Tertian arithmetic - the idea

Okay, this has been stewing around in my head for a little while now, and I think there's something significant in it, but I have not yet found the pow! way to explain it. So, please forgive me if this discussion still seems a bit formative--it is.

The topic is looking at extended complex chords (ninths, elevenths, thirteenths) as polychords. The intent here is to come up with a deliberate device to understand these complex chords better, by viewing them as the products of multiple simpler chords (triads, sevenths) that one may already have in the hands. What I like is that there is a very simple logic at work that makes this daunting subject rather easy to grasp--at least in a practical way.

And that is my goal. Many of us find ourselves in a group context in which we are one voice among several, and so this concept of reducing a complex chord into two simpler chords, each to be played by a separate person, has a great deal of appeal. And for the improvising musician, the ability to add harmonic complexity spontaneously (without having to know where, say, a G13 or an Am11 is) is a real bonus.

You've probably heard the phrase "chords are built in thirds", and the term "tertian chords". It turns out that there's a lot more to this than you might think. Most of our chords are indeed built from stacked thirds, but the stacking can be applied further to whole chords a diatonic third apart. Somewhere in there is a sort of "tertian arithmetic" that can be described, that just unlocks the whole mess like a master key. It is the description of this arithmetic that I continue to struggle with; I can see it by permutation, but the teacher in me wants to be able to distill out the best way to 'splain it. (I'll get there.)

So, here we go. The next post will lay out the examples.