Half-diminished seventh chord
Encyclopedia
In music theory
, the half-diminished seventh chord (also known as a half-diminished chord or a minor seventh flat five) is created by taking the root
, minor third
, diminished fifth and minor seventh
(1, 3, 5 and 7) of any major scale
; for example, C half-diminished is (C E G B). Its consecutive intervals are minor 3rd, minor 3rd, major 3rd. In diatonic harmony
, the half-diminished chord naturally occurs on the 7th scale degree (for example, Bm7(5) in C major). By the same virtue, it also occurs on the second degree of natural minor (e.g. Dm7 (5) in C minor). It occurs as a leading-tone seventh chord
in major and can be represented by the integer notation {0, 3, 6, 10}.
Half-diminished seventh chords are often symbolized as a circle with a diagonal line through it, as in C. It also can be represented as m75, -75, m7(5) etc.
The terms and symbols for this chord break expectations that derive from the usual system of chord nomenclature. Normally a symbol like "Bdim" indicates a diminished triad and "B7" indicates a major triad plus a minor seventh. Thus one would expect the term "Bdim7" to indicate a diminished triad plus a minor seventh. Instead, it means a diminished triad plus a diminished seventh
. To make this distinction clear, the term "half-diminished" and the symbol (ø) were invented. Since the term dim7 (as in Bdim7) meant something else, the accurate but unwieldy term "minor seventh flat five" (as in Bm7(5)) came to be used. "Despite the appearance of the word 'diminished' in the name of this type of seventh chord, its sound differs considerably from that of a diminished seventh chord. In fact, the only sonic connection between the two chords is the single diminished triad found in the half-diminished seventh chord. As composer-theorist Milton Babbitt has astutely pointed out, the 'half-diminished' seventh chord should be called the 'one-third' diminished seventh chord....Whatever its deficiencies might be in the label department, however, the half-diminished seventh chord is in many respects the star of the seventh chord harmonic cast. Many songs in the classic American popular song repertoire reserve it for their most intensely expressive moments".
Jazz
musicians typically consider the half-diminished chord as built from one of three scales: the seventh (Locrian mode
) of the major scale, the sixth mode of the melodic minor scale (the latter scale is nearly identical to the Locrian mode, except that it has a natural 9 rather than a 9, giving it a somewhat more consonant quality), or the "half-whole" diminished scale (see octatonic scale
s.) See: chord-scale system
.
The "Tristan chord
" is sometimes described as a half-diminished seventh chord; however, the term "Tristan chord" is typically reserved for a very specific harmonic function, especially determined by the order of the notes from bottom to top, and sometimes even the way the chord is spelled (e.g. is it G or F?).
The half-diminished chord has three functions in contemporary harmony: predominant
function, diminished
, and dominant
function. The vast majority of its occurrence is on the II chord in the minor mode, wherein it takes a predominant function, leading naturally to the dominant V chord. Not including the root motion, there is only a one note difference between a half diminished chord and a V chord with a 9th. Since it is built on the diatonic II chord of the minor scale, most of the time the II-V pattern resolves to a minor tonic (such as in the progression Dm7(5) - G7(9) - Cm)., but there are instances where there is a major tonic resolution.
Diminished chord function is rarer, but it still exists. Half-diminished chords can function in the same way as fully diminished chords do, such as in the chord progression Cmaj7 - Cdim7 - Dm7, or Em7 - Edim7 - Dm7, where the diminished chord serves as a chromatic passing chord preceding a chord with a diatonic root. A typical example of this is when IVm7(5) progresses to IVm7, such as in the Cole Porter
song "Night and Day
", where you have the progression Fm7(5) - Fm7 - Em7 - Edim7 - Dm7 - G7 - Cmaj7. If analyzed in its predominant function, it wouldn't sufficiently explain how it functions preceding the Fm7 chord.
In dominant function, the VII half diminished chord, like its fully diminished counterpart, can take the place of the dominant V chord at a point of cadential
motion. This generally occurs in a major key, since the flattening of the sixth degree in the natural minor scale renders a dominant diminished seventh chord fully diminished if played within the scale. Indeed, the VII half diminished chord in a major key is identical to a dominant ninth chord (a dominant seventh
with an added ninth) but with its root omitted.
The dominant function of the half-diminished seventh chord may also occur in a secondary dominant
context, i.e., as part of a progression where the chord performs the dominant function with respect to the overall key's dominant chord. In this scenario, the half-diminished seventh chord is built on the tritone
of the overall key and is equivalent to a secondary dominant seventh chord with added ninth and omitted root. If written with respect to the overall key, this chord is styled "#ivø7," but in terms of its function in the progression, the styling "viiø7/V" is more descriptive. Examples of the #ivø7-to-V or viiø7/V-to-V transition include the half-line "know when to run" in the Kenny Rogers
song "The Gambler"
, the opening bars of the Super Mario Bros.
theme
, and measures 11-12 of Scott Joplin
's "The Entertainer
".
is represented with the Roman numeral notation vii7. In the key of C
, this is Bdim7, the root of which is the leading-tone to the tonic
.
seventh chord is the supertonic half-diminished seventh (ii7) in minor. It may be considered a minor seventh chord
with a flatted fifth
(e.g., ACEG rather than ACEG) and is used in the ii-V-I in minor. For example, over the first three bars of the Ciaccona or Chaconne
movement of J.S. Bach's Violin Partita No. 2 in D minor
, the tonic in the first measure progresses to the ii7 chord (here in third inversion: DGBE) for the first beat of the second measure, then to the dominant (here a V7 in first inversion: C#GAE) for the second and third beats of the second measure, and then back to the tonic for the first beat of the third measure.
, which equals the lowered third
through enharmonic equivalence (in C: D=E).
DFA C = FA CE
d7 = fmADD7
is represented with the Roman numeral notation iv7; the root of this chord is the raised subdominant
(sharpened fourth). That root also serves as the leading tone to the dominant when used in the vii7/V function described above; such a function is the diminished, secondary-dominant equivalent of a backdoor progression
. For example, in the key
of C major
, the chord playing this role is f7, which can be heard in the above-mentioned passages from "The Entertainer" and from the Super Mario Bros. theme.
Music theory
Music theory is the study of how music works. It examines the language and notation of music. It seeks to identify patterns and structures in composers' techniques across or within genres, styles, or historical periods...
, the half-diminished seventh chord (also known as a half-diminished chord or a minor seventh flat five) is created by taking 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....
, 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...
, diminished fifth and minor seventh
Minor seventh
In classical music from Western culture, a seventh is a musical interval encompassing seven staff positions , and the minor seventh is one of two commonly occurring sevenths. The minor quality specification identifies it as being the smallest of the two: the minor seventh spans ten semitones, the...
(1, 3, 5 and 7) 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 half-diminished is (C E G B). Its consecutive intervals are minor 3rd, minor 3rd, major 3rd. In diatonic harmony
Harmony
In music, harmony is the use of simultaneous pitches , or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic...
, the half-diminished chord naturally occurs on the 7th scale degree (for example, Bm7(5) in C major). By the same virtue, it also occurs on the second degree of natural minor (e.g. Dm7 (5) in C minor). 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 major and can be represented by the integer notation {0, 3, 6, 10}.
Half-diminished seventh chords are often symbolized as a circle with a diagonal line through it, as in C. It also can be represented as m75, -75, m7(5) etc.
The terms and symbols for this chord break expectations that derive from the usual system of chord nomenclature. Normally a symbol like "Bdim" indicates a diminished triad and "B7" indicates a major triad plus a minor seventh. Thus one would expect the term "Bdim7" to indicate a diminished triad plus a minor seventh. Instead, it means a diminished triad plus a diminished seventh
Diminished seventh chord
A diminished seventh chord is a four note chord that comprises a diminished triad plus the interval of a diminished seventh above the root. Thus it is , or enharmonically , of any major scale; for example, C diminished-seventh would be , or enharmonically...
. To make this distinction clear, the term "half-diminished" and the symbol (ø) were invented. Since the term dim7 (as in Bdim7) meant something else, the accurate but unwieldy term "minor seventh flat five" (as in Bm7(5)) came to be used. "Despite the appearance of the word 'diminished' in the name of this type of seventh chord, its sound differs considerably from that of a diminished seventh chord. In fact, the only sonic connection between the two chords is the single diminished triad found in the half-diminished seventh chord. As composer-theorist Milton Babbitt has astutely pointed out, the 'half-diminished' seventh chord should be called the 'one-third' diminished seventh chord....Whatever its deficiencies might be in the label department, however, the half-diminished seventh chord is in many respects the star of the seventh chord harmonic cast. Many songs in the classic American popular song repertoire reserve it for their most intensely expressive moments".
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...
musicians typically consider the half-diminished chord as built from one of three scales: the seventh (Locrian mode
Locrian mode
The Locrian mode is either a musical mode or simply a diatonic scale. Although the term occurs in several classical authors on music theory, including Cleonides and Athenaeus , there is no warrant for the modern usage of Locrian as equivalent to Glarean's Hyperaeolian mode, in either classical,...
) of the major scale, the sixth mode of the melodic minor scale (the latter scale is nearly identical to the Locrian mode, except that it has a natural 9 rather than a 9, giving it a somewhat more consonant quality), or the "half-whole" diminished scale (see octatonic 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...
s.) See: chord-scale system
Chord-scale system
The chord-scale system is a method of matching, from a list of possible chords, a list of possible scales. The system has been widely used since the 1970s and is "generally accepted in the jazz world today"...
.
The "Tristan chord
Tristan chord
The Tristan chord is a chord made up of the notes F, B, D and G. More generally, it can be any chord that consists of these same intervals: augmented fourth, augmented sixth, and augmented ninth above a root...
" is sometimes described as a half-diminished seventh chord; however, the term "Tristan chord" is typically reserved for a very specific harmonic function, especially determined by the order of the notes from bottom to top, and sometimes even the way the chord is spelled (e.g. is it G or F?).
Function
It is described as a "considerable instability".The half-diminished chord has three functions in contemporary harmony: predominant
Predominant
In music theory, a predominant chord is any chord which normally resolves to a dominant chord. Examples of predominant chords are the subdominant , supertonic , Neapolitan sixth and German sixth. Other examples are the submediant , secondary dominant , iv and ii°...
function, diminished
Diminished
Diminished is to make smaller or less or to cause to appear so.Diminished may also refer to:*Diminution in Music*Diminished: A song in alternative rock band R.E.M.'s 1998 album Up↑...
, and 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...
function. The vast majority of its occurrence is on the II chord in the minor mode, wherein it takes a predominant function, leading naturally to the dominant V chord. Not including the root motion, there is only a one note difference between a half diminished chord and a V chord with a 9th. Since it is built on the diatonic II chord of the minor scale, most of the time the II-V pattern resolves to a minor tonic (such as in the progression Dm7(5) - G7(9) - Cm)., but there are instances where there is a major tonic resolution.
Diminished chord function is rarer, but it still exists. Half-diminished chords can function in the same way as fully diminished chords do, such as in the chord progression Cmaj7 - Cdim7 - Dm7, or Em7 - Edim7 - Dm7, where the diminished chord serves as a chromatic passing chord preceding a chord with a diatonic root. A typical example of this is when IVm7(5) progresses to IVm7, such as in the Cole Porter
Cole Porter
Cole Albert Porter was an American composer and songwriter. Born to a wealthy family in Indiana, he defied the wishes of his domineering grandfather and took up music as a profession. Classically trained, he was drawn towards musical theatre...
song "Night and Day
Night and Day (song)
"Night and Day" is a popular song by Cole Porter. It was written for the 1932 musical play Gay Divorce. It is perhaps Porter's most popular contribution to the Great American Songbook and has been recorded by dozens of artists....
", where you have the progression Fm7(5) - Fm7 - Em7 - Edim7 - Dm7 - G7 - Cmaj7. If analyzed in its predominant function, it wouldn't sufficiently explain how it functions preceding the Fm7 chord.
In dominant function, the VII half diminished chord, like its fully diminished counterpart, can take the place of the dominant V chord at a point of cadential
Cadence (music)
In Western musical theory, a cadence is, "a melodic or harmonic configuration that creates a sense of repose or resolution [finality or pause]." A harmonic cadence is a progression of two chords that concludes a phrase, section, or piece of music...
motion. This generally occurs in a major key, since the flattening of the sixth degree in the natural minor scale renders a dominant diminished seventh chord fully diminished if played within the scale. Indeed, the VII half diminished chord in a major key is identical to a dominant ninth chord (a dominant seventh
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...
with an added ninth) but with its root omitted.
The dominant function of the half-diminished seventh chord may also occur in a secondary dominant
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...
context, i.e., as part of a progression where the chord performs the dominant function with respect to the overall key's dominant chord. In this scenario, the half-diminished seventh chord is built on the 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...
of the overall key and is equivalent to a secondary dominant seventh chord with added ninth and omitted root. If written with respect to the overall key, this chord is styled "#ivø7," but in terms of its function in the progression, the styling "viiø7/V" is more descriptive. Examples of the #ivø7-to-V or viiø7/V-to-V transition include the half-line "know when to run" in the Kenny Rogers
Kenny Rogers
Kenneth Donald "Kenny" Rogers is an American singer-songwriter, photographer, record producer, actor, and entrepreneur...
song "The Gambler"
The Gambler (song)
"The Gambler" is the title of a song written by Don Schlitz and recorded by American country music artist Kenny Rogers. It was released in November 1978 as the title track from his album The Gambler which won him the Grammy award for best male country vocal performance in 1980. Bobby Bare had...
, the opening bars of the Super Mario Bros.
Super Mario Bros.
is a 1985 platform video game developed by Nintendo, published for the Nintendo Entertainment System as a sequel to the 1983 game Mario Bros. In Super Mario Bros., the player controls Mario as he travels through the Mushroom Kingdom in order to rescue Princess Toadstool from the antagonist...
theme
Super Mario Bros. theme
-Composition:This theme took the longest of the six tracks of Super Mario Bros. to compose, according to its composer Koji Kondo. He stated that he would write one piece, and the team would put it in the game. If it did not accentuate the action, did not time up with Mario running and jumping, or...
, and measures 11-12 of Scott Joplin
Scott Joplin
Scott Joplin was an American composer and pianist. Joplin achieved fame for his ragtime compositions, and was later dubbed "The King of Ragtime". During his brief career, Joplin wrote 44 original ragtime pieces, one ragtime ballet, and two operas...
's "The Entertainer
The Entertainer (rag)
"The Entertainer" is sub-titled "A rag time two step", which was a form of dance popular until about 1911, and a style which was common among rags written at the time.Its structure is: Intro AA BB A CC Intro2 DD....
".
Leading-tone with minor seventh
The leading-tone diminished triad with minor seventh chordChord (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 represented with the Roman numeral notation vii7. 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 Bdim7, the root of which is the leading-tone to 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...
.
Supertonic with minor seventh in minor
One variant of the supertonicSupertonic
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 half-diminished seventh (ii7) in minor. It may be considered a minor seventh chord
Minor seventh chord
In music, a minor seventh chord is any nondominant seventh chord where the "third" note is a minor third above the root.Most typically, minor seventh chord refers to where the "seventh" note is a minor seventh above the root...
with a flatted fifth
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...
(e.g., ACEG rather than ACEG) and is used in the ii-V-I in minor. For example, over the first three bars of the Ciaccona or Chaconne
Chaconne
A chaconne ; is a type of musical composition popular in the baroque era when it was much used as a vehicle for variation on a repeated short harmonic progression, often involving a fairly short repetitive bass-line which offered a compositional outline for variation, decoration, figuration and...
movement of J.S. Bach's Violin Partita No. 2 in D minor
Solo Violin Partita No. 2 (Bach)
The Partita in D minor for solo violin by Johann Sebastian Bach was written during the period 1717–1723 and one scholar, Professor Helga Thoene, suggests this partita, and especially its last movement, was a tombeau, written in memory of Bach's first wife, Maria Barbara Bach , though this...
, the tonic in the first measure progresses to the ii7 chord (here in third inversion: DGBE) for the first beat of the second measure, then to the dominant (here a V7 in first inversion: C#GAE) for the second and third beats of the second measure, and then back to the tonic for the first beat of the third measure.
Sharpened supertonic with minor seventh
One variant of the supertonic seventh chord is the supertonic half-diminished seventh (ii7) with the raised supertonicMinor 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...
, which equals the lowered third
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...
through enharmonic equivalence (in C: D=E).
DFA C = FA CE
d7 = fmADD7
Sharpened subdominant with minor seventh
The sharpened subdominant diminished triad with minor seventh chordChord (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 represented with the Roman numeral notation iv7; the root of this chord is the raised subdominant
Subdominant
In music, the subdominant is the technical name for the fourth tonal degree of the diatonic scale. It is so called because it is the same distance "below" the tonic as the dominant is above the tonic - in other words, the tonic is the dominant of the subdominant. It is also the note immediately...
(sharpened fourth). That root also serves as the leading tone to the dominant when used in the vii7/V function described above; such a function is the diminished, secondary-dominant equivalent of a backdoor progression
Backdoor progression
In jazz and jazz harmony, the chord progression from iv7 to VII7 to I has been nicknamed the backdoor progression or the backdoor ii-V. This name derives from an assumption that the normal progression to the tonic, the ii-V-I turnaround is, by inference, the front door...
. For example, in the key
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...
of C major
C major
C major is a musical major scale based on C, with pitches C, D, E, F, G, A, and B. Its key signature has no flats/sharps.Its relative minor is A minor, and its parallel minor is C minor....
, the chord playing this role is f7, which can be heard in the above-mentioned passages from "The Entertainer" and from the Super Mario Bros. theme.
Half-diminished seventh chord table
| Chord | Root | Minor Third | Diminished Fifth | Minor Seventh |
|---|---|---|---|---|
| C | E | G | B | |
| C | E | G | B | |
| D | F (E) | A (G) | C (B) | |
| D | F | A | C | |
| D | F | A | C | |
| E | G | B (A) | D | |
| E | G | B | D | |
| F | A | C (B) | E | |
| F | A | C | E | |
| G | B (A) | D (C) | F (E) | |
| G | B | D | F | |
| G | B | D | F | |
| A | C (B) | E (D) | G | |
| A | C | E | G | |
| A | C | E | G | |
| B | D | F (E) | A | |
| B | D | F | A | |