A diminished seventh chord is a four note chord

Chord (music)

A chord in music is any harmonic set of two–three or more notes that is heard as if sounding simultaneously. These need not actually be played together: arpeggios and broken chords may for many practical and theoretical purposes be understood as chords...

 that comprises a diminished triad

Diminished chord

A diminished triad chord or diminished chord is a triad consisting of two minor thirds above the root — if built on C, a diminished chord would have a C, an E and a G. It resembles a minor triad with a lowered fifth....

 plus the interval

Interval (music)

In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...

 of a diminished seventh

Diminished seventh

In classical music from Western culture, a diminished seventh is an interval produced by narrowing a minor seventh by a chromatic semitone. For instance, the interval from A to G is a minor seventh, ten semitones wide, and both the intervals from A to G, and from A to G are diminished sevenths,...

 (alternatively regarded enharmonically as a major sixth

Sixth

Sixth can refer to:* The ordinal form of the number six* Sixth Amendment to the U.S. Constitution* A keg of beer equal to 5 U.S. gallons or 1/6 barrel of beer.* A fraction, such as 1/6-Music:*Interval*Major sixth*Minor sixth...

) above the root

Root (chord)

In music theory, the root of a chord is the note or pitch upon which a triadic chord is built. For example, the root of the major triad C-E-G is C....

. Thus it is (1, 3, 5, 7), or enharmonically (1, 3, 5, 6), of any major scale

Major scale

In music theory, the major scale or Ionian scale is one of the diatonic scales. It is made up of seven distinct notes, plus an eighth which duplicates the first an octave higher. In solfege these notes correspond to the syllables "Do, Re, Mi, Fa, Sol, La, Ti/Si, ", the "Do" in the parenthesis at...

; 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

Leading-tone seventh chord

In music theory, the leading-tone seventh chords are vii7 and vii7, the half-diminished and diminished seventh chords on the seventh scale degree, or leading-tone, in major and harmonic minor, resolving to the tonic...

 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

Minor third

In classical music from Western culture, a third is a musical interval encompassing three staff positions , and the minor third is one of two commonly occurring thirds. The minor quality specification identifies it as being the smallest of the two: the minor third spans three semitones, the major...

. The diminished seventh contains two diminished fifths, which often resolve inwards.

In most sheet music books, Cdim or C° 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° 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

Submediant

In music, the submediant is the sixth scale degree of the diatonic scale, the 'lower mediant' halfway between the tonic and the subdominant or 'lower dominant'...

) scale degrees

Degree (music)

In music theory, a scale degree or scale step is the name of a particular note of a scale in relation to the tonic...

. 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

Borrowed chord

A borrowed chord is a chord borrowed from the parallel key . Borrowed chords are typically used as "color chords", providing variety through contrasting scale forms, major and the three forms of minor...

" from the parallel minor.

Seventh chords may also be rooted on other scale degrees, either as secondary function

Secondary dominant

Secondary dominant is an analytical label for a specific harmonic device, prevalent in the tonal idiom of Western music beginning in the common practice period...

 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

Jazz

Jazz is a musical style that originated at the beginning of the 20th century in African American communities in the Southern United States. It was born out of a mix of African and European music traditions. From its early development until the present, jazz has incorporated music from 19th and 20th...

, the diminished seventh chord is often based on the lowered third scale degree (the flat mediant

Mediant

In music, the mediant is the third scale degree of the diatonic scale, being the note halfway between the tonic and the dominant. Similarly, the submediant is halfway between the tonic and subdominant...

) and acts as a passing chord

Passing chord

In music, a passing chord is, "a nondiatonic chord that connects, or passes between, the notes of two diatonic chords." "Any chord that moves between one diatonic chord and another one nearby may be loosely termed 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

Dominant seventh chord

In music theory, a dominant seventh chord, or major minor seventh chord,is a chord composed of a root, major third, perfect fifth, and minor seventh. It can be also viewed as a major triad with an additional minor seventh...

, 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 C13911). The diminished seventh chord should not be confused with the half-diminished seventh chord

Half-diminished seventh chord

In music theory, the half-diminished seventh chord is created by taking the root, minor third, diminished fifth and minor seventh of any major scale; for example, C half-diminished is . Its consecutive intervals are minor 3rd, minor 3rd, major 3rd...

, 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, each being a minor third

Minor third

In classical music from Western culture, a third is a musical interval encompassing three staff positions , and the minor third is one of two commonly occurring thirds. The minor quality specification identifies it as being the smallest of the two: the minor third spans three semitones, the major...

.
The diminished scale

Octatonic scale

An octatonic scale is any eight-note musical scale. Among the most famous of these is a scale in which the notes ascend in alternating intervals of a whole step and a half step, creating a symmetric scale...

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

Sharpened subdominant with diminished seventh

The sharpened subdominant with added diminished seventh chord

Chord (music)

A chord in music is any harmonic set of two–three or more notes that is heard as if sounding simultaneously. These need not actually be played together: arpeggios and broken chords may for many practical and theoretical purposes be understood as chords...

 is another common use of the chord. It can be simply represented with 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

Key (music)

In music theory, the term key is used in many different and sometimes contradictory ways. A common use is to speak of music as being "in" a specific key, such as in the key of C major or in the key of F-sharp. Sometimes the terms "major" or "minor" are appended, as in the key of A minor or in the...

, this is Fdim7, which may be used for a strikingly fearful effect, as its root is a tritone

Tritone

In classical music from Western culture, the tritone |tone]]) is traditionally defined as a musical interval composed of three whole tones. In a chromatic scale, each whole tone can be further divided into two semitones...

 (augmented fourth) from the tonic

Tonic (music)

In music, the tonic is the first scale degree of the diatonic scale and the tonal center or final resolution tone. The triad formed on the tonic note, the tonic chord, is thus the most significant chord...

. It is also a common chord in jazz

Jazz

Jazz is a musical style that originated at the beginning of the 20th century in African American communities in the Southern United States. It was born out of a mix of African and European music traditions. From its early development until the present, jazz has incorporated music from 19th and 20th...

 and ragtime

Ragtime

Ragtime is an original musical genre which enjoyed its peak popularity between 1897 and 1918. Its main characteristic trait is its syncopated, or "ragged," rhythm. It began as dance music in the red-light districts of American cities such as St. Louis and New Orleans years before being published...

 music. A common traditional jazz or Dixieland

Dixieland

Dixieland music, sometimes referred to as Hot jazz, Early Jazz or New Orleans jazz, is a style of jazz music which developed in New Orleans at the start of the 20th century, and was spread to Chicago and New York City by New Orleans bands in the 1910s.Well-known jazz standard songs from the...

 progression in E may go:

A - A dim - B7,

which is

IV - iv7 - V7

Another common usage of iv7 is often found in Gospel music

Gospel music

Gospel music is music that is written to express either personal, spiritual or a communal belief regarding Christian life, as well as to give a Christian alternative to mainstream secular music....

 and jazz progressions

Chord progression

A chord progression is a series of musical chords, or chord changes that "aims for a definite goal" of establishing a tonality founded on a key, root or tonic chord. In other words, the succession of root relationships...

 such as in the song "I Got Rhythm

I Got Rhythm

"I Got Rhythm" is a song composed by George Gershwin with lyrics by Ira Gershwin and published in 1930, which became a jazz standard. Its chord progression, known as the "rhythm changes", is the foundation for many other popular jazz tunes such as Charlie Parker's and Dizzy Gillespie's Bebop...

".

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

Supertonic diminished seventh chord

One variant of the supertonic

Supertonic

In music or music theory, the supertonic is the second degree or note of a diatonic scale, one step above the tonic. In music theory, the supertonic chord is symbolized by the Roman numeral ii in a major scale, indicating that the chord is a minor chord , or ii in a natural minor scale, indicating...

 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

Chord substitution

In music theory, chord substitution is the use of a chord in the place of another related chord in a chord progression. Jazz musicians often substitute chords in the original progression to create variety and add interest to a piece. The substitute chord must have some harmonic quality and degree...

.

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, the most common being the raised supertonic seventh, which resolves to the tonic in major keys and the raised submediant, which resolves to dominant triad or seventh in major keys, with the altered tones resolving upward by half step.
The diminished chord may also resolve through lowering two of the bottom three voices producing a supertonic seventh chord that may lead to a conventional dominant cadence.

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 chord

Seventh chord

A seventh chord is a chord consisting of a triad plus a note forming an interval of a seventh above the chord's root. When not otherwise specified, a "seventh chord" usually means a major triad with an added minor seventh...

s are analyzed.
The other method is to analyze the chord as an "incomplete dominant ninth", that is a ninth chord

Ninth chord

A ninth chord is a chord that encompasses the interval of a ninth when arranged in close position with the root in the bass.A dominant ninth is a dominant chord with a ninth. A ninth chord, as an extended chord, typically includes the seventh along with the basic triad structure. Thus, a Cmaj9...

 with its root on the dominant, whose root is missing or implied. A vii°7 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. Walter Piston

Walter Piston

Walter Hamor Piston Jr., , was an American composer of classical music, music theorist and professor of music at Harvard University whose students included Leroy Anderson, Leonard Bernstein, and Elliott Carter....

 has long been the champion of this analysis.

The dominant ninth theory has been questioned by Heinrich Schenker

Heinrich Schenker

Heinrich Schenker was a music theorist, best known for his approach to musical analysis, now usually called Schenkerian analysis....

. 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.

Rameau

Jean-Philippe Rameau

Jean-Philippe Rameau was one of the most important French composers and music theorists of the Baroque era. He replaced Jean-Baptiste Lully as the dominant composer of French opera and is also considered the leading French composer for the harpsichord of his time, alongside François...

 explained the diminished seventh chord as a dominant seventh chord whose supposed fundamental bass

Bass note

In music theory, the bass note of a chord or sonority is the lowest note played or notated. If there are multiple voices it is the note played or notated in the lowest voice. While the bass note is often the root or fundamental of the chord, it does not have to be, and sometimes one of the other...

 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 minor produces A-B-D-F. He observed in his Treatise on Harmony

Treatise on Harmony

Treatise on Harmony is a music treatise written by Jean-Philippe Rameau. The first publication of the treatise was in Paris, 1722 by Jean-Baptiste-Christophe Ballard....

 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

Quarter-comma meantone

Quarter-comma meantone, or 1/4-comma meantone, was the most common meantone temperament in the sixteenth and seventeenth centuries, and was sometimes used later. This method is a variant of Pythagorean tuning...

, a tuning he favored, which is close to the just septimal minor third

Septimal minor third

In music, the septimal minor third , also called the subminor third, is the musical interval exactly or approximately equal to a 7/6 ratio of frequencies. In terms of cents, it is 267 cents, a quartertone of size 36/35 flatter than a just minor third of 6/5...

 of 7/6.

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 Edim7 in its third inversion:

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

It can also be viewed as a Gdim7 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 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 Fdim7).

C + D (enharmonic equivalent of E) + F (enharmonic equivalent of G) + A (enharmonic equivalent of B) (third inversion Ddim7).

B (enharmonic equivalent of C) + D (enharmonic equivalent of E) + F (enharmonic equivalent of G) + A (enharmonic equivalent of B) (root position Bdim7).

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 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

Inversion (music)

In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices...

. Each inversion is enharmonic

Enharmonic

In modern musical notation and tuning, an enharmonic equivalent is a note , interval , or key signature which is equivalent to some other note, interval, or key signature, but "spelled", or named, differently...

 with another diminished seventh chord, and 19th-century composers in particular often make use of this enharmonic to use these chords for modulation

Modulation (music)

In music, modulation is most commonly the act or process of changing from one key to another. This may or may not be accompanied by a change in key signature. Modulations articulate or create the structure or form of many pieces, as well as add interest...

s. 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

Dominant (music)

In music, the dominant is the fifth scale degree of the diatonic scale, called "dominant" because it is next in importance to the tonic,and a dominant chord is any chord built upon that pitch, using the notes of the same diatonic scale...

, tonic

Tonic (music)

In music, the tonic is the first scale degree of the diatonic scale and the tonal center or final resolution tone. The triad formed on the tonic note, the tonic chord, is thus the most significant chord...

, or supertonic

Supertonic

In music or music theory, the supertonic is the second degree or note of a diatonic scale, one step above the tonic. In music theory, the supertonic chord is symbolized by the Roman numeral ii in a major scale, indicating that the chord is a minor chord , or ii in a natural minor scale, indicating...

, giving twelve possibilities.

Diminished seventh chord table

Chord	Root	Minor Third	Diminished Fifth	Diminished Seventh
Cdim7	C	E	G	B (A)
	C	E	G	B
	D	F (E)	A (G)	C (B)
Ddim7	D	F	A	C (B)
	D	F	A	C
	E	G	B (A)	D (C)
Edim7	E	G	B	D
Fdim7	F	A	C (B)	E (D)
	F	A	C	E
	G	B (A)	D (C)	F (E)
Gdim7	G	B	D	F (E)
	G	B	D	F
	A	C (B)	E (D)	G (F)
Adim7	A	C	E	G
	A	C	E	G
	B	D	F (E)	A (G)
Bdim7	B	D	F	A