Hi, Alan--
Please excuse if this is information you already know.
Any aerial fingering technique exploits your ability to control the movements of small muscles (e.g., in your fingers) more precisely than those of large ones (e.g., in your arm).
GENERAL DEFINITION
Within any one position of your arm, the range of available pitches is defined by two extremes:
a) The lowest pitch is produced by closing your hand; this represents arranging the mass of your hand farthest from the pitch rod (that is, farthest [i]without[/i] moving your arm or wrist).
b) The highest pitch is produced by opening your hand; this represents extending the mass of your hand closest to the pitch rod (again, closest [i]without[/i] moving your arm or wrist).
That much may be intuitively obvious. One of the major non-obvious aspects of the technique (whether you opt for "four," "nine," or whatEVERrrr) is that if you literally open your hand, extending all your digits, then four of them (the fingers) move closer to the pitch rod, BUT the fifth (a.k.a. your thumb) is moving [i]away[/i] from it. Ergo, for consistent control of pitch, it's important to keep your thumb and forefinger together. So, absent photos, let's refine the above:
IMPROVED DEFINITION
Within any one position of your arm, the range of available pitches is defined by two extremes:
a) The lowest pitch is produced by closing your hand--not into a fist, but with your thumb and index finger forming a circle, and the tips of the other three fingers (let's call them "the active fingers") resting comfortably on the base of your thumb.
b) The highest pitch is produced by opening your hand--not completely, but by maintaining that thumb-and-forefinger circle, while extending the active fingers toward the pitch rod, so that your hand forms the traditional "Okay" gesture.
So, them's your extremes. Intermediate pitches are produced by extending your knuckles, without fully unfolding your active fingers. Try moving your active fingers as slowly as you can from closed to open position, and back. Your next step is to find the intermediate positions that correspond to the pitches you want to produce, and then to train your muscles to go to those intermediate positions instantly.
CALIBRATION*
I think it's safe to say (and I trust others to correct me as needed) that the above features are common to the aerial techniques we've been discussing. The fundamental differences lie in how you calibrate the pitch control field of your instrument.
Opting for the "four"-position technique means setting your control field so that moving from closed position to open position (without moving your arm or wrist) would produce the first two notes of Wagner's wedding march ("HERE COMES the bride..."), a.k.a. the first two pitches of "Shenandoah" ("OH SHENANDOAH, ..."), a.k.a. the first two pitches of "Loch Lomond" ("OH, YOU take the high road...").
Opting for the "nine"-position technique means setting your control field so that moving from closed to open position (without moving your arm or wrist) would produce the first two notes of "Over the rainbow" ("SOME-WHERE... over the rainbow..."), a.k.a. the first two notes of "Bali Hai" from [i]South Pacific[/i], a.k.a. the first two notes of "Singin' in the rain" ("I'M SING-in' in the rain...")
I hope this helps. In particular, I hope that you can better follow what Kevin demonstrates in his videos, especially the one where he demonstrates how to handle large melodic leaps using a "four"-position technique (this video provides an excellent, protracted close-up shot of his pitch hand).
P.S. The number labels come from the basic seven-note scale that underlies most European music (Do-Re-Mi-Fa-Sol-La-Ti-Do, a.k.a. "only the white keys on a piano keyboard"). I put the quotation marks around them, because in each technique you're actually learning to find other notes in between, such that