Relatively new fan of Ted Greene and first time poster here. Been playing guitar for 20 years or so and don't know how I was never exposed to his work until now... I'm under a rock I tell ya.
In an effort to further unveil for myself the immediate usefulness of all 35 of the qualities in the V-System, and as a complimentary dimension to practicing and learning chord streams, I've mapped out where each bottom set V-2 shape naturally occurs in harmony using relative notation as coordinates (roman numeral chord names as coordinates).
How to Read the Chart Next to Each Shape:
-Note that the term "Chord" represents a specific quality with a chosen specific root note (Like "C Dominant 7" and its four shapes).
-Note that the term "Shape" represents a specific shape in a quality without a specific root note chosen (Like Quality 1, Shape 1).
-The chart to the right of each shape is divided into specific key types; major, minor, harmonic minor, and melodic minor.
-The roman numeral triads indicated in these charts share the same bass note as the shape they reside next to. That is, the lists to the right of each shape aren't meant to highlight what each shape is functionally (although frequently it does, I would guess), but rather highlight WHERE each shape occurs naturally in harmony.
-The roman numerals are all color coordinated using the same palette with permission from the guys at hooktheory.com to make it easier to see where any particular shape occurs at any particular scale degree at a glance. (Just visual scan for a red 'I' across all six pages to get a feel for it.)
Take the dominant 7th quality on the first page (the first quality at the top of the page consisting of 4 shapes). Lining up the bass note of the shape and the bass note of the indicated roman numeral triads, we can see that the first shape of the dominant 7th quality occurs at the 'V' chord of a major key, at the 'VII' chord of a minor key, at the 'V' chord when chords are built from the harmonic minor scale, at the 'IV' chord from chords built from the melodic minor scale, and at the 'V' chord from chords built from the melodic minor scale.
How Often do these Shapes Occur Naturally in Harmony?:
It's also interesting to note, at a glance looking at all 35 qualities, how different shapes naturally occur much more frequently than others in harmony (and is probably by no means an indication of how often or in what capacity these shapes are actually used in the real world).
Implications Beyond the V-2 Family:
So, I haven't done a ton of playing around with the other families (still focusing on learning/studying V-2 mainly), but I'm pretty sure these coordinates transfer seamlessly between them. As an example, the first V-2 shape of the plain dominant 7th quality should have the same coordinates as the first V-3, V-4, etc shape of the same quality.
Anyway, let me know if I can clarify anything. I just attached this coordinate work on top of my existing "V-2 35 Qualities plus Modes" sheet found in the "From Students" section, so the mode stuff is still in there for now. I may remove the mode stuff at a later date when I get some time because one can figure out the mode just by looking at the chord type, "I" in a major key means Ionian, "ii" in a major key means Dorian, etc.
Finally, I'm still learning, so while I feel the work is pretty solid and adds an interesting bird's eye view of the physical link between different qualities and links within a quality, I have very likely made a few mistakes. Feel free to let me know and I'll make the appropriate changes.
As an aside, I am using odd labels for the modes, and for that I'm sorry (my wife is a real composer and cringes when I refer to Super Locrian as Mixolydian#7#1). I think of all of these patterns and stuff in terms of relative dots in space and the theoretic labels became kind of secondary. There is an index of modes at the end with 3-note per string shapes to help with this.