Chord Terminology: Dm7b5, Dø7, or Fm6?

"Minor 7 flat five," "half-diminished," or "IVm6"?

These three progressions all express pretty much the same thing, II V I in the key of C minor:

Dm7b5    G7b9    Cm
Dø7        G7b9    Cm
Fm6        G7b9    Cm

One of my first jazz teachers felt that the most accurate way to notate the first chord in this progression would be "m7b5," rather than "half-diminished." His reasoning was that its usual function had more in common with m7 chords than it did with diminished chords. That made sense to me then, and still does now.

The m7b5 chord is usually encountered as II (dominant preparation) in minor, as in the examples above. In major keys, II is a m7 chord. So in C major, II would be Dm7, and in C minor, II would be Dm7b5. It makes sense to use similar terminology - m7 and m7b5 - to describe similarly functioning chords.

The m7b5 chord is often called "half-diminished" because of its construction: diminished triad, with a minor seventh. It's only one accidental away from a "fully" diminished seventh chord. But these chords are not functionally related: The "fully" diminished seventh chord does not occur as a II (dominant preparation) in either major or minor. Rather, it virtually always functions as either a dominant chord (Bdim7 = G7b9 minus the root), or as a passing chord (supplying chromatic passing tones between two other chords). Here are two common turnaround progressions illustrating these usages:

Cmaj7   C#dim7   Dm7   G7    (here the C#dim7 has a dominant function, substituting for A7b9 as a V of II) 

Em7   Ebdim7   Dm7    G7    (here the Ebdim7 is a passing chord)

It's true that a m7b5 chord could serve as a dominant 9 chord minus the root (Bm7b5 = G9), but you'll rarely see it used that way in jazz lead sheets.

It's also true that you will sometimes see the m7b5 chord used in a sort of "passing" context in what I'd call an extended turnaround:

F#m7b5  Fm7   Em7   Ebdim7  Dm7  G7   (e.g., Cole Porter's "Night and Day")

Or sometimes as a VII in major, as part of the "circle within a key" (diatonic circle of fourths):

Cmaj7  Fmaj7  Bm7b5  Em7  Am7  Dm7  G7  Cmaj7

And yes, it's quicker to write a circle with a slash through it (or type option - o) than to write "m7b5."

But I'd still argue that "m7b5" better describes this chord, given its most common function.

In older fakebooks, you'll often see m7b5 expressed as a IVm6 chord:

As you can see, Fm6 is an inversion of Dm7b5; the only difference is that Fm6 implies F in the bass rather than D. In the context of a progression like  Fm6  G7b9  Cm, Fm6 has the same "dominant preparation," minor-key function. Most modern fakebooks would relabel this chord as Dm7b5 (or Dø7), making it easier for players to recognize it (and deal with it) as part of a II V.

In his autobiography To Be, or Not...to Bop, Dizzy Gillespie credits Thelonious Monk with showing him how to use a "minor sixth chord with the sixth in the bass." Of course, voicing it this way gives you exactly a "minor seven flat five."

In current usage, you are more likely to see minor 6 chords occurring as I or IV in a minor key, or as IVm in a major key (e.g., Fm6  Bb7  Cmaj7, where the Fm6 and Bb7 are "borrowed from the parallel minor," adding temporary minor color via the notes Ab and Bb). 

I don't want to digress too much. But the next point of discussion might be: In the progression  Fm6  Bb7  Cmaj7  (or  Fm7  Bb7  Cmaj7), is the Fm6 (or Fm7) just a substitute for Dm7b5, as mentioned above, and is Bb7 just a substitute for G7b9 (e.g., see the bridge to "Stella by Starlight," where bVIIdom sustitutes for V)? One might make that argument, at least on the level of "dominant preparation, dominant substitute, tonic." However, the "IVm bVIIdom" formula tends to occur in specific harmonic situations, and I see it as a rather different thing.