What is the minor ii V i matrix?
Utilizing certain harmonic minor scales, we can construct a matrix of possible chord substitutions that may be used over the minor ii – V, or minor ii – V – i chord progressions. This approach is actually awesome for times when it is just ii – V’s that don’t resolve to i. The example I will use for this post is the last eight bars of “Stella by Starlight”. Most beginning players who study this tune have a hard time with the last eight bars because of the fact that the first three ii-V’s don’t resolve to i. Just playing in each of the minor keys doesn’t really get the job done.
Here is the last 8 bars of “Stella” :
E-7b5 | A7b9 | D-7b5 | G7b9 |
C-7b5 | F7b9 | Bb Maj7 | Bb maj7 |
As you can see we have a series of minor ii V’s descending in whole steps, ending with a “minor” ii V in Bb resolving to a Bb Major. What gets tricky with these chords is that just playing “D minor” over E-7b5 A7b9, “C minor” over D-7b5 G7b9, “Bb minor” over C-7b5 F7b9, doesn’t really sound that great. When the chords don’t resolve it doesn’t really work well. This is where are melodic minor matrix kicks but!
Lets build our Matrix.
We have to figure which melodic minor scales we are going to use to construct the matrix.
- Step 1. Figure out which melodic minor scale we need for the ii chord. For the ii chord we will play a harmonic minor scale starting a minor 3rd above the root. For example: E-7b5 = G harmonic minor scale.
- Step 2. Figure out which scale for the V chord. For the V chord we will play a harmonic minor scale a minor 2nd ( 1 1/2 step or semi-tone) above the root. for example: A7b9 = Bb harmonic Minor.
- Step 3. Build the matrix. We are going to build chords off of the scale leaving out scale degree “2” and “5”. Example: G Har Min. we will build chords off of scale degrees 1, 3, 4, 6, 7 …..giving us….. G, Bb, C, E, and F#. For each of those notes we can just simply stack thirds except for the 7th scale degree. we will come back to that in a bit so lets start making our matrix.
| ii Chord | Scale degree |
| E-7b5 | 6 |
| G min +7 | 1 |
| Bb maj7 #5 | 3 |
| C7 #11 | 4 |
| F# 7 alt (#5, #9) | 7 |
Notice we did not just stack 3rds for the 7th scale degree “F#”. Instead of naturally occurring F# -7 b5, F#, A, C, E , We use Bb, and D and Get F#, Bb(A#), D, E. giving us the F# Alt chord. Pretty Hip! Lets do the same for the V chord.
| V Chord | Scale degree |
| A7b9 (A7 Alt (#9, # 5)) | 7 |
| Bb min +7 | 1 |
| Db maj7 #5 | 3 |
| Eb #11 | 4 |
| G -7 b5 | 6 |
In this case our V chord is an A7 b9 chord. The “A” being the 7th scale degree of the Bb Harmonic minor scale. We already have a Dominant 7th chord (A7) so we don’t have to worry about it like the ii chord. The scale lets us “alter” the A7 we already have giving us the A7 alt chord.
- Step 4. Put it together! We can take a look at the Completed matrix
ii V E-7b5 G-7b5 G min +7 Bb min +7 Bb maj7 #5 Db Maj 7 #5 C7 #11 Eb7 #11 F# 7 alt (#5, #9) A7 alt (#5, #9)
Now that we did the first one. Lets write out the other three:
| ii (G Har min) |
V (Bb Har Min) |
| E-7b5 | G-7b5 |
| G min +7 | Bb min +7 |
| Bb maj7 #5 | Db Maj 7 #5 |
| C7 #11 | Eb7 #11 |
| F# 7 alt (#5, #9) | A7 alt (#5, #9) |
| ii (F Har Min) |
V (Ab Har Min) |
| D-7b5 | F-7b5 |
| F min +7 | Ab min +7 |
| Ab maj7 #5 | Cb(B) Maj 7 #5 |
| Bb7 #11 | Db7 #11 |
| E 7 alt (#5, #9) | G7 alt (#5, #9) |
| ii (Eb Har Min) |
V (F#(Gb) Har Min) |
| C-7b5 | D#-7b5 |
| Eb min +7 | F# min +7 |
| Gb maj7 #5 | A Maj 7 #5 |
| Ab7 #11 | B7 #11 |
| D 7 alt (#5, #9) | (E#)F7 alt (#5, #9) |
I wrote it out so that the same chord types are across from each other. I think it is visually more pleasing that way. What make this really great is now you can substitute any chord in each column for one another.
examples:
G min +7 | A7 alt | Fmin +7 | Db7 #11 |
Gb maj7 #5 | B7 #11 | Bbmaj | ||
You can cris-cross, zig-zag, mix-match, whatever you want. Pick one chord from column one and pick one chord from column two.
It is important to mention in the case of a minor ii V i we can build the matrix including the “i” chord as well. If | E-7b5| A7 b5| went to D -7 we could play a D har min scale and build chords off of scale degrees 1,3,4,6,7 just like the other two chords.
| ii | V | i |
| E-7b5 | G-7b5 | B-7b5 |
| G min +7 | Bb min +7 | D min +7 |
| C7 #11 | Eb7 #11 | G7 #11 |
| F# 7 Alt (#5, #9) | A 7 Alt (#5, #9) | C# 7 Alt (#5, #9) |
For me this is one of those essential “tools” to have in the “tool box”. Not only does it offer you a way to deal with minor ii V’s, and minor ii V i’s, it sounds freakin’ awesome! Have fun experimenting and let me know what you think.