Secondary chord

{{Short description|Harmonic device in Western music}} {{Distinguish|Secondary triad|Subsidiary chord}} {{Image frame|content=<div style="zoom: 65%;"><score sound="1" override_midi="Secondary chords in Mozart K 475.mid"> { \override Score.SpacingSpanner.uniform-stretching = ##t \set Score.proportionalNotationDuration = #(ly:make-moment 1/8) \new PianoStaff << \new Staff << \new Voice \relative c'' { \override DynamicLineSpanner.staff-padding = #4 \set Score.currentBarNumber = #86 \bar "" \tempo "Andantino" \key bes \major \time 3/4 \stemUp d8.^( c32 bes a8) r r r16. c32 es8.^( d32 c bes8) r16. d32\f f8.^( es32 d) c8^> <d g>^> r8 f16^( es) es^( d) d^( c) \stemNeutral bes4( a8) } \new Voice \relative c' { \stemDown f4_~\p f8 s s4 a4_( bes8) s <f b>4 g8 g s g\p f es } >> \new Staff << \new Voice \relative c' { \clef F \key bes \major \time 3/4 <bes d>4(_\markup { \concat { \translate #'(-5.5 . 0) { "B♭: I" \hspace #7 "V" \combine \raise #1 \small 4 \lower #1 \small 3 \hspace #23 "I" \raise #1 \small "6" \hspace #6 "vii" \raise #1 \small "o6" "/ii" \hspace #4 "ii" \raise #1 \small "6" \hspace #1 "V" \raise #1 \small "6" "/ii" \hspace #4 "ii" \hspace #5.2 "ii" \raise #1 \small "6" \hspace #3 "V" } } } <c es>8) r r4 <c f>4( <d f>8) r <d, d'>4 <es es'>8 <b b'> r c d es <f_~ d'>4( <f c'>8) } >> >> } </score></div>|caption=Secondary chords in Mozart's Fantasia in C minor, K. 475{{sfn|Benward|Saker|2003|p=275}}}} '''Secondary chords''' are a type of altered or borrowed chord, chords that are not part of the music piece's key. They are the most common type of altered chord in tonal music.{{sfn|Kostka|Payne|2004|p=246}} 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 or minor triad on any diatonic scale degree may have any secondary function applied to it; secondary functions may even be applied to diminished triads in some special circumstances.

Secondary chords were not used until the Baroque period and are found more frequently and freely in the Classical period, even more so in the Romantic period. 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.{{sfn|Benward|Saker|2003|pp=273–277}}

==Secondary dominant== {{redirect|V/V|other uses|VV (disambiguation)}} {{Image frame|content=<score sound="1"> { \new PianoStaff << \new Staff << \new Voice \relative c'' { \stemUp c2 b c1 } \new Voice \relative c' { \stemDown fis2 d e1 } >> \new Staff << \new Voice \relative c' { \stemUp \clef F a2 g g1 } \new Voice \relative c { \stemDown d2_\markup { \translate #'(-5.5 . 0) { "C: V/V" \hspace #1 "V" \hspace #5 "I" } } g c,1 \bar "||" } >> >> } </score>|width=300|caption=V7 of V in C, four-part harmony{{sfn|Benward|Saker|2003|p=269}}}}

A '''secondary dominant''' (also '''applied dominant''', '''artificial dominant''', or '''borrowed dominant''') is a major triad or dominant seventh chord built and set to resolve to a scale degree other than the tonic. The dominant (seventh) of the dominant (written as V⁷/V or V⁷ of V) is the most frequently encountered.{{sfn|Kostka|Payne|2004|p=250}} The chord that the secondary dominant is the dominant of is said to be a temporarily ''tonicized chord''. The secondary dominant is normally, though not always, followed by the tonicized chord. Tonicizations that last longer than a phrase are generally regarded as modulations to a new key (or new tonic).

According to music theorists David Beach and Ryan C. McClelland, "[t]he purpose of the secondary dominant is to place emphasis on a chord within the diatonic progression."{{sfn|Beach|McClelland|2012|p=32}} 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.{{sfn|Rawlins|Bahha|2005|p=59}}

===Definition===

The major scale contains seven diatonic triads. Because tonic triads tend to be either major or minor, one would not expect to find diminished chords (either the vii{{music|dim}} in major or the ii{{music|dim}} in minor) tonicized by a secondary dominant.{{sfn|Kostka|Payne|2004|p=246}} And the tonic of the key itself is not an applicable target to be tonicized, by definition.

In the key of C major, the five remaining chords are:

:<score sound="1"> { \relative c' { <d f a>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" } <e g b> <f a c> <g b d> <a c e> } } </score>

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.

:<score sound="1"> { \relative c' { <a cis e>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" } <d f a> <b dis fis> <e g b> <c e g> <f a c> <d fis a> <g b d> <e gis b> <a c e> } } </score>

Like most chords, secondary dominants may be seventh chords or chords with other upper extensions.{{efn|For example, {{harvnb|Ottman|1992|p=308}} discusses secondary dominant ninth chords, such as V⁹/V.}} Dominant seventh chords are commonly used as secondary dominants. The notation below shows the same secondary dominants as above but with dominant seventh chords. :<score sound="1"> { \relative c' { <a cis e g>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" } } <d f a> <b dis fis a> <e g b> <c e g bes> <f a c> <d fis a c> <g b d> <e gis b d> <a c e> } } </score>

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:{{sfn|White|1976|p=5}}

:<score sound="1" override_midi="Beethoven - Symphony No. 1, introduction secondary dominants.mid"> { \new PianoStaff << \new Staff << \relative c'' { \tempo "Adagio molto" <e g bes e>2(\fp <f a f'>8) r r4 \override DynamicLineSpanner.staff-padding = #3 <b,! d f b!>2(\fp <c e c'>8) r r4 <fis a c fis>2\cresc <fis a c fis>4-.\!( <fis a c fis>-.) <g b d g>4\f } >> \new Staff << \new Voice \relative c { \clef F <c c'>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" } } } <f, f' c'>8) r r4 <g g'>2( <a a'>8) r r4 <d, d'>2 <d d'>4-.( <d d'>-.) <g, g'> } >> >> } </score>

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 scale (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 analysis revealing the distinction.{{sfn|Benward|Saker|2003|pp=201–204}}

=== History === {{Image frame|content=<div style="zoom: 75%;"><score sound="1"> { \new PianoStaff << \new Staff << \new Voice \relative c { \override DynamicLineSpanner.staff-padding = #2.5 \set Score.currentBarNumber = #17 \bar "" \set Score.tempoHideNote = ##t \tempo 4 = 84 \clef F <d f b>8-. r <e g c>-.\sf r <e g cis>-. r <f a d>-.\sf r <fis a dis>-. r <g b e>-.\sf r <g b f'>2~\sf <g b f'>4(\p <g c e> <f! c' d!> < a c f>) <g c e>8-. r <f b d>-. r <e g c>-. r } >> \new Staff << \new Voice \relative c { \clef F g8-._\markup { \translate #'(-5.5 . 0) \concat { { "C: V" \raise #1 \small "7" \hspace #2.5 "I" \hspace #2 "V" \raise #1 \small "7" "/ii" \hspace #2.2 "ii" \hspace #4.5 "V" \raise #1 \small "7" "/iii" \hspace #1.7 "iii" \hspace #3 "V" \combine \raise #1 \small 4 \lower #1 \small 3 \hspace #4.5 "I" \hspace #6 "ii" \combine \raise #1 \small 4 \lower #1 \small 3 \hspace #1.5 "IV" \hspace #3 "V" \hspace #3.2 "V" \raise #1 \small "7" \hspace #2.5 "I" } } } r c,-. r a'-. r d,-. r b'-. r e,-. r <d! d'!>2( c4)( c' a f) g8-. r g,-. r c-. r } >> >> } </score></div>|width=430|caption=Secondary dominants in Beethoven's Piano Sonata No. 10, op. 14, no. 2, mvmt. II{{sfn|Benward|Saker|2003|p=274}}}} Before the 20th century, in the music of J.S. Bach, Mozart, Beethoven, and Brahms, a secondary dominant, along with its chord of resolution, was considered a modulation.{{Citation needed|date=April 2015}} Since this was a rather self-contradictory description, theorists in the early 1900s, such as Hugo Riemann (who used the term "Zwischendominante"—"intermediary dominant", still the usual German term for a secondary dominant), searched for a better description of the phenomenon.{{Citation needed|date=April 2015|reason=In which of Riemann's numerous publications did he make this search?}}

Walter Piston first used the analysis "V⁷ of IV" in a monograph entitled ''Principles of Harmonic Analysis''.{{sfn|Piston|1933}}{{efn|Notably, Piston's analytical symbol always used the word "of"—e.g. "V⁷ of IV" rather than the virgule V⁷/IV.}} In his 1941 book ''Harmony'', Piston used the term "secondary dominant".<ref>{{harvnb|Piston|1941|p=151}}: "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."</ref> 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''.<ref>{{harvnb|Schoenberg|1954|pp=15–29, 197}}. The term "artificial", however, appears to refer to the alteration 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.)</ref>

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.{{sfn|Piston|1987|p=257}} 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.

:<score sound="1"> { \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 <gis d'>-. r <g! cis>( <fis c'>-.) r <f b>( <e c'>-.) <d fis!>-. r <e g>-. \stemUp g4 fis8 g^. } \new Voice \relative c' { \stemDown s4. s s s c8 a d g } >> >> } </score>

===In jazz and popular music=== {{Image frame|content=<score sound="1" override_midi="Bop V of II cliche arpeggio.mid"> { \relative c' { e4 f8 fis g f e d cis e g bes r a4. } } </score>|width=350|caption=Measure 2 shows a bebop cliché arpeggio upwards from the third to the ninth of A^{7{{music|b}}9}, which is the secondary dominant of D minor, the ii chord in the key of C (V/ii).{{sfn|Spitzer|2001|p=62}}}} [[File:I'd Like to Teach the World to Sing secondary dominant.png|thumb|upright=2|Secondary dominant in "I'd Like to Teach the World to Sing" (1971), mm. 1–8{{sfn|Benward|Saker|2003|p=277}}File:I'd Like to Teach the World to Sing secondary dominant.mid]]

In jazz harmony, a secondary dominant is any dominant seventh chord on a weak beat{{Citation needed|date=April 2019}} and resolves downward by a perfect fifth. Thus, a chord is a secondary dominant when it functions as the dominant of some harmonic element other than the key's tonic and resolves to that element. This is slightly different from the traditional use of the term, where a secondary dominant does not have to be a seventh chord, occur on a weak beat, or resolve downward. If a non-diatonic dominant chord is used on a strong beat, it is considered an extended dominant. If it doesn't resolve downward, it may be a borrowed chord.{{Citation needed|date=January 2016}}

Secondary dominants are used in jazz harmony in the bebop blues and other blues progression variations, as are substitute dominants and turnarounds.{{sfn|Spitzer|2001|p=62}} 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.{{Citation needed|date=January 2016}}

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)".<ref>{{harvnb|Everett|2009|p=198}}. Everett notates major-minor sevenths X^m7.</ref> "Five Foot Two, Eyes of Blue" features chains of secondary dominants.{{sfn|Shepherd|2003|p=10}} "Sweet Georgia Brown" opens with V/V/V–V/V–V–I. {{audio|Sweet Georgia Brown V of V.mid|Play}}

===Extended dominant<!--Extended dominant redirects directly here-->=== {{for|a chord with extensions past the seventh|Extended chord}} {{Image frame|content=<score sound="1"> { \relative c' { <c e g>2_\markup { \concat { \translate #'(-3 . 0) { "C: I" \hspace #2.8 "vi" \raise #1 \small "7" \hspace #3 "ii" \raise #1 \small "7" \hspace #1.5 "V" \raise #1 \small "7" \hspace #4.8 "I" } } } <a e' g c> <d f a c> <g, d' f b> <c e g c>1 } } </score>

<score sound="1"> { \relative c' { <c e g>2_\markup { \concat { \translate #'(-3 . 0) { "C: I" \hspace #2.5 "VI" \raise #1 \small "7" \hspace #3.8 "II" \raise #1 \small "7" \hspace #1.5 "V" \raise #1 \small "7" \hspace #4.8 "I" } } } <a e' g cis> <d fis a c!> <g, d' f b> <c e g c>1 } } </score>|width=300|caption=A diatonic I–vi–ii–V turnaround{{sfn|Boyd|1997|p=43}} and a progression with secondary dominants: I–V/V/V–V/V–V–I}}

An '''extended dominant''' chord is a secondary dominant seventh chord that resolves down by a fifth to another dominant seventh chord. A series of extended dominant chords continues to resolve downwards by the circle of fifths until it reaches the tonic chord. The most common extended dominant chord is the '''tertiary dominant''',{{Citation needed|date=April 2019}} which resolves to a secondary dominant. For example, V/V/V (in C major, A⁽⁷⁾) resolves to V/V (D⁽⁷⁾), which resolves to V (G⁽⁷⁾), which resolves to I. Note that V/V/V is the same chord as V/ii, but differs in its resolution to a major dominant rather than a minor chord.

'''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){{sfn|Benward|Saker|2003|p=276}} has a quaternary dominant in the second beat (V/ii = V/V/V, V/vi = V/V/V/V).

:<score sound="1" override_midi="Successive secondary dominants in Chopin op 26 no 1.mid"> { #(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 <es bes'>16] r\fermata r8 } >> \new Staff << \new Voice \relative c' { \clef F \key des \major \time 3/4 <es ges>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" } } } <es ges> <f, f'> <f es'> <bes d> <bes d> <es, des'!>[ <es des'> <aes c> <aes c> <des, aes' des> <g des'>16] r\fermata aes,8-. } >> >> } </score>

== Secondary leading-tone == {{Image frame|content=<div style="zoom: 85%;"><score sound="1" override_midi="Half-diminished secondary leading-tone chord in Brahms op 119 no 3.mid"> { \new PianoStaff << \new Staff << \new Voice \relative c' { \stemUp \time 6/8 <f g>4.^~ <f g>4^~ <e g>8 d'4^( c8 e4 c8) b^( c d) <f, g>4^~ <e g>8 } \new Voice \relative c' { \stemDown \override DynamicText.X-offset = #-4 \override DynamicLineSpanner.staff-padding = #4 b8_(\p c d g,4 c8) <f aes>4.\< <e a>4.\> <f g>4\! f8 e,4_( c'8) } >> \new Staff << \new Voice \relative c, { \clef F \time 6/8 \stemUp g8^( g' b d c e) \stemNeutral f,,( f' aes fis fis' a) \stemUp g,,8^( g' b d c e) } \new Voice \relative c { \stemDown s4._\markup { \concat { "V" \raise #1 \small "7" \hspace #16 "ii" \raise #1 \small "o" \combine \raise #1 \small 6 \lower #1 \small 5 \hspace #6 "vii" \raise #1 \small "ø7" "/V" \hspace #5 "V" \raise #1 \small "7" } } g s2. s4. g } >> >> } </score></div>|caption=A secondary leading-tone half-diminished chord in<br />Brahms's Intermezzo, op. 119, no. 3 (1893){{sfn|Benward|Saker|2003|p=276}}}} {{Image frame|content=<div style="zoom: 90%;"><score sound="1" override_midi="Easy Living diminished seventh chord harmonization.mid"> << #(set-global-staff-size 18) \chords { f2:maj7 fis:dim7 g:min7 gis:dim7 a:min7 } \relative c'' { \key f \major a4_\markup { \concat { "I" \raise #1 \small "MA7" \hspace #2.5 "vii" \raise #1 \small "o7" "/ii" \hspace #1.5 "ii" \raise #1 \small "min7" \hspace #4 "vii" \raise #1 \small "o7" "/iii" \hspace #3 "iii" \raise #1 \small "min7" } } d8 c es,2 r8 d g bes d f4 es8 b4 d8 c r2 } >> </score></div>|caption=Three measures from "Easy Living"<br />showing secondary leading-tone chords.{{sfn|Lawn|Hellmer|1996|pp=97–98}}}}

In music theory, a '''secondary leading-tone chord''' is a secondary chord that is rooted on a tone that is a leading-tone of (in short, has a strong affinity to resolve to) a tone just 1 semitone from that root (typically 1 semitone above, though can be below).{{sfn|Benward|Saker|2003|p=271}} Like the secondary ''dominant'' it can be used as tonicization of only one subsequent chord (which will be rooted in the resolution tone), or the music can continue with other chords/notes in the key of that chord's root for a phrase, or even longer to be considered a modulation to that key. This one-semitone-apart resolution of the secondary ''leading-tone'' is in contrast to the secondary ''dominant'' which resolves through a wider distance of perfect fifth below or perfect fourth above the chord's root (as per the two distances between dominant and tonic).

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{{sfn|Blatter|2007|pp=132–133}} or one of the diminished sevenths (as in seventh scale degree{{sfn|Blatter|2007|pp=132–133}} or leading-tone, not necessarily seventh chord) where the type of the diminished seventh is typically related to the type of tonicized triad: # If the tonicized triad is minor, the leading-tone chord is fully diminished seventh chord. # If it is major, the leading-tone chord may be either half-diminished or fully diminished, though fully diminished chords are used more often.{{sfn|Kostka|Payne|2004|p=263}}

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 or minor diatonic triads:{{sfn|Benward|Saker|2003|p=271}}

:In major keys: ii, iii, IV, V, vi :In minor keys: III, iv, V, VI

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,{{sfn|Benward|Saker|2003|p=272}} as the example below{{sfn|Benward|Saker|2003|p=270}} shows.

:<score sound="1"> { \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 "||" } >> >> } </score>

Secondary leading-tone chords were not used until the Baroque period 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{{music|dim}}{{sup|7}}/V–V–I is quite common in ragtime music.{{sfn|Benward|Saker|2003|p=271}}

== Secondary supertonic == {{Image frame|content=<score sound="1"> { \new PianoStaff << \new Staff << \new Voice \relative c'' { \stemUp g2 fis g1 } \new Voice \relative c' { \stemDown c2 c d1 } >> \new Staff << \new Voice \relative c' { \stemUp \clef F a2 a b1 } \new Voice \relative c { \stemDown a2_\markup { \translate #'(-7 . 0) { \concat { "C: ii" \raise #1 \small "7" "/V" \hspace #1 "V" \raise #1 \small "7" "/V" \hspace #3.2 "V" } } } d g1 \bar "||" } >> >> } </score>|width=300|caption=A secondary supertonic chord: ii⁷/V–V/V–V in C major (a⁷–D⁷–G)}}The '''secondary supertonic chord''', or '''secondary second''', is a secondary chord that is on the supertonic scale degree. Rather than tonicizing a degree other than the tonic, as does a secondary dominant, it creates a temporary dominant.{{sfn|Blatter|2007|pp=132–133}} Examples include ii⁷/III (F{{music|#}}min.⁷, in C major), ii⁷/II (Amin.⁷, in F major), ii⁷/V (Emin.⁷, in G major), and ii⁷/IV (Bmin.⁷, in E major).{{sfn|Russo|2015|p=80}} {{Clear}}

== Secondary subdominant == The '''secondary subdominant''' is the subdominant (IV) of the tonicized chord. For example, in G major, the supertonic chord is A minor and the IV of ii chord is D major.

==Others== The other secondary functions are the secondary mediant, the secondary submediant, and the secondary subtonic.

==See also== *{{annotated link|Barbershop seventh chord}} *{{annotated link|Backdoor progression}} *{{annotated link|Circle progression}} *{{annotated link|Common-tone diminished seventh chord}} *{{annotated link|ii–V–I progression}} *{{annotated link|Secondary development}} *{{annotated link|Subtonic}}

==Notes== {{notelist}}

==References== {{reflist}}

==Bibliography== {{refbegin}} * {{cite book |last1=Beach |first1=David |last2=McClelland |first2=Ryan C. |date=2012 |title=Analysis of 18th- and 19th-century Musical Works in the Classical Tradition |publisher=Routledge |isbn=9780415806657 }} * {{cite book |last1=Benward |first1=Bruce |last2=Saker |first2=Marilyn Nadine |date=2003 |title=Music: In Theory and Practice |volume=I |edition=7th |publisher=McGraw-Hill |isbn=978-0-07-294262-0 |url=https://archive.org/details/musicintheorypra0001benw_b9i1 |url-access=registration }} * {{cite book |last=Blatter |first=Alfred |date=2007 |title=Revisiting Music Theory: A Guide to the Practice |isbn=0-415-97440-2 }} * {{cite book |last=Boyd |first=Bill |date=1997 |title=Jazz Chord Progressions |isbn=0-7935-7038-7 }} * {{cite book |last=Everett |first=Walter |date=2009 |title=The Foundations of Rock |isbn=978-0-19-531023-8 |url=https://archive.org/details/foundationsofroc0000ever |url-access=registration }} * {{cite book |last1=Kostka |first1=Stefan |last2=Payne |first2=Dorothy |date=2004 |title=Tonal Harmony |edition=5th |location=Boston |publisher=McGraw-Hill |isbn=0072852607 |oclc=51613969 |url=https://archive.org/details/tonalharmonywith0000kost |url-access=registration }} * {{cite book |last=Ottman |first=Robert W. |date=1992 |orig-date=1961 |title=Advanced Harmony: Theory and Practice |edition=4th |location=Englewood Cliffs, NJ |publisher=Prentice Hall |isbn=0-13-006016-X |url=https://archive.org/details/advancedharmonyt00ottm |url-access=registration }} * {{cite book |last=Piston |first=Walter |author-link=Walter Piston |date=1933 |title=Principles of Harmonic Analysis |edition= |location=Boston |publisher=E. C. Schirmer |url=https://archive.org/details/principlesofharm0000walt_i7h6 |url-access=registration }} {{pre-ISBN}} * {{cite book |last=Piston |first=Walter |author-link=Walter Piston |date=1941 |title=Harmony |edition= |location=New York |publisher=W. W. Norton & Company, Inc. }} {{pre-ISBN}} * {{cite book |last=Piston |first=Walter |author-link=Walter Piston |date=1987 |orig-date=First published 1941 |others=Revised and expanded by Mark Devoto |title=Harmony |edition=5th |location=New York |publisher=W. W. Norton & Company, Inc. |isbn=978-0-393-95480-7 |url=https://archive.org/details/harmony0000pist_l8w3 |url-access=registration }} * {{cite book |last1=Rawlins |first1=Robert |last2=Bahha |first2=Nor Eddine |date=2005 |title=Jazzology: The Encyclopedia of Jazz Theory for All Musicians |isbn=0-634-08678-2 |url=https://archive.org/details/jazzologyencyclo0000rawl |url-access=registration }} * {{cite book |last1=Lawn |first1=Richard |last2=Hellmer |first2=Jeffrey L. |date=1996 |title=Jazz: Theory and Practice |isbn=978-0-88284-722-1 }} * {{cite book |last=Russo |first=William |author-link=William Russo (musician) |date=2015 |orig-date=1961 |title=Composing for the Jazz Orchestra |publisher=University of Chicago |isbn=978-0-226-73209-1 }} * {{cite book |last=Schoenberg |first=Arnold |author-link=Arnold Schoenberg |date=1954 |title=Structural Functions of Harmony |editor-last=Searle |editor-first=Humphrey |editor-link=Humphrey Searle |publisher=W. W. Norton & Company, Inc. |location=New York }} * {{cite book |last=Shepherd |first=John |date=2003 |title=Continuum Encyclopedia of Popular Music of the World |volume=II: Performance and Production |publisher=A&C Black |isbn=9780826463227 }} * {{cite book |last=Spitzer |first=Peter |date=2001 |title=Jazz Theory Handbook |isbn=0-7866-5328-0 }} * {{cite book |last=White |first=John D. |date=1976 |title=The Analysis of Music |isbn=0-13-033233-X |url=https://archive.org/details/analysisofmusic00whit |url-access=registration }} {{refend}}

==Further reading== *Nettles, Barrie & Graf, Richard (1997). ''The Chord Scale Theory and Jazz Harmony''. Advance Music, {{ISBN|3-89221-056-X}} *Thompson, David M. (1980). ''A History of Harmonic Theory in the United States''. Kent, Ohio: The Kent State University Press.

{{Chords}} {{Tonality}} {{Chromaticism}}

Category:Secondary chords Category:Chromaticism Category:Diatonic functions Category:Dominant chords