Diminished seventh chord

The diminished seventh chord is a four-note chord (a seventh chord) composed of a root note, together with a minor third, a diminished fifth, and a diminished seventh above the root: (1, 3, 5, 7). For example, the diminished seventh chord built on B, commonly written as B⁷, has pitches B-D-F-A:

:<score sound="1">

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

</score>

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,&nbsp;3,&nbsp;6,&nbsp;9}.

Since the diminished seventh interval is enharmonically equivalent to a major sixth, the chord is enharmonically equivalent to (1,&nbsp;3,&nbsp;5,&nbsp;6). This may be labeled as a minor sixth chord with a flattened fifth.

The diminished seventh chord occurs as a leading-tone seventh chord in the harmonic minor scale. It typically has dominant function and contains two diminished fifths, which often resolve inwards.

The chord notation for the diminished seventh chord with C as the root is Cdim⁷ or C⁷ (or Cm⁶⁵ for the enharmonic variant). The notation Cdim or C 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.

François-Joseph Fétis tuned the chord 10:12:14:17 (17-limit tuning).

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 vii⁷ 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 79 chord (G–B–D–F–A) without its root.

:<score sound="1"> {

\omit Score.TimeSignature \relative c {

<\parenthesize g b d f aes>1 \bar "||"

}

}

</score>

This was already proposed by Arnold Schoenberg, and Walter Piston championed this analysis. 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. 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.

Jean-Philippe Rameau explained the diminished seventh chord as a dominant seventh chord whose supposed fundamental bass is borrowed from the sixth degree in minor, raised a semitone producing a stack of minor thirds. 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. The passing chord is used widely in Brazilian music such as choro, samba and bossa nova.

Other functions

Another common use of the chord is as a sharpened subdominant with diminished seventh chord. This is represented by the Roman notation iv⁷, but in classical music is more correctly represented as vii⁷/V, being a very common way for a composer to approach the dominant of any key. In the key of C, this is Fdim⁷. It is also a common chord in jazz and ragtime music. A common traditional jazz or Dixieland progression is IV–iv⁷–V⁷ (in C major: F–F⁷–G⁷). Another common usage of iv⁷ is often found in Gospel music and jazz progressions such as in the song "I Got Rhythm":

:In C: | C C/E | F Fdim⁷ | C/G A⁷ | Dm⁷ G⁷ |

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