Diminished seventh chord

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The diminished seventh chord is commonly used in the harmony of both Western classical music and also in jazz and popular music of the twentieth and twenty-first centuries. Classical composers of the eighteenth and nineteenth centuries imaginatively exploited the chord's dramatic and expressive potential. (See below).

Video Diminished seventh chord

Definition

A diminished seventh chord is a four note chord that comprises 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 minor scale; for example, C diminished-seventh would be (C, E?, G?, B), or enharmonically (C, E?, G?, A). It occurs as a leading-tone seventh chord in harmonic minor and can be represented by the integer notation {0, 3, 6, 9}.

Because of this it can also be viewed as four notes all stacked in intervals of a minor third. The diminished seventh contains two diminished fifths, which often resolve inwards.

In most sheet music books, Cdim or C^o denotes a diminished seventh chord with root C; but it may also happen, mostly in modern jazz books and some music theory literature, that Cdim or C^o or Cm^?5 denotes a diminished triad, while Cdim⁷ or C^o7 or Cm^6?5 denotes a diminished seventh chord.

Maps 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. Fétis tuned the chord 10:12:14:17.

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. Because these chords have no leading tone in relation to the chords to which they resolve, they can not properly have "dominant" function. They are therefore referred to commonly as "non-dominant" diminished seventh chords or "common tone" diminished seventh chords. (See "common tone diminished seventh chord" below)

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 chord, "plays no role in...jazz." The passing chord is used widely in Brazilian music such as choro, samba and bossa nova.

The diminished seventh chord normally possesses a "dominant" function, 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?. (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 very common "7?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 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, each being a minor third.

The diminished scale may be conceived of as two interlocking diminished seventh chords, which may be rearranged into the alpha chord.

Sharped subdominant with diminished seventh

The sharped subdominant with added diminished seventh chord is another common use of the chord. It can be simply represented with the Roman notation ?iv^o7, but in classical music is more correctly represented as vii^o7/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, which may be used for a strikingly fearful effect, as its root is a tritone (augmented fourth) from the tonic. It is also a common chord in jazz and ragtime music. A common traditional jazz or Dixieland progression in E? may go:

A? - A dim - B?⁷,

which is

IV - ?iv^o7 - V⁷

Another common usage of ?iv^o7 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 |

Supertonic diminished seventh chord

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

Common-tone diminished seventh chord

A diminished seventh chord may alternatively resolve to a major or major-minor 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 (?ii^o7 - I) and the raised submediant, which resolves to dominant triad or seventh in major keys (?vi^o7 - V), with the altered tones resolving upward by half step in both cases.

The ct^o chord, whose function, "is simply one of embellishment," most often spelled ?ii^o when embellishing I or ?vi^o when embellishing V, is distinguished from the vii^o/V chord by common tone chords resolving to I or I⁶ while vii^o/V resolves to V or I⁶
₄. They may be confused, due to enharmonic equivalency, but resolution is a better indicator of function than spelling. In C:

ct^o/I = d?^o = D? F? A C

vii^o/V = f?^o = F? A C E?(=D?)

The diminished chord may also resolve through lowering two of the bottom three voices producing a supertonic seventh chord (ii) that may lead to a conventional dominant cadence.

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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. A vii^o7 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. This was already proposed by Arnold Schoenberg, and Walter Piston has long been the champion of 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 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.

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. He observed in his Treatise on Harmony 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.

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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 third 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 first inversion, is very clumsy and not very useful as it requires the use a triple-flatted note, something that is hardly ever 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?dim 7.

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 dim⁷ 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."

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 min.). 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. More conservatively, each assumed root may be used as a dominant, tonic, or supertonic, giving twelve possibilities.

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Diminished seventh chord table

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Expressive potential

During the Baroque era (1600-1750), European composers became aware of the expressive potential of the diminished seventh chord. In operas and other dramatic works, the chord was frequently used to heighten the sense of passion, anger, danger or mystery. One famous example can be found in J. S. Bach's St. Matthew Passion, (1737) where 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 'Barabbas' is a diminished seventh chord.

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 in the opera Don Giovanni by Wolfgang Amadeus Mozart (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 .

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 Schwanengesang (1828), Franz Schubert conjures "the pianistic elaboration of a diminished seventh over an octave tremolo" to convey the sinister rippling of the oars as the protagonist is rowed across a lake towards the town where his lost beloved once lived. "This famous arpeggiation seems to arise from nowhere to create an atmospheric prelude.. and it dies away to nothing in a postlude." The song ends on the diminished seventh chord; there is no resolution, "the dissonance is terminal.":

The operas of Carl Maria von Weber, particularly Der Freischutz and Euryanthe featured many passages using this chord. The Wolf's Glen scene in Der Freischutz (1821) is an example. According to his early biographer, Alexander Wheelock Thayer, Ludwig van Beethoven spoke disparagingly of the 'accumulation of diminished seventh chords' in Euryanthe (1823). However, it should be pointed out that 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, his piano sonata No. 23, 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, a sharp, stabbing fortissimo.

By the end of the nineteenth 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) 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, Haydn, Mozart, Beethoven, Weber, etc. Even in 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."

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See also

• Enharmonic scale
• Irregular resolution
• Half diminished chord
• Subtonic

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References

Source of the article : Wikipedia