Concise Guide To Jazz 7th Edition Pdf Download Updated

Concise Guide To Jazz 7th Edition Pdf Download

Harmonic set of three or more notes

A chord, in music, is whatever harmonic set of pitches/frequencies consisting of multiple notes (also called "pitches") that are heard every bit if sounding simultaneously.^[a] For many practical and theoretical purposes, arpeggios and broken chords (in which the notes of the chord are sounded one afterwards the other, rather than simultaneously), or sequences of chord tones, may also be considered as chords in the correct musical context.

In tonal Western classical music (music with a tonic key or "home central"), the most oft encountered chords are triads, so chosen because they consist of three distinct notes: the root note, and intervals of a third and a fifth above the root note. Chords with more than three notes include added tone chords, extended chords and tone clusters, which are used in contemporary classical music, jazz and almost whatsoever other genre.

A series of chords is chosen a chord progression.^[1] I example of a widely used chord progression in Western traditional music and dejection is the 12 bar blues progression. Although whatever chord may in principle be followed past whatever other chord, sure patterns of chords are more than common in Western music, and some patterns have been accustomed as establishing the key (tonic note) in common-practice harmony—notably the resolution of a dominant chord to a tonic chord. To describe this, Western music theory has developed the practise of numbering chords using Roman numerals^[two] to represent the number of diatonic steps up from the tonic note of the calibration.

Common means of notating or representing chords^[3] in Western music (other than conventional staff annotation) include Roman numerals, the Nashville Number System, figured bass, chord letters (sometimes used in modern musicology), and chord charts.

Definition [edit]

The English discussion chord derives from Middle English string, a back-formation of accord ^[4] in the original sense of understanding and later, harmonious audio.^[5] A sequence of chords is known as a chord progression or harmonic progression. These are oft used in Western music.^[6] A chord progression "aims for a definite goal" of establishing (or contradicting) a tonality founded on a key, root or tonic chord.^[ii] The report of harmony involves chords and chord progressions and the principles of connection that govern them.^[vii]

${ #(set-global-staff-size eighteen) \new PianoStaff << \new Staff << \new voice \relative c'' { \set Score.tempoHideNote = ##t \tempo 4 = 112 \clef treble \key bes \major \time 5/iv <bes, d g>4 <a c f> <bes d bes'> \stemDown <c a'> \stemNeutral <f a d> \fourth dimension 6/four \stemDown <c a'> \stemNeutral <f bes d> <d g bes> <e g c> <g, c g'> <a c f> } \new Voice \relative c'' { \time 5/4 s2. \stemUp c8^( f d4) \time 6/4 \stemUp c8^( f d4) s1 } >> \new Staff << \clef bass \key bes \major \relative c { \time v/4 <g g'>4 <a f'> <g g'> <f f'> <d d'> \time 6/4 <f f'> <bes bes'> <g g'> <c, c'> <e e'> <f f'> } >> >> }$

Ottó Károlyi^[ix] writes that, "Two or more notes sounded simultaneously are known as a chord," though, since instances of whatever given note in different octaves may be taken as the aforementioned notation, it is more precise for the purposes of analysis to speak of distinct pitch classes. Furthermore, as iii notes are needed to ascertain any mutual chord, three is often taken as the minimum number of notes that course a definite chord.^[10] Hence, Andrew Surmani, for example, states, "When iii or more notes are sounded together, the combination is called a chord."^[11] George T. Jones agrees: "Two tones sounding together are ordinarily termed an interval, while three or more than tones are called a chord."^[12] According to Monath, "a chord is a combination of three or more tones sounded simultaneously", and the distances between the tones are called intervals.^[13] However, sonorities of ii pitches, or even unmarried-notation melodies, are commonly heard equally implying chords.^[fourteen] A unproblematic example of ii notes beingness interpreted as a chord is when the root and tertiary are played simply the fifth is omitted. In the key of C major, if the music stops on the two notes G and B, most listeners hear this equally a G major chord.

Since a chord may be understood equally such fifty-fifty when all its notes are not simultaneously aural, there has been some academic discussion regarding the point at which a group of notes may be called a chord. Jean-Jacques Nattiez explains that, "We can run across 'pure chords' in a musical work", such as in the "Promenade" of Modest Mussorgsky's Pictures at an Exhibition but, "often, we must become from a textual given to a more abstruse representation of the chords being used", as in Claude Debussy's Première arabesque.^[8]

History [edit]

In the medieval era, early on Christian hymns featured organum (which used the simultaneous perfect intervals of a quaternary, a fifth, and an octave^[15]), with chord progressions and harmony - an incidental result of the emphasis on melodic lines during the medieval and and then Renaissance (15th to 17th centuries).^[16] ^[17]

The Baroque period, the 17th and 18th centuries, began to feature the major and small scale based tonal organisation and harmony, including chord progressions and circle progressions.^[iii] It was in the Bizarre period that the accessory of melodies with chords was developed, as in figured bass,^[17] and the familiar cadences (perfect authentic, etc.).^[18] In the Renaissance, certain anomalous sonorities that suggest the dominant seventh occurred with frequency.^[19] In the Baroque period, the dominant seventh proper was introduced and was in constant use in the Classical and Romantic periods.^[19] The leading-tone 7th appeared in the Bizarre period and remains in employ.^[twenty] Composers began to employ nondominant seventh chords in the Baroque menstruum. They became frequent in the Classical menses, gave manner to altered dominants in the Romantic period, and underwent a resurgence in the Post-Romantic and Impressionistic period.^[21]

The Romantic flow, the 19th century, featured increased chromaticism.^[3] Composers began to apply secondary dominants in the Baroque, and they became common in the Romantic catamenia.^[22] Many gimmicky popular Western genres continue to rely on simple diatonic harmony, though far from universally:^[23] notable exceptions include the music of film scores, which oftentimes apply chromatic, atonal or post-tonal harmony, and modern jazz (particularly circa 1960), in which chords may include upwards to seven notes (and occasionally more than).^[24] When referring to chords that practise not role as harmony, such as in atonal music, the term "sonority" is often used specifically to avoid whatever tonal implications of the word "chord"^{[ commendation needed ]}.

Chords are also used for timbre effects. In organ registers, certain chords are activated by a single key so that playing a tune results in parallel voice leading. These voices, losing independence, are fused into one with a new timbre. The aforementioned effect is also used in synthesizers and orchestral arrangements; for instance, in Ravel's Bolero #5 the parallel parts of flutes, horn and celesta, existence tuned equally a chord, resemble the sound of an electrical organ.^[25] ^[26]

Annotation [edit]

${ \override Score.TimeSignature #'stencil = ##f \relative c' { \clef treble \time four/4 <c e g>1 } }$

A C major triad in staff notation

Chords can exist represented in various ways. The most common notation systems are:^[3]

Plain staff notation, used in classical music
Roman numerals, normally used in harmonic assay to denote the scale step on which the chord is built.^[2]
Figured bass, much used in the Baroque era, uses numbers added to a bass line written on a staff, to enable keyboard players to improvise chords with the correct mitt while playing the bass with their left.
Chord letters, sometimes used in modern musicology, to denote chord root and quality.
Diverse chord names and symbols used in pop music lead sheets, fake books, and chord charts, to apace lay out the harmonic ground programme of a slice and then that the musician may improvise, jam, or vamp on information technology.

Roman numerals [edit]

${ \relative c' { \clef treble \time 4/4 <c e a>1_\markup { \concat { \translate #'(-4 . 0) { "C: vi" \raise #ane \small "6" \hspace #5.5 "two" \hspace #6.5 "Five" \enhance #ane \small "6" \hspace #half dozen.2 "I" } } } <d f a> <b d g> <c e g> \bar "||" } }$

The chord progression vi–ii–Five–I in the fundamental of C major. Using pb canvas chord names, these chords could exist referred to as A minor, D minor, G major and C major.^[27]

While scale degrees are typically represented in musical analysis or musicology articles with Arabic numerals (eastward.g., 1, 2, 3, ..., sometimes with a circumflex to a higher place the numeral: , , , ...), the triads (3-notation chords) that have these degrees as their roots are often identified by Roman numerals (e.g., I, IV, V, which in the fundamental of C major would be the triads C major, F major, G major).

In some conventions (as in this and related articles) upper-case Roman numerals bespeak major triads (e.g., I, Iv, V) while lower-case Roman numerals indicate modest triads (e.g., I for a major chord and i for a small-scale chord, or using the major key, two, three and vi representing typical diatonic pocket-sized triads); other writers (due east.yard., Schoenberg) use upper case Roman numerals for both major and minor triads. Some writers employ 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 calibration. Diminished triads may be represented past lower-case Roman numerals with a degree symbol (eastward.thou., seven ^o ⁷ indicates a diminished 7th chord congenital on the seventh calibration degree; in the key of C major, this chord would exist B diminished seventh, which consists of the notes B, D, F and A ♭ ).

Roman numerals can too be used in stringed instrument notation to betoken the position or string to play. In some string music, the cord on which it is suggested that the performer play the notation is indicated with a Roman numeral (e.k., on a four-string orchestral cord instrument, I indicates the highest-pitched, thinnest cord and 4 indicates the everyman-pitched, thickest bass cord). In some orchestral parts, chamber music and solo works for cord instruments, the composer tells the performer which string to use with the Roman numeral. Alternately, the composer starts the note proper noun with the sting to use—e.g., "sul G" ways "play on the G string".

Figured bass annotation [edit]

Mutual conventional symbols for figured bass
Triads
Inversion	Intervals above bass	Symbol	Case
Root position	^five _iii	None	${ \override Score.TimeSignature #'stencil = ##f \new PianoStaff << \new Staff << \relative c' { \clef treble \fourth dimension three/4 <e g c>4 <c g' c> <c e g> } >> \new Staff << \relative c { \clef bass \time three/iv c4 e 1000 } \figures { < _ >4 <6> <6 4> } >> >> }$
1st inversion	⁶ ₃	^vi
2nd inversion	⁶ ₄	^six ₄
Seventh chords
Inversion	Intervals above bass	Symbol	Example
Root position	vii 5 3	⁷	${ \override Score.TimeSignature #'stencil = ##f \new PianoStaff << \new Staff << \relative c' { \clef treble \time 4/4 <b d f>4 <g d' f> <b f' g > <b d g> } >> \new Staff << \relative c { \clef bass \time iv/4 g4 b d f } \figures { <7>4 <6 5> <4 3> <4 2> } >> >> }$
1st inversion	6 5 3	⁶ _five
2d inversion	6 4 3	⁴ _three
3rd inversion	6 4 two	⁴ ₂ or ²

Figured bass or thoroughbass is a kind of musical notation used in almost all Baroque music (c. 1600–1750), though rarely in music from later than 1750, to indicate harmonies in relation to a conventionally written bass line. Figured bass is closely associated with chord-playing basso continuo accessory instruments, which include harpsichord, pipe organ and lute. Added numbers, symbols, and accidentals below the staff indicate the intervals in a higher place the bass annotation to play; that is, the numbers stand for the number of scale steps above the written note to play the figured notes.

For example, in the figured bass beneath, the bass note is a C, and the numbers 4 and 6 bespeak that notes a 4th and a sixth above (F and A) should exist played, giving the second inversion of the F major triad.

${ \clef bass \time 4/4 << \override Score.TimeSignature #'stencil = ##f \relative c { <c>ane } \figures { <6 4> } >> }$

can be realized every bit

${ \clef bass \fourth dimension four/four << \override Score.TimeSignature #'stencil = ##f \relative c { <c f a>1 } >> }$

If no numbers are written below a bass note, the figure is assumed to exist ⁵
₃ , which calls for a third and a 5th above the bass annotation (i.e., a root position triad).

In the 2010s, some classical musicians who specialize in music from the Baroque era tin can all the same perform chords using figured bass notation; in many cases, yet, the chord-playing performers read a fully notated accompaniment that has been prepared for the piece past the music publisher. Such a part, with fully written-out chords, is called a "realization" of the figured bass part.

Chord messages [edit]

${ \relative c' { \clef treble \fourth dimension 4/four <c e g>i^\markup { "C" } <c es g>1^\markup { "c" } <c e gis>1^\markup { "C+" } <c es ges>1^\markup { \concat { "c" \raise #1 \small "o" } } } }$

Chord letters for triads on C

Chord messages are used by musicologists, music theorists and advanced university music students to analyze songs and pieces. Chord letters use upper-instance and lower-case letters to indicate the roots of chords, followed by symbols that specify the chord quality.^[28]

Annotation in popular music [edit]

In most genres of popular music, including jazz, pop, and stone, a chord name and the corresponding symbol are typically equanimous of i or more than parts. In these genres, chord-playing musicians in the rhythm department (e.g., electric guitar, acoustic guitar, piano, Hammond organ, etc.) typically improvise the specific "voicing" of each chord from a song's chord progression by interpreting the written chord symbols appearing in the lead canvass or fake book. Usually, these chord symbols include:

A (big) alphabetic character indicating the root note (due east.g., C).
A symbol or abbreviation indicating the chord quality (east.g., minor, aug or ^o ). If no chord quality is specified, the chord is assumed to be a major triad by default.
Number(due south) indicating the stacked intervals above the root annotation (east.thousand., seven or 13).
Boosted musical symbols or abbreviations for special alterations (e.g., ♭ 5, ♯ v or add13).
An added slash "/" and an upper case alphabetic character indicates that a bass notation other than the root should be played. These are called slash chords. For instance, C/F indicates that a C major triad should exist played with an added F in the bass. In some genres of modern jazz, two chords with a slash between them may betoken an advanced chord blazon chosen a polychord, which is the playing of two chords simultaneously. The right notation of this should be F / C , which sometimes go mixed up with slash chords.

Chord qualities are related with the qualities of the component intervals that define the chord. The master chord qualities are:

Major and small (a chord is "Major" past default and contradistinct with added info: "C" = C major, "Cm" = c small-scale).
augmented, diminished, and half-diminished,
ascendant 7th.

Symbols [edit]

The symbols used for notating chords are:

m, min, or − indicates a minor chord. The "g" must be lowercase to distinguish it from the "Thou" for major.
M, Ma, Maj, Δ , or (no symbol) indicates a major chord. In a jazz context, this typically indicates that the player should use any suitable chord of a major quality, for case a major seventh chord or a 6/nine chord. In a lot of jazz styles, an unembellished major triad is rarely if ever played, simply in a lead sheet the choice of which major quality chord to apply is left to the performer.
+ or aug indicates an augmented chord (A or a is not used).
^o or dim indicates a diminished chord, either a diminished triad or a macerated seventh chord (d is non used).
^ø indicates a one-half-diminished 7th chord. In some imitation books, the abridgement m^{7( ♭ five)} is used as an equivalent symbol.
2 is mostly used as an extra note in a chord (e.grand., add2, sus2).
iii is the minor or major quality of the chord and is rarely written as a number.
4 is by and large used as an extra notation in a chord (e.1000., add4, sus4).
5 is the (perfect) 5th of the chord and is only written every bit a number when contradistinct (e.g., F7^{( ♭ v)}). In guitar music, like rock, a "5" indicates a power chord, which consists of only the root and fifth, mayhap with the root doubled an octave higher.
6 indicates a sixth chord. There are no rules if the 6 replaces the 5th or not.
7 indicates a dominant 7th chord. Still, if Maj7, M7 or Δ7 is indicated, this is a major 7th chord (e.one thousand., G^M7 or F^Δ7). Very rarely, too dom is used for dominant 7th.
9 indicates a 9th chord, which in jazz usually includes the dominant seventh as well, if it is a ascendant chord.
11 indicates an eleventh chord, which in jazz commonly includes the dominant seventh and 9th as well, if it is a dominant chord.
13 indicates a thirteenth chord, which in jazz usually includes the ascendant seventh, ninth and eleventh equally well.
6/9 indicates a triad with the addition of the sixth and ninth.
sus4 (or simply 4) indicates a sus chord with the third omitted and the fourth used instead. Other notes may be added to a sus4 chord, indicated with the word "add" and the scale degree (e.g., A^sus4(add9) or A^sus4(add7)).
sus2 (or simply 2) indicates a sus chord with the third omitted and the second (which may also be called the ninth) used instead. As with "sus4", a "sus2" chord can have other scale degrees added (e.g., A^{sus2(add ♭ 7)} or A^sus2(add4)).
( ♭ ix) (parenthesis) is used to indicate explicit chord alterations (e.g., A^{7( ♭ 9)}). The parenthesis is probably left from older days when jazz musicians weren't used to "contradistinct chords". Albeit important, the parenthesis tin can be left unplayed (with no "musical harm").
add together indicates that an additional interval number should exist added to the chord. (e.g., C^7add13 is a C 7th chord plus an added 13th).
alt or alt dom indicates an contradistinct dominant seventh chord (due east.g., G^{seven ♯ 11}).
omit5 (or simply no5) indicates that the (indicated) note should be omitted.

Examples [edit]

The table below lists common chord types, their symbols, and their components.

Chord			Components
Proper name	Symbol (on C)		Interval	P1	m2	M2	m3	M3	P4	d5	P5	A5	M6/d7	m7	M7
Proper name	Short	Long	Semitones	0	i	ii	three	4	v	6	7	8	9	ten	11
Major triad	C CΔ			P1				M3			P5
Major sixth chord	C^six CM⁶	Cmaj6		P1				M3			P5		M6
Dominant seventh chord	C⁷	Cdom7		P1				M3			P5			m7
Major seventh chord	CM⁷ C^∆7	Cmaj⁷		P1				M3			P5				M7
Augmented triad	C+	Caug		P1				M3				A5
Augmented seventh chord	C+^vii	Caug⁷		P1				M3				A5		m7
Pocket-size triad	Cm	Cmin		P1			m3				P5
Minor sixth chord	Cm^{half dozen}	Cmin^vi		P1			m3				P5		M6
Pocket-size seventh chord	Cm⁷	Cmin^vii		P1			m3				P5			m7
Minor-major seventh chord	Cm^M7 Cm/M7 Cm(M7)	Cmin^maj7 Cmin/maj7 Cmin(maj7)		P1			m3				P5				M7
Macerated triad	C ^o	Cdim		P1			m3			d5
Diminished seventh chord	C ^o ⁷	Cdim⁷		P1			m3			d5			d7
One-half-macerated 7th chord	C ^ø C ^ø ⁷			P1			m3			d5				m7

Utilise [edit]

The bones role of chord symbols is to eliminate the demand to write out sheet music. The modern jazz player has extensive knowledge of the chordal functions and can more often than not play music by reading the chord symbols only. Advanced chords are common especially in modernistic jazz. Altered 9ths, 11ths and 5ths are not mutual in popular music. In jazz, a chord chart is used by comping musicians (jazz guitar, jazz pianoforte, Hammond organ) to improvise a chordal accessory and to play improvised solos. Jazz bass players improvise a bassline from a chord chart. Chord charts are used past horn players and other solo instruments to guide their solo improvisations.

Interpretation of chord symbols depends on the genre of music being played. In jazz from the bebop era or later, major and minor chords are typically realized every bit 7th chords even if only "C" or "Cm" appear in the nautical chart. In jazz charts, seventh chords are often realized with upper extensions, such as the ninth, sharp eleventh, and thirteenth, even if the chart just indicates "A⁷". In jazz, the root and 5th are often omitted from chord voicings, except when there is a diminished fifth or an augmented fifth.

In a popular or rock context, nonetheless, "C" and "Cm" would most always be played as triads, with no sevenths. In popular and stone, in the relatively less mutual cases where songwriters wish a dominant seventh, major 7th, or minor seventh chord, they signal this explicitly with the indications "C⁷", "C^maj7" or "Cm^seven".

Characteristics [edit]

Within the diatonic scale, every chord has certain characteristics, which include:

the number of pitch classes (distinct notes without respect to octave) in the chord,
the calibration degree of the root note,
the position or inversion of the chord,
the full general type of intervals it is synthetic from—for example, seconds, thirds, or fourths, and
counts of each pitch course every bit occur between all combinations of notes the chord contains.

Number of notes [edit]

No.	Proper noun	Alternate name
ane	Monad	Monochord
ii	Dyad	Dichord
iii	Triad	Trichord
4	Tetrad	Tetrachord
5	Pentad	Pentachord
6	Hexad	Hexachord
vii	Heptad	Heptachord
8	Octad	Octachord
9	Ennead	Nonachord
x	Decad	Decachord

Two-note combinations, whether referred to equally chords or intervals, are called dyads. In the context of a specific section in a slice of music, dyads can be heard every bit chords if they contain the almost important notes of a certain chord. For example, in a piece in C Major, after a section of tonic C Major chords, a dyad containing the notes B and D sounds to nigh listeners as a start inversion K Major chord. Other dyads are more than ambiguous, an attribute that composers can use creatively. For example, a dyad with a perfect fifth has no tertiary, so it does not sound major or minor; a composer who ends a department on a perfect fifth could subsequently add the missing third. Another example is a dyad outlining the tritone, such as the notes C and F# in C Major. This dyad could be heard as implying a D7 chord (resolving to G Major) or as implying a C diminished chord (resolving to Db Major). In unaccompanied duos for 2 instruments, such as flute duos, the just combinations of notes that are possible are dyads, which ways that all of the chord progressions must be implied through dyads, as well equally with arpeggios.

Chords constructed of iii notes of some underlying scale are described every bit triads. Chords of 4 notes are known as tetrads, those containing five are called pentads and those using half-dozen 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 mostly played simultaneously. Chords that may contain more than three notes include pedal bespeak chords, ascendant 7th chords, extended chords, added tone chords, clusters, and polychords.

Polychords are formed past ii or more chords superimposed.^[29] Oftentimes these may exist analysed equally extended chords; examples include tertian, altered chord, secundal chord, quartal and quintal harmony and Tristan chord. Another example is when G^{7( ♯ 11 ♭ ix)} (G–B–D–F–A ♭ –C ♯ ) is formed from G major (G–B–D) and D ♭ major (D ♭ –F–A ♭ ).^[thirty] A nonchord tone is a anomalous or unstable tone that lies outside the chord currently heard, though often resolving to a chord tone.^[31]

Calibration degree [edit]

Roman Numerals and Calibration Degrees for Major Keys
Roman Numeral	Scale Caste
I	tonic
two	supertonic
3	mediant
IV	subdominant
V	dominant
vi	submediant
vii ^o / ♭ Vii	leading tone / subtonic

In the key of C major, the kickoff degree of the scale, chosen the tonic, is the note C itself. A C major chord, the major triad built on the notation C (C–E–Grand), is referred to as the one chord of that fundamental and notated in Roman numerals as I. The same C major chord can be plant in other scales: it forms chord Three in the key of A minor (A→B→C) and chord Four in the key of Grand major (Yard→A→B→C). This numbering indicates the chords's function.

Many analysts use lower-example Roman numerals to indicate minor triads and upper-case numerals for major triads, 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 apartment/sharp sign before the chord—for example, the chord Due east ♭ major in the key of C major is represented by ♭ 3. The tonic of the scale may be indicated to the left (due east.chiliad., "F ♯ :") or may be understood from a fundamental signature or other contextual clues. Indications of inversions or added tones may be omitted if they are non relevant to the assay. Roman numeral assay indicates the root of the chord as a scale degree inside a particular major central as follows.

Inversion [edit]

In the harmony of Western art music, a chord is in root position when the tonic note is the lowest in the chord (the bass note), and the other notes are in a higher place information technology. When the lowest notation is non the tonic, the chord is inverted. Chords that accept many constituent notes can have many different inverted positions as shown below for the C major chord:

Bass note	Position	Lodge of notes (starting from the bass)	Annotation
C	root position	C–Eastward–K or C–1000–Due east	⁵ ₃ as Grand is a fifth to a higher place C and Due east is a third to a higher place C
Eastward	first inversion	Due east–G–C or E–C–Chiliad	⁶ _iii equally C is a 6th to a higher place E and M is a 3rd above E
G	second inversion	G–C–E or G–E–C	^six _four as E is a sixth above M and C is a fourth above G

Further, a 4-note chord can be inverted to four different positions by the same method every bit triadic inversion. For example, a K⁷ chord can exist in root position (G every bit bass note); first inversion (B as bass note); second inversion (D as bass annotation); or third inversion (F as bass notation).

${ \override Score.TimeSignature #'stencil = ##f \override Score.SpacingSpanner.strict-annotation-spacing = ##t \set Score.proportionalNotationDuration = #(ly:brand-moment one/4) \time four/four \relative c' { <g b d f>1^\markup { \column { "Root" "position" } } <b d f g>1^\markup { \cavalcade { "Offset" "inversion" } } <d f g b>1^\markup { \column { "2nd" "inversion" } } <f g b d>1^\markup { \column { "Third" "inversion" } } } }$

Where guitar chords are concerned, the term "inversion" is used slightly differently; to refer to stock fingering "shapes".^[32]

Secundal, tertian, and quartal chords [edit]

Type	Component intervals
Secundal	Seconds: major 2d, small 2nd
Tertian	Thirds: major third, modest 3rd
Quartal	Fourth: perfect fourth, augmented quaternary
Quintal	Fifths: diminished 5th, perfect fifth

Many chords are a sequence of notes separated by intervals of roughly the same size. Chords tin can be classified into different categories past this size:

Tertian chords can be decomposed into a series of (major or modest) thirds. For example, the C major triad (C–E–Thou) is divers by a sequence of 2 intervals, the outset (C–Eastward) beingness a major third and the second (E–Chiliad) being a small-scale third. Most common chords are tertian.
Secundal chords can be decomposed into a serial of (major or minor) seconds. For example, the chord C–D–East ♭ is a serial of seconds, containing a major 2nd (C–D) and a pocket-sized second (D–E ♭ ).
Quartal chords tin can exist decomposed into a series of (perfect or augmented) fourths. Quartal harmony commonly works with a combination of perfect and augmented fourths. Diminished fourths are enharmonically equivalent to major thirds, so they are uncommon.^[33] For example, the chord C–F–B is a serial of fourths, containing a perfect fourth (C–F) and an augmented fourth/tritone (F–B).

These terms can become ambiguous when dealing with not-diatonic scales, such as the pentatonic or chromatic scales. The use of accidentals tin can also complicate the terminology. For example, the chord B ♯ –E–A ♭ appears to be quartal, as a series of macerated fourths (B ♯ –E and E–A ♭ ), but it is enharmonically equivalent to (and sonically indistinguishable from) the tertian chord C–E–G ♯ , which is a series of major thirds (C–E and East–Thousand ♯ ).

Harmonic content [edit]

The notes of a chord form intervals with each of the other notes of the chord in combination. A iii-note chord has iii of these harmonic intervals, a 4-note chord has half dozen, a 5-note chord has 10, a vi-note chord has xv.^[34] The absenteeism, presence, and placement of certain key intervals plays a big 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 7th chords, giving their sound a feature tension, and making the tritone interval likely to move in sure stereotypical means to the following chord.^[35] Tritones are also present in diminished seventh and half-diminished chords.

A chord containing semitones, whether actualization every bit minor seconds or major sevenths, is called hemitonic; 1 without semitones is anhemitonic. Harmonic semitones are an important part of major seventh chords, giving their sound a feature high tension, and making the harmonic semitone probable to motility in certain stereotypical means to the following chord.^[36] A chord containing major sevenths only no pocket-size seconds is much less harsh in sound than 1 containing minor seconds besides.

Other chords of interest might include the

Diminished triad, which has many pocket-sized thirds and no major thirds, many tritones but no perfect fifths
Augmented triad, which has many major thirds and no pocket-size thirds or perfect fifths
Ascendant seventh flat five chord, which has many major thirds and tritones and no minor thirds or perfect fifths

Common types of chords [edit]

Triads [edit]

Triads, also chosen triadic chords, are tertian chords with 3 notes. The 4 basic triads are described below.

Blazon	Component intervals		Chord symbol	Notes	Sound
Blazon	3rd	Fifth	Chord symbol	Notes	Sound
Major triad	major	perfect	C, CM, Cmaj, CΔ, Cma	C E G	play(assist·info)
Minor triad	minor	perfect	Cm, Cmin, C−, Cmi	C Eastward ♭ G	play(help·info)
Augmented triad	major	augmented	Caug, C ⁺ , C+	C Eastward Thousand ♯	play(help·info)
Diminished triad	minor	diminished	Cdim, C ^o , Cm^{( ♭ v)}	C Due east ♭ G ♭	play(assist·info)

Seventh chords [edit]

Seventh chords are tertian chords, synthetic by adding a 4th note to a triad, at the interval of a third to a higher place the fifth of the chord. This creates the interval of a 7th above the root of the chord, the next natural footstep in composing tertian chords. The seventh chord built on the fifth pace of the calibration (the dominant 7th) is the only dominant seventh chord available in the major scale: information technology contains all three notes of the diminished triad of the seventh and is ofttimes used as a stronger substitute for it.

There are diverse types of 7th 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 (eastward.g., Dm7, Dm⁷, and D^m7 are all identical).

Type	Component intervals			Chord symbol	Notes	Sound
Type	Third	Fifth	Seventh	Chord symbol	Notes	Sound
Diminished seventh	minor	diminished	diminished	C ^o ^seven, Cdim^seven	C E ♭ G ♭ B	Play(help·info)
One-half-diminished seventh	pocket-size	diminished	minor	C ^ø ^vii, Cm^{7 ♭ 5}, C−^{( ♭ v)}	C East ♭ One thousand ♭ B ♭	Play(help·info)
Minor 7th	small	perfect	minor	Cm⁷, Cmin^seven, C−^seven ,	C E ♭ G B ♭	Play(help·info)
Minor major seventh	pocket-size	perfect	major	Cm^M7, Cm^maj7 , C−^(j7) , C−^Δ7 , C−^M7	C E ♭ K B	Play(assistance·info)
Dominant seventh	major	perfect	modest	C⁷, Cdom⁷	C East 1000 B ♭	Play(aid·info)
Major seventh	major	perfect	major	CM^seven, C^M7, C^maj7, C^Δ7, C^j7	C E G B	Play(aid·info)
Augmented 7th	major	augmented	minor	C+⁷, Caug⁷, C⁷⁺, C^7+five, C^{vii ♯ v}	C Due east Thousand ♯ B ♭	Play(help·info)
Augmented major seventh	major	augmented	major	C+^M7, C^M7+5, C^{M7 ♯ 5}, C+^j7, C+^Δ7	C East G ♯ B	Play(assistance·info)

Extended chords [edit]

Extended chords are triads with further tertian notes added beyond the seventh: the ninth, eleventh, and thirteenth chords. For example, a dominant thirteenth chord consists of the notes C–E–Grand–B ♭ –D–F–A:

${ \override Score.TimeSignature #'stencil = ##f \new Staff << \new Voice \relative c' { \clef treble \time four/4 \central c \major \voiceOne <c e g bes>1 } \new Voice \relative c'' { \clef treble \time 4/4 \key c \major \voiceOne \override NoteHead.color = #red <d f a>1 } >> }$

The upper structure or extensions, i.eastward., notes beyond the 7th, are shown in red. This chord is just a theoretical analogy of this chord. In practice, a jazz pianist or jazz guitarist would not usually play the chord all in thirds as illustrated. Jazz voicings typically use the tertiary, seventh, and then the extensions such as the 9th and thirteenth, and in some cases the eleventh. The root is often omitted from chord voicings, as the bass histrion will play the root. The fifth is often omitted if it is a perfect fifth. Augmented and diminished fifths are normally included in voicings. Afterwards the thirteenth, any notes added in thirds duplicate notes elsewhere in the chord; all seven notes of the scale are present in the chord, so adding more than notes does not add new pitch classes. Such chords may be constructed only past using notes that lie outside the diatonic vii-note scale.

Type	Components				Chord symbol	Notes	Audio
Type	Chord	Extensions			Chord symbol	Notes	Audio
Dominant 9th	dominant seventh	major ninth	—	—	C⁹	C E G B ♭ D	Play(assist·info)
Dominant eleventh	ascendant seventh (the tertiary is usually omitted)	major 9th	perfect eleventh	—	C¹¹	C E G B ♭ D F	Play(help·info)
Ascendant thirteenth	dominant 7th	major ninth	perfect eleventh (normally omitted)	major thirteenth	C¹³	C E K B ♭ D F A	Play(assist·info)

Other extended chords follow similar rules, so that for instance maj⁹, maj¹¹, and maj¹³ contain major seventh chords rather than ascendant seventh chords, while m^ix, one thousand^eleven, and k¹³ contain minor seventh chords.

Altered chords [edit]

${ \override Score.TimeSignature #'stencil = ##f \relative c' { \clef treble \time 4/four <c e ges bes des>1 } }$

An altered chord on C with a diminished fifth and a modest seventh and ninth.

The third and seventh of the chord are e'er determined by the symbols shown higher up. The root cannot be then altered without changing the name of the chord, while the tertiary cannot be altered without altering the chord's quality. Nevertheless, the fifth, 9th, eleventh and thirteenth may all exist chromatically altered past accidentals.

These are noted alongside the altered element. Accidentals are most oft used with dominant 7th chords. Altered dominant seventh chords (C^7alt) may accept a modest ninth, a sharp 9th, a diminished fifth, or an augmented fifth. Some write this as C⁷⁺⁹, which assumes too the pocket-sized ninth, diminished fifth and augmented 5th. The augmented ninth is frequently referred to in blues and jazz equally a blue annotation, being enharmonically equivalent to the minor third or 10th. When superscripted numerals are used the dissimilar numbers may be listed horizontally or vertically.

Type	Components		Chord symbol	Notes	Audio
Type	Chord	Alteration	Chord symbol	Notes	Audio
Seventh augmented fifth	dominant seventh	augmented fifth	C^vii+v, C^{vii ♯ 5}	C E Grand ♯ B ♭	Play(help·info)
Seventh pocket-sized ninth	ascendant seventh	minor ninth	C^seven−9, C^{7 ♭ 9}	C Due east G B ♭ D ♭	Play(help·info)
Seventh sharp ninth	dominant seventh	augmented ninth	C^seven+9, C^{7 ♯ 9}	C E G B ♭ D ♯	Play(help·info)
Seventh augmented eleventh	ascendant seventh	augmented eleventh	C⁷⁺¹¹, C^{7 ♯ 11}	C E K B ♭ D F ♯	Play(help·info)
Seventh macerated thirteenth	ascendant 7th	modest thirteenth	C^seven−13, C^{seven ♭ 13}	C E G B ♭ D F A ♭	Play(help·info)
Half-diminished seventh	minor seventh	diminished fifth	C ^ø , C ^ø ⁷, Cm^{7 ♭ 5}	C Due east ♭ Grand ♭ B ♭	Play(assistance·info)

Added tone chords [edit]

An added tone chord is a triad with an added, non-tertian note, such as an added 6th or a chord with an added second (ninth) or quaternary (eleventh) or a combination of the iii. These chords do not include "intervening" thirds as in an extended chord. Added chords tin can also have variations. Thus, one thousand^add9, m⁴ and 1000⁶ are pocket-sized triads with extended notes.

Sixth chords can belong to either of two groups. I is first inversion chords and added 6th chords that contain a sixth from the root.^[38] The other group is inverted chords in which the interval of a 6th appears above a bass notation that is not the root.^[39]

The major sixth chord (also called, sixth or added sixth with the chord note half-dozen, eastward.g., C⁶) is by far the nigh common type of 6th chord of the first group. Information technology comprises a major triad with the added major sixth higher up the root, mutual in pop music.^[3] For example, the chord C⁶ contains the notes C–E–M–A. The minor sixth chord (min⁶ or m⁶, e.thousand., Cm⁶) is a pocket-sized triad, still with a major vi. For example, the chord Cm^{half dozen} contains the notes C–E ♭ –Chiliad–A.

The augmented sixth chord usually appears in chord notation every bit 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 more often than not used as a dissonant interval nearly ordinarily used in motility towards a ascendant 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 instance, the tonic notation 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 sixth chord: A ♭ , C, F ♯
French sixth chord: A ♭ , C, D, F ♯
German 6th chord: A ♭ , C, E ♭ , F ♯

The augmented sixth family unit of chords exhibits certain peculiarities. Since they are not based on triads, equally are seventh chords and other 6th chords, they are not more often than not regarded as having roots (nor, therefore, inversions), although i re-voicing of the notes is common (with the namesake interval inverted to create a diminished third).^[40]

The second group of sixth chords includes inverted major and minor chords, which may exist called sixth chords in that the half dozen-three ( ^vi
₃ ) and six-four ( ^half-dozen
_iv ) chords contain intervals of a sixth with the bass note, though this is not the root. Nowadays, this is mostly for academic study or assay (meet figured bass) but the Neapolitan 6th chord is an of import example; a major triad with a apartment supertonic scale degree as its root that is chosen a "sixth" because it is well-nigh always institute in kickoff inversion. Though a technically accurate Roman numeral analysis would be ♭ II, information technology is generally labelled N^six. In C major, the chord is notated (from root position) D ♭ , F, A ♭ . Because it uses chromatically altered tones, this chord is ofttimes grouped with the borrowed chords merely the chord is not borrowed from the relative major or minor and it may appear in both major and pocket-sized keys.

Blazon	Components			Chord symbol	Notes	Audio
Blazon	Chord	Interval(s)		Chord symbol	Notes	Audio
Add nine	major triad	major ninth	—	C^two, C^add9	C E Chiliad D	Play(help·info)
Add together fourth	major triad	perfect fourth	—	C⁴, C^add11	C E M F	Play(help·info)
Add 6th	major triad	major sixth	—	C^{half dozen}	C E Chiliad A	Play(help·info)
Six-nine	major triad	major sixth	major ninth	C^6/9	C E G A D	—
Vii-half dozen	major triad	major 6th	minor 7th	C^7/6	C Due east G A B ♭	—
Mixed-tertiary	major triad	small third	—	—	C E ♭ E K	Play(aid·info)

Suspended chords [edit]

${ \override Score.TimeSignature #'stencil = ##f \relative c' { \clef treble \time 4/4 \textLengthOn <c f g>1 } }$

A C^sus4 chord

A suspended chord, or "sus chord", is a chord in which the tertiary is replaced by either the 2d or the fourth. This produces two main chord types: the suspended second (sus2) and the suspended fourth (sus4). The chords, C^sus2 and C^sus4, 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 nowadays, for example the chord with the notes C–D–F–Thousand.

The proper name suspended derives from an early on polyphonic technique adult during the common practice period, in which a stepwise melodic progress to a harmonically stable note in any item role was oft 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 3rd in either chord would negate the pause, and then such chords would be chosen added ninth and added eleventh chords instead.

In modern lay usage, the term is restricted to the displacement of the third simply, and the anomalous second or fourth no longer must 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 mail service-bop and modal jazz compositions and improvisations, suspended seventh chords are often used in nontraditional ways: these often do not office equally 5 chords and do not resolve from the fourth to the third. The lack of resolution gives the chord an cryptic, static quality. Indeed, the 3rd 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 C^7sus4. C^sus4 is sometimes written C^sus since the sus4 is more common than the sus2.

Blazon	Components				Chord symbol	Notes	Audio
Blazon	Chord	Interval(south)			Chord symbol	Notes	Audio
Suspended second	open up fifth	major second	—	—	C^sus2	C D G	Play(help·info)
Suspended fourth	open fifth	perfect fourth	—	—	C^sus4	C F G	Play(help·info)
Jazz sus	open 5th	perfect 4th	minor seventh	major 9th	C^9sus4	C F G B ♭ D	Play(help·info)

Borrowed chords [edit]

${ \override Score.TimeSignature #'stencil = ##f \relative c' { \clef treble \fourth dimension four/4 <d f aes>1_\markup { \translate #'(-7.5 . 0) { \concat { \small "C Maj.:" \hspace #1 \normalsize "ii" \raise #1 \small-scale "o" \hspace #vi "ii" \enhance #1 \pocket-size "ø7" \hspace #4 "♭III" \hspace #5.viii "iv" \hspace #five.5 "♭Half-dozen" \hspace #five.5 "vii" \raise #1 \small "o7" } } } <d f aes c> <es g bes> <f aes c> <aes c es> <b d f aes> \bar "||" } }$

A borrowed chord is one from a unlike key than the home key, the central of the piece it is used in. The most mutual occurrence of this is where a chord from the parallel major or pocket-size key is used. Particularly skilful 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 (e.m., an East ♭ major chord) would be borrowed, as this chord appears only in the key of C minor. Although borrowed chords could theoretically include chords taken from any key other than the home fundamental, this is not how the term is used when a chord is described in formal musical analysis.

When a chord is analysed equally "borrowed" from some other key information technology may be shown past the Roman numeral corresponding with that central afterward a slash. For example, V/5 (pronounced "five of five") indicates the dominant chord of the dominant primal of the present abode-key. The dominant key of C major is G major so this secondary dominant is the chord of the fifth degree of the One thousand major scale, which is D major (which tin can also be described every bit II relative to the fundamental of C major, not to be confused with the supertonic ii namely D pocket-size.). If used for a significant elapsing, the apply of the D major chord may cause a modulation to a new central (in this example to K major).

Borrowed chords are widely used in Western popular music and rock music. For example, there are a number of songs in E major which use the ♭ III chord (e.g., a G major chord used in an Due east major song), the ♭ Seven chord (e.k., a D major chord used in an Due east major song) and the ♭ VI chord (e.chiliad., a C major chord used in an E major vocal). All of these chords are "borrowed" from the primal of Eastward minor.

References [edit]

Notes [edit]

^ Benward & Saker 2003, p. 67 note that "A chord is a harmonic unit of measurement with at least iii unlike tones sounding simultaneously." And Benward & Saker 2003, p. 359 "A combination of three or more than pitches sounding at the same time." Károlyi 1965, p. 63 notes "2 or more notes sounding simultaneously are known as a chord".

Citations [edit]

^ Moylan 2014, p. 39.
^ ^a ^b ^c Schoenberg 1983, pp. i–2.
^ ^a ^b ^c ^d ^e Benward & Saker 2003, p. 77.
^ "Chord". Merriam-Webster'southward dictionary of English usage. Merriam-Webster. 1995. p. 243. ISBN978-0-87779-132-4.
^ "Chord". Oxford Dictionaries.
^ Malm 1996, p. 15, "Indeed, this harmonic orientation is one of the major differences between Western and much non-Western music."
^ Dahlhaus 2001. sfn error: no target: CITEREFDahlhaus2001 (assistance)
^ ^a ^b Nattiez 1990, p. 218.
^ Károlyi 1965, p. 63.
^ Schoenberg 2010, p. 26, "It is required of a chord that it consist of three different tones."
^ Surmani 2004, p. 72.
^ Jones 1994, p. 43.
^ Monath 1984, p. 37.
^ Schellenberg et al. 2005, pp. 551–566.
^ Duarter 2008, p. 49.
^ Benward & Saker 2003, p. 185.
^ ^a ^b Benward & Saker 2003, p. 70.
^ Benward & Saker 2003, p. 100.
^ ^a ^b Benward & Saker 2003, p. 201.
^ Benward & Saker 2003, p. 220.
^ Benward & Saker 2003, p. 231.
^ Benward & Saker 2003, p. 274.
^ Harrison 2005, p. 33.
^ Pachet 1999, pp. 187–206.
^ Tanguiane 1993.
^ Tanguiane 1994.
^ Andrews & Sclater 2000, p. 227.
^ Benward & Saker 2003, pp. 74–75.
^ Haerle 1982, p. 30.
^ Policastro 1999, p. 168.
^ Benward & Saker 2003, p. 92.
^ Weedon 2007.
^ Mayfield 2012, p. 523.
^ Hanson 1960, p. 7.
^ Benjamin et al. 2014, pp. 46–47.
^ Benjamin et al. 2014, pp. 48–49.
^ Hawkins 1992, pp. 325–335.
^ Miller 2005, p. 119.
^ Piston 1987, p. 66.
^ Bartlette & Laitz 2010.

Sources [edit]

Andrews, William K; Sclater, Molly (2000). Materials of Western Music Part 1. ISBNane-55122-034-2.
Bartlette, Christopher; Laitz, Steven K. (2010). Graduate Review of Tonal Theory. New York: Oxford University Press. ISBN978-0-19-537698-2.
Benjamin, T.; Horvit, K.; Nelson, R.; Koozin, T. (2014). Techniques and Materials of Music: From the Common Practise Menstruum Through the Twentieth Century (Enhanced ed.). Cengage Learning. ISBN978-i-285-96580-ii.
Benward, Bruce; Saker, Marilyn (2003). Music in Theory and Practice. Vol. I (' (seventh ed.). New York: McGraw Hill. ISBN9780072942620. OCLC 61691613.
Dahlhaus, Carl (2001). "Harmony". In Sadie, Stanley; Tyrrell, John (eds.). The New Grove Dictionary of Music and Musicians (2nd ed.). London: Macmillan. ‎
Duarter, John (2008). Melody & Harmony for Guitarists. ISBN978-0-7866-7688-0.
Harrison, Winston (2005). The Rockmaster System: Relating Ongoing Chords to the Keyboard – Stone, Book one. Dellwin. ISBN9780976526704.
Haerle, Dan (1982). The Jazz Language: A Theory Text for Jazz Composition and Improvisation. ISBN978-0-7604-0014-two.
Hanson, Howard (1960). Harmonic Materials of Modern Music. New York: Appleton-Century-Crofts. LOC 58-8138.
Hawkins, Stan (October 1992). "Prince- Harmonic Assay of 'Anna Stesia'". Popular Music. 11 (iii): 329, 334n7. doi:x.1017/S0261143000005171.
Jones, George T. (1994). College Outline Music Theory. HarperCollins. ISBN0-06-467168-2.
Károlyi, Otto (1965). Introducing Music. Penguin. ISBN9780140206593.
Malm, William P. (1996). Music Cultures of the Pacific, the About East, and Asia (third ed.). ISBN0-13-182387-6.
Mayfield, Connie E. (2012). Theory Essentials. ISBN978-i-133-30818-8.
Miller, Michael (2005). The Complete Idiot'due south Guide to Music Theory. ISBN978-1-59257-437-vii.
Monath, Norman (1984). How to Play Popular Pianoforte in x Piece of cake Lessons. Fireside Books. ISBN0-671-53067-4.
Moylan, William (2014). Understanding and Crafting the Mix: The Fine art of Recording. CRC Press. ISBN9781136117589.
Nattiez, Jean-Jacques (1990) [1987 as Musicologie générale et sémiologue]. Music and Discourse: Toward a Semiology of Music. Translated by Carolyn Abbate. ISBN0-691-02714-5.
Pachet, François (1999). "Surprising Harmonies". International Periodical on Computing Anticipatory Systems.
Piston, Walter (1987). Harmony (5th ed.). New York: W.W. Norton & Company. ISBN0-393-95480-3.
Policastro, Michael A. (1999). Agreement How to Build Guitar Chords and Arpeggios. ISBN978-0-7866-4443-8.
Schellenberg, E. Glenn; Bigand, Emmanuel; Poulin-Charronnat, Benedicte; Garnier, Cecilia; Stevens, Catherine (Nov 2005). "Children's implicit noesis of harmony in Western music". Developmental Science. eight (half dozen): 551–566. doi:10.1111/j.1467-7687.2005.00447.x. PMID 16246247.
Schoenberg, Arnold (1983). Structural Functions of Harmony. Faber and Faber.
Schoenberg, Arnold (2010). Theory of harmony. Berkeley, Calif: University of California. ISBN978-0-520-26608-7. OCLC 669843249.
Surmani, Andrew (2004). Essentials of Music Theory: A Complete Self-Report Course for All Musicians. ISBN0-7390-3635-1.
Tanguiane, Andranick (1993). Artificial Perception and Music Recognition. Lecture Notes in Bogus Intelligence. Vol. 746. Berlin-Heidelberg: Springer. ISBN978-3-540-57394-four.
Tanguiane, Andranick (1994). "A principle of correlativity of perception and its application to music recognition". Music Perception. 11 (4): 465–502. doi:ten.2307/40285634. JSTOR 40285634.
Weedon, Bert (2007). Play in a Solar day. Faber Music. ISBN978-0-571-52965-0.

External links [edit]