One of my private instructors, Richard Thompson, has had me working on what he calls "upper structure triads" on dominant chords. I've explored this concept before, but not in as much detail as he summarized to me in half a minute. The idea is to use triadic shapes on various altered extensions of dominant chords to create a specific kind of tension.

I wrote about my previous explorations in this area in a couple posts two years ago: 7-9-11-13 Arpeggios and Über Arpeggios. The extent of my abilities on this front went little beyond knowing that such arpeggios can be employed. I still do exercises along these lines, but it kind of melts my brain when I try to use these in real improvising situations.

So the new approach to which Professor Thompson has introduced me is to only worry about dominant chords and to target certain major triads that can be created with collections of altered or unaltered extensions. He said the minor triads aren't as potent and can be ignored when getting into this kind of playing, but I'll buy that when I can hear it.

Here are the specific triads he recommended, over a C7:
Eb G Bb: #9 5 b7
Gb Bb Db: b5 b7 b9
A C# E: 13 b9 3
D F# A: 9 #11 13
Ab C Eb: #5 1 #9

He said the triad built on Eb is lukewarm, and I can see that; usually a #9 is accompanied by an altered 5 in jazz harmony. The triads built on Gb and A are his favorites. I'm digging the one on D, as it's been showing up all over a couple transcriptions I've been working on this semester, of Pat Martino and John McLaughlin. However, those applications are clearly Lydian Dominant, so this triad falls right inside it. The point of this exercise is to get outside and create extra tension over a vanilla dominant chord, and I can see and hear how the triads on Gb and A are more effective at that.

This got me wondering whether there are others. So I wrote out the rest of the triads built from all 12 notes relative to the root. Pardon the enharmonic spellings.

Major Triads
1 3 5
b2 4 b6
2 b5 6
b3 5 b7
3 b6 7
4 6 1
b5 b7 b2
5 7 2
b6 1 b3
6 b2 3
b7 2 4
7 b3 b5

If I apply the simple rule of excluding any triad with the 4 or 7, then Thompson has already exhausted everything left except 1 3 5, which won't add much tension. Because I'm curious, on to minor triads!

Minor Triads
1 b3 5
b2 3 b6
2 4 6
b3 b5 b7
3 5 7
4 b6 1
b5 6 b2
5 b7 2
b6 7 b3
6 1 3
b7 b2 4
7 2 b5

Applying the same rule, excluding any with the 4 or 7, I get some interesting possibilities: 1 b3 5, b2 3 b6, b3 b5 b7, b5 6 b2, 5 b7 2, 6 1 3. Some of those won't add anything, but some sound just as fascinating as the best major triads.

Now I just gotta figure out how to start using these. Maybe write a bunch of licks with them.