Ok jazz nerds, I have SSG Michael Kramer (guitarist, Army Blues) to thank for this little project. He told me about this great idea, and I’ve decided to blow some time at BCT cataloging its results. Behold:

1. This first item is matrix of standard ii/V7/I’s, separated by minor thirds (repeat this matrix for the other two transpositions). Your standard jazz changes building block.

The theory here is that, due to the tensions and tendencies made possible by dominant/diminished scales (half-whole) and their limited transpositions (sharing content with similar scales built on roots an m3 away), one can draw any 3-chord path across this matrix from left to right as a substitute pathway for a typical ii/V/I. Using such substitutions instead of the half-whole scale should add tension, harmonic interest, and additional options in jazz improvisation or composition. It’s a way out of the ii/V jail cell, without totally leaving the complex.

This leaves a lot of possibilities, and some paths across this matrix will be redundant. Therefore, the matrix is of limited use when really approaching this idea in practice.

So, in an attempt to reduce the theory to a more readily usable form:

2. This second pic shows all the prime (reduced) forms of paths across the matrix, and is organized by root motion contour (or shape). For cleanliness’ sake, I’ve excluded the work I did cataloging all products of the matrix, and organized the paths into 6 basic shapes. One can see that regardless of starting point, we are left with a total of 16 possibilities, including our basic ii/V/I motion. Each of the 16 paths will has a signature sound and feel, though some have special relationships to each other (i.e., the nonlinear paths are all retrograde-invertible). Some paths are well-trodden, like the basic ii/V, the tritone substitution, and the “back door” ii/V. Some are not as common, and should provide some exotic alternatives.

3. Here’s a quick couple of PDF exercises with all 16 pathways, strung together in order by shape class, and then in order of net harmonic shift:

16 ii-V Paths By Shape Class Exercise (Herbie Hancock)

16 ii-V Paths By Net Shift Exercise (Herbie Hancock)

I wish I had a horn to practice these with, but I think I’ll have to wait until BCT is over (unless the 399th decides to toss me an ax: standby to standby). I hope it’s useful to the rest of you. Again, thanks to SSG Kramer (and Herbie Hancock) for the killer idea!