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{{Short description|Tonal degree of the diatonic scale}}
{{for|the term "dominant function" on the Myers-Briggs Type Indicator|Myers-Briggs Type Indicator#Dominant function}}{{Image frame|content=<score vorbis="1" lang="lilypond">
{{Image frame|content=<score sound="1">
{
{
\override Score.TimeSignature #'stencil = ##f
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\time 4/4 <g b d>1 \bar "||"
\time 4/4 <g b d>1 \bar "||"
} }
} }
</score>|width=310|caption=C major scale and dominant triad}}
</score>|width=310|caption=The C major scale and dominant triad}}In [[music]], the '''dominant''' is the fifth [[degree (music)|scale degree]] ({{music|scale|5}}) of the [[diatonic scale]]. It is called the ''dominant'' because it is next in importance to the first scale degree, the [[tonic (music)|tonic]].<ref>
Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.33. Seventh Edition. {{ISBN|978-0-07-294262-0}}. "So called because its function is next in importance to the tonic."</ref><ref>[[Allen Forte|Forte, Allen]] (1979). ''Tonal Harmony'', p.118. 3rd edition. Holt, Rinehart, and Wilson. {{ISBN|0-03-020756-8}}. "V serves to establish the tonic triad...particularly evident at the cadence."</ref> In the [[Solfège#Movable do solf%C3%A8ge|movable do solfège]] system, the dominant note is sung as ''so(l)''.{{Image frame|content=<score vorbis="1" lang="lilypond">
In [[music]], the '''dominant''' is the fifth [[degree (music)|scale degree]] ({{music|scale|5}}) of the [[diatonic scale]]. It is called the ''dominant'' because it is second in importance to the first scale degree, the [[tonic (music)|tonic]].<ref>Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p. 33. Seventh Edition. {{ISBN|978-0-07-294262-0}}. "So called because its function is next in importance to the tonic."</ref><ref>{{cite book|last=Forte|first=Allen|author-link=Allen Forte|year=1979|title=Tonal Harmony|page=118|edition=3rd|publisher=Holt, Rinehart, and Wilson|isbn=0-03-020756-8|quote=V serves to establish the tonic triad...particularly evident at the cadence.}}</ref> In the [[Solfège#Movable do solf%C3%A8ge|movable do solfège]] system, the dominant note is sung as "So(l)".
{{Image frame|content=<score sound="1">
{
{
#(set-global-staff-size 16)
#(set-global-staff-size 16)
Line 23: Line 25:
<g b d f aes>
<g b d f aes>
} }
} }
</score>|width=355|caption=Chords with a dominant function: dominant chords ([[seventh chord|seventh]], [[ninth chord|ninth]], and [[dominant ninth chord|dominant ninth]]) and [[leading-tone]] chords ([[diminished triad|diminished]], [[half-diminished seventh chord|half-diminished seventh]], and [[diminished seventh chord|diminished seventh]]).<ref>Berry, Wallace (1976/1987). ''Structural Functions in Music'', p.54. {{ISBN|0-486-25384-8}}.</ref>}}
</score>|width=442|caption=Chords with a dominant function: dominant chords ([[seventh chord|seventh]], [[ninth chord|ninth]], and [[dominant ninth chord|dominant ninth]]) and [[leading-tone]] chords ([[diminished triad|diminished]], [[half-diminished seventh chord|half-diminished seventh]], and [[diminished seventh chord|diminished seventh]]).<ref>{{cite book|last=Berry|first=Wallace|author-link=Wallace Berry|orig-year=1976|year=1987|title=Structural Functions in Music|page=54|isbn=0-486-25384-8}}</ref>}}
The [[Triad (music)|triad]] built on the dominant note is called the '''dominant chord'''. This chord is said to have dominant [[Function (music)|function]], which means that it creates an instability that requires the [[tonic (music)|tonic]] for [[resolution (music)|resolution]]. Dominant triads, [[Seventh chord|seventh chords]], and [[Ninth chord|ninth chords]] typically have dominant function. [[Leading-tone triad|Leading-tone triads]] and [[Leading-tone seventh chord|seventh chords]] may also have dominant function.
The [[Triad (music)|triad]] built on the dominant note is called the '''dominant chord'''. This chord is said to have dominant [[Function (music)|function]], which means that it creates an instability that requires the [[tonic (music)|tonic]] for [[resolution (music)|resolution]]. Dominant triads, [[Seventh chord|seventh chords]], and [[Ninth chord|ninth chords]] typically have dominant function. [[Leading-tone triad|Leading-tone triads]] and [[Leading-tone seventh chord|leading-tone seventh chords]] may also have dominant function.
{{quote|In very much conventionally [[tonality|tonal music]], harmonic analysis will reveal a broad prevalence of the [[primary triad|primary]] (often triadic) harmonies: tonic, dominant, and [[subdominant]] (i.e., I and its chief auxiliaries a 5th removed), and especially the first two of these.|Berry (1976)<ref name="Berry">Berry, Wallace (1976/1987). ''Structural Functions in Music'', p.62. {{ISBN|0-486-25384-8}}.</ref>|source=}}
{{quote|In very much conventionally [[tonality|tonal music]], harmonic analysis will reveal a broad prevalence of the [[primary triad|primary]] (often triadic) harmonies: tonic, dominant, and [[subdominant]] (i.e., I and its chief auxiliaries a 5th removed), and especially the first two of these.|[[Wallace Berry]] (1976)<ref name="Berry">{{harvnb|Berry|1987|p=62}}</ref>|source=}}


{{quote|The scheme I-x-V-I symbolizes, though naturally in a very summarizing way, the harmonic course of any composition of the [[Classical period (music)|Classical period]]. This ''x'', usually appearing as a [[chord progression|progression of chords]], as a whole series, constitutes, as it were, the actual "music" within the scheme, which through the annexed formula V-I, is made into a unit, a group, or even a whole piece.|[[Rudolph Reti]]|(1962)<ref>Reti, Rudolph (1962). ''Tonality in Modern Music'', p.28.</ref> quoted in<ref>Kostka & Payne (1995). ''Tonal Harmony'', p.458. {{ISBN|0-07-035874-5}}.</ref>}}
{{quote|The scheme I-x-V-I symbolizes, though naturally in a very summarizing way, the harmonic course of any composition of the [[Classical period (music)|Classical period]]. This ''x'', usually appearing as a [[chord progression|progression of chords]], as a whole series, constitutes, as it were, the actual "music" within the scheme, which through the annexed formula V-I, is made into a unit, a group, or even a whole piece.|[[Rudolph Reti]]|(1962)<ref>[[Rudolph Reti|Reti, Rudolph]] (1962). ''Tonality in Modern Music'', p. 28, quoted in [[Stefan Kostka|Kostka]] & Payne (1995). ''Tonal Harmony'', p. 458. {{ISBN|0-07-035874-5}}.</ref>}}


== Dominant chords ==
== Dominant chords ==
{{Image frame|content=<score vorbis="1" lang="lilypond">
{{Image frame|content=<score sound="1">
{
{
\override Score.TimeSignature #'stencil = ##f
\override Score.TimeSignature #'stencil = ##f
Line 38: Line 40:
\time 4/4 <g bes d>1 <g b! d> \bar "||"
\time 4/4 <g bes d>1 <g b! d> \bar "||"
} }
} }
</score>|width=365|caption=The C minor scale and dominant triad, first with a [[subtonic]] ({{music|flat}}{{music|scale|7|}}) and then with a [[leading tone]] ({{music|natural}}{{music|scale|7|}})}}
</score>|width=365|caption=C minor scale and dominant triad, first with a [[subtonic]] ({{music|flat}}{{music|scale|7|}}) and then with a [[leading tone]] ({{music|natural}}{{music|scale|7|}})}}


In [[music theory]], the dominant [[triad (music)|triad]] is a [[major chord]], symbolized by the [[Roman numeral analysis|Roman numeral]] "V" in the [[major scale]]. In the [[natural minor scale]], the triad is a [[minor chord]], denoted by "v". However, in a minor [[Key (music)|key]], the seventh scale degree is often raised by a [[half step]] ({{music|flat}}{{music|scale|7}} to {{music|natural}}{{music|scale|7}}), creating a [[major chord]].
In [[music theory]], the dominant [[triad (music)|triad]] is a [[major chord]], symbolized by the [[Roman numeral analysis|Roman numeral]] "V" in the [[major scale]]. In the [[natural minor scale]], the triad is a [[minor chord]], denoted by "v". However, in a minor [[Key (music)|key]], the seventh scale degree is often raised by a [[half step]] ({{music|flat}}{{music|scale|7}} to {{music|natural}}{{music|scale|7}}), creating a [[major chord]].


These chords may also appear as [[Seventh chord|seventh chords]]: typically as a [[dominant seventh chord]], but occasionally in minor as a [[minor seventh chord]] v<sup>7</sup> with [[Passing chord|passing function]]:<ref name="K&P 2463">{{Cite book|url=https://www.worldcat.org/oclc/51613969|title=Tonal Harmony|last=Kostka|first=Stefan|last2=Payne|first2=Dorothy|date=2004|publisher=McGraw-Hill|others=|year=|isbn=0072852607|edition=5th|location=Boston|pages=197|oclc=51613969}}</ref>
These chords may also appear as [[Seventh chord|seventh chords]]: typically as a [[dominant seventh chord]], but occasionally in minor as a [[minor seventh chord]] v<sup>7</sup> with [[Passing chord|passing function]]:<ref name="K&P 2463">{{Cite book|title=Tonal Harmony|url=https://archive.org/details/workbookfortonal00kost_245|url-access=limited|last1=Kostka|first1=Stefan|author1-link=Stefan Kostka|last2=Payne|first2=Dorothy|date=2004|publisher=McGraw-Hill|isbn=0072852607|edition=5th|location=Boston|pages=[https://archive.org/details/workbookfortonal00kost_245/page/n185 197]|oclc=51613969}}</ref>


:<score lang="lilypond">
:<score lang="lilypond">
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</score>
</score>


As defined by the 19th century musicologist [[François-Joseph Fétis|Joseph Fétis]], the ''dominante'' was a seventh chord over the first note of a descending perfect fifth in the ''[[basse fondamentale]]'' or root progression, the [[common practice period]] dominant seventh he named the ''dominante tonique''.<ref>Dahlhaus, Carl. Gjerdingen, Robert O. trans. (1990). ''Studies in the Origin of Harmonic Tonality'', p.143. Princeton University Press. {{ISBN|0-691-09135-8}}.</ref>
As defined by the 19th century musicologist [[François-Joseph Fétis|Joseph Fétis]], the ''dominante'' was a seventh chord over the first note of a descending perfect fifth in the ''[[basse fondamentale]]'' or root progression, the [[common practice period]] dominant seventh he named the ''dominante tonique''.<ref>Dahlhaus, Carl. Gjerdingen, Robert O. trans. (1990). ''Studies in the Origin of Harmonic Tonality'', p. 143. Princeton University Press. {{ISBN|0-691-09135-8}}.</ref>


Dominant chords are important to [[Cadence|cadential]] [[Chord progression|progressions]]. In the strongest cadence, the [[authentic cadence]] (example shown below), the dominant chord is followed by the tonic chord. A cadence that ends with a dominant chord is called a ''[[half cadence]]''.
Dominant chords are important to [[Cadence|cadential]] [[Chord progression|progressions]]. In the strongest cadence, the [[authentic cadence]] (example shown below), the dominant chord is followed by the tonic chord. A cadence that ends with a dominant chord is called a ''[[half cadence]]'' or an "imperfect cadence".


: <score vorbis="1" lang="lilypond">
:<score sound="1">
\new PianoStaff <<
\new PianoStaff <<
\new Staff <<
\new Staff <<
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[[File:Circle of fifths deluxe 4.svg|thumb|The key immediately clockwise is the dominant key of the key immediately counterclockwise, and features either one more sharp or one less flat.]]
[[File:Circle of fifths deluxe 4.svg|thumb|The key immediately clockwise is the dominant key of the key immediately counterclockwise, and features either one more sharp or one less flat.]]


The '''dominant key''' is the [[key (music)|key]] whose tonic is a [[perfect fifth]] above (or a [[perfect fourth]] below) the [[tonic (music)|tonic]] of the main key of the piece. Put another way, it is the key whose tonic is the dominant scale degree in the main key.<ref>{{cite web |url= |title=Dominant |date= |website=Grove Music Online |publisher= |accessdate=}}{{full citation needed|date=May 2013}}</ref> If, for example, a piece is written in the key of [[C major]], then the tonic key is C major and the dominant key is [[G major]] since G is the dominant note in C major.<ref>{{cite web |url=http://www.britannica.com/eb/article-9030871/dominant#94697.hook |title=Dominant |last1=DeVoto |first1=Mark |date= |website=Encyclopædia Britannica |publisher= |accessdate=22 May 2013}}</ref> With a key signature of one sharp, G major has one more sharp than C major.
The '''dominant key''' is the [[key (music)|key]] whose tonic is a [[perfect fifth]] above (or a [[perfect fourth]] below) the [[tonic (music)|tonic]] of the main key of the piece. Put another way, it is the key whose tonic is the dominant scale degree in the main key.<ref>"Dominant", ''[[Grove Music Online]]''{{full citation needed|date=May 2013|reason=There are 2 articles, both by Janna Saslaw; which one?}}</ref> If, for example, a piece is written in the key of [[C major]], then the tonic key is C major and the dominant key is [[G major]] since G is the dominant note in C major.<ref>{{cite web |url=http://www.britannica.com/eb/article-9030871/dominant#94697.hook |title=Dominant |last1=DeVoto |first1=Mark |website=Encyclopædia Britannica |access-date=22 May 2013}}</ref>


[[File:Harmonic axis in C major and minor.png|300px|thumb|"Essentially, there are two harmonic directions: toward I and toward V. These primary diatonic triads form the harmonic axis of tonal music."{{sfn|Forte|1979|p=103}}]]
In [[sonata form]] in major keys, the second subject group is usually in the dominant key.{{quote|The movement to the dominant was part of musical grammar, not an element of form. Almost all music in the eighteenth century went to the dominant: before 1750 it was not something to be emphasized; afterward, it was something that the composer could take advantage of. This means that every eighteenth-century listener expected the movement to the dominant in the sense that [one] would have been puzzled if [one] did not get it; it was a necessary condition of intelligibility.|[[Charles Rosen]] (1972)<ref>Rosen, Charles (1972). ''[[The Classical Style]]''. W.W. Norton & Company Inc. Cited in White, John D. (1976). ''The Analysis of Music'', p.56. {{ISBN|0-13-033233-X}}.</ref>}}


In [[sonata form]] in major keys, the second subject group is usually in the dominant key.{{quote|The movement to the dominant was part of musical grammar, not an element of form. Almost all music in the eighteenth century went to the dominant: before 1750 it was not something to be emphasized; afterward, it was something that the composer could take advantage of. This means that every eighteenth-century listener expected the movement to the dominant in the sense that [one] would have been puzzled if [one] did not get it; it was a necessary condition of intelligibility.|[[Charles Rosen]] (1972)<ref>[[Charles Rosen|Rosen, Charles]] (1972). ''[[The Classical Style]]''. W. W. Norton. Cited in White, John D. (1976). ''The Analysis of Music'', p. 56. {{ISBN|0-13-033233-X}}.</ref>}}
[[File:Harmonic axis in C major and minor.png|300px|thumb|"Essentially, there are two harmonic directions: toward I and toward V. These primary diatonic triads form the harmonic axis of tonal music."<ref>Forte (1979), p.103.</ref>]]


Music which [[Modulation (music)|modulates]] (changes key) often modulates to the dominant key. Modulation to the dominant often creates a sense of increased tension; as opposed to modulation to the [[subdominant]] (fourth note of the scale), which creates a sense of musical relaxation.
Music which [[Modulation (music)|modulates]] (changes key) often modulates to the dominant key. Modulation to the dominant often creates a sense of increased tension; as opposed to modulation to the [[subdominant]] (fourth note of the scale), which creates a sense of musical relaxation.


{{quote|The vast majority of harmonies designated as "essential" in the basic frame of structure must be I and V–the latter, ''when tonal music is viewed in broadest terms'', an auxiliary support and embellishment of the former, for which it is the principal medium of [[tonicization]].|Berry (1976)<ref name="Berry"/>}}{{Clear}}
{{quote|The vast majority of harmonies designated as "essential" in the basic frame of structure must be I and V–the latter, ''when tonal music is viewed in broadest terms'', an auxiliary support and embellishment of the former, for which it is the principal medium of [[tonicization]].|Berry (1976)<ref name="Berry"/>}}
{{Clear}}



== In non-Western music ==
== In non-Western music ==
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* [[Nondominant seventh chord]]
* [[Nondominant seventh chord]]


== Sources ==
== References ==
{{reflist}}
{{reflist}}



Latest revision as of 17:49, 25 February 2024


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\relative c' { 
  \clef treble 
  \time 7/4 c4 d e f \once \override NoteHead.color = #red g a b \time 2/4 c2 \bar "||"
  \time 4/4 <g b d>1 \bar "||"
} }
C major scale and dominant triad

In music, the dominant is the fifth scale degree (scale degree 5) of the diatonic scale. It is called the dominant because it is second in importance to the first scale degree, the tonic.[1][2] In the movable do solfège system, the dominant note is sung as "So(l)".


{
#(set-global-staff-size 16)
\override Score.TimeSignature #'stencil = ##f
\relative c'' { 
  \clef treble 
  \time 4/4 
  <g b d>1_\markup{ \concat{ "V" \hspace #6 "V" \raise #1 "7" \hspace #5.5 "vii" \raise #1 "o" \hspace #4.5 "vii" \raise #1 "ø7" \hspace #3 "vii" \raise #1 "o7" \hspace #4 "V" \raise #1 "9" \hspace #4 "V" \raise #1 "7♭9" } }
  <g b d f>
  <b d f>
  <b d f a>
  <b d f aes>
  <g b d f a>
  <g b d f aes>
} }
Chords with a dominant function: dominant chords (seventh, ninth, and dominant ninth) and leading-tone chords (diminished, half-diminished seventh, and diminished seventh).[3]

The triad built on the dominant note is called the dominant chord. This chord is said to have dominant function, which means that it creates an instability that requires the tonic for resolution. Dominant triads, seventh chords, and ninth chords typically have dominant function. Leading-tone triads and leading-tone seventh chords may also have dominant function.

In very much conventionally tonal music, harmonic analysis will reveal a broad prevalence of the primary (often triadic) harmonies: tonic, dominant, and subdominant (i.e., I and its chief auxiliaries a 5th removed), and especially the first two of these.

— Wallace Berry (1976)[4]

The scheme I-x-V-I symbolizes, though naturally in a very summarizing way, the harmonic course of any composition of the Classical period. This x, usually appearing as a progression of chords, as a whole series, constitutes, as it were, the actual "music" within the scheme, which through the annexed formula V-I, is made into a unit, a group, or even a whole piece.

— Rudolph Reti, (1962)[5]

Dominant chords

[edit]

{
\override Score.TimeSignature #'stencil = ##f
\relative c' { 
  \clef treble 
  \time 7/4 c4 d es f \once \override NoteHead.color = #red g aes bes \time 2/4 c2 \bar "||"
  \time 4/4 <g bes d>1 <g b! d> \bar "||"
} }
C minor scale and dominant triad, first with a subtonic (scale degree 7) and then with a leading tone (scale degree 7)

In music theory, the dominant triad is a major chord, symbolized by the Roman numeral "V" in the major scale. In the natural minor scale, the triad is a minor chord, denoted by "v". However, in a minor key, the seventh scale degree is often raised by a half step (scale degree 7 to scale degree 7), creating a major chord.

These chords may also appear as seventh chords: typically as a dominant seventh chord, but occasionally in minor as a minor seventh chord v7 with passing function:[6]


{
\override Score.TimeSignature #'stencil = ##f
\relative c'' {
   \clef treble 
   \time 4/4
   \key c \major
   <g b d f>1_\markup { \concat { "V" \raise #1 \small "7" } } \bar "||"

   \clef treble 
   \time 4/4
   \key c \minor
   <g b d f>1_\markup { \concat { "V" \raise #1 \small "7" } }
   <g bes! d f>^\markup { "rare" }_\markup { \concat { "v" \raise #1 \small "7" } } \bar "||"
} }

As defined by the 19th century musicologist Joseph Fétis, the dominante was a seventh chord over the first note of a descending perfect fifth in the basse fondamentale or root progression, the common practice period dominant seventh he named the dominante tonique.[7]

Dominant chords are important to cadential progressions. In the strongest cadence, the authentic cadence (example shown below), the dominant chord is followed by the tonic chord. A cadence that ends with a dominant chord is called a half cadence or an "imperfect cadence".


   \new PianoStaff <<
      \new Staff <<
         \new Voice \relative c'' {
             \stemUp \clef treble \key c \major \time 4/4
             b1 c 
             }
         \new Voice \relative c'' {
             \stemDown
              g1 g
              }
            >>
     \new Staff <<
         \new Voice \relative c' {
             \stemUp \clef bass \key c \major \time 4/4
             d1 e
             }
         \new Voice \relative c' {
             \stemDown
             g1_\markup { \concat { \translate #'(-4 . 0) { "C:   V" \hspace #7 "I" } } }
             c, \bar "||"
             }
         >>
    >>

Dominant key

[edit]
The key immediately clockwise is the dominant key of the key immediately counterclockwise, and features either one more sharp or one less flat.

The dominant key is the key whose tonic is a perfect fifth above (or a perfect fourth below) the tonic of the main key of the piece. Put another way, it is the key whose tonic is the dominant scale degree in the main key.[8] If, for example, a piece is written in the key of C major, then the tonic key is C major and the dominant key is G major since G is the dominant note in C major.[9]

"Essentially, there are two harmonic directions: toward I and toward V. These primary diatonic triads form the harmonic axis of tonal music."[10]

In sonata form in major keys, the second subject group is usually in the dominant key.

The movement to the dominant was part of musical grammar, not an element of form. Almost all music in the eighteenth century went to the dominant: before 1750 it was not something to be emphasized; afterward, it was something that the composer could take advantage of. This means that every eighteenth-century listener expected the movement to the dominant in the sense that [one] would have been puzzled if [one] did not get it; it was a necessary condition of intelligibility.

— Charles Rosen (1972)[11]

Music which modulates (changes key) often modulates to the dominant key. Modulation to the dominant often creates a sense of increased tension; as opposed to modulation to the subdominant (fourth note of the scale), which creates a sense of musical relaxation.

The vast majority of harmonies designated as "essential" in the basic frame of structure must be I and V–the latter, when tonal music is viewed in broadest terms, an auxiliary support and embellishment of the former, for which it is the principal medium of tonicization.

— Berry (1976)[4]


In non-Western music

[edit]

The dominant is an important concept in Middle Eastern music. In the Persian Dastgah, Arabic maqam and the Turkish makam, scales are made up of trichords, tetrachords, and pentachords (each called a jins in Arabic) with the tonic of a maqam being the lowest note of the lower jins and the dominant being that of the upper jins. The dominant of a maqam is not always the fifth, however; for example, in Kurdish music and Bayati, the dominant is the fourth, and in maqam Saba, the dominant is the minor third. A maqam may have more than one dominant.

See also

[edit]

References

[edit]
  1. ^ Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p. 33. Seventh Edition. ISBN 978-0-07-294262-0. "So called because its function is next in importance to the tonic."
  2. ^ Forte, Allen (1979). Tonal Harmony (3rd ed.). Holt, Rinehart, and Wilson. p. 118. ISBN 0-03-020756-8. V serves to establish the tonic triad...particularly evident at the cadence.
  3. ^ Berry, Wallace (1987) [1976]. Structural Functions in Music. p. 54. ISBN 0-486-25384-8.
  4. ^ a b Berry 1987, p. 62
  5. ^ Reti, Rudolph (1962). Tonality in Modern Music, p. 28, quoted in Kostka & Payne (1995). Tonal Harmony, p. 458. ISBN 0-07-035874-5.
  6. ^ Kostka, Stefan; Payne, Dorothy (2004). Tonal Harmony (5th ed.). Boston: McGraw-Hill. pp. 197. ISBN 0072852607. OCLC 51613969.
  7. ^ Dahlhaus, Carl. Gjerdingen, Robert O. trans. (1990). Studies in the Origin of Harmonic Tonality, p. 143. Princeton University Press. ISBN 0-691-09135-8.
  8. ^ "Dominant", Grove Music Online[full citation needed]
  9. ^ DeVoto, Mark. "Dominant". Encyclopædia Britannica. Retrieved 22 May 2013.
  10. ^ Forte 1979, p. 103.
  11. ^ Rosen, Charles (1972). The Classical Style. W. W. Norton. Cited in White, John D. (1976). The Analysis of Music, p. 56. ISBN 0-13-033233-X.