- This article describes pitch simultaneity and harmony in music. For other meanings of the word, see Chord.
A chord, in music, is any harmonic set of three or more notes that is heard as if sounding simultaneously. These need not actually be played together: arpeggios and broken chords may, for many practical and theoretical purposes, constitute chords. Chords and sequences of chords are frequently used in modern Western, West African and Oceanian music, whereas they are absent from the music of many other parts of the world.
The most frequently encountered chords are triads, so called because they consist of three distinct notes: further notes may be added to give seventh chords, extended chords, or added tone chords. The most common chords are the major and minor triads and then the augmented and diminished triads. The descriptions major, minor, augmented, and diminished are sometimes referred to collectively as chordal quality. Chords are also commonly classed by their root note—so, for instance, the chord C major may be described as a triad of major quality built upon the note C. Chords may also be classified by inversion, the order in which the notes are stacked.
A series of chords is called a chord progression. Although any chord may in principle be followed by any other chord, certain patterns of chords have been accepted as establishing key in common-practice harmony. To describe this, chords are numbered, using Roman numerals, upwards from the key-note (See diatonic function). Common ways of notating or representing chords in western music other than conventional staff notation include Roman numerals, figured bass (much used in the Baroque era), macro symbols (sometimes used in modern musicology), and various systems of chord charts typically found in the lead sheets used in popular music to lay out the sequence of chords so that the musician may play accompaniment chords or improvise a solo.
- 1 Definition and history
- 2 Notation
- 3 Characteristics
- 4 Triads
- 5 Seventh chords
- 6 Extended chords
- 7 Altered chords
- 8 Added tone chords
- 9 Suspended chords
- 10 Borrowed chords
- 11 References
- 12 Sources
- 13 Further reading
- 14 External links
Definition and history
The English word chord derives from Middle English cord, a shortening of accord in the original sense of agreement and later, harmonious sound. A sequence of chords is known as a chord progression or harmonic progression. These are frequently used in Western music. A chord progression "aims for a definite goal" of establishing (or contradicting) a tonality founded on a key, root or tonic chord. The study of harmony involves chords and chord progressions, and the principles of connection that govern them.
interval, while three or mores tones are called a chord." According to Monath (1984, p. 37); "A chord is a combination of three or more tones sounded simultaneously," and the distances between the tones are called intervals. However sonorities of two pitches, or even single-note melodies, are commonly heard as implying chords.
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 may be called a chord. 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.
The Baroque period, the 17th and 18th centuries, began to feature the major and minor scale based tonal system and harmony, including chord progressions and circle progressions. It was in the Baroque period that the accompaniment of melodies with chords was developed, as in figured bass, and the familiar cadences (perfect authentic, etc.). In the Renaissance, certain dissonant sonorities that suggest the dominant seventh occurred with frequency. In the Baroque period the dominant seventh proper was introduced, and was in constant use in the Classical and Romantic periods. The leading-tone seventh appeared in the Baroque period and remains in use. Composers began to use nondominant seventh chords in the Baroque period. They became frequent in the Classical period, gave way to altered dominants in the Romantic period, and underwent a resurgence in the Post-Romantic and Impressionistic period.
The Romantic period, the 19th century, featured increased chromaticism. Composers began to use secondary dominants in the Baroque, and they became common in the Romantic period. Many contemporary popular Western genres continue to rely on simple diatonic harmony, though far from universally: notable exceptions include the music of film scores, which often use chromatic, atonal or post-tonal harmony, and modern jazz (especially circa 1960), in which chords may include up to seven notes (and occasionally more).
Triads consist of three notes; the root or first note, the third, and the fifth. For example the C major scale consists of the notes C D E F G A B: a triad can be constructed on any note of such a major scale, and all are minor or major except the triad on the seventh or leading-tone, which is a diminished chord. A triad formed using the note C itself consists of C (the root note), E (the third note of the scale) and G (the fifth note of the scale). The interval from C to E is of four semitones, a major third, and so this triad is called C Major. A triad formed upon the same scale but with D as the root note, D (root), F (third), A (fifth), on the other hand, has only three semitones between the root and third and is called D minor, a minor triad.
Chords can be represented in various ways. The most common notation systems are:
- Plain staff notation, used in classical music (see figure).
- Roman numerals, commonly used in harmonic analysis to denote the scale step on which the chord is built. See: Roman numeral analysis.
- Figured bass, much used in the Baroque era, uses numbers added to a bass line written on staff (music), to enable keyboard players to improvise chords with the right hand while playing the bass with their left.
- Macro symbols, sometimes used in modern musicology, to denote chord root and quality.
- Various chord names and symbols used in popular music lead sheets, fake books, and chord charts, to quickly lay out the harmonic groundplan of a piece so that the musician may improvise, jam, or vamp on it.
While scale degrees are typically represented with Arabic numerals, the triads that have these degrees as their roots are often identified by Roman numerals. In some conventions (as in this and related articles) upper-case Roman numerals indicate major triads while lower-case Roman numerals indicate minor triads: other writers, (e.g. Schoenberg) use upper case Roman numerals for both major and minor triads. Some writers use upper-case Roman numerals to indicate the chord is diatonic in the major scale, and lower-case Roman numerals to indicate that the chord is diatonic in the minor scale. Diminished triads may be represented by lower-case Roman numerals with a degree symbol. Roman numerals can also be used in stringed instrument notation to indicate the position or string to play.
Figured bass notation
Figured bass or thoroughbass is a kind of musical notation used in almost all Baroque music, though rarely in modern music, to indicate harmonies in relation to a conventionally written bass line. Figured bass is closely associated with basso continuo accompaniment. Added numbers and accidentals beneath the staff indicate at the intervals to play, the numbers stand for the number of scale steps above the written note to play the figured notes.
In the illustration the bass note is a C, and the numbers 4 and 6 indicate that notes a fourth and a sixth above, that is F and A, should be played, giving the second inversion of the F major triad.
Macro analysis uses upper-case and lower-case letters to indicate the roots of chords, followed by symbols that specify the chord quality.
- The root note (e.g. C).
- The chord quality (e.g. major, maj, or M).
- The number of an interval (e.g. seventh, or 7), or less often its full name or symbol (e.g. major seventh, maj7, or M7).
- The altered fifth (e.g. sharp five, or ♯5).
- An additional interval number (e.g. add 13 or add13), in added tone chords.
For instance, the name C augmented seventh, and the corresponding symbol Caug7, or C+7, are both composed of parts 1, 2, and 3.
None of these parts, except for the root, directly refer to the notes forming the chord, but to the intervals they form with respect to the root. For instance, Caug7 is formed by the notes C-E-G♯-B♭. However, its name and symbol refer only to the root note C, the augmented (fifth) interval from C to G♯, and the (minor) seventh interval from C to B♭. The interval from C to E (a major third) sets the chord quality (major). A set of decoding rules is applied to deduce the missing information.
Some of the symbols used for chord quality are similar to those used for interval quality:
- m, or min for minor,
- M, maj, or no symbol (see rule 2 below) for major,
- aug for augmented,
- dim for diminished.
In addition, however,
- Δ is sometimes used for major, instead of the standard M, or maj,
- − is sometimes used for minor, instead of the standard m or min,
- +, or aug, is used for augmented (A is not used),
- o, °, dim, is used for diminished (d is not used),
- ø, or Ø is used for half diminished,
- dom is used for dominant.
Every chord has certain characteristics, which include:
- Number of pitch classes (distinct notes without respect to octave) that constitute the chord.
- Scale degree of the root note
- Position or inversion of the chord
- General type of intervals it appears constructed from—for example seconds, thirds, or fourths
- Counts of each pitch class as occur between all combinations of notes the chord contains
Number of notes
|Number of notes||Name||Alternate name|
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. 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 notes include pedal point chords, dominant seventh chords, extended chords, added tone chords, clusters, and polychords.
Polychords are formed by two or more chords superimposed. Often these may be analysed as extended chords (See: tertian, altered chord, secundal chord, quartal and quintal harmony and Tristan chord). For example G7(♯11♭9) (G-B-D-F-A♭-C♯) is formed from G major (G-B-D) and D♭ major (D♭-F-A♭). A nonchord tone is a dissonant or unstable tone that lies outside the chord currently heard, though often resolving to a chord tone.
|Roman numeral||Scale degree|
|viio / ♭VII||leading tone / subtonic|
In the key of C major the first degree of the scale, called the tonic, is the note C itself, 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 numbering lets us see the job a 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 may be upper-case and the qualities of the chords 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 tonic of the scale may be indicated to the left (e.g. F♯:) or may be understood from a key signature or other contextual clues. 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:
In the harmony of Western art music a chord is in root position when the tonic note is the lowest in the chord, and the other notes are above it. When the lowest note is not the tonic, the chord is inverted. Chords, having many constituent notes, can have many different inverted positions as shown below for the C major chord:
|Bass note||Position||Order of notes||Notation|
|C||root position||C E G||
3 as G is a 5th above C and E is a 3rd above C
|E||1st inversion||E G C||
3 as C is a 6th above E and G is a 3rd above E
|G||2nd inversion||G C E||
4 as E is a 6th above G and C is a 4th above G
Further, a four-note chord can be inverted to four different positions by the same method as triadic inversion. Where guitar chords are concerned the term "inversion" is used slightly differently; to refer to stock fingering "shapes".
Secundal, tertian, and quartal chords
|Secundal||2nd's : major 2nd, minor 2nd|
|Tertian||3rd's : major 3rd, minor 3rd|
|Quartal||4th's : perfect 4th, augmented 4th|
Many chords are a sequence of ascending notes separated by intervals of roughly the same size. Chords can be classified into different categories by this size:
- Tertian chords can be decomposed into a series of (major or minor) thirds. For example, the C major triad (C-E-G) is defined by a sequence of two intervals, the first (C-E) being a major third and the second (E-G) being a minor third. Most common chords are tertian.
- Secundal chords can be decomposed into a series of (major or minor) seconds. For example, the chord C-D-E♭ is a series of seconds, containing a major second (C-D) and a minor second (D-E♭).
- Quartal chords can be decomposed into a series of (perfect or augmented) fourths. Quartal harmony normally works with a combination of perfect and augmented fourths. Diminished fourths are enharmonically equivalent to major thirds, so they are uncommon. For example, the chord C-F-B is a series of fourths, containing a perfect fourth (C-F) and an augmented fourth/tritone (F-B).
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 notes of a chord form intervals with each of the other notes of the chord in combination. A 3-note chord has 3 of these harmonic intervals, a 4-note chord has 6, a 5-note chord has 10, a 6-note chord has 15. The absence, presence, and placement of certain key intervals plays a large part in the sound of the chord, and sometimes of the selection of the chord that follows.
A chord containing tritones is called tritonic; one without tritones is atritonic. Harmonic tritones are an important part of Dominant seventh chords, giving their sound a characteristic tension, and making the tritone interval likely to move in certain stereotypical ways to the following chord.
A chord containing semitones, whether appearing as Minor seconds or Major sevenths, is called hemitonic; one without semitones is anhemitonic. Harmonic semitones are an important part of Major seventh chords, giving their sound a characteristic high tension, and making the harmonic semitone likely to move in certain stereotypical ways to the following chord. A chord containing Major sevenths but no Minor seconds is much less harsh in sound than one containing Minor seconds as well.
Other chords of interest might include the
- Diminished chord, which has many Minor thirds and no Major thirds, many Tritones but no Perfect fifths
- Augmented chord, which has many Major thirds and no Minor thirds or Perfect fifths
- Dominant seventh flat five chord, which has many Major thirds and Tritones and no Minor thirds or Perfect fifths
Triads, also called triadic chords, are tertian chords (see above) with three notes. The four basic triads are described below.
|Component intervals||Chord symbol||Notes||Audio|
|Major triad||major||perfect||C, CM, Cmaj, CΔ, Cma||C E G||play|
|Minor triad||minor||perfect||Cm, Cmin, C-, Cmi||C E♭ G|
|Augmented triad||major||augmented||Caug, C+, C+||C E G♯|
|Diminished triad||minor||diminished||Cdim, Co, Cm(♭5)||C E♭ G♭|
Seventh chords are tertian chords (see above), 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).
|Component intervals||Chord symbol||Notes||Audio|
|Diminished seventh||minor||diminished||diminished||Co7, Cdim7||C E♭ G♭ B|
|Half-diminished seventh||minor||diminished||minor||Cø7, Cm7♭5, C−7(♭5)||C E♭ G♭ B♭|
|Minor seventh||minor||perfect||minor||Cm7, Cmin7, C−7, C−7||C E♭ G B♭|
|Minor major seventh||minor||perfect||major||Cm(M7), Cm maj7, C−(j7), C−Δ7, C−M7||C E♭ G B|
|Dominant seventh||major||perfect||minor||C7, C7, Cdom7||C E G B♭|
|Major seventh||major||perfect||major||CM7, Cmaj7, CΔ7, CΔ7, CΔ7, Cj7||C E G B|
|Augmented seventh||major||augmented||minor||C+7, Caug7, C7+, C7+5, C7♯5||C E G♯ B♭|
|Augmented major seventh||major||augmented||major||C+(M7), CM7+5, CM7♯5, C+j7, C+Δ7||C E G♯ B|
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 duplicate notes elsewhere in the chord. All seven notes of the scale are present in the chord and adding more notes does not add new pitch classes. Such chords may be constructed only by using notes that lie outside the diatonic seven-note scale (See #Altered chords below).
|Dominant ninth||dominant seventh||major ninth||-||-||C9||C E G B♭ D|
(the third is usually omitted)
|major ninth||eleventh||-||C11||C E G B♭ D F|
|Dominant thirteenth||dominant seventh||major ninth||
|major thirteenth||C13||C E G B♭ D F A|
Other extended chords follow similar rules, so that for example maj9, maj11, and maj13 contain major seventh chords rather than dominant seventh chords, while min9, min11, and min13 contain minor seventh 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 altered element. Accidentals are most often used 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.
|Seventh augmented fifth||dominant seventh||augmented fifth||C7+5, C7♯5|
|Seventh flat ninth||dominant seventh||minor ninth||C7-9, C7♭9|
|Seventh sharp ninth||dominant seventh||augmented ninth||C7+9, C7♯9|
|Seventh augmented eleventh||dominant seventh||augmented eleventh||C7+11, C7♯11|
|Seventh flat thirteenth||dominant seventh||minor thirteenth||C7-13, C7♭13|
|Half-diminished seventh||minor seventh||diminished fifth||Cø, Cm7♭5|
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.
Sixth chords can belong to either of two groups. One is first inversion chords and added sixth chords that contain a sixth from the root. The other group is inverted chords in which the interval of a sixth appears above a bass note that is not the root.
The major sixth chord (also called, sixth or added sixth with the chord notation 6, e.g., "C6") is by far the most common type of sixth chord of the first group. It comprises a major triad with the added major sixth above the root, common in popular music. For example, the chord C6 contains the notes C-E-G-A. The minor sixth chord (min6 or m6, e.g., "Cm6") is a minor triad 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 a major sixth rather than a minor sixth, however a minor sixth interval may be indicated in the notation as, for example, "Cm(m6)", or Cmm6.
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 the augmented sixth chord resolves to) 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 based on triads, 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 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.
|Add nine||major triad||major ninth||-||C2, Cadd9||C E G D|
|Add fourth||major triad||perfect fourth||-||C4, Cadd11||C E G F|
|Add sixth||major triad||major sixth||-||C6||C E G A|
|Six-nine||major triad||major sixth||major ninth||C6/9||C E G A D||-|
|Mixed-third||major triad||minor third||-||-||C E♭ E G|
A suspended chord, or "sus chord" (sometimes wrongly thought to mean sustained chord), is a chord in which the third is replaced by either the second or the fourth. This produces two main 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. There is also a third type of suspended chord, in which both the second and fourth are present, for example the chord with the notes C D F G.
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 layman 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 . Csus4 is sometimes written Csus since the sus4 is more common than the sus2.
|Sus2||open fifth||major second||-||-||Csus2||C D G|
|Sus4||open fifth||perfect fourth||-||-||Csus4||C F G|
|Jazz sus||open fifth||perfect fourth||minor seventh||major ninth||C9sus4||C F G B♭ D|
A borrowed chord is one from a different key than the home key, the key of the piece it is used in. The most common occurrence of this is where a chord from the parallel major or minor key is used. Particularly good examples can be found throughout the works of composers such as Schubert.
For instance, for a composer working in the C major key, a major ♭III chord would be borrowed, as this appears only in the C minor key. Although borrowed chords could theoretically include chords taken from any key other than the home key, this is not how the term is used when a chord is described in formal musical analysis.
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 is the chord of the fifth degree of the G major scale, which is D major. If used, this chord causes a modulation.
- Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p. 67&359. Seventh Edition. ISBN 978-0-07-294262-0."A chord is a harmonic unit with at least three different tones sounding simultaneously." "A combination of three or more pitches sounding at the same time."
Károlyi, Otto (1965). Introducing Music. Penguin Books. p. 63.
Two or more notes sounding simultaneously are known as a chord.
- Mitchell, Barry (January 16, 2008). "An explanation for the emergence of Jazz (1956)", Theory of Music.
- Linkels, Ad, The Real Music of Paradise", In Broughton, Simon and Ellingham, Mark with McConnachie, James and Duane, Orla (Ed.), World Music, Vol. 2: Latin & North America, Caribbean, India, Asia and Pacific, pp 218–229. Rough Guides Ltd, Penguin Books. ISBN 1-85828-636-0
- Malm, William P. (1996). Music Cultures of the Pacific, the Near East, and Asia. p.15. ISBN 0-13-182387-6. Third edition: "Indeed this harmonic orientation is one of the major differences between Western and much non-Western music."
- Arnold Schoenberg, Structural Functions of Harmony, Faber and Faber, 1983, p.1-2.
- Benward & Saker (2003), p. 77.
- Merriam-Webster, Inc. (1995). "Chord", Merriam-Webster's dictionary of English usage, p.243. ISBN 978-0-87779-132-4.
- "Chord", Oxford Dictionaries.
- Dahlhaus, Car. "Harmony", Grove Music Online, ed. L. Macy (accessed 24 February 2007), grovemusic.com (subscription access).
- Károlyi, Ottó, Introducing Music, p. 63. England: Penguin Books.
- Schellenberg, E. Glenn; Bigand, Emmanuel; Poulin-Charronnat, Benedicte; Garnier, Cecilia; Stevens, Catherine (Nov 2005). "Children's implicit knowledge of harmony in Western music". Developmental Science 8 (8): 551–566.
- Duarter, John (2008). Melody & Harmony for Guitarists, p.49. ISBN 978-0-7866-7688-0.
- Benward & Saker (2003), p.70.
- Benward & Saker (2003), p.100.
- Benward & Saker (2003), p.201.
- Benward & Saker (2003), p.220.
- Benward & Saker (2003), p.231.
- Benward & Saker (2003), p.274.
- Winston Harrison, The Rockmaster System: Relating Ongoing Chords to the Keyboard – Rock, Book 1, Dellwin Publishing Co. 2005, p. 33 
- Pachet, François, Surprising Harmonies, International Journal on ComputingAnticipatory Systems, 1999. 
- Pen, Ronald (1992). Introduction to Music, p.81. McGraw-Hill, ISBN 0-07-038068-6. "In each case the note that forms the foundation pitch is called the root, the middle tone of the chord is designated the third (because it is separated by the interval of a third from the root), and the top tone is referred to as the fifth (because it is a fifth away from the root)."
- William G Andrews and Molly Sclater (2000). Materials of Western Music Part 1, p.227. ISBN 1-55122-034-2.
- The symbol Δ is ambiguous, as it is used by some as a synonym for M (e.g. CΔ=CM and CΔ7=CM7), and by others as a synonym of M7 (e.g. CΔ=CM7).
- Haerle, Dan (1982). The Jazz Language: A Theory Text for Jazz Composition and Improvisation, p.30. ISBN 978-0-7604-0014-2.
- Policastro, Michael A. (1999). Understanding How to Build Guitar Chords and Arpeggios, p.168. ISBN 978-0-7866-4443-8.
- Benward & Saker (2003), p.92.
- Bert Weedon, Play in a Day, Faber Music Ltd, ISBN 0-571-52965-8, passim - among a wide range of other guitar tutors
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• How to Interpret Chord Symbols