Diminished seventh chord

Source: Wikipedia, the free encyclopedia.
Not to be confused with
diminished fifth (tritone)minor thirdrootTuning125:150:180:216[1]Forte no. / Complement
4–28 / 8–28

The diminished seventh chord is a four-note chord (a

written
as Bo7, has pitches B-D-F-A♭:

{ \omit Score.TimeSignature \relative c' { <b d f aes>1 } }

The chord consists of a diminished triad plus the diminished seventh above the root. These four notes form a stack of three intervals which are all minor thirds. Since stacking yet another minor third returns to the root note, the four inversions of a diminished seventh chord are symmetrical. The integer notation is {0, 3, 6, 9}.

Since the diminished seventh interval is

enharmonically equivalent to a major sixth
, the chord is enharmonically equivalent to (1, ♭3, ♭5, ♮6).

The diminished seventh chord occurs as a

dominant function and contains two diminished fifths, which often resolve inwards.[2]

The chord notation for the diminished seventh chord (assuming root C) is Cdim7 or Co7 (or Cm6♭5 for the enharmonic variant). The notation Cdim or Co normally denotes a (three-note) diminished triad, but some jazz charts or other music literature may intend for these to denote the four-note diminished seventh chord instead.

17-limit tuning).[3]

Analysis

Music theorists have struggled over the centuries to explain the meaning and function of diminished seventh chords. Currently, two approaches are generally used.

The less complex method treats the leading tone as the root of the chord and the other chord members as the third, fifth, and seventh of the chord, the same way other seventh chords are analyzed.

The other method is to analyze the chord as an "incomplete dominant ninth", that is a ninth chord with its root on the dominant, whose root is missing or implied. A viio7 chord in the minor key (for example, in C minor, B♮–D–F–A♭) occurs naturally in the harmonic minor scale and is equivalent to the dominant 7♭9 chord (G–B–D–F–A♭) without its root.

{ \omit Score.TimeSignature \relative c'' { <\parenthesize g b d f aes>1 \bar "||" } }

This was already proposed by Arnold Schoenberg,[4] and Walter Piston championed this analysis.[5] Jazz guitarist Sal Salvador, and other jazz theorists, also advocated this view, rewriting chord charts to reflect this and supplying the "missing" root as part of their bass lines.[6] The dominant ninth theory was questioned by Heinrich Schenker. He explained that although there is a kinship between all univalent chords rising out of the fifth degree, the dominant ninth chord is not a real chord formation.[7]

supposed fundamental bass is borrowed from the sixth degree in minor, raised a semitone producing a stack of minor thirds.[8] Thus, in C, the dominant seventh is G7 (G–B–D–F) and the sixth degree borrowed from the minor scale produces A♭–B–D–F.[8]

{ \omit Score.TimeSignature \relative c'' { <g b d f>1 <aes b d f> \bar "||" } }

In his

Treatise on Harmony, he observed that three minor thirds and an augmented second make up a chord where the augmented second is such that "the ear is not offended" by it. He may have been talking of the augmented second in quarter-comma meantone, a tuning he favored, which is close to the just septimal minor third
of 7:6.

Function

Most common functions

\new PianoStaff << \new Staff << \new Voice \relative c'' { \stemUp \key c \minor aes1 g } \new Voice \relative c' { \stemDown d1 es } >> \new Staff << \new Voice \relative c { \stemUp \clef F \key c \minor f1 es } \new Voice \relative c { \stemDown b1_\markup { \concat { "vii" \raise #1 \small "o7" \hspace #4.3 "i" } } c \bar "||" } >> >>

The most common form of the diminished seventh chord is that rooted on the

parallel minor
.

The chord possesses a

dominant function when rooted on the leading tone (otherwise it doesn't, but can serve other functions - see below), and this is most straightforwardly shown when the root of a dominant seventh chord
is omitted. The remaining third, fifth and seventh of that chord form a diminished triad (whose new root is the third of the former chord), to which a diminished seventh can be added. Thus, in C (major or minor), a dominant seventh chord consisting of G–B–D–F can be replaced by a diminished seventh chord B–D–F–A♭.

{ \omit Score.TimeSignature \relative c'' { <g b d f>1 <b d f aes> \bar "||" } }

In jazz harmony, a combination of the original chord with its substitute (with G in the bass and A♭ simultaneously in an upper voice) yields the seven flat-9 chord, which intensifies the dominant function of either a diminished seventh or dominant seventh chord. Other transformations of this kind facilitate a variety of substitutions and modulations: any of the four notes in a diminished seventh chord are raised by a semitone, that raised note is then the flat-seventh of a half-diminished seventh chord. Similarly, if any of the four notes in the diminished seventh chord are lowered by a semitone, that lowered note is then the root of a dominant seventh chord.

Diminished seventh chords may also be rooted on scale degrees other than the leading-tone, either as

secondary function chords temporarily borrowed from other keys, or as appoggiatura chords: a chord rooted on the raised second scale degree (D♯–F♯–A–C in the key of C) acts as an appoggiatura to the tonic (C major) chord, and one rooted on the raised sixth scale degree (A♯–C♯–E–G in C major) acts as an appoggiatura to the dominant (G major) chord. Such chords however, having no leading tone in relation to the chords to which they resolve, cannot properly have a dominant function. They are therefore referred to commonly as non-dominant diminished seventh chords or common tone diminished seventh chords (see below
).

In jazz, the diminished seventh chord is often based on the ♭

Brazilian music such as choro, samba and bossa nova
.

Other functions

\new PianoStaff << \new Staff << \new Voice \relative c'' { \stemUp f2 es d1 c } \new Voice \relative c'' { \stemDown <a c>1 <f b> <e g> } >> \new Staff << \new Voice \relative c { \clef F f2 fis g1 c \bar "||" } >> >>
A chord progression with a sharpened subdominant with diminished seventh chord

Another common use of the chord is as a sharpened subdominant with diminished seventh chord. This is represented by the Roman notation ♯ivo7, but in classical music is more correctly represented as viio7/V, being a very common way for a composer to approach the dominant of any key. In the key of C, this is F♯dim7. It is also a common chord in

Dixieland progression is IV–♯ivo7–V7 (in C major: F–F♯o7–G7). Another common usage of ♯ivo7 is often found in Gospel music and jazz progressions such as in the song "I Got Rhythm
":

In C: | C C/E | F F♯dim7 | C/G A7 | Dm7 G7 |

One variant of the supertonic seventh chord is the supertonic diminished seventh[10] with the raised supertonic, which is enharmonically equivalent to the lowered third (in C: D♯ = E♭). It may be used as a dominant substitute.[11]

{ \new StaffGroup << \new Staff << \new Voice \relative c' { \stemUp \clef "G_8" \key bes \major \time 3/4 es4 es2 cis2 cis4 d2 d4 es2 r4 } \new Voice \relative c' { \stemDown bes4 c2 bes2 g4 f2._~ f2 s4 } \addlyrics { good old sum mer time __ } >> \new Staff << \new Voice \relative c' { \stemUp \clef F \key bes \major \time 3/4 g4 g2 g2 bes4 bes2 aes4 a!2 r4 } \new Voice \relative c { \stemDown es4 es2 es2 es4 bes2 b4 c2 s4 \bar "||" } \addlyrics { good old sum mer, sum mer time __ } >> >> }
According to Benward and Saker, "The... [♯iio7 and ♯vio7] chords are very common in 20th-century 'barbershop' quartet music."[12] The music shows the chord progression IV–vi6–Ger+6–I ♯vio6
5–V4
3.
{ \new PianoStaff << \new Staff << \relative c' { \tempo "Tempo di Valse" \key d \major \time 3/4 \override DynamicText.X-offset = #-4 \once \override DynamicLineSpanner.staff-padding = #3 <e a>4--\f <e a cis>-- <e a cis e>-- <fis a bis fis'>2->\sf <e a cis e>4-- <e a cis e>2.~ <e a cis e>8 r r4 r } >> \new Staff << \new Voice \relative c { \clef F \key d \major \time 3/4 <a e' a cis>4--_\markup { \concat { "V" \hspace #10 "♯vi" \raise #1 \small "o" \combine \raise #1 \small 4 \lower #1 \small 2 \hspace #1 "V" } } <a e' a cis>-- <a e' a cis>-- <a dis a' bis>2-> <a e' a cis>4-- <a e' a cis>2.~ <a e' a cis>8 r r4 r } >> >> }
Example (B♯o4
2) in the Waltz of the Flowers (1892)[13][12]

A diminished seventh chord may function as a common-tone diminished seventh chord. In this role, a diminished seventh chord resolves to a

dominant seventh chord whose root is one of the notes of the diminished seventh chord (common tone), the most common being the raised supertonic seventh, which resolves to the tonic in major keys (♯iio7–I, shown below) and the raised submediant, which resolves to dominant triad or seventh in major keys (♯vio7–V, shown right), with the altered tones resolving upward by half step in both cases.[12]

{ \omit Score.TimeSignature \relative c' { <dis a' c fis>1_\markup { \concat { "♯ii" \raise #1 \small "o7" \hspace #4 "I" \raise #1 \small "6" } } <e g c g'> \bar "||" } }

The cto7 chord, whose function, "is simply one of embellishment," most often spelled ♯iio7 when embellishing I or ♯vio7 when embellishing V, is distinguished from the viio7/V chord by common tone chords resolving to I or I6 while viio7/V resolves to V or I6
4.[13] They may be confused, due to enharmonic equivalency, but resolution is a better indicator of function than spelling. In C:

cto7/I = d♯o7 = D♯–F♯–A–C
viio7/V = f♯o7 = F♯–A–C–E♭ (= D♯)

The diminished chord may also resolve through lowering two of the chord tones producing a supertonic seventh chord (ii7) that may lead to a conventional cadence:[14]

{ \set Score.proportionalNotationDuration = #(ly:make-moment 1/4) \omit Score.TimeSignature \key d \major \relative c'' { <b d f aes>2_\markup { \concat { "vii" \raise #1 \small "o7" \hspace #1.2 "ii" \raise #1 \small "7" \hspace #4.7 "V" \raise #1 \small "7" \hspace #4 "I" } } <b d e g> <a cis e g> <a d fis> \bar "||" } }

Expressive potential

During the

St. Matthew Passion (1737), in which he sets verses from the Gospel of Matthew
, chapter 27, verses 20–21: "But the chief priests and elders persuaded the multitude that they should ask Barabbas, and destroy Jesus. The governor [Pilate] answered and said unto them, 'Whether of the twain will ye that I release unto you?' They said, 'Barabbas'." Bach sets the text so that the angry multitude's harsh reply on the word Barabbam is a diminished seventh chord:

{ \new StaffGroup << \new Staff << \set Staff.midiInstrument = #"voice oohs" \key d \minor \relative c' { \set Score.tempoHideNote = ##t \tempo 8 = 120 \time 2/4 <fis a c fis>8.^"Choir" <fis a c fis>16 <fis a c fis>4 } \addlyrics { Ba -- rab -- bam! } >> \new Staff << \set Staff.midiInstrument = #"church organ" \clef F \key d \minor \time 2/4 \new Voice \relative c { <dis dis'>8. <dis dis'>16 <dis dis'>4 } >> >> }

After Bach, diminished sevenths were to feature regularly in music to evoke the uncanny or sense of impending danger. A powerful diminished seventh chord heralds the resurrection of the murdered Commendatore in the final scene of Mozart's Don Giovanni (1787). The dead man's statue comes to life and takes the Don down to Hell in one of the most chilling episodes in the entire operatic repertoire (Listen):

{ << \new Staff << \tempo Andante \relative c' { \set Score.tempoHideNote = ##t \tempo 4 = 86 \set Staff.midiInstrument = #"trombone" \clef F \key d \minor R1 R1 R1 r2 a4.^"COMMENDATORE" a8 d2 d, r4 d f d a'2 a } \addlyrics { Don Gio -- van -- ni! A ce -- nar te -- co } >> \new PianoStaff << \new Staff << \set Staff.midiInstrument = #"string ensemble 1" \key d \minor \relative c'' { \override DynamicLineSpanner.staff-padding = #3 <d f gis d'>4\ff <d f gis d'>2 <d f gis d'>4~ <d f gis d'>4 r4 r2 <a e' g! a>4 <a e' g a>2 <a e' g a>4~ <a e' g a>4 r4 r2 <a, f'>4.\p <a f'>8 <a f'>4. <a f'>8 <a f'>4. <a f'>8 <a f'>4. <a f'>8 <a e'>4. <a e'>8 <a e'>4. <a e'>8 } >> \new Staff << \clef F \key d \minor \relative c, { <b b'>2 <b b'> <b b'> r <cis cis'> <cis cis'> <cis cis'> r d'4. d8 d4. d8 d4. d8 d4. d8 c4. c8 c4. c8 } >> >> >> }

In the early years of the 19th century, composers used the diminished seventh with increasing frequency. In "Die Stadt", one of his darkest and most melancholy songs from

dissonance is terminal":[15]

{ #(set-global-staff-size 17) << \new PianoStaff << \new Staff << \tempo "Mässig geschwind" \key c \minor \time 3/4 \set Score.currentBarNumber = #35 \bar "" \relative c'' { R2. R \tuplet 9/8 { a32([ c es fis a fis es c a)] } <c, es fis a>8->([ a16)] r \clef bass <c, es fis a>8->([ a16)] r \clef G \tuplet 9/8 { a''32([ c es fis a fis es c a)] } <c, es fis a>8->([ a16)] r \clef F <c, es fis a>8->([ a16)] r \clef G \tuplet 9/8 { a''32([ c es fis a fis es c a)] } <c, es fis a>8->([ a16)] r \clef F <c, es fis a>8->([ a16)] r R2.\fermata } >> \new Staff << \clef F \key c \minor \time 3/4 \relative c, { c32^\markup {\dynamic pp \italic "con pedale" } c' c, c' c, c' c, c' c,8 r c r c32 c' c, c' c, c' c, c' c,8 r c r c32 c' c, c' c, c' c, c' c,8 r c r c32 c' c, c' c, c' c, c' c,8 r c r c32 c' c, c' c, c' c, c' c,8 r c r c2.\fermata \bar "|." } >> >> >> }

The operas of Carl Maria von Weber, particularly Der Freischütz and Euryanthe, featured many passages using this chord. The Wolf's Glen scene in Der Freischütz (1821) is an example.

Wolf's Glen music from Der Freischütz (orchestra only)
Wolf's Glen music from Der Freischütz (orchestra only)

According to his early biographer, Alexander Wheelock Thayer,[16] Ludwig van Beethoven spoke disparagingly of the 'accumulation of diminished seventh chords' in Euryanthe (1823).

Beethoven was himself rather fond of the chord and was well aware of its dramatic potential. Perhaps the clearest instance of the diminished seventh's power to evoke mystery and terror can be found in the passage linking the two final movements of Beethoven's Appassionata sonata, Op. 57 (1806). The placid conclusion of the andante movement is interrupted first by a slowly rolled diminished seventh arpeggio played pianissimo, followed by the same chord played an octave above in a sharp, stabbing fortissimo.[17]

{ << \new PianoStaff << \new Staff << \key des \major \time 2/4 \relative c'' { <ges bes es>4(_\markup { \dynamic p \italic dim. } <es aes>) <des e g des'>2\pp\arpeggio\fermata <des' e g des'>2_\markup { \dynamic ff \italic secco }\arpeggio\fermata } >> \new Staff << \clef F \key des \major \time 2/4 \relative c' { <ges bes>4( <aes c>) <bes, des e g bes>2\arpeggio\fermata \clef treble <bes' des e g bes>2\arpeggio\fermata \bar "||" } >> >> >> }

The final movement of

Symphonie Fantastique reflects the influence of Weber [18] in its copious use of diminished seventh chords to evoke the spooky atmosphere of a Witch's Sabbath: "a sinister gathering of spectres, monsters and weird, infernal mocking creatures":[19]

Berlioz's Symphonie Fantastique finale, bars 1–4
Berlioz's Symphonie Fantastique finale, bars 1-4

By the end of the 19th century, composers had used the diminished seventh so much that it became a cliché of musical expression and consequently lost much its power to shock and thrill. By the turn of the 20th century, many musicians were getting weary of it. In his Harmonielehre (1911),[20] Arnold Schoenberg wrote:

Whenever one wanted to express pain, excitement, anger, or some other strong feeling – there we find, almost exclusively, the diminished seventh chord. So it is in the music of Bach,

Wagner
's early works it plays the same role. But soon the role was played out. This uncommon, restless, undependable guest, here today, gone tomorrow, settled down, became a citizen, was retired a philistine. The chord had lost that appeal of novelty, hence, it had lost its sharpness, but also its luster. It had nothing more in say to a new era. Thus, it fell from the higher sphere of art music to the lower of music for entertainment. There it remains, as a sentimental expression of sentimental concerns. It became banal and effeminate.

Symmetry

{ \omit Score.TimeSignature \relative c'' { <gis b d f>1 <aes b d f> <aes ces d f> <aes ces eses f> \bar "||" } }
The same four pitch classes spelled as four different diminished seventh chords: G♯dim7, Bdim7, Ddim7, and Fdim7.

Because a diminished seventh chord is composed of three stacked

enharmonically equivalent
to three other inverted diminished chords with roots on the other three pitches in the chord:

  1. Bdim7 (A♭–B–D–F)
  2. Ddim7 (A♭–C♭–D–F)
  3. Fdim7 (A♭–C♭–Edouble flat–F)

Nineteenth-century composers in particular often make use of this enharmonic to use these chords for modulations. Percy Goetschius calls it the "enharmonic chord."[21]

{ \omit Score.TimeSignature \relative c' { <cis e g bes c es fis a>1 } }
{ \omit Score.TimeSignature \relative c' { \once \override NoteHead.color = #red des8 \once \override NoteHead.color = #blue es \once \override NoteHead.color = #red e! \once \override NoteHead.color = #blue fis \once \override NoteHead.color = #red g \once \override NoteHead.color = #blue a \once \override NoteHead.color = #red bes \once \override NoteHead.color = #blue c } }
Two diminished seventh chords in the octatonic scale (one red, one blue) may be rearranged as the alpha chord

Given the symmetry of the chord (and ignoring enharmonic spelling), it follows that there are only three distinct diminished seventh chords (as opposed to twelve), each a conflation of four enharmonic equivalents. Using

V/ii, V/III (in minor), V/iii (in major), V/iv, V/V, V/VI (in minor), V/vi (in major), V/VII (in minor). Since the chord may be enharmonically written in four different ways without changing the sound, the above can be multiplied by four, yielding a total of forty-eight possible interpretations.[22] More conservatively, each assumed root may be used as a dominant, tonic, or supertonic, giving twelve possibilities.[23]

The

alpha chord
.

Diminished seventh chord table

Chord Root Minor third Dim. fifth Dim. seventh
C♭o7 C♭ Edouble flat (D) Gdouble flat (F) Btriple flat (A♭)
Co7 C E♭ G♭ Bdouble flat (A)
C♯o7 C♯ E G B♭
D♭o7 D♭ F♭ (E) Adouble flat (G) Cdouble flat (B♭)
Do7 D F A♭ C♭ (B)
D♯o7 D♯ F♯ A C
E♭o7 E♭ G♭ Bdouble flat (A) Ddouble flat (C)
Eo7 E G B♭ D♭
E♯o7 E♯ G♯ B D
F♭o7 F♭ Adouble flat (G) Cdouble flat (B♭) Etriple flat (D♭)
Fo7 F A♭ C♭(B) Edouble flat(D)
F♯o7 F♯ A C E♭
G♭o7 G♭ Bdouble flat (A) Ddouble flat (C) Fdouble flat (E♭)
Go7 G B♭ D♭ F♭ (E)
G♯o7 G♯ B D F
A♭o7 A♭ C♭ (B) Edouble flat (D) Gdouble flat (F)
Ao7 A C E♭ G♭
A♯o7 A♯ C♯ E G
B♭o7 B♭ D♭ F♭ (E) Adouble flat (G)
Bo7 B D F A♭
B♯o7 B♯ D♯ F♯ A

See also

References

  1. ISBN 978-1-4510-1534-8
    . "G♯–B–D–F."
  2. ISBN 978-0-07-294262-0
    .
  3. ISBN 978-0-945193-51-7
    .
  4. ^ Schoenberg, Arnold. Harmonielehre, chapter IX, Wien, Universal Edition, 1911
  5. OCLC 2082824
    .
  6. OCLC 21109944
    .
  7. OCLC 280916
    .
  8. ^
    ISBN 978-0-521-61709-3
    .
  9. ISBN 978-0-19-538458-1
    .
  10. ISBN 1-4067-9372-8
    .
  11. ISBN 1-57623-875-X
    .
  12. ^
    ISBN 978-0-07-310188-0
    .
  13. ^
    ISBN 0-07-300056-6 "The cto7 chords... embellish [the] dominant chord. While the cto7
    chords are clearly ornamental, their flavor is crucial to this passage and to the waltz that follows."
  14. ^ Alchin, Carrie Adelaide (1917). Applied Harmony, p. 99. Los Angeles: C. A. Alchin. [ISBN unspecified] [1].
  15. ^
    OCLC 670430565
    .
  16. ^ Thayer, A. W. (1921) Life of Beethoven. Princeton: Princeton University Press (1879)
  17. ^ Rosen, C. (2002, p. 196) Beethoven's Piano Sonatas, a Short Companion Yale University Press.
  18. ^ Hovland, E. (2019, p. 20) "Who's afraid of Berlioz?" Studia Musicologica Norvegica, vol 45, no. 1, pp. 9–30.
  19. ^ Macdonald, H. (1969, p. 37) Berlioz Orchestral Music. London, BBC.
  20. ^ Schoenberg, Arnold (1911) Harmonielehre, Wien, Universal Edition.
  21. ^ Goetschius, Percy (1913). The Material Used in Musical Composition: A System of Harmony. p. 159, G. Shirmer, Inc.
  22. OCLC 2082824
    .
  23. ^ Adela Harriet Sophia Bagot Wodehouse (1890). A Dictionary of Music and Musicians: (A.D. 1450–1889), p. 448. Macmillan and Co., Ltd.
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