Half diminished chords are also called minor seventh flat fives. They are notated either as m7b5 or with a small bisected circle to the top right of the letter of the chord. When studying chordal theory, it is seen that as chords progress from major to minor and so forth, they get smaller. That is, the intervals within the chord shrink. A major seventh is larger than a dominant and a minor seventh, respectively.
Building the Chord
After the minor seventh, the next smallest chord is the half diminished. A Cm7 is composed of C Eb G Bb. In intervals, this is a minor third followed by a major third followed by a minor third. Compare this to a Cm7b5 which is composed of C Eb Gb Bb.
Notice that the difference between these chords is the Gb. Cm7 contains a perfect fifth (C-G) while Cm7b5 contains a diminished fifth (C-Gb).
In all chords with at least four notes there is another chord within. There is an inverse relationship between major chords and their "inside" chords. The same is true with minor sevenths. Spelling out Cm7 reveals a major triad: Eb G Bb. This is important because it frees up harmonic instruments. Since the bass will hold down the C, it's possible to substitute EbM for Cm7.
The inverse relationship does not apply to half diminished chords, however. As a result of the diminished fifth interval, a minor triad occurs within Cm7b5. Spell out the chord and see that Eb Gb Bb is purely minor. The same principle can still be used, though. If the bass plays the root of the chord (C), then the harmonic instrument can substitute a Ebm chord for the Cm7b5.
Half Diminished Chords within the Diatonic Scale
There are two naturally occurring half diminished chords, one within the minor mode and one in the major. In major, it is on the vii (seventh position) and in minor on the ii (second position). For example, in C minor, D is half diminished. Since the key signature for C minor is Bb Eb Ab, the ii chord is D F Ab C.
Note the F minor triad within the Dm7b5 as previously mentioned. In CM, a half diminished occurs on B.
The role of half diminished chords is to approach the dominant (V). The most common progression in jazz is the ii-V-I (note that capitalized Roman Numerals indicate major chords, whereas lower case indicates minor). A ii-V-I progression in C minor would occur as follows: Dm7b5-G7-Cm7. It is a good idea to spell each chord out to see the notes.
Dm7b5: D F Ab C
G7: G B D F (note that there are very many alterations that are possible when dealing with dominant seventh chords)
Cm7: C Eb G Bb
Notice the relationship between Dm7b5 and G7. D is the V (dominant) of G and so D has a strong urge to move to G just as G7 has a natural attraction to C. This is known as the circle of fifths and is a very important concept in all of western music. The circle can move up a fifth or down a fourth over the entire chromatic scale until it returns to the original starting point. Try this beginning on C-G-D-A, etc.
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