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Contents 1 Diminished Seventh Interval 2 Diminished Seventh Chord 2.1 Theoretically Explained 2.2 Basic Sound Qualities and Structure 2.3 Harmonic Function 3 References

[edit] Diminished Seventh Interval

A diminished seventh interval is a chromatically reduced minor seventh interval. It is also known as an enharmonic interval.^[1] The prefix 'diminished' identifies a minor or perfect interval that has been chromatically reduced by a half-tone.^[2] Its inversion is the augmented second, and its enharmonic equivalent is the major sixth.

The diminished seventh has no 'natural' diatonic occurrence.

As music became increasingly chromatic, the diminished seventh was used with correspondingly greater freedom and also became a common component of jazz chords.

In an equal tempered tuning, a diminished seventh is equal to nine semitones, a ratio of 1:2^9/12 (approximately 1.682), or 900 cents.

The diminished seventh is a context dependent dissonance. That is, when heard in certain contexts, such as that described above, the interval will sound dissonant. In other contexts, however, the same nine semitone interval will simply be heard (and notated) as its consonant enharmonic equivalent, the major sixth.

[edit] Diminished Seventh Chord

[edit] Theoretically Explained

The diminished seventh chord is often considered as an incomplete dominant minor ninth. These chords, belonging to the group of dominant ninth chords, are most often found with their roots omitted. Even though the root is not sounded, its function is implied.^[3] The diminished seventh interval occurs as part of the minor dominant ninth chord: (G) B D F Ab.

The diminished seventh chord is a nondiatonic chord.^[4]

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.^[5]

[edit] Basic Sound Qualities and Structure

This chord may be regarded as three superimposed minor third intervals (e.g. B-D-F-Ab) or two tritones (e.g. C-F#, Eb-A).

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 pitches), there are only three different diminished seventh chords possible.

[edit] Harmonic Function

Each of the diminished seventh chord's tones can be traced to its own hidden root. It is unclear to which key the chord belongs whenever it appears out of context or in an ambiguous one. The functional ambiguity of the diminished seventh chord makes it particularly useful in facilitating modulation, though overuse of this hermaphroditic chord can produce a feeble, bland sound.^[6]

The most usual progression is the strong movement (or leap a fourth upward) with a tacit root ((V)-I).^[7]

This is the best chord for simple enharmonic changes, the properties of which in this particular are so remarkable and manifold that it is often called the "enharmonic chord."^[8]

A single diminished seventh chord, without enharmonic change, is capable, like any dominant chord, 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.^[9]

[edit] References

1. ^ Piston, Walter: "Harmony", pp. 5-8, Third Edition, W. W. Norton & Company, 1962
2. ^ ibid, pg. 5
3. ^ ibid, pg. 191
4. ^ Schoenberg, Arnold: "Theory of Harmony", pp. 192 & 194, Third Edition (1922), University of California Press ISBN 0-520-04944-6
5. ^ Schenker, Heinrich: "Harmony", pg. 192, The University of Chicago Press, 1954, Library of Congress - 54-11213
6. ^ Schoenberg, Arnold: "Theory of Harmony", pp. 194-195, Third Edition (1922), University of California Press ISBN 0-520-04944-6
7. ^ ibid, pg. 199
8. ^ Goetschius, Percy: "The Material Used in Musical Composition - A System of Harmony", pg. 159, G. Shirmer, Inc., 1913
9. ^ Piston, Walter: "Harmony", pg. 201, Third Edition, W. W. Norton & Company, 1962