As a jazz musician, I love learning new jazz theory tricks to apply to my playing. While learning jazz language by ear should be the primary way we learn to play, conceptualizing different ideas through music theory can be a really helpful tool.
So here’s a simple but quite useful theory tip for you to use today: how to substitute a dominant 7 for a diminished 7. Using diminished ideas over dominant chords can be a refreshing approach when used in the proper context. Here’s the rule:
The Dominant 7 and Diminished 7 Rule
A diminished 7 chord can replace an altered dominant 7 chord (commonly b9 or #9) when the root of the diminished 7 is a half-step above the root of the altered dominant 7.
Essentially, if you see a dominant 7 chord resolving to another chord, it can be altered. For example, a ii-V-I chord progression.
The G7 is resolving to a Cmaj7. Since the G7 is a V chord resolving to a I, you can add tension by adding an altered extension to it (b9, #9, b13, #11).
This is the same case in a I-VI-ii-V.
To be diatonically authentic, the vi chord would be minor (Amin7), but in jazz we often turn this chord into a dominant 7 chord (A7), to add some color in the voice leading. Therefore, the A7 now resolves to the ii (Dmin7) and the V (G7) is presumably resolving to the I chord. Both the VI7 chord and the V chord can be altered. Because they can be altered, we can apply a diminished sound to them.
If you think about it, a diminished scale a half step above the dominant 7 chord would be starting on the b9 of the dominant 7.
For easy demonstration purposes, let’s look at a C diminished scale. This scale is also called a Whole Half Diminished Scale because it is built off of these alternating intervals.
Whole Half Diminished Scale
Intervallic formula: W-H-W-H-W-H-W-H
Scale tone formula: 1-2-b3-4-#4-#5-6-7-8
C whole half diminished scale: C-D-Eb-F-Gb-G#-A-B
Which dominant 7 chord would we play this over? B7(b9). Of course, it could be a #9 as well because D natural (second note in the scale) is the #9 of B7. The F natural in C diminished is the #11 you could apply to the B7.
But if you know anything about diminished 7 chords it’s that they are symmetrical. Here’s the rule:
Diminished 7th Chord Rule
Because of the symmetrical intervals, there are only 3 possible diminished chords. All 12 keys are related to one of those 3 chords. A diminished 7 chord can be moved up or down in minor 3rds and be thought of as an inversion of the original or a new key entirely.
In other words, if we take our Cdim7 chord up a minor third it becomes and Ebdim7 chord. Or you can think of it as a Cdim7 first inversion. They are the same notes, just shifted. If you move the Eb up a minor 3rd it becomes a Gbdim7. Same exact chord. Move the Gb up a minor 3rd and its an Adim7. Same exact chord. Move the A up a minor 3rd and we are back to Cdim7.
So if you think of this rule in the context of altered dominant 7 chords, if you had a D7(b9) chord, you could play and Eb diminished scale, C, Gb, or A. Because of diminished symmetry, they are all the same.
Now, because the diminished scale moves symmetrically in its intervals using alternating whole steps and half steps, you can also start the scale on a half step. That’s where the Half Whole Diminished Scale comes in. This scale is specifically used to play over altered dominant chords starting on their root.
Half Whole Diminished Scale
Intervallic formula: H-W-H-W-H-W-H-W
Scale tone formula: 1-b2-b3-3-#4-5-6-b7-8
C half whole diminished scale: C-Db-Eb-E-F#-G-A-Bb
In this case, the diminished scale starts on the root of the dominant 7 chord. So what dominant 7 chord would we use the C half whole diminished scale over? C7(b9).
This is just another way to look at it. So either you play a Whole Half diminished scale a half step up from the root of the dominant 7 chord, or you play a half whole diminished scale starting on the root.
Let’s do one last example and move away from scales and focus more on the chords. Let’s say we are applying the diminished half step up rule over a Bb7(b9) chord. So we will be playing a Bdim7 sound over this chord.
Let’s start by asking the question: what notes are in Bb7(b9) and Bdim7 chord?
Bb7(b9): Bb (root) D (3rd) F (5th) Ab (b7) B (b9)
Bdim7: B (root) D (b3) F (b5) Ab (bb7)
So what notes do these two chords share? B-F-D-Ab.
In fact, the only note they don’t have in common is the Bb. But you don’t need the root of the chord, especially since this is a tension chord that needs to be resolved.
There is a lot of interesting diminished theory out there, but this is just a simple one to take home and practice. Spend some time playing around with this idea using both kinds of diminished scales, and applying the Diminished 7 Chord Rule.