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A secondary chord is an music analysis label for a specific harmony device that is prevalent in the tonality idiom of Western music beginning in the common practice period: the use of diatonic functions for tonicization.
Secondary chords are a type of altered chord or borrowed chord, chords that are not part of the music piece's key. They are the most common sort of altered chord in tonal music. Secondary chords are referred to by the function they have and the key or chord in which they function. In Roman numeral analysis, they are written with the notation " function/ key". Thus, one of the most common secondary chords, the dominant of the dominant, is written "V/V" and read as "five of five" or "the dominant of the dominant". The Major triad or minor triad on any diatonic scale degree may have any secondary function applied to it; secondary functions may even be applied to in some special circumstances.
Secondary chords were not used until the Baroque music and are found more frequently and freely in the Classical period, even more so in the Romantic music. Composers began to use them less frequently with the breakdown of conventional harmony in modern classical music—but secondary dominants are a cornerstone of popular music and jazz in the 20th century.
According to music theorists David Beach and Ryan C. McClelland, "the purpose of the secondary dominant is to place emphasis on a chord within the diatonic progression." The secondary-dominant terminology is still usually applied even if the chord resolution is nonfunctional. For example, the V/ii label is still used even if the V/ii chord is not followed by ii.
In the key of C major, the five remaining chords are:
} }1_\markup { \translate #'(-4 . 0) { "C: ii" \hspace #7 "iii" \hspace #6.5 "IV" \hspace #6.5 "V" \hspace #6.8 "vi" } }_\markup { \translate #'(-2 . 0) "d minor" \hspace #1 "e minor" \hspace #1 "F major" \hspace #1 "G major" \hspace #1 "a minor" }
Of these chords, the V chord (G major) is said to be the dominant of C major. However, each of the chords from ii to vi also has its own dominant. For example, V (G major) has a D major triad as its dominant. These extra dominant chords are not part of the key of C major as such because they include notes that are not part of the C major scale. Instead, they are secondary dominants.
The notation below shows the secondary-dominant chords for C major. Each chord is accompanied by its standard number in harmonic notation. In this notation, a secondary dominant is usually labeled with the formula "V of ..." (dominant chord of); thus "V of ii" stands for the dominant of the ii chord, "V of iii" for the dominant of iii, and so on. A shorter notation, used below, is "V/ii", "V/iii", etc.
2_\markup { \translate #'(-4 . 0) { "C: V/ii ii" \hspace #4.5 "V/iii iii" \hspace #1.8 "V/IV IV" \hspace #2.2 "V/V V" \hspace #2.8 "V/vi vi" } }_\markup { "A Dm" \hspace #4.5 "B Em" \hspace #2.5 "C F" \hspace #4.2 "D G" \hspace #4.3 "E Am" }} }
Like most chords, secondary dominants may be or chords with other upper Extended chord. Dominant seventh chords are commonly used as secondary dominants. The notation below shows the same secondary dominants as above but with dominant seventh chords.
2_\markup { \concat { \translate #'(-4 . 0) { "C: V" \raise #1 \small "7" "/ii ii" \hspace #4.2 "V" \raise #1 \small "7" "/iii iii" \hspace #2.3 "V" \raise #1 \small "7" "/IV IV" \hspace #2.0 "V" \raise #1 \small "7" "/V V" \hspace #2.3 "V" \raise #1 \small "7" "/vi vi" } } }_\markup { \concat { "A" \raise #1 \small "7" " Dm" \hspace #4 "B" \raise #1 \small "7" " Em" \hspace #3.5 "C" \raise #1 \small "7" " F" \hspace #4 "D" \raise #1 \small "7" " G" \hspace #3.8 "E" \raise #1 \small "7" " Am" } }} }
Note that the triad V/IV is the same as the I triad. When a seventh is added (V7/IV), it becomes an altered chord because the seventh is not a diatonic pitch. Beethoven's Symphony No. 1 begins with a V7/IV chord:
{
\new PianoStaff <<
\new Staff <<
\relative c'' {
\tempo "Adagio molto"
2(\fp 8) r r4
\override DynamicLineSpanner.staff-padding = #3
2(\fp 8) r r4 2\cresc 4-.\!( -.) 4\f
}
>>
\new Staff <<
\new Voice \relative c {
\clef F
2(_\markup { \concat { \translate #'(-6 . 0) { "C: V" \raise #1 \small "7" "/IV" \hspace #1.5 "IV" \hspace #7 "V" \raise #1 \small "7" \hspace #3 "vi" \hspace #6.5 "V" \raise #1 \small "7" "/V" \hspace #10.5 "V" } } }
8) r r4 2( 8) r r4 2 4-.( -.)
}
>>
>> }
According to the principles exposed above, in fact, V7/IV, which means the C7 chord, i.e. the dominant seventh chord on the F major (C–E–G–B♭), does not represent the tonic because it contains a B♭, which isn't included in the main key, as Beethoven's Symphony No. 1 is written in the key of C major. The chord then resolves on the natural IV (F major) and in the following bar the V7, i.e. G7 (dominant seventh chord on the C major key), is presented.
Chromatic mediants, for example VI is also a secondary dominant of ii (V/ii) and III is V/vi, are distinguished from secondary dominants with context and musical analysis revealing the distinction.
Walter Piston first used the analysis "V7 of IV" in a monograph entitled Principles of Harmonic Analysis. In his 1941 book Harmony, Piston used the term "secondary dominant".: "These temporary dominant chords have been referred to by theorists as attendant chords, parenthesis chords, borrowed chords, etc. We shall call them secondary dominants, in the belief that the term is slightly more descriptive of their function." At around the same time (1946–48), Arnold Schoenberg created the expression "artificial dominant" to describe the same phenomenon, in his posthumously published book Structural Functions of Harmony.. The term "artificial", however, appears to refer to the altered chord by which a chord changes into another: "By substituting for altering the third in minor triads, they produce 'artificial' major triads and 'artificial' dominant seventh chords. Substituting for altering the fifth changes minor triads to 'artificial' diminished triads, commonly used with an added seventh, and changes major triads to augmented. Artificial dominants, artificial dominant seventh chords, and artificial diminished seventh chords are normally used in progressions according to the models V–I, V—VI and V—IV. (p. 16.)
In the fifth edition of Walter Piston's Harmony, a passage from the last movement of Mozart's Piano Sonata K. 283 in G major serves as one illustration of secondary dominants. This passage has three secondary dominants. The final four chords form a circle of fifths progression, ending in a standard dominant-tonic cadence, which concludes the phrase.
\set Score.proportionalNotationDuration = #(ly:make-moment 1/12)
\new PianoStaff <<
\new Staff <<
\relative c''' {
\set Score.currentBarNumber = #247
\bar ""
\tempo "Presto"
\key g \major \time 3/8
\override DynamicLineSpanner.staff-padding = #2
f8(\p e) e-.
e4( a,8)
d4( g,8)
c8-. r b-.
\grace { b8( } a4.)\trill
g8-.
}
>>
\new Staff <<
\new Voice \relative c'' {
\key g \major \time 3/8
r8_\markup { \concat { \translate #'(-5 . 0) { "G: V" \combine \raise #1 \small 6 \lower #1 \small 5 "/ii" \hspace #7 "vii" \raise #1 \small "o" \combine \raise #1 \small 6 \lower #1 \small 4 "/V" \hspace #1.2 "vii" \raise #1 \small "o" \combine \raise #1 \small 5 \lower #1 \small 3 \hspace #1 "vii" \raise #1 \small "o" \combine \raise #1 \small 6 \lower #1 \small 4 "/IV" \hspace #1 "IV" \raise #1 \small "6" \hspace #2 "V" \raise #1 \small "7" \hspace #4.5 "vi" \hspace #4 "ii" \hspace #5.8 "V" \hspace #4 "I" } } }
r -.
r ( -.)
r ( -.)
-. r -.
\stemUp g4 fis8
g^.
}
\new Voice \relative c' {
\stemDown
s4. s s s
c8 a d g
}
>>
>> }
Secondary dominants are used in jazz harmony in the bebop blues and other blues progression variations, as are substitute dominants and turnarounds. In some jazz tunes, all or almost all of the chords that are used are dominant chords. For example, in the standard jazz chord progression ii–V–I, which would normally be Dm–G7–C in the key of C major, some tunes will use D7–G7–C7. Since jazz tunes are often based on the circle of fifths, this creates long sequences of secondary dominants.
Secondary dominants are also used in popular music. Examples include II7 (V7/V) in Bob Dylan's "Don't Think Twice, It's All Right" and III7 (V7/vi) in Betty Everett's "The Shoop Shoop Song (It's in His Kiss)".. Everett notates major-minor sevenths Xm7. "Five Foot Two, Eyes of Blue" features chains of secondary dominants. "Sweet Georgia Brown" opens with V/V/V–V/V–V–I.
Quaternary dominants are rarer, but an example is the bridge section of the rhythm changes, which starts from V/V/V/V (in C major, E(7)). The example below from Chopin's Polonaises, Op. 26, No. 1 (1835) has a quaternary dominant in the second beat (V/ii = V/V/V, V/vi = V/V/V/V).
{
#(set-global-staff-size 16)
\new PianoStaff <<
\new Staff <<
\new Voice \relative c''' {
\set Score.currentBarNumber = #62
\bar ""
\key des \major \time 3/4
\voiceOne ges8 des16 es f8 c f c 16 d
es8 bes es bes16 c \tuplet 3/2 { des16\prall[ c des] } f16[ r32\fermata es](
aes,4)
}
\new Voice \relative c'' {
\key des \major \time 3/4
\voiceTwo bes!8 bes a a aes aes
g[ g ges ges f 16] r\fermata
r8
}
>>
\new Staff <<
\new Voice \relative c' {
\clef F \key des \major \time 3/4
8_\markup { \concat { \translate #'(-6 . 0) { "D♭: ii" \raise #1 \small "7" \hspace #8.5 "V" \raise #1 \small "7" "/vi" \hspace #5 "V" \raise #1 \small "7" "/ii" \hspace #10 "V" \raise #1 \small "7" "/V" \hspace #6 "V" \raise #1 \small "7" \hspace #10 "I" \hspace #6.5 "V" \combine \raise #1 \small 6 \lower #1 \small 5 "/V" \hspace #6.7 "V" } } }
[ 16] r\fermata
aes,8-.
}
>>
>> }
While the root of a secondary leading-tone chord needs to be the leading-tone, the other notes may vary and form with it one of: the triad or one of the diminished sevenths (as in seventh scale degree or leading-tone, not necessarily seventh chord) where the type of the diminished seventh is typically related to the type of tonicized triad:
Because of their symmetry, secondary leading-tone diminished seventh chords are also useful for modulation; all four notes may be considered the root of any diminished seventh chord. They may resolve to these major chord or minor chord diatonic triads:
Especially in four-part writing, the seventh should resolve downwards by step and if possible the lower tritone should resolve appropriately, inwards if a diminished fifth and outwards if an Augmented Fourth, as the example below shows.
{
\new PianoStaff <<
\new Staff <<
\new Voice \relative c'' {
\stemUp
a2 g g1
}
\new Voice \relative c' {
\stemDown
es2\glissando d e1
}
>>
\new Staff <<
\new Voice \relative c' {
\stemUp \clef F
c2\glissando b c1
}
\new Voice \relative c {
\stemDown
fis2\glissando_\markup { \translate #'(-7 . 0) { \concat { "C: vii" \raise #1 \small "o7" "/V" \hspace #1 "V" \hspace #5.2 "I" } } }
g c,1 \bar "||"
}
>>
>> }
Secondary leading-tone chords were not used until the Baroque music and are found more frequently and less conventionally in the Classical period. They are found even more frequently and freely in the Romantic period, but they began to be used less frequently with the breakdown of conventional harmony.
The chord progression vii/V–V–I is quite common in ragtime music.
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