chord construction and functional harmony with half diminished (m7b5) chords.

Minor Seventh Flat Five Chords

The last set of keyboard chords we shall look at are minor seventh flat five chords. To form this chord, combine the root, flat 3rd, flat fifth and flat seventh of the major scale.created by playing the tonic, flattened third, flattened fifth, and flatted seventh degrees of any major scale (1, ♭3, ♭5 and ♭7)—for example, C half-diminished is (C E♭ G♭ B♭). Alternatively, it can be derived simply by raising (by a semitone) the root note of the major seventh chord.Half-diminished seventh chords are often symbolized as a circle with a diagonal line through it, as in Cø7 or simply Cø. It also can be represented as m7♭5, −7♭5, m7(♭5) etc.

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 ø 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 Bø7) came to be used.  another perspective is that we can see our chord as a Diminished chord of which the Seventh is raised by a 1/2 step-- that is why some other people prefer to call it a Half-Diminished chord. By the way, remember that the 7th of a Diminished chord is actually a M6th.

The half-diminished chord has three functions in contemporary harmony: predominant function, diminished, and dominant function. The vast majority of its occurrences are on the II chord in the minor mode—where 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 V7 chord with a flat ninth. 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 CM7 – C♯dim7 – Dm7, or Em7 – E♭dim7 – 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 there is the progression F♯m7♭5 – Fm7 – Em7 – E♭dim7 – Dm7 – G7 – CM7. 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", and measures 11–12 of Scott Joplin "The Entertainer".

FUNCTIONAL HARMONY:

Now, with those considerations out of the way, where can we find the m7(b5) or Half-Diminished chord?

When deriving the diatonic seventh chords from the 4 Parent Scales (also called Source Scales: see my other article on Chords & Scales) we will find our chord as:

--the vii chord in Major, which is also the ii chord in its relative Minor (Natural Minor scale).

--the ii chord in Harmonic Minor.

--the ii chord in Harmonic Major.

--the vi and vii chords in Melodic Minor.

If we look at a simple turnaround in a minor key, we generally expect to find:

im6 - vim7(b5) - iim7(b5) - V7.

In Cm this progression would give us:

Cm6 - Am7(b5) - Dm7(b5) - G7

Let's look at some other examples:

In the tune "Autumn Leaves" (in the key of Gm) the Am7(b5) in the 5th measure is both the vii in Bb and the ii in Gm (the relative minor). Such a chord is known as a "pivot chord" because it serves a function in the key that it is leaving, as well as a function in the key that it is entering. A "pivot chord" usually makes a modulation less abrupt.

In "All The Things You Are" (in the key of Ab) the F#m7(b5) in the 21st measure is also a "pivot chord". It is the vii in G (the key that is is leaving) as well as the ii in E (the key that it is entering). Some of you might ask why the ii of a Major key such as E can be a Half-Diminished chord when it should be a simple m7 chord? It is what we call a "borrowed" chord: we can see it as coming from either the parallel key of Em, or even from the E Harmonic Major diatonic system. The main reason anyway is that the F#m7(b5) achieves a smoother modulation from G to E.

USING THE CHORD AS A SUBSTITUTION:

A simple substitution is to turn the m7 of a ii-V7 into a Half-Diminished chord. The flatted 5th provides a peculiar tension without truly altering the quality of the chord.

If and when the melody allows it, a biim7(b5) can be substituted for a IMaj7 chord. In "Meditation" by Antonio Carlos Jobim (in the key of C) an F#m7(b5) can be used instead of the usual FMaj7 for the first two measures of the bridge. Think about it: F#m7(b5) and FMaj7 have no less that 3 notes in common!

USING THE CHORD AS AN UPPER-STRUCTURE:

An upper-structure is a chord or an arpeggio that can be played OVER another chord (and not necessarily INSTEAD of the original chord). The chosen upper-structure will be played as a chord when comping, or as an arpeggiated single-note line when improvising.

Remember that a Half-Diminished chord is an inversion of a m6 chord. When playing the i chord in a Minor key (Tonic Minor) you can play a Half-Diminished chord from the 6th of that chord.

Ex. for Dm6 play Bm7(b5)

(You may want to take a look at my essay on Minor Chords and Minor Keys for some thoughts on m6 chords).

The most interesting uses of the Half-Diminished chord as an upper-structure are found over Dominant chords:

For C7(9) play Em7(b5)           (Half-Diminished upper-structure from the 3rd of the dominant)

For C+7(b9) play Bbm7(b5)          (Half-Diminished upper-structure from the 7th of the dominant)

For C7(#9 #11) play Cm7(b5)          (Half-Diminished upper-structure from the Root of the dominant)

For C7(#9 13) play Am7(b5)             (Half-Diminished upper-structure from the 13th of the dominant)

For C7(#11 13) play F#m7(b5)         (Half-Diminished upper-structure from the #11th of the dominant)

For C7(b9 #9 #11 13) play D#m7(b5)  (Half-Diminished upper-structure from the #9th of the dominant)

SUBSTITUTIONS FOR THE HALF-DIMINISHED CHORD:

In the context of a iim7(b5)-V7 here are two common (but interesting) diatonic substitutions for the ii chord:

--At the very beginning of "Night & Day" instead of Dm7(b5) - G7 we can substitute AbMaj7 - G7.

The formula is to play a Maj7 chord from the b5 of the iim7(b5)

--At the very beginning of "I Love You" instead of Gm7(b5) - C7 we can substitute Bbm7(9) - C7.

The formula is to play a m7 chord from the m3 of the iim7(b5)

Both examples work nicely because the V7 chord is approached either by a 1/2 step (down) or by a whole-step (up) -- two pleasing root movements which also break the monotony of a bass moving in perfect fourths.

   

Chord	Root	Minor third	Diminished fifth	Flat seventh
Cm7♭5	C	E♭	G♭	B♭
C♯m7♭5	C♯	E	G	B
D♭m7♭5	D♭	F♭ (E)	A (G)	C♭ (B)
Dm7♭5	D	F	A♭	C
D♯m7♭5	D♯	F♯	A	C♯
E♭m7♭5	E♭	G♭	B (A)	D♭
Em7♭5	E	G	B♭	D
Fm7♭5	F	A♭	C♭ (B)	E♭
F♯m7♭5	F♯	A	C	E
G♭m7♭5	G♭	B (A)	D (C)	F♭ (E)
Gm7♭5	G	B♭	D♭	F
G♯m7♭5	G♯	B	D	F♯
A♭m7♭5	A♭	C♭ (B)	E (D)	G♭
Am7♭5	A	C	E♭	G
A♯m7♭5	A♯	C♯	E	G♯
B♭m7♭5	B♭	D♭	F♭ (E)	A♭
Bm7♭5	B	D	F	A