THE MINOR 7(b5) OR HALF-DIMINISHED CHORD:
First of all we need to understand that the two names: either m7(b5) or Half-Diminished indifferently refer to the exact same chord. It really is just a matter of semantics or personal choice...
Let's examine the chord:
Built on a C root, we have: C Eb Gb Bb, respectively the Root, the m3, the dim 5, and the m7. In a chart it may be found written as Cm7(b5) or as CØ
We have three basic (but a bit conflicting) ways to look at the chord:
1) We can see it as a Minor 7th chord of which the Fifth is lowered by a 1/2 step-- that is why some people call it a m7(b5) chord.
It should be noted here that the Half-Diminished chord pretty much always functions as a ii of something (often a ii of iii, or ii of ii) which is why it seems convenient to think of it as a variation of a ii chord-- hence the appellation m7(b5).
2) The 4 notes of the Half-Diminished chord are also the notes of an inverted Minor 6 chord (third inversion). For instance:
Cm7(b5) = Ebm6 with the 6th in the bass (sometimes written as Ebm6/C or simply Ebm/C)
Which means that in the key of Db, Cm7(b5) is both vii and/or an inversion of ii... but it is also ii of vi...
Dizzy Gillespie, in his autobiography, talks about his discovery of the "m6 chord with the 6th in the bass" and how it had a huge impact on his music.
3) Finally, 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...
Since the chord is built on a Diminished Triad (C Eb Gb) it seems that it would make sense to think of it as belonging to the Diminished family.
The confusing thing is that theorists tend to be very opinionated sometimes, and they like to think that only one definition is valid...
The important point here, regardless of which camp we choose, is to realize that we will definitely encounter those various names in books, on charts, and in conversations with other musicians. We just need to accept the fact that they all refer to the same chord, and not worry too much about it.
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.
If you are interested in modes that can be played over the m7(b5) chord, see my other article on Chords & Scales
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