Half-diminished seventh chord

half-diminished seventh chord
Component intervals fromroot
	minor seventh
	diminished fifth(tritone)
	minor third
	root
Tuning
	5:6:7:9or 25:30:36:45
Forte no./Complement
	4-27 /8-27

Inmusic theory,thehalf-diminished seventh chord(also known as ahalf-diminished chordor aminor seventh flat five chord) is aseventh chordcomposed of aroot note,together with aminor third,adiminished fifth,and aminor seventh(1,♭3,♭5,♭7). For example, the half-diminished seventh chord built on B, commonlywrittenas Bm7(♭5), or B^ø⁷,has pitches B-D-F-A:

${ \omit Score.TimeSignature \relative c' { <b d f a>1 } }$

It can be represented by theinteger notation{0, 3, 6, 10}.

The half-diminished seventh chord exists inroot positionand in three inversions. The first inversion is enharmonic to a minorsixth chord:

Half-diminished chord inversions

Indiatonic harmony,the half-diminished seventh chord occurs naturally on the seventhscale degreeof anymajor scale(for example, B^ø⁷in C major) and is thus aleading-tone seventh chordin themajor mode.^[3]Similarly, the chord also occurs on the second degree of anynatural minor scale(e.g., D^ø⁷in C minor). It has been described as a "considerable instability".^[4]

Expressive potential

The half-diminished seventh chord is frequently used in passages that convey heightened emotion. For example, the "mournfulaffect"^[5]of the sombre opening Chorus ofJ. S. Bach'sSt Matthew Passion(1727) features the chord on the seventh beat of its first bar and on the first beat of its third bar:

Bach,St Matthew Passion,opening

Similarly in theEt carnatus estsection fromMichael Haydn'sMissa Sancti Nicolai Tolentini(1768):

Et incarnatus estonYouTubefrom Michael Haydn's Missa Sancti Nicolai Tolentini, MH 109 performed by Le Choeur de Filles de la Maîtrise de Bordeaux

Et incarnatus estfrom Michael Haydn'sMissa Sancti Nicolai Tolentini(1768)

In contrast, however, one of the most striking and best known examples of a half diminished seventh can be found in a piece that expresses joyful celebration, namely the chord that follows the fanfare at the start of theWedding MarchfromMendelssohn's incidental music toA Midsummer Night's Dream(1842).

Mendelssohn, Wedding March

An instance of the power latent in this "quintessentially dramatic chord"^[6]can be found in the "shriek of despair" that launches the "torrent of fury" that isChopin'sScherzo No. 1(1835):^[7]

Chopin, Scherzo No. 1 bars 1–8

Wagner frequently used the chord for dramatic and expressive effect. (Thechordthat opensTristan und Isolde(1859) is the best known and most-discussed example.)^[8]However, in his final operaParsifal(1882), the composer used the half-diminished seventh to colour aleitmotifthat conveys how its hero develops as the story progresses. In the first Act, the music portrays Parsifal as vigorous, youthful and naïve. His leitmotif consists almost entirely ofdiatonicchords:

Wagner, fromParsifal,act 1

"As the hero grows in wisdom, so his music develops."^[9]When Parsifal re-appears in the final act, set many years later, half-diminished chords permeate the leitmotif. Thechromaticharmony here conveys "a deeply sad and resigned impression"^[10]

Wagner, fromParsifalact 3

In the opening section of his Fantasy-Overture,Romeo and Juliet(1880),Tchaikovskyfollows a minor chord with a half-diminished chord to striking effect:

Tchaikovsky Romeo & Juliet bars 28-33

Gustav Mahlersaw the opening movement of hisSymphony No. 7"(1905) as a tragic night without stars or moonlight."^[11]The lowregisterof the half-diminished chord at the start appropriately conveys a dark, brooding character. A striking phrase on the tenor horn unfolds the chord as anarpeggioin the second bar.

Mahler, Symphony No. 7, opening

In his book celebrating popular songs of the first half of the twentieth century, musicologistAllen Fortewrites, "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."^[12]Forte cites as a particular exampleGeorge Gershwin's use of the chord in his song "Embraceable You".^[13]Other examples in the popular song repertoire that use the half-diminished seventh chord include "From This Moment On"byCole Porter,where the opening phrase of the melody unfolds the chord as anarpeggio^[14]and "Because"by theBeatles.^[15]

Chord symbols and terminology

Half-diminished seventh chords areoften symbolizedas a circle with a diagonal line through it, as in B^ø⁷or simply B^ø.It also can be represented as a minor seventh chord with a superscript "^♭5"(sometimes enclosed in parentheses).

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 adiminished triadplus a minor seventh. Instead, it means adiminished triad plus a diminished seventh.To make this distinction clear, the term "half-diminished" and the^øsymbol (ø) were invented. Since the term dim⁷(as in Bdim⁷) meant something else, the accurate but unwieldy term "minor seventh flat five" (as in B^ø⁷) came to be used.^[16]

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-theoristMilton Babbitthas astutely pointed out, the "half-diminished" seventh chord should be called the "one-third" diminished seventh chord.^[17]

Jazzmusicians typically consider the half-diminished chord (more commonly known as the minor seventh flat five chord, m7♭5) as built from one of the following scales:

the seventhmode(theLocrian mode) of the major scale;
the sixthmode of the melodic minor scale—this scale is nearly identical to the Locrian mode, except that it has a♮2 rather than a♭2, giving it a somewhat more consonant quality; or
the second mode of theharmonic minor scale.

Jazz pianistBarry Harrisexplained that bebop musicians would play a descending dominant seventh (Mixolydian) scale with an added half-step to keep all the chord tones on the beat. For example, for the chords "Dm7♭5 G7♭9, play down the B♭7 scale from its seventh to B "(B being the added half-step" bebop note "and third of the G7♭9 chord). This works because the notes of the Dm7♭5 chord { D F A♭C } are also chord tones of B♭9 { B♭D F A♭C }. This scale is sometimes called thePhrygian dominant scaleand is the only scale that keeps all the chord tones on the beat across the $ii-V$ sequence.

The "Tristan chord"is sometimes described as a half-diminished seventh chord; however, the term" Tristan chord "is typically reserved for a very specificharmonic function,especially determined by thechord voicingand sometimes even the way the chord isspelled.

Function

Most common functions

The half-diminished seventh chord has threefunctionsin contemporary harmony:predominant(also called "subdominant" ),diminished,^{[further explanation needed]}anddominantfunction.

The vast majority of its occurrences are on the II chord in theminor mode,^{[citation needed]}where it takes a predominant function, leading naturally to the dominant V chord. Not including therootmotion, there is only a one-note difference between a half-diminished seventh chord and a V⁷chord with a flat ninth. Since it is built on thediatonicII chord of the minor scale, most of the time theII-Vpattern resolves to a minortonic(such as in the progression D^ø⁷– G^7♭9– Cm), but there are also instances where there is a major tonic resolution.

The first three measures of theCiacconamovement ofJ. S. Bach'sViolin Partita No. 2 in D minor

For example, over the first three bars of theCiacconamovement ofJ.S. Bach'sViolin Partita No. 2 in D minor,the tonic in the first measure progresses to the ii^ø⁷chord (inthird inversion) for the first beat of the second measure, then to the dominant (a V⁷infirst inversion), and then back to the tonic in the third measure.

Diminished chord function is rarer but still exists. Half-diminished chords can function in the same way asfully diminishedchords, such as in the chord progression CM⁷– C♯dim⁷– Dm⁷,or Em⁷– E♭dim⁷– Dm⁷,where the diminished chord serves as achromatic passing chordpreceding a chord with a diatonic root. A typical example of this is when♯IV^ø⁷progresses to IVm⁷,such as in theCole Portersong "Night and Day",where there is the progression F♯^ø⁷– Fm⁷– Em⁷– E♭dim⁷– Dm⁷– G⁷– CM⁷.If analyzed in its predominant function, it wouldn't sufficiently explain how it functions preceding the Fm⁷chord.

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 ofcadentialmotion. This chord, sometimes called aleading-tone diminished seventh chord,is represented by theRoman numeral notationvii^ø⁷,the root of which is theleading-toneto the tonic.^[3]In the key of C, this is chord is B^ø⁷,as shown below.

This generally occurs in amajor key,since the flattening of the sixth degree in thenatural minor scalerenders a dominant diminished seventh chordfullydiminished if played within the scale. Indeed, the VII half diminished chord in a major key is identical to adominant ninth chord(adominant seventhwith amajor ninth) with its root omitted.

Secondary leading-tone half-diminished chord in Brahms'sIntermezzo, Op. 119,no. 3 (1893)^[18]

The dominant function of the half-diminished seventh chord may also occur in asecondary dominantcontext, 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 thetritoneof 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 "♯iv^ø⁷,"but in terms of its function in the progression, the styling" vii^ø7/V "is more descriptive.

Other functions

A variant of the supertonic seventh chord (ii^ø⁷) is the supertonic half-diminished seventh with theraised supertonic(♯ii^ø⁷), which isenharmonically equivalentto the loweredthird(in C: D♯= E♭).

D♯–F♯–A–C♯= F♯–A–C♯–E♭

D♯^ø⁷= F♯m^{add dim7}

The sharpened subdominant diminished triad with minor seventh chord is represented with the Roman numeral notation♯iv^ø⁷;the root of this chord is the raisedsubdominant(sharpened fourth). That root also serves as the leading tone to the dominant when used in the vii^ø⁷/V function described above; such a function is the diminished, secondary-dominant equivalent of abackdoor progression.For example, in thekeyofC major,the chord playing this role is F♯^ø⁷.

The half-diminished seventh chord may also be enharmonically interpreted as anaugmented sixth chord.Theminor seventhinterval (between root and seventh degree, i.e.: { C B♭} in { C E♭G♭B♭} ) is enharmonically equivalent to anaugmented sixth{ C E♭G♭A♯}.^[19]Transposing this gives { A♭C♭D F♯}, a virtual minor version of theFrench augmented sixthchord.^[20]Like the typical augmented sixth chord, this enharmonic interpretation gives on aresolution irregularfor the half-diminished seventh but regular for theaugmented sixth chord,where the two voices at thediminished third(enharmonicmajor second) converge tounisonor diverge tooctave.^[21]