For those of you who can appreciate stream-of-consciousness thinking, here's how the sequence went: I started by revisiting the first suggested "alter the first-inversion triad to get a dominant seventh" suggestion, on G major. On the mandolin and other fifths tunings, that looks like this:
Well, what about going the other way? If we can take that root down a whole step to get G7, what about going up a whole step to get the ninth? It's probably fudging the point a bit from a Juilliard/Berklee point of view, but that could probably serve as both Gadd9 and as Gmaj9, depending on what notes others are holding down.
And that's got to be so much easier to think of doing, at speed, in an improvisational context. If we consider the mandolin (or the Guitar Craft guitar, for that matter) as but one voice among other instruments, this would promise to be a very effective way of adding color notes with less risk of bumping into others' territory.
From here, it can start to get pretty fast and furious. On that first-inversion triad (third in bass), I just started permuting:
That rather neatly covers those*; then, you could start walking the fifth around as well (for this diagram, read down, not across, to see the permutations):
This could get out of hand in a hurry, but on the other hand (and with apologies to Frank Zappa), great googly-moogly! And that is just the first-inversion triad...I'll try my hand at root-inversion and second-inversion next time, and holy cow, then there's ninths.
I suspect that there are a couple of goals with going further down this approach:
- The real goal here is not just to build a library of chords to memorize, but to become competent at finding a triad and altering it on the spot (and herein is where the value of reducing from four strings to three becomes obvious, saving what must be a fairly staggering amount of complexity)
- With the enharmonic equivalents starting to pop off the page (with just three strings to keep track of, it's much easier, isn't it?), it seems that using this approach will also underscore the need to better understand polychords, both from the standpoint of deliberate construction of polychords by multiple members of the group playing simple chords, and also from the standpoint of reduction of polychords into smaller constituent pieces that a player can grab onto either at speed, or to allow a humane fingering. (I think I'm going to have to chew on that one for a while.)
- One nice thing about using three strings instead of four is that it does leave the player more room to wander about the registers, in effect "playing his harmony with more melody". I suppose that a complete player would want both full voicings and the three-string variants at his disposal, but the potential for improvisation here is pretty huge.
* How about the bender of the enharmonic equivalents, as well? That three-string Gmaj7 is also known as Bm, which is a standard third-up substitution...also check out Bb augmented aka Gm/maj7, Bb major aka Gm7 (diatonic third up and relative major).