Microtonal, just intonation, electronic music software Microtonal, just intonation, electronic music software

Encyclopedia of Microtonal Music Theory

@ 00 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Login   |  Encyclopedia Index

diminished-7th (chord) / dim7 / o7

[Joe Monzo]

The diminished-7th chord is formally a chord containing 4 notes, built upward in pitch from the root with the intervals of three successive minor-3rds, resulting in the chord-members identified as root, 3rd, 5th, and 7th. The actual intervals above the root are thus the minor-3rd, diminished-5th, and diminished-7th.

The diminished-7th chord does not arise naturally from the diatonic major scale, however, it is present as a tetrad whose root is the seventh degree (VII) of the harmonic-minor scale. A common abbreviation for the diminished chord quality is a small circle after the letter of the root-note: VIIo7. For example:

     key of A-minor (harmonic-minor):

     F   G#  A   B C   D   E F   G#  A
         |       |     |     |
        root    3rd   5th    7th
          \_____/ \___/ \___/
         min-3rd min-3rd min-3rd

Because the V7 chord is so important in the harmonic-minor scale, it is easy to view the diminished-7th chord on VII as an extension of the V7 E:G#:B:D to include the 9th, which is specifically a minor-9th -- in the above example, (E):F -- but with the root omitted. In fact, a listener who hears this diminished-7th chord as the proportion 10:12:14:17 is likely to imagine the presence of the difference-tones 2, 3, 4, and 5 where 2 and 4 both provide the "missing root".

Interestingly, because of the theoretical similarity of the intervals (all minor-3rds), and especially because of the actual similarity of these same intervals as 300 cents each in 12-edo tuning, a composer may manipulate this chord in such a way that the enharmonic-equivalences are exploited, and allow the listener to imagine 3 other "missing roots". The above example may be reinterpreted thus:

root 3rd  5th 7th 9th

(E)   G#   B   D   F    in A-minor
(G)   B    D   F   Ab   in C-minor
(Bb)  D    F   Ab  Cb   in Eb-minor  \ enharmonically equivalent
(A#)  Cx   E#  G#  B    in D#-minor  /
(C#)  E#   G#  B   D    in F#-minor

This flexible reinterpretation allows the diminished-7th chord to act as a pivot between keys which are not closely related. Note that in 12-edo, there are only three diminished-7th chords available, and that the "missing roots" of this example chord form one of the other two diminished-7th chords, and that the tonics of the minor keys form the other of the two.

The growing acceptance of 12-edo during the 1800s led to a wider use of diminished-7th chords and the resultant modulations to remote key relationships. Eventually, the greater use of these diminished-7th chord interlockings led to experimentation with 12-edo as a member of the diminished family of temperaments which featured a new type of scale: the octatonic diminished scale (which see).

The first composer to make heavy use of the diminished-7th chord was Beethoven, and the first to base whole sections of a piece on it was Chopin (see, for example, the middle section of his Etude in E-major, op.10,no.3, which keeps alternating all three of the diminished-7th chords).

. . . . . . . . .

The tonalsoft.com website is almost entirely the work of one person: me, Joe Monzo. Please reward me for my knowledge and effort by choosing your preferred level of financial support. Thank you.

support level