:: Intro
In my crash course on jazz piano, I described the grammatical/functional use of diatonic chords, modal chords, and augmented chords. I also talked at good length about diminished chords, but I didn't present a grammar for using them in relation to diatonic tetrads. I'm going to do that here and now.
:: Dim7 Chords In The Barry Harris System
In the Barry Harris jazz piano system, there's a diminished seventh chord that you can play before or after almost any other chord.
Here are out main diatonic tetrads in C major for concreteness:
[C.maj6, C.maj7, D.m7, E.m7, F.maj7, G.7, A.m7, B.m7b5]
We'll target each of those with a .dim7 chord. In lots of jazz, C.maj6 and C.maj7 are played fairly interchangeably, but my understanding is that they're quite distinct in the Harris system, so we'll treat them separately in this section.
Let's write out the .dim7 options that alternate against diatonic tetrads in the key of C major.
C.maj6 ↔ B.dim7
C.maj7 ↔ F#.dim7
D.m7 ↔ E.dim7
E.m7 ↔ F#.dim7
F.maj7 ↔ B.dim7
G.7 ↔ C#.dim7 or B.dim7.
A.m7 ↔ B.dim7
B.m7b5 ↔ C#.dim7
If you've already learned about the Barry Harris system, here's a refresher on where these come from:
C.maj6 and B.dim7 are the two chords that alternate in the C major-diminished scale at the heart of the method.
Since A.m7 is an inversion of C.maj6, you play B.dim7, which comes from the C maj6-dim scale.
Since D.m7 is an inversion of F.maj6, you play C#.dim7, which comes from the F maj6-dim scale.
Since E.m7 is an inversion of G.maj6, you play F#.dim7, which comes from the G maj6-dim scale.
Since F.maj9 is A.m7 over F, and we play B.dim7 against A.m7, we also play B.dim7 against F.maj7.
Since C.maj9 is E.m7 over C, and we play F#.dim7 against E.m7, we also play F#.dim7 against C.maj7.
Since B.m7b5 is an inversion of D.m6, you play C#.dim7, which comes from the D m6-dim scale.
G.7 is treated in the Barry Harris system as G.9 or G.7b9.
G.9 is B.m7b5 over G, and we play C#.dim7 against B.m7b5, so we also play C#.dim7 against G.9.
G.7b9 is B.dim7 over G, and B.dim7, so when you want a .dim7 chord that sounds good with G.7b9, obviously you can play B.dim7.
:: Dim7 Chords As Chromatic Approach Chords
Let's get away from the Barry Harris method now. Much like the idiom of approaching a note chromatically from below, there is an often used idiom of preceding a chord with a /dim7 chord whose root is a m2 below the root of the target chord. In the key of C major, that looks like
1. B.dim7 → [C.maj6 or C.maj7]
2. C#.dim7 → D.m7
3. D#.dim7 → E.m7
4. E.dim7 → F.maj7
5. F#.dim7 → G.7
6. G#.dim7 → A.m7
7. A#.dim7 → B.m7b5
Rule 7 here sounds a little worse than the others, but you can make it work. Rule 1 is partly familiar from Barry Harris (B.dim7 → C.maj6) and partly new. Rule 6 is also accounted for by the Harris system if you're working in a tuning such as 12-TET where G#.dim7 is enharmonic with B.dim7. The dim7 chords from rules 2, 4, and 7, namely (C#.dim7, E.dim7, and A#.dim7) are also enharmonic with each other. G.dim7 is also enharmonic with those three, so if you see a G.dim7 chord in a piece in C.maj, and you're struggling to analyze it, you might check if one of its enharmonic re-spellings makes more sense.
:: Half Diminished Chords As Secondary Dominants
Next let's talk about half diminished chords as secondary dominants. Since V.7 and VII.m7b5 both have dominant functions, we can talk about secondary VII.m7b5 chords just as much as secondary V.7 chords. In the key of C major, this gives us the following relations:
B.m7b5 → C.maj
C#.m7b5 → D.m7
D#.m7b5 → E.m7
E.m7b5 → F.maj7
F#.m7b5 → G.7
G#.m7b5 → A.m7
A#.m7b5 → B.m7b5
You'll notice these are all just have diminished versions of the full diminished chord rules in the previous section. Easy. No sweat. Actually, we could also consider these chords to be rootless V.9 secondary dominants, and the .dim7 chords in the previous section could be thought of as rootless V.7b9 seconary dominants. If you're feeling sassy.
:: Dim7 Chords As Descending Chromatic Line Cliches
In addition to preceding a diatonic chord with a .dim7 approach from below, you can often follow a minor chord on a root with a .dim7 chord that has the same root, for a sound that is something like a chromatic line cliche. Here are some examples:
D.m7 → D.dim7 → C.maj7
F.maj7 → F.m7 → F.dim7 → ?(G.7) → C.maj7
A.m7 → A.dim7 → ?
E.m7 → E.dim7 → ?
The question marks are there as placeholders until I sit down at a piano and verify what my memory is telling me about these.
:: Dim7 Chords On Flat Three
Another pretty common use for .dim7 chords that you see in jazz is the [I → bIII] transition. Here are two ways to continue that:
C.maj7 → Eb.dim7 → D.m7
? C.maj7 → Eb.dim7 → F.maj7 ?
I think this just has to be analyzed as a passing chord, which is to say that I don't know why it sounds so good.
Let's work through some ways that these two progressions don't make sense, so you can see why I'm confused.
From all our previous experience with diminished chords, we'd expect that here, before D.m7, we'd see an E.dim7 in the Harris system or C#.dim7 in the chromatic approach idiom, or C#.m7b5 as a half-diminished secondary dominant. But Eb.dim7 isn't any of those. Eb.dim7 happens to be enharmonic in 12-TET with chords such as D#.dim7, Gb.dim7, F#.dim7, A.dim7, and C.dim7. No match, no cigar.
Before F.maj7 we'd expect B.dim7 (Harris) or E.dim7 (chromatic approach) or E.m7b5 (half diminished secondary dominant). Still no dice.
Maybe the bIII dim7 chord is a rootless secondary dominant! You can add one of these notes [B, D, F, G#] to Eb.dim7 and get one of these dominant chords, [B.7b9, D.7b9, F.7b9, or G#.7b9], respectively, which means that Eb.dim7 can act like a rootless version of any of those. But none of those are secondary dominants to D.m7 or F.maj7. So I still don't know why I -> bIII.dim7 works so well. I guess you could call it a chromatic mediant relation, but I thought those were mostly restricted to invole major and minor chord sonorities.
:: Outro
If you know any other uses of .dim7 or .m7b5 chords that aren't accounted for by the above rules, or if you have a different analysis of I.maj7 → bIII.dim7, please do let me know.
