Diminished seventh chord

A diminished seventh chord ( play (help·info)) is a four note chord comprising a diminished triad plus the interval of a diminished seventh (alternatively regarded enharmonically as a major sixth) above the root. Thus it is (1, ♭3, ♭5, 7), or enharmonically (1, ♭3, ♭5, 6), of any major scale; for example, C diminished-seventh would be (C, E♭, G♭, B), or enharmonically (C, E♭, G♭, A).

In most sheet music books, Cdim or C° denotes a diminished seventh chord with root C. However, in some modern jazz books and some music theory literature, Cdim or C° denotes a diminished triad chord, while Cdim7 or C°7 denotes a diminished seventh chord.

Uses

The most common form of the diminished seventh chord is that rooted on the leading tone; for example, in the key of C, the chord (B, D, F, A♭). So its other constituents are the second, fourth, and flatted sixth (flat submediant) scale degrees. These notes occur naturally in the harmonic minor scale. But this chord also appears in major keys, especially after the time of Bach, where it is "borrowed" from the parallel minor.

Seventh chords may also be rooted on other scale degrees, 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. These chords may be referred to as "secondary diminished seventh chords" or as a subclass of secondary dominants.

In jazz, the diminished seventh chord is often based on the lowered third scale degree (the flat mediant) and acts as a passing chord between the mediant triad (or first-inversion tonic triad) and the supertonic triad: in C major, this would be the chord progression E minor - E♭ diminished - D minor.

The diminished seventh chord can also be conceived of (and used in practice) as a dominant seventh chord, to which the third, fifth and flat-seventh have been lowered by a semi-tone while the root remains fixed; e.g., lowering the third, fifth and flat-seventh of C7 (C, E, G, B♭) each by a semi-tone yields C, D♯, F♯, A which is enharmonically equivalent to C, E♭, G♭, B. In this context the diminished seventh chord is instead conceptualized as a dominant thirteen ♯9 ♯11 (e.g., the previous example may be thought of as C13♯9♯11). The diminished seventh chord should not be confused with the half-diminished seventh chord, in which the seventh is not diminished but rather minor (♭7). This said, if any of the four notes in a diminished seventh chord are raised by a semi-tone, 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 semi-tone, that lowered note is then the root of a dominant seventh chord.

The diminished seventh chord comprises frequencies that are equally spaced when considered on a logarithmic axis, and thus divides the octave into four logarithmically equal portions.

Diminished seventh root

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. VIIdim7 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(b9) chord (G, B, D, F, A♭) without its root. Walter Piston has long been the champion of this analysis.^[1]

The dominant ninth theory has been 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.^[2]

Inversions

The fundamental tone or root of any diminished seventh chord, being composed of three stacked minor thirds, is ambiguous. For example, Cdim7 in root position: C + E♭ + G♭ + B (each has one and half interval), is just as easily viewed as an E♭dim7 in its first inversion:

D (enharmonic equivalent of C) + E♭ + G♭ + B.

It can also be viewed as a G♭dim7 in its second inversion:

D + F (enharmonic equivalent of E♭) + G♭ + B.

Delineating this chord in its last possibility, that of Bdim7 in its third inversion, is very clumsy and not very useful as it requires the use a triple-flatted note, something that is never used in a musical score:

D + F + A♭♭♭ (enharmonic equivalent of G♭) + B.

However, by enharmonically respelling the B to A, this can also be viewed as a first inversion Adim7 chord:

C + E♭ + G♭ + A (enharmonic equivalent of B).

Other possibilities present themselves by respelling the various roots; for instance:

C + E♭ + F♯ (enharmonic equivalent of G♭) + A (enharmonic equivalent of B) (second inversion F♯dim7).

C + D♯ (enharmonic equivalent of E♭) + F♯ (enharmonic equivalent of G♭) + A (enharmonic equivalent of B) (third inversion D♯dim7).

B♯ (enharmonic equivalent of C) + D♯ (enharmonic equivalent of E♭) + F♯ (enharmonic equivalent of G♭) + A (enharmonic equivalent of B) (root position B♯dim7).

All of the chord's inversions have the same sound harmonically. Because of the chord's symmetrical nature (superimposing more minor thirds on top of the the dim 7 produces no new notes), there are only three different diminished seventh chords possible.

The diminished seventh chord can appear in first, second, or (least common) third inversion. Each inversion is enharmonic with another diminished seventh chord, and 19th-century composers in particular often make use of this enharmonic to use these chords for modulations. Percy Goetschius calls it the "enharmonic chord."^[3]

Using Piston's incomplete-ninth analysis, a single diminished seventh chord, without enharmonic change, is capable of the following analyses: V, V of II, V of III (in min.), V of III (in maj.), V of IV, V of V, V of VI (in min.), V of VI (in maj.), V of VII (in maj.). Since the chord may be enharmonically written in four different ways without changing the sound, we may multiply the above by four, making a total of forty-eight possible interpretations.^[4]

References