chords, a [[psychoacoustic]] phenomenon resulting from a lifetime of exposure to the conventional harmonies of music so that the brain "completes" the chord.<ref> {{Cite journal | last = Schellenberg
Theorists differ as to whether chords consist of at least three pitches. Otto Karolyi ({{citequote}}, p.&nbsp;63), disagrees, writing that, "two or more notes sounded simultaneously are known as a chord. The vertical combination of three sounds: fundamental note, third and fifth, gives us a chord known as a triad." In contrast, Andrew Surmani (2004, p.&nbsp;72), writes that, "when three or more notes are sounded together, the combination is called a chord," and George T. Jones explains (1994, p.&nbsp;43) "two tones sounding together are usually termed an ''interval'', while three or mores tones are called a ''chord''." According to Monath (1984, p.&nbsp;37) "A chord is a combination of three or more tones sounded simultaneously for which the distances (called intervals) between the tones are based on a particular formula. (Two notes sounded simultaneously are not considered to be chords and are simply called intervals.)"
| first = E. Glenn | last2 = Bigand | first2 = Emmanuel | last3 = Poulin-Charronnat | first3 = Benedicte | last4 = Garnier | first4 = Cecilia | last5 = Stevens | first5 = Catherine | title = Children's implicit knowledge of harmony in Western music | journal = Developmental Science | volume = 8 | issue = 8 | pages = 551–566 | date = Nov. | year = 2005 | doi = 10.1111/j.1467-7687.2005.00447.x | pmid = 16246247}}</ref> Otto Karolyi<ref>Károlyi, Otto, ''Introducing Music''. England: Penguin Books., p.&nbsp;63</ref> writes that "two or more notes sounded simultaneously are known as a chord."


Two-note combinations, whether referred to as chords or intervals, are called ''[[dyad (music)|dyads]]''. Chords constructed of three notes of some underlying [[musical scale|scale]] are described as triads. They may be understood to be constructed from a stack of two [[third]] intervals. Chords of four notes are known as [[tetrad]]s, those containing five are called [[pentad]]s and those using six are [[hexad]]s. Sometimes the terms "[[trichord]]", "[[tetrachord]]", "[[pentachord]]" and "[[hexachord]]" are used, though these more usually refer to the pitch classes of any [[Scale (music)|scale]], not generally played simultaneously. Chords that may contain more than three chords include [[suspended chord]]s [[pedal point]] chords, '''dominant seventh''' chords and others termed [[extended chord]]s, [[added tone chord]]s, clusters and [[polychord]]s.
=== Type of interval ===
{{main|Interval (music)}}

Many chords can be arranged as a series whose elements are separated by [[interval (music)|intervals]] that are all roughly the same size. For example, a C major triad contains the notes C, E, and G. These notes can be arranged in the series C-E-G, in which the first interval (C-E) is a [[major third]], while the second interval (E-G) is a [[minor third]]. Any chord that can be arranged as a series of (major or minor) thirds is called a '''[[tertian]]''' chord. A chord such as C-D-E{{music|flat}} is a series of seconds, containing a [[major second]] (C-D) and a [[minor second]] (D-E{{music|flat}}). Such chords are called [[secundal]]. The chord C-F-B, which consists of a [[perfect fourth]] C-F and an augmented fourth ([[tritone]]) F-B is called [[quartal harmony|quartal]]. Most Western music uses [[tertian]] chords.

On closer examination, however, the terms "secundal", "tertian" and "quartal" can become ambiguous. The terms "second," "third," and "fourth" (and so on) are often understood relative to a scale, but it is not always clear which scale they refer to. For example, consider the pentatonic scale G-A-C-D-F. Relative to the pentatonic scale, the intervals G-C and C-F are "thirds," since there is one note between them. Relative to the chromatic scale, however, the intervals G-C and C-F are "fourths" since they are five semitones wide. For this reason the chord G-C-F might be described both as "tertian" and "quartal," depending on whether one is measuring intervals relative to the pentatonic or chromatic scales.

The use of [[Accidental (music)|accidentals]] complicates the picture. The chord B{{music|sharp}}-E-A{{music|flat}} is notated as a series of diminished fourths (B{{music|sharp}}-E) and (E-A{{music|flat}}). However, the chord is [[enharmonic equivalence|enharmonically equivalent]] to (and sonically indistinguishable from) C-E-G{{music|sharp}}, which is a series of [[major third]]s (C-E) and (E-G{{music|sharp}}). Notationally, then, B{{music|sharp}}-E-A{{music|flat}} is a "fourth chord," even though it sounds identical to the tertian chord C-E-G{{music|sharp}}. In some circumstances it is useful to talk about how a chord is notated, while in others it is useful to talk about how it sounds. Terms such as "tertian" and "quartal" can be used in either sense, and it is important to be clear about which is intended.


=== Scale degree ===
=== Scale degree ===
[[File:C Major scale (up and down).svg|412px|right|thumb|C major scale {{Audio|C major scale.mid|play}}]]
Chords are also distinguished and notated by the scale [[Degree (music)|degree]] of their [[root note]] or [[bass note]].
In the key of C major the first degree of thescale is the note C, so a C major chord, a triad built on the note C, may be called the ''one'' chord of that key and notated in Roman numerals as '''I'''. The same C major chord can be found in other scales: it forms chord '''III''' in the key of A minor ('''A'''-B-'''C''') and chord '''IV''' in the key of G major ('''G'''-A-B-'''C'''). This lets us see the job the chord is doing in the current key and tonality.


Many analysts use lower-case Roman numerals to indicate minor triads and upper-case for major ones, and "degree" and "plus" signs ('''<sup>o</sup>''' and '''<sup>+</sup>''') to indicate diminished and augmented triads respectively. Otherwise all the numerals are capital and the qualities of the chords are inferred from the scale degree. Chords outside the scale can be indicated by placing a flat/sharp sign before the chord — for example, the chord of E flat major in the key of C major is represented by {{music|flat}}III. The scale to whose scale degrees the Roman numerals refer may be indicated to the left (e.g. '''F{{music|sharp}}:'''), but may also be understood from the key signature or other contextual clues. Roman numerals are used primarily as analytical tools so indications of inversions or added tones may be omitted if they are not relevant to the analysis. [[Roman numeral]]s indicate the root of the chord as a [[scale degree]] within a particular major [[key (music)|key]] as follows:
For example, since the first scale degree of the C major scale is the note C, a triad built on top of the note C would be called the ''one'' chord, which might be notated 1, I, or even C, in which case the assumption would be made that the [[key signature]] of the particular piece of music in question would indicate to the musician what function a C major triad was fulfilling, and that any special role of the chord outside of its normal diatonic function would be inferred from the context.


When taking any major ([[Ionian mode|Ionian]]) scale and building a triad with a base in the scale, the second, third, and sixth intervals, when used as a root, will form a minor triad. The root, fourth, and fifth form a major triad, whereas the seventh will form a diminished triad. When in minor modes, building a triad upon the tonic, fourth and fifth degrees of the scale will result in a minor chord. Building upon scale degree two will result in a diminished chord, while building a triad upon scale degrees three, six and seven will yield major chords.

[[Roman numeral]]s indicate the root of the chord as a [[scale degree]] within a particular major [[key (music)|key]] as follows:
{| class="wikitable" style="margin:auto; text-align: center; width:85%"
{| class="wikitable" style="margin:auto; text-align: center; width:85%"
|'''Roman numeral''' || I || ii || iii || IV || V || vi || vii<sup>o</sup>/bVII
|'''Roman numeral''' || I || ii || iii || IV || V || vi || vii<sup>o</sup>/bVII
Line 60: Line 52:
|'''Scale degree''' || [[tonic (music)|tonic]] || [[supertonic]] || [[mediant]] || [[subdominant]] || [[dominant (music)|dominant]] || [[submediant]] || [[leading tone]]/[[subtonic]]
|'''Scale degree''' || [[tonic (music)|tonic]] || [[supertonic]] || [[mediant]] || [[subdominant]] || [[dominant (music)|dominant]] || [[submediant]] || [[leading tone]]/[[subtonic]]
|}
|}
Many analysts use lower-case Roman numerals to indicate minor triads and upper-case for major ones, with degree and plus signs ('''<sup>o</sup>''' and '''<sup>+</sup>''') to indicate diminished and augmented triads, respectively. When they are not used, all the numerals are capital, and the qualities of the chords are inferred from the other scale degrees that chord contains; for example, a chord built on '''VI''' in C major would contain the notes A, C, and E, and would therefore be a minor triad.
Chords that are not on the scale can be indicated by placing a flat/sharp sign before the chord — for example, the chord of E flat major in the key of C major is represented by {{music|flat}}III.

The scale to whose scale degrees the Roman numerals refer may be indicated to the left (e.g. '''F{{music|sharp}}:'''), but may also be understood from the key signature or other contextual clues.

Unlike pop chord symbols, which are used as a guide to players, Roman numerals are used primarily as analytical tools, and so indications of inversions or added tones are sometimes omitted if they are not relevant to the analysis being performed.


=== Inversion ===
=== Inversion ===
{{listen|filename=Chord-triad-C-major-inversions.ogg|title=Inverted triads|description=the first three chords played are C major root position, first inversion, second inversion.}}
{{Main article|Inversion (music)}}
{{Main article|Inversion (music)}}
[[Image:Frets, guitar neck, C-major chord.jpg|thumb|left|200px|Fingering a [[second inversion]] chord]]
When the bass is not the same as the root, the chord is [[Inversion (music)|inverted]].


A chord is said to be in root position when the root note is in the bass and the third and the fifth above it: it is marked in [[figured bass]] notation as '3/5'. When the bass is not the same as the root, the chord is said to be [[Inversion (music)|inverted]]. C major chord on a [[guitar]].]]But triads, having three constituent notes, can have three positions, two of which are [[inversion (music)|inversions]]. In the first inversion the third is in the bass, and above it are the fifth and the root. This creates an interval of a sixth and a third above the bass note and so is marked in a [[figured bass]] as '6/3', commonly abbreviated to 'I6' (or 'Ib') since the sixth is the characteristic interval of the inversion, and so always implies '6/3'. The second inversion has the fifth in the bass and above it the root and third. This creates an interval of a sixth and a fourth above the bass note, and so is marked as 'I6/4' or 'Ic'.
The number of inversions that a chord can have is one fewer than the number of constituent notes. Triads, for example, (having three constituent notes) can have three positions, two of which are [[inversion (music)|inversions]]:
* Root position
:The root note is in the bass, and above that are the third and the fifth. A triad built on the first scale degree, for example, is marked 'I'
* First inversion
:The third is in the bass, and above it are the fifth and the root. This creates an interval of a sixth and a third above the bass note, and so is marked in figured Roman notation as '6/3'. This is commonly abbreviated to 'I6' (or 'Ib') since the sixth is the characteristic interval of the inversion, and so always implies '6/3'.
* Second inversion
:The fifth is in the bass, and above it are the root and the third. This creates an interval of a sixth and a fourth above the bass note, and so is marked as 'I6/4' or 'Ic'. Second inversion is the most unstable chord position.


=== Intervals in chords ===
{{listen|filename=Chord-triad-C-major-inversions.ogg|title=Inverted triads|description=the first three chords played are C major root position, first inversion, second inversion.}}
{{main|Interval (music)}}

Many chords can be arranged as a series of ascending notes separated by [[interval (music)|intervals]] of roughly the same size. For example the C major triad's notes, C, E, and G, can be arranged in the series C-E-G, the first interval (C-E) being a [[major third]] and the second (E-G) a [[minor third]]. Any such chord that can be arranged as a series of (major or minor) thirds may be called a '''[[tertian]]''' chord. Most common chords are tertian.

A chord such as C-D-E{{music|flat}}, though, is a series of seconds, containing a [[major second]] (C-D) and a [[minor second]] (D-E{{music|flat}}). Such chords are called [[secundal]]. The chord C-F-B, which consists of a [[perfect fourth]] C-F and an augmented fourth ([[tritone]]) F-B is called [[quartal harmony|quartal]].

However all these terms can become ambiguous when dealing with non-diatonic scales such as the pentatonic or chromatic scales. The use of [[Accidental (music)|accidentals]] can also complicate the terminology. For example the chord B{{music|sharp}}-E-A{{music|flat}} appears to be a series of diminished fourths (B{{music|sharp}}-E) and (E-A{{music|flat}}) but is [[enharmonic equivalence|enharmonically equivalent]] to (and sonically indistinguishable from) the chord C-E-G{{music|sharp}}, which is a series of [[major third]]s (C-E) and (E-G{{music|sharp}}).


The important triads are described below:
== Types of chords ==
=== Tertian triads ===
Tertian triads can be described as a series of three notes. The first element is called the [[root note]] of the chord, the second note is called the "third" of the chord, and the last note is called the "fifth" of the chord. These are described below:


{| class="wikitable" style="text-align: center;"
{| class="wikitable" style="text-align: center;"
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|}
|}


== Seventh and extended chords ==
As an example, consider an [[octave]] of the C [[major scale]], consisting of the notes C D E F G A B C.
{{main|Seventh chord|Extended chord}}
Seventh chords are constructed by adding a fourth note to a triad, at the interval of a third above the fifth of the chord. This creates the interval of a seventh above the root of the chord, the next natural step in composing [[tertian]] chords. The seventh chord on the fifth step of the scale (the dominant seventh) is the only one available in the major scale: it contains all three notes of the diminished triad of the seventh and is frequently used as a stronger substitute for it.


There are various [[Seventh chord#Types of seventh chords|types of seventh chords]] depending on the quality of both the chord and the seventh added. In chord notation the chord type is sometimes superscripted and sometimes not (e.g. ''Dm7'', ''Dm<sup>7</sup>'', and ''D<sup>m7</sup>'' are all identical).
[[File:C Major scale (up and down).svg|512px|center|thumb|C major scale {{Audio|C major scale.mid|play}}]]

[[File:C major triad.png|50px|thumb|left|The C major triad consists of the notes C, E and G {{Audio|C major triad.mid|play}}]]
The major triad formed using the C note as the root would consist of C (the root note of the scale), E (the third note of the scale) and G (the fifth note of the scale). This triad is major because the interval from C to E is a [[major third]].
[[File:d minor triad.png|50px|thumb|right|The D minor triad consists of the notes D, F and A {{Audio|D minor triad.mid|play}}]]
Using the same scale (and thus, implicitly, the [[Key (music)|key]] of C major) a minor chord may be constructed using the D as the root note. This would be D (root), F (third note), A (fifth note).

Examination at the piano keyboard will reveal that there are four [[semitone]]s between the root and third of the chord on C, but only 3 semitones between the root and third of the chord on D (while the outer notes are still a perfect fifth apart). Thus the C triad is major while the D triad is minor.

A triad can be constructed on any note of the C major scale. These will all be either minor or major, with the exception of the triad on B, the [[leading-tone]] (the last note of the scale before returning to a C, in this case), which is diminished. For more detail see the article on the [[Music and mathematics#Mathematics of musical scales|mathematics of the Western music scale]].

=== Seventh chords ===
{{main|Seventh chord}}
Seventh chords may be thought of as the next natural step in composing [[tertian]] chords after triads. Seventh chords are constructed by adding a fourth note to a triad, at the interval of a third above the fifth of the chord. This creates the interval of a seventh above the root of the chord. The chords can be performed using equal tuning or any form of just tuning.

There are various [[Seventh chord#Types of seventh chords|types of seventh chords]] depending on the quality of the original chord and the quality of the seventh added. The chord quality indications are sometimes superscripted and sometimes not (e.g. ''Dm7'', ''Dm<sup>7</sup>'', and ''D<sup>m7</sup>'' are all identical).


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When a dominant seventh chord (a major minor seventh in its most common function) is borrowed from another key, the Roman numeral corresponding with that key is shown after a slash. For example, '''V/V''' indicates the ''[[dominant (music)|dominant]] of the dominant''. In the key of C major, where the dominant (V) chord is G major, this [[secondary dominant]] is the chord on the fifth degree of the G major scale, i.e. D major. Note that while the chord built on D ('''ii''') in the key of C major would normally be a minor chord, the '''V/V''' chord, also built on D, is major.
When a chord is analysed as "borrowed" from another key, it may be shown by the Roman numeral corresponding with that key after a slash so, for example, '''V/V''' indicates the [[dominant (music)|dominant]] chord of the dominant key of the present home-key. The dominant key of C major is G major so this [[secondary dominant]] will be the chord of the fifth degree of the G major scale, which is D major. If used, this chord will cause a [[modulation]].


'''Extended chords''' are triads with further tertian notes added beyond the seventh; the ninth, eleventh, and thirteenth chords. After the thirteenth any notes added in thirds will duplicate notes elsewhere in the chord: all seven notes of the scale are present in the chord and further added notes will not give new [[pitch class]]es. Such chords may be constructed only by using notes that lie outside the diatonic seven-note scale ''(See '''Altered chords''' below)''.
=== Extended chords ===
{{main|Extended chord}}
Extended chords are tertian chords (built from thirds) or triads with notes extended, or added, beyond the seventh. Thus ninth, eleventh, and thirteenth chords are extended chords. After the thirteenth, any notes added in thirds duplicate notes elsewhere in the chord, so there are no fifteenth chords, seventeenth chords, and so on in [[tonal]] music theory, though such chords may be constructed with up to all twelve unique tones (this would obviously imply that the chord lies outside the diatonic seven-note scale) and doublings; such a chord may be of arbitrarily large size, though large names such as "23rd chord" and "25th chord" are not particularly useful.


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Other extended chords follow the same rules as shown above, so that for example ''Maj9'', ''Maj11'' and ''Maj13'', shown above are with major sevenths rather than minor sevenths: similarly ''m9'', ''m11'' and ''m13'' will have minor thirds and minor sevenths.
Other extended chords follow the logic of the rules shown above.


== Altered chords ==
Thus ''Maj9'', ''Maj11'' and ''Maj13'' chords are the extended chords shown above with major sevenths rather than minor sevenths. Similarly, ''m9'', ''m11'' and ''m13'' have minor thirds and minor sevenths.
Although the third and seventh of the chord are always determined by the symbols shown above the fifth, ninth, eleventh and thirteenth may all be chromatically altered by [[Accidental (music)|accidentals]] (the root cannot be so altered without changing the name of the chord, while the third cannot be altered without altering the chord's quality). These are noted alongside the element to be altered. Accidentals are most often used in conjunction with dominant seventh chords. "Altered" dominant seventh chords (C<sup>7alt</sup>) may have a flat ninth, a sharp ninth, a diminished fifth or an augmented fifth (see Levine's ''Jazz Theory''). Some write this as C<sup>7+9</sup>, which assumes also the flat ninth, diminished fifth and augmented fifth (see Aebersold's ''Scale Syllabus''). The augmented ninth is often referred to in [[blues]] and [[jazz]] as a [[blue note]], being enharmonically equivalent to the flat third or tenth. When superscripted numerals are used the different numbers may be listed horizontally (as shown) or else vertically.

=== Chromatic alterations ===
Although the third and seventh of the chord are always determined by the symbols shown above, the fifth, as well as the extended intervals 9, 11, and 13, may be altered through the use of [[Accidental (music)|accidentals]]. These are indicated along with the corresponding number of the element to be altered.

Accidentals are most often used in conjunction with dominant seventh chords. For example:


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== Added tone chords ==
"Altered" dominant seventh chords (C<sup>7alt</sup>) have a flat ninth, a sharp ninth, a diminished fifth and an augmented fifth (see Levine's ''Jazz Theory''). Some write this as C<sup>7+9</sup>, which assumes also the flat ninth, diminished fifth and augmented fifth (see Aebersold's ''Scale Syllabus'').
{{main|Added tone chord}}
An added tone chord is a triad chord with an added, non-tertian note, such as the commonly added sixth as well as chords with an added second (ninth) or fourth (eleventh) or a combination of the three. These chords do not include "intervening" thirds as in an [[extended chord]]. Added chords can also have variations. Thus ''madd9'', ''m4'' and ''m6'' are minor triads with extended notes.


Added sixth chords can be considered as belonging to either of two separate groups; chords that contain a ''sixth'' chord member, i.e., a note separated by the interval of a sixth from the chord's root an inverted chords in which the interval of a sixth appears above the bass note when this is not the root.
The augmented ninth is often referred to as a [[blue note]], being enharmonically equivalent to the flatted third or tenth, and is used as such, particularly in [[blues]] and other [[jazz standard]]s.


The major sixth chord (also called, ''sixth'' or ''added sixth'' with chord notation: 6, e.g., 'C6') is by far the most common type of sixth chord of the first group. It comprises a major chord with the added [[major sixth]] above the root. For example, the chord C6 contains the notes C-E-G-A. The minor sixth chord (min 6 or m6, e.g., Cm6) is a minor chord with the same added note. For example, the chord Cmin6 contains the notes C-E{{music|flat}}-G-A. In chord notation, the sixth of either chord is always assumed to be a major sixth rather than a [[minor sixth]]. Minor versions exist and may be indicated in notation as, e.g., Cmin (min6), or Cmin (Aeolian). Such chords, however, are very rare due to the semitone clash between the sixth and fifth. The [[augmented sixth chord]] usually appears in chord notation as its enharmonic equivalent, the seventh chord. This chord contains two notes separated by the interval of an augmented sixth (or, by inversion, a diminished third, though this inversion is rare). The augmented sixth is generally used as a dissonant interval most commonly used in motion towards a dominant chord in root position (with the root doubled to create the octave to which the augmented sixth chord resolves) or to a tonic chord in second inversion (a tonic triad with the fifth doubled for the same purpose). In this case, the tonic note of the key is included in the chord, sometimes along with an optional fourth note, to create one of the following (illustrated here in the key of C major):
When superscripted numerals are used, the different numbers may be listed horizontally (as shown), or vertically.


* Italian augmented sixth: A{{music|flat}}, C, F{{music|sharp}}
=== Added tone chords ===
* French augmented sixth: A{{music|flat}}, C, D, F{{music|sharp}}
{{main|Added tone chord}}
* German augmented sixth: A{{music|flat}}, C, E{{music|flat}}, F{{music|sharp}}
An added tone chord is a traditional chord with an extra "added" note, such as the commonly added sixth (see following section). This includes chords with an added second (ninth) or fourth (eleventh), or a combination of the three. These chords do not include "intervening" thirds as in an [[extended chord]].

The augmented sixth family of chords exhibits certain peculiarities. Since they are not triad-based, as are seventh chords and other sixth chords, they are not generally regarded as having roots (nor, therefore, inversions), although one [[chord voicing|re-voicing]] of the notes is common (with the namesake interval inverted so as to create a diminished third).

The second group of sixth chords includes inverted major and minor chords, which may be called ''sixth'' chords in that the ''six-three'' (6/3)and ''six-four'' (6/4) chords contain intervals of a sixth with the bass note, though this is not the root. Nowadays this is mostly for academic study or analysis (see [[figured bass]]) but the [[Neapolitan sixth|neapolitan sixth chord]] is an important example; a major triad with a flat supertonic scale degree as its root that is called a "sixth" because it is almost always found in first inversion. Though a technically accurate Roman numeral analysis would be ♭II, it is generally labelled N<sup>6</sup>. In C major, the chord is notated (from root position) D{{music|flat}}, F, A{{music|flat}}. Because it uses chromatically [[altered tone]]s this chord is often grouped with the borrowed chords (''see below'') but the chord is not borrowed from the relative major or minor and it may appear in both major and minor keys.


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== Suspended chords ==
Added chords can also have variations. Thus ''madd9'', ''m4'' and ''m6'' are minor triads with extended notes.

=== Sixth chords ===
Sixth chords are chords that contain any of the various intervals of a sixth as a defining characteristic. They can be considered as belonging to either of two separate groups:

==== Group 1 ====
Chords that contain a ''sixth'' chord member, i.e., a note separated by the interval of a sixth from the chord's root, such as:

#The major sixth chord (also called, ''sixth'' or ''added sixth'' with chord notation: 6, e.g., 'C6')
#:This is by far the most common type of sixth chord of this group, and comprises a major chord plus a note forming the interval of a [[major sixth]] above the root. For example, the chord C6 contains the notes C-E-G-A.
#The minor sixth chord (with chord notation: min 6 or m6, e.g., Cm6)
#:This is a minor chord plus a note forming the interval of a major sixth above the root. For example, the chord Cmin6 contains the notes C-E{{music|flat}}-G-A
#:In chord notation, the sixth of either chord is always assumed to be a major sixth rather than a [[minor sixth]]. Minor versions exist, and in chord notation this is indicated as, e.g., Cmin (min6), or Cmin (aeolian). Such chords, however, are very rare, as the minor sixth chord member is considered an "[[avoid tone]]" due to the semitone clash between it and the chord's fifth.
#The [[augmented sixth chord]] (usually appearing in chord notation as an enharmonically equivalent seventh chord)
#:An augmented sixth chord is a chord which contains two notes that are separated by the interval of an augmented sixth (or, by inversion, a diminished third - though this inversion is rare in compositional practice). The augmented sixth is generally used as a dissonant interval which ''resolves'' by both notes moving outward to an octave.

In Western music, the most common use of augmented sixth chords is to resolve to a dominant chord in root position (that is, a dominant triad with the root doubled to create the octave to which the augmented sixth chord resolves), or to a tonic chord in second inversion (a tonic triad with the fifth doubled for the same purpose). In this case, the tonic note of the key is included in the chord, sometimes along with an optional fourth note, to create one of the following (illustrated here in the key of C major):
* Italian augmented sixth: A{{music|flat}}, C, F{{music|sharp}}
* French augmented sixth: A{{music|flat}}, C, D, F{{music|sharp}}
* German augmented sixth: A{{music|flat}}, C, E{{music|flat}}, F{{music|sharp}}

The augmented sixth family of chords exhibits certain peculiarities. Since they are not triad-based, as are seventh chords and other sixth chords, they are not generally regarded as having roots (nor, therefore, inversions), although one [[chord voicing|re-voicing]] of the notes is common (with the namesake interval inverted so as to create a diminished third).

==== Group 2 ====
Inverted chords, in which the interval of a sixth appears above the bass note rather than the root; inversions, traditionally, being so named from their characteristic interval of a sixth from the bass.

#Inverted major and minor chords
#:Inverted major and minor chords may be called ''sixth'' chords. More specifically, their first and second inversions may be called ''six-three'' (6/3)and ''six-four'' (6/4) chords respectively, to indicate the intervals that the upper notes form with the bass note. Nowadays, however, this is mostly done for purposes of academic study or analysis. (see [[figured bass]])
#The [[Neapolitan sixth|neapolitan sixth chord]]
#:This chord is a major triad with the lowered supertonic scale degree as its root. The chord is referred to as a "sixth" because it is almost always found in first inversion Though a technically accurate Roman numeral analysis would be ♭II, it is generally labelled N<sup>6</sup>. In C major, the chord is spelled (assuming root position) D{{music|flat}}, F, A{{music|flat}}.
#:Because it uses lowered [[altered tone]]s, this chord is often grouped with the borrowed chords. However, the chord is not borrowed from the parallel major or minor, and may appear in both major and minor keys.

=== Suspended chords ===
{{main|Suspended chord}}
{{main|Suspended chord}}
A '''suspended chord''', or "sus chord" (sometimes improperly called ''sustained chord''), is a chord in which the ''third'' has been displaced by either of its dissonant neighbouring notes, forming intervals of a major second or (more commonly) a perfect fourth with the root. This results in two distinct chord types: the ''suspended second'' (sus2) and the ''suspended fourth'' (sus4). The chords, '''C<sup>sus2</sup>''' and '''C<sup>sus4</sup>''', for example, consist of the notes ''C D G'' and ''C F G'', respectively. Extended versions are also possible, such as the ''seventh suspended fourth'', for example, which, with root ''C'', contains the notes ''C F G B{{music|flat}}'' and is notated as '''C7<sup>sus4</sup>''' {{Audio|7sus4 chord on C.mid|play}}. '''C<sup>sus4</sup>''' is sometimes written '''C<sup>sus</sup>''' since the sus4 is more common than the sus2.
A '''suspended chord''', or "sus chord" (sometimes wrongly thought to mean ''sustained chord''), is a chord in which the ''third'' is delayed by either of its dissonant neighbouring notes, forming intervals of a major second or (more commonly) a perfect fourth with the root. This results in two distinct chord types: the ''suspended second'' (sus2) and the ''suspended fourth'' (sus4). The chords, '''C<sup>sus2</sup>''' and '''C<sup>sus4</sup>''', for example, consist of the notes ''C D G'' and ''C F G'', respectively.


The name ''[[suspension (music)|suspended]]'' derives from an early [[voice leading]] technique developed during the [[common practice period]] of composition, in which an anticipated stepwise melodic progression to a harmonically stable note in any particular part (voice) was often momentarily delayed or ''suspended'' simply by extending the duration of the previous note. The resulting unexpected dissonance could then be all the more satisfyingly resolved by the eventual appearance of the displaced note.
The name ''[[suspension (music)|suspended]]'' derives from an early [[polyphonic]] technique developed during the [[common practice period]], in which a stepwise melodic progress to a harmonically stable note in any particular part was often momentarily delayed or ''suspended'' by extending the duration of the previous note. The resulting unexpected dissonance could then be all the more satisfyingly resolved by the eventual appearance of the displaced note. In traditional music theory the inclusion of the ''third'' in either chord would negate the suspension, so such chords would be called ''added ninth'' and ''added eleventh'' chords instead.


In modern usage, without regard to such considerations of voice leading, the term ''suspended'' is restricted to those chords involving the displacement of the ''third'' only, and the dissonant ''second'' or ''fourth'' no longer needs to be prepared from the previous chord. Neither is it now obligatory for the displaced note to make an appearance at all. However, in the majority of occurrences of suspended chords, the conventional stepwise resolution to the ''third'' is still observed.
In modern usage the term is restricted to the displacement of the ''third'' only and the dissonant ''second'' or ''fourth'' no longer needs to be held over ("prepared") from the previous chord. Neither is it now obligatory for the displaced note to make an appearance at all though in the majority of cases the conventional stepwise resolution to the ''third'' is still observed. In [[post-bop]] and [[modal jazz]] compositions and improvisations suspended seventh chords are often used in nontraditional ways: these often do not function as '''V''' chords, and do not resolve from the fourth to the third. The lack of resolution gives the chord an ambiguous, static quality. Indeed, the third is often played on top of a sus4 chord. A good example is the jazz standard, [[Maiden Voyage]].


Extended versions are also possible, such as the ''seventh suspended fourth'' which, with root ''C'', contains the notes ''C F G B{{music|flat}}'' and is notated as '''C7<sup>sus4</sup>''' {{Audio|7sus4 chord on C.mid|play}}. '''C<sup>sus4</sup>''' is sometimes written '''C<sup>sus</sup>''' since the sus4 is more common than the sus2.
Note that, in traditional music theory, the inclusion of the ''third'' in either the ''suspended second'' or ''suspended fourth'' chords negates the effect of suspension, and such chords are properly called ''added ninth'' and ''added eleventh'' chords rather than ''suspended'' chords.


== Borrowed chords ==
A notable exception to this analysis of suspended chords occurs in jazz theory. In [[post-bop]] and [[modal jazz]] compositions and improvisations, suspended seventh chords are often used in nontraditional ways. In these contexts, they often do not function as V chords, and do not resolve the fourth to the third; the lack of resolution gives the chord an ambiguous, static quality. Indeed, the third is often played on top of a sus4 chord; in jazz theory, this doesn't negate the quality of the chord as a suspended chord. A good example is the jazz standard, [[Maiden Voyage]].

=== Borrowed chords ===
{{main|Borrowed chord}}
{{main|Borrowed chord}}
Borrowed chords are chords taken for use from a [[parallel key|parallel minor or major]] key. If the root of the borrowed chord is not in the original key, then they are named by the accidental. For instance, in major, a chord built on the parallel minor's sixth degree is a "flat six chord", written {{music|flat}}VI. Borrowed chords are an example of [[mode mixture]].
Borrowed chords are taken from a [[parallel key|relative minor or major]] key. If the root of the borrowed chord is not in the original key, then it is named by the accidental it introduces. For instance, in a major tonality a chord built on the parallel minor's sixth degree is a "flat six chord", written {{music|flat}}VI. Borrowed chords are an example of [[mode mixture]].


If a chord is [[Borrowed chord|borrowed]] from the [[parallel key]], this is usually indicated directly (e.g. '''IV (minor)''') or explained in a footnote or accompanying text. If there is no mention of tonality upper case can be taken as the major and lower case as minor.
If a chord is borrowed from the [[parallel key]], this is usually indicated directly (e.g. '''IV (minor)''') or explained in a footnote or accompanying text. If there is no mention of tonality upper case can be taken as the major and lower case as minor.


== Progression and notation ==
=== Polychords ===
{{listen|filename=Satie_Sarabande_3_chord_sequence.ogg|title=Chord sequence|description=from [[Erik Satie]]'s ''Sarabande'' no. 3}}
[[Polychord]]s are two or more chords superimposed on top of one another. See also [[altered chord]], [[secundal|secundal chord]], [[Quartal and quintal harmony]] and [[Tristan chord]].
{{main|Chord progression|Chord notation}}

== Pop chord notation ==
{{main|Chord notation}}
Chords can be notated in abbreviated manner using '''pop chord symbols''', usually written above the given [[lyrics]] or [[musical staff|staff]]. Although these symbols are used occasionally in classical music as well, they are most common for [[lead sheet]]s and [[fake book]]s in [[jazz]] and other [[popular music]].
Chords can be notated in abbreviated manner using '''pop chord symbols''', usually written above the given [[lyrics]] or [[musical staff|staff]]. Although these symbols are used occasionally in classical music as well, they are most common for [[lead sheet]]s and [[fake book]]s in [[jazz]] and other [[popular music]].
Pop chord symbols are given under the '''Chord symbol''' column in the tables of this article.
Pop chord symbols are given under the '''Chord symbol''' column in the tables of this article.

== Chord sequence ==
{{main|Chord progression}}


Chords are commonly played in sequence, much as notes are played in sequence to form melodies. [[Chord sequence]]s can be conceptualised either in a simplistic way, in which the [[root note]]s of the chords play simple melodies while tension is created and relieved by increasing and decreasing dissonance, or full attention can be paid to each note in every chord, in which case chord sequences can be regarded as multi-part [[harmony]] of unlimited complexity.
Chords are commonly played in sequence, much as notes are played in sequence to form melodies. [[Chord sequence]]s can be conceptualised either in a simplistic way, in which the [[root note]]s of the chords play simple melodies while tension is created and relieved by increasing and decreasing dissonance, or full attention can be paid to each note in every chord, in which case chord sequences can be regarded as multi-part [[harmony]] of unlimited complexity.


According to Goldman (1965, p.&nbsp;26); "the sense of harmonic relation, change, or effect depends on ''speed'' (or tempo) as well as on the relative duration of single notes or triadic units. Both absolute time (measurable length and speed) and relative time (proportion and division) must at all times be taken into account in harmonic thinking or analysis."
{{listen|filename=Satie_Sarabande_3_chord_sequence.ogg|title=Chord sequence|description=from [[Erik Satie]]'s ''Sarabande'' no. 3}}

== Nonchord tones and dissonance ==
A [[nonchord tone]] is a [[Consonance and dissonance|dissonant]] or unstable tone which is not a part of the chord that is currently playing and in most cases quickly [[resolution (music)|resolves]] to a chord tone.

== Simultaneity ==
{{main|Simultaneity (music)}}
A chord is only the harmonic function of a group of notes, and it is unnecessary for all the notes to be played together. For example, [[broken chord]]s and [[arpeggio]]s are ways of playing notes in succession so that they form chords. One of the most familiar broken chord figures is [[Alberti bass]].

Since simultaneity is not a required feature of chords, there has been some academic discussion regarding the point at which a group of notes can be called a ''chord''. [[Jean-Jacques Nattiez]] (1990, p.&nbsp;218) explains that, "we can encounter 'pure chords' in a musical work," such as in the "Promenade" of [[Modest Mussorgsky]]'s ''[[Pictures at an Exhibition]]''.
[[File:Mussorgsky Pictures at an Exhibition, chords.PNG|400px|center|Mussorgsky's ''Pictures at an Exhibition'' "Promenade"|thumb]]

However, "often, we must go from a textual given to a more ''abstract'' representation of the chords being used," as in Claude Debussy's ''[[Arabesques (Debussy)|Première Arabesque]]''. The chords on the second stave shown here are abstracted from the notes in the actual piece, shown on the first. "For a sound configuration to be recognized as a chord, it must have a certain duration."
[[File:Debussy Premiere Arabesque melody and chords.PNG|400px|center|Upper stave: [[Claude Debussy]]'s ''[[Arabesques (Debussy)|Première Arabesque]]''|thumb]]

Goldman (1965, p.&nbsp;26) elaborates: "the sense of harmonic relation, change, or effect depends on ''speed'' (or tempo) as well as on the relative duration of single notes or triadic units. Both absolute time (measurable length and speed) and relative time (proportion and division) must at all times be taken into account in harmonic thinking or analysis."

== See also ==
== See also ==
* [[Chord notation]]
* [[Chord notation]]

Revision as of 19:41, 11 December 2009

Instruments playing different notes create chords.
This article describes pitch simultaneity and harmony in music. For other meanings of the word, see Chord.

A chord in music is any set of harmonically-related notes that is heard as if sounding simultaneously (a "harmonic simultaneity", see Simultaneity (music)). The most common chords are the major and minor, and then the augmented and diminished triads, types of chord that are sometimes referred to generically as the chord's "quality". Triads are so called because they consist of three distinct notes: further notes may be added to give extended chords and added tone chords. Chords are also commonly classed by their root note so, for instance, the chord C Major is a three-note chord of major quality built upon the note C. However, since the structural meaning of a chord depends exclusively upon the degree of the scale upon which it is built,[1] chords are usually analysed by numbering them, using Roman numerals, upwards from the key-note. A chord may also be classified by its inversion, the order in which its notes are stacked from lowest to highest.

A chord, then, is the harmonic or "vertical" function of any group of notes. These need not actually be played together: arpeggios and broken chord figures may for many practical and theoretical purposes be understood as chords. Polychords are formed by two or more chords superimposed. Often these may be analysed as extended chords but some examples lack the tertian sonority of triads (See: altered chord, secundal chord, quartal and quintal harmony and Tristan chord). A nonchord tone is a dissonant or unstable tone that lies outside the chord currently heard, though often resolving to a chord tone.

A succession of chords is called a chord progression. There are four common ways of notating or representing chords as such (Benward & Saker 2003, p. 77):- Roman numerals are commonly used in harmonic analysis to denote the step of the scale upon which the chord is built and its quality. Figured bass, much used in the Baroque era, added numbers to a written bass line to enable keyboard players to improvise chords with the right hand while playing the bass with their left. Macro symbols are a technique of modern musicology while various popular music symbols, such as chord charts for guitarists, can quickly lay out the harmonic groundplan of a piece so that the musician may improvise, "jam", "vamp", "busk" or "head arrange" a part.

C Major triad Play in just intonation Play in equal temperament Audio file "Lucy Tuning major chord on C.mid" not found Play in Quarter-comma meantone tuning Play in Young temperament Play in Pythagorean tuning

Definition and history

Mussorgsky's Pictures at an Exhibition "Promenade", a piece showing an explicit chord progression

The English word "chord" derives from "cord", a Middle English shortening of "accord" in the sense of "in tune with one another".

Since a chord may be understood as such even when all its notes are not simultaneously audible there has been some academic discussion regarding the point at which a group of notes can be called a chord. Jean-Jacques Nattiez (1990, p. 218) explains that "we can encounter 'pure chords' in a musical work," such as in the "Promenade" of Modest Mussorgsky's Pictures at an Exhibition but "often, we must go from a textual given to a more abstract representation of the chords being used" - as in Claude Debussy's Première Arabesque.

File:Debussy Premiere Arabesque melody and chords.PNG
Upper stave: Claude Debussy's Première Arabesque. Lower stave: implied chord progression.

The chords on the lower stave on the left are constructed from the notes in the actual piece, shown above. For a sound configuration to be recognized as a chord it must have a certain duration.

In the Middle Ages, Western harmony featured the perfect intervals of a fourth, a fifth, and an octave. In the 15th and 16th centuries, the major and minor triads became increasingly common, and were soon established as the default sonority for Western music. Such triads can be described as a series of three notes; the root note, the "third", and the "fifth" of the chord. As an example, the C major scale consists of the notes C D E F G A B C. The major triad formed using the C note as the root consists of C itself (the root note of the scale), E (the third note of the scale) and G (the fifth note of the scale). This triad is major because the interval from C to E, of four semitones, is a major third. Using the same scale a chord may be constructed using the D as the root note; D (root), F (third), A (fifth). While there were four semitones between the root and third of the chord on C there are here only 3 semitones between the root and third (the outer notes are still a perfect fifth apart). Thus, while the C triad is major, the D triad is minor. A triad can be constructed on any note of the C major scale and all will be minor or major, with the exception of the triad on the leading-tone which is diminished. Taking any other major scale (Ionian mode), the first, fourth and fifth intervals, when used as roots, form major triads. Similarly, as any major scale can also yield a relative minor, in any natural minor scale (Aeolian mode) minor triads are found on the tonic, fourth and fifth degrees of the scale. Each seven-note diatonic scale can provide three major and three minor chords, both sets of three standing in the same I-IV-V relationship to one another. The seventh degree of the major (degree two of the relative minor) will result in a diminished chord. See Music and mathematics#Mathematics of musical scales.

Four-note "seventh chords" were widely adopted from the 17th century. The harmony of many contemporary popular Western genres continues to be founded in the use of triads and seventh chords, though far from universally. Notable exceptions include: modern jazz (especially circa 1960), in which chords often include at least five notes, with seven (and occasionally more) being quite common; and atonal or post-tonal contemporary classical music (including the music of some film scores), whose chords can be far more complex, rooted in such disparate harmonic philosophies that traditional terms such as triad are rarely useful.

Chord characteristics

Every chord has certain characteristics, which include:

  • the number of pitch classes or chromas (distinct notes without respect to octave) that constitute the chord.
  • the scale degree of the root note
  • The position or inversion of the chord
  • the general type of intervals it contains: for example seconds, thirds, or fourths

Number of distinct notes

Chords may be classified according to the number of notes they contain. More precisely, since instances of any given note in different octaves may be taken as the same note for the purposes of analysis, it is better to speak of the number of distinct pitch classes or "chromas" used in their construction. Three such pitch classes are needed to define any common chord, therefore two notes sounded simultaneously is sometimes classed as an interval rather than a chord. Hence Andrew Surmani (2004, p. 72) states; "when three or more notes are sounded together, the combination is called a chord" and George T. Jones (1994, p. 43) explains; "two tones sounding together are usually termed an interval, while three or mores tones are called a chord" while, according to Monath (1984, p. 37); "A chord is a combination of three or more tones sounded simultaneously for which the distances (called intervals) between the tones are based on a particular formula."

Chords, however, are so well-established in Western music that sonorities of two pitches, or even single-note melodies, are commonly heard as "implying" chords, a psychoacoustic phenomenon resulting from a lifetime of exposure to the conventional harmonies of music so that the brain "completes" the chord.[2] Otto Karolyi[3] writes that "two or more notes sounded simultaneously are known as a chord."

Two-note combinations, whether referred to as chords or intervals, are called dyads. Chords constructed of three notes of some underlying scale are described as triads. They may be understood to be constructed from a stack of two third intervals. Chords of four notes are known as tetrads, those containing five are called pentads and those using six are hexads. Sometimes the terms "trichord", "tetrachord", "pentachord" and "hexachord" are used, though these more usually refer to the pitch classes of any scale, not generally played simultaneously. Chords that may contain more than three chords include suspended chords pedal point chords, dominant seventh chords and others termed extended chords, added tone chords, clusters and polychords.

Scale degree

C major scale play

In the key of C major the first degree of thescale is the note C, so a C major chord, a triad built on the note C, may be called the one chord of that key and notated in Roman numerals as I. The same C major chord can be found in other scales: it forms chord III in the key of A minor (A-B-C) and chord IV in the key of G major (G-A-B-C). This lets us see the job the chord is doing in the current key and tonality.

Many analysts use lower-case Roman numerals to indicate minor triads and upper-case for major ones, and "degree" and "plus" signs (o and +) to indicate diminished and augmented triads respectively. Otherwise all the numerals are capital and the qualities of the chords are inferred from the scale degree. Chords outside the scale can be indicated by placing a flat/sharp sign before the chord — for example, the chord of E flat major in the key of C major is represented by III. The scale to whose scale degrees the Roman numerals refer may be indicated to the left (e.g. F:), but may also be understood from the key signature or other contextual clues. Roman numerals are used primarily as analytical tools so indications of inversions or added tones may be omitted if they are not relevant to the analysis. Roman numerals indicate the root of the chord as a scale degree within a particular major key as follows:

Roman numeral I ii iii IV V vi viio/bVII
Scale degree tonic supertonic mediant subdominant dominant submediant leading tone/subtonic

Inversion

Fingering a second inversion chord

A chord is said to be in root position when the root note is in the bass and the third and the fifth above it: it is marked in figured bass notation as '3/5'. When the bass is not the same as the root, the chord is said to be inverted. C major chord on a guitar.]]But triads, having three constituent notes, can have three positions, two of which are inversions. In the first inversion the third is in the bass, and above it are the fifth and the root. This creates an interval of a sixth and a third above the bass note and so is marked in a figured bass as '6/3', commonly abbreviated to 'I6' (or 'Ib') since the sixth is the characteristic interval of the inversion, and so always implies '6/3'. The second inversion has the fifth in the bass and above it the root and third. This creates an interval of a sixth and a fourth above the bass note, and so is marked as 'I6/4' or 'Ic'.

Intervals in chords

Many chords can be arranged as a series of ascending notes separated by intervals of roughly the same size. For example the C major triad's notes, C, E, and G, can be arranged in the series C-E-G, the first interval (C-E) being a major third and the second (E-G) a minor third. Any such chord that can be arranged as a series of (major or minor) thirds may be called a tertian chord. Most common chords are tertian.

A chord such as C-D-E, though, is a series of seconds, containing a major second (C-D) and a minor second (D-E). Such chords are called secundal. The chord C-F-B, which consists of a perfect fourth C-F and an augmented fourth (tritone) F-B is called quartal.

However all these terms can become ambiguous when dealing with non-diatonic scales such as the pentatonic or chromatic scales. The use of accidentals can also complicate the terminology. For example the chord B-E-A appears to be a series of diminished fourths (B-E) and (E-A) but is enharmonically equivalent to (and sonically indistinguishable from) the chord C-E-G, which is a series of major thirds (C-E) and (E-G).

The important triads are described below:

Chord name Component intervals Example Chord symbol Audio
major triad major third perfect fifth C-E-G C, CM, Cma, Cmaj, CΔ play
minor triad minor third perfect fifth C-E-G Cm, Cmi, Cmin, C- play
augmented triad major third augmented fifth C-E-G C+, C+, Caug play
diminished triad minor third diminished fifth C-E-G Cm(5), Cº, Cdim, C play

Seventh and extended chords

Seventh chords are constructed by adding a fourth note to a triad, at the interval of a third above the fifth of the chord. This creates the interval of a seventh above the root of the chord, the next natural step in composing tertian chords. The seventh chord on the fifth step of the scale (the dominant seventh) is the only one available in the major scale: it contains all three notes of the diminished triad of the seventh and is frequently used as a stronger substitute for it.

There are various types of seventh chords depending on the quality of both the chord and the seventh added. In chord notation the chord type is sometimes superscripted and sometimes not (e.g. Dm7, Dm7, and Dm7 are all identical).

Chord name Component notes (intervals) Chord symbol Example (C root) Audio
diminished seventh minor third diminished fifth diminished seventh Co7, Cdim7 C E G Bdouble flat Play
half-diminished seventh minor third diminished fifth minor seventh Cø7, Cm75, C-7(5) C E G B Play
minor seventh minor third perfect fifth minor seventh Cm7, C−7, C−7 C E G B Play
minor major seventh minor third perfect fifth major seventh Cm(Maj7), C−(j7), Cm7, C−Δ7, C−maj7 C E G B Play
dominant seventh major third perfect fifth minor seventh C7, C7, Cdom7 C E G B Play
major seventh major third perfect fifth major seventh CMaj7, CM7, CΔ7, Cj7, C+7 C E G B Play
augmented seventh major third augmented fifth minor seventh C+7, C7+, C7+5, C75 C E G B Play
augmented major seventh major third augmented fifth major seventh C+(Maj7), CMaj7+5, CMaj75, C+j7, CΔ+7 C E G B Play

When a chord is analysed as "borrowed" from another key, it may be shown by the Roman numeral corresponding with that key after a slash so, for example, V/V indicates the dominant chord of the dominant key of the present home-key. The dominant key of C major is G major so this secondary dominant will be the chord of the fifth degree of the G major scale, which is D major. If used, this chord will cause a modulation.

Extended chords are triads with further tertian notes added beyond the seventh; the ninth, eleventh, and thirteenth chords. After the thirteenth any notes added in thirds will duplicate notes elsewhere in the chord: all seven notes of the scale are present in the chord and further added notes will not give new pitch classes. Such chords may be constructed only by using notes that lie outside the diatonic seven-note scale (See Altered chords below).

Chord name Component notes (chord and interval) Chord symbol Audio
Dominant ninth dominant seventh major ninth - - C9 Play
Dominant eleventh dominant seventh
the third is usually omitted
major ninth perfect eleventh - C11 Play
Dominant thirteenth dominant seventh
the eleventh is usually omitted
major ninth perfect eleventh major thirteenth C13 Play

Other extended chords follow the same rules as shown above, so that for example Maj9, Maj11 and Maj13, shown above are with major sevenths rather than minor sevenths: similarly m9, m11 and m13 will have minor thirds and minor sevenths.

Altered chords

Although the third and seventh of the chord are always determined by the symbols shown above the fifth, ninth, eleventh and thirteenth may all be chromatically altered by accidentals (the root cannot be so altered without changing the name of the chord, while the third cannot be altered without altering the chord's quality). These are noted alongside the element to be altered. Accidentals are most often used in conjunction with dominant seventh chords. "Altered" dominant seventh chords (C7alt) may have a flat ninth, a sharp ninth, a diminished fifth or an augmented fifth (see Levine's Jazz Theory). Some write this as C7+9, which assumes also the flat ninth, diminished fifth and augmented fifth (see Aebersold's Scale Syllabus). The augmented ninth is often referred to in blues and jazz as a blue note, being enharmonically equivalent to the flat third or tenth. When superscripted numerals are used the different numbers may be listed horizontally (as shown) or else vertically.

Chord name Component notes Chord symbol Audio
Seventh augmented fifth dominant seventh augmented fifth C7+5, C75 Play
Seventh flat nine dominant seventh minor ninth C7-9, C79 Play
Seventh sharp nine dominant seventh augmented ninth C7+9, C79 Play
Seventh augmented eleventh dominant seventh augmented eleventh C7+11, C711 Play
Seventh flat thirteenth dominant seventh minor thirteenth C7-13, C713 Play
Half-diminished seventh minor seventh diminished fifth Cø, Cm75 Play

Added tone chords

An added tone chord is a triad chord with an added, non-tertian note, such as the commonly added sixth as well as chords with an added second (ninth) or fourth (eleventh) or a combination of the three. These chords do not include "intervening" thirds as in an extended chord. Added chords can also have variations. Thus madd9, m4 and m6 are minor triads with extended notes.

Added sixth chords can be considered as belonging to either of two separate groups; chords that contain a sixth chord member, i.e., a note separated by the interval of a sixth from the chord's root an inverted chords in which the interval of a sixth appears above the bass note when this is not the root.

The major sixth chord (also called, sixth or added sixth with chord notation: 6, e.g., 'C6') is by far the most common type of sixth chord of the first group. It comprises a major chord with the added major sixth above the root. For example, the chord C6 contains the notes C-E-G-A. The minor sixth chord (min 6 or m6, e.g., Cm6) is a minor chord with the same added note. For example, the chord Cmin6 contains the notes C-E-G-A. In chord notation, the sixth of either chord is always assumed to be a major sixth rather than a minor sixth. Minor versions exist and may be indicated in notation as, e.g., Cmin (min6), or Cmin (Aeolian). Such chords, however, are very rare due to the semitone clash between the sixth and fifth. The augmented sixth chord usually appears in chord notation as its enharmonic equivalent, the seventh chord. This chord contains two notes separated by the interval of an augmented sixth (or, by inversion, a diminished third, though this inversion is rare). The augmented sixth is generally used as a dissonant interval most commonly used in motion towards a dominant chord in root position (with the root doubled to create the octave to which the augmented sixth chord resolves) or to a tonic chord in second inversion (a tonic triad with the fifth doubled for the same purpose). In this case, the tonic note of the key is included in the chord, sometimes along with an optional fourth note, to create one of the following (illustrated here in the key of C major):

  • Italian augmented sixth: A, C, F
  • French augmented sixth: A, C, D, F
  • German augmented sixth: A, C, E, F

The augmented sixth family of chords exhibits certain peculiarities. Since they are not triad-based, as are seventh chords and other sixth chords, they are not generally regarded as having roots (nor, therefore, inversions), although one re-voicing of the notes is common (with the namesake interval inverted so as to create a diminished third).

The second group of sixth chords includes inverted major and minor chords, which may be called sixth chords in that the six-three (6/3)and six-four (6/4) chords contain intervals of a sixth with the bass note, though this is not the root. Nowadays this is mostly for academic study or analysis (see figured bass) but the neapolitan sixth chord is an important example; a major triad with a flat supertonic scale degree as its root that is called a "sixth" because it is almost always found in first inversion. Though a technically accurate Roman numeral analysis would be ♭II, it is generally labelled N6. In C major, the chord is notated (from root position) D, F, A. Because it uses chromatically altered tones this chord is often grouped with the borrowed chords (see below) but the chord is not borrowed from the relative major or minor and it may appear in both major and minor keys.

Chord name Component notes (chord and interval) Chord symbol Audio
Add nine major triad major ninth - C2, Cadd9 Play
Major 4th major triad perfect fourth - C4, Cadd11 Play
Major sixth major triad major sixth - C6 Play
Six-nine major triad major sixth major ninth C6/9

Suspended chords

A suspended chord, or "sus chord" (sometimes wrongly thought to mean sustained chord), is a chord in which the third is delayed by either of its dissonant neighbouring notes, forming intervals of a major second or (more commonly) a perfect fourth with the root. This results in two distinct chord types: the suspended second (sus2) and the suspended fourth (sus4). The chords, Csus2 and Csus4, for example, consist of the notes C D G and C F G, respectively.

The name suspended derives from an early polyphonic technique developed during the common practice period, in which a stepwise melodic progress to a harmonically stable note in any particular part was often momentarily delayed or suspended by extending the duration of the previous note. The resulting unexpected dissonance could then be all the more satisfyingly resolved by the eventual appearance of the displaced note. In traditional music theory the inclusion of the third in either chord would negate the suspension, so such chords would be called added ninth and added eleventh chords instead.

In modern usage the term is restricted to the displacement of the third only and the dissonant second or fourth no longer needs to be held over ("prepared") from the previous chord. Neither is it now obligatory for the displaced note to make an appearance at all though in the majority of cases the conventional stepwise resolution to the third is still observed. In post-bop and modal jazz compositions and improvisations suspended seventh chords are often used in nontraditional ways: these often do not function as V chords, and do not resolve from the fourth to the third. The lack of resolution gives the chord an ambiguous, static quality. Indeed, the third is often played on top of a sus4 chord. A good example is the jazz standard, Maiden Voyage.

Extended versions are also possible, such as the seventh suspended fourth which, with root C, contains the notes C F G B and is notated as C7sus4 play. Csus4 is sometimes written Csus since the sus4 is more common than the sus2.

Borrowed chords

Borrowed chords are taken from a relative minor or major key. If the root of the borrowed chord is not in the original key, then it is named by the accidental it introduces. For instance, in a major tonality a chord built on the parallel minor's sixth degree is a "flat six chord", written VI. Borrowed chords are an example of mode mixture.

If a chord is borrowed from the parallel key, this is usually indicated directly (e.g. IV (minor)) or explained in a footnote or accompanying text. If there is no mention of tonality upper case can be taken as the major and lower case as minor.

Progression and notation

Chords can be notated in abbreviated manner using pop chord symbols, usually written above the given lyrics or staff. Although these symbols are used occasionally in classical music as well, they are most common for lead sheets and fake books in jazz and other popular music. Pop chord symbols are given under the Chord symbol column in the tables of this article.

Chords are commonly played in sequence, much as notes are played in sequence to form melodies. Chord sequences can be conceptualised either in a simplistic way, in which the root notes of the chords play simple melodies while tension is created and relieved by increasing and decreasing dissonance, or full attention can be paid to each note in every chord, in which case chord sequences can be regarded as multi-part harmony of unlimited complexity.

According to Goldman (1965, p. 26); "the sense of harmonic relation, change, or effect depends on speed (or tempo) as well as on the relative duration of single notes or triadic units. Both absolute time (measurable length and speed) and relative time (proportion and division) must at all times be taken into account in harmonic thinking or analysis."

See also

References

  1. ^ Arnold Schoenberg, Structural Functions of Harmony, Faber and Faber, 1983, p.1-2.
  2. ^ Schellenberg, E. Glenn; Bigand, Emmanuel; Poulin-Charronnat, Benedicte; Garnier, Cecilia; Stevens, Catherine (Nov.). "Children's implicit knowledge of harmony in Western music". Developmental Science. 8 (8): 551–566. doi:10.1111/j.1467-7687.2005.00447.x. PMID 16246247. {{cite journal}}: Check date values in: |date= and |year= / |date= mismatch (help)
  3. ^ Károlyi, Otto, Introducing Music. England: Penguin Books., p. 63
  • Grout, Donald Jay (1960). A History Of Western Music. Norton Publishing.
  • Benward & Saker (2003). Music: In Theory and Practice, Vol. I. Seventh Edition. ISBN 978-0-07-294262-0.
  • Dahlhaus, Carl. Gjerdingen, Robert O. trans. (1990). Studies in the Origin of Harmonic Tonality, p. 67. Princeton University Press. ISBN 0-691-09135-8.
  • Goldman (1965). Cited in Nattiez (1990).
  • Jones, George T. (1994). HarperCollins College Outline Music Theory. ISBN 0-06-467168-2.
  • Károlyi, Otto (). Introducing Music. England: Penguin Books.
  • Nattiez, Jean-Jacques (1990). Music and Discourse: Toward a Semiology of Music (Musicologie générale et sémiologue, 1987). Translated by Carolyn Abbate (1990). ISBN 0-691-02714-5.
  • Norman Monath, Norman (1984). How To Play Popular Piano In 10 Easy Lessons. Fireside Books. ISBN 0-671-53067-4.
  • Stanley Sadie and John Tyrrell, eds. (2001). The New Grove Dictionary of Music and Musicians. ISBN 1-56159-239-0.
  • Surmani, Andrew (2004). Essentials of Music Theory: A Complete Self-Study Course for All Musicians. ISBN 0-7390-3635-1.

Further reading

  • Schejtman, Rod (2008). Music Fundamentals. The Piano Encyclopedia. ISBN 978-987-25216-2-2.
  • Persichetti, Vincent (1961). Twentieth-century Harmony: Creative Aspects and Practice. New York: W. W. Norton. ISBN 0-393-09539-8. OCLC 398434.
  • Benward, Bruce & Saker, Marilyn (2002). Music in Theory and Practice, Volumes I & II (7th ed.). New York: McGraw Hill. ISBN 0-07-294262-2.
  • Piston, Walter (1987). Harmony (5th ed.). New York: W.W. Norton & Company. ISBN 0-393-95480-3.

External links