Theory 101

I'm going to have to explain my rationale at some point, so it might as well be today, since I screwed up the labeling my sets a couple of days ago. This is the hard stuff.

After looking more closely at my sets, I discovered two more sets that overlap by 4 pitches. To classify them I had to resort to my pivot pitches. One of those sets shared an additional pivot pitch. Two of the sets that shared 3 main pitches contained both pivot pitches.

So I've got:

I is O0a
V is O0b
O5b shares 4 +1
O11b shares 3 +2
O1b shares 3 +2
O6b shares 4
O7b shares 4
the rest except O3b share 3 +1
O3b shares 3

My classification system mimmicks traditional tonality using substitutions (like jazz). And my substitutions are classed by how many notes they share with the tonic.

I shares all
V7 shares none (my dominant complex is really the vii, not V)
VI7 shares 3
III7 shares 2
IV7 shares 2
II7 shares 1

Using that hierarchy my sets are classed as:

Tonic
I O0a (+O6a as V/IV)

Dominant
V O0b

Subdominant
IV O6b
II O7b (+O5a as V/V)

Pre-subdominant
VI O5b (+O7a as V/II)
III O11b, 01b

The complement (a) sets of the above become V of x. Choosing between IV and II was arbitrary and may be adjusted when I start comparing the secondary dominant sets. I've discarded all the 3 and 3+1 sets, since they are all the grey in-between harmonies. They won't show much in the way of harmonic progression.

During the main tonal centre parts of the piece, these are probably the only sets I will use. That will probably be the first and third movement. Generally, I'll use them in "functional" harmonic progressions. I've used this method before, and it really does create harmonic motion.

For the middle movement, I may invert the row and re-classify. I haven't decided yet.

Thus endeth the lesson.

Tomorrow I may post an excerpt from the story this is based on.