In the man's own words:
The sound of a Tri-sonic pickup is not like a Stratocaster single-coil, or a Gibson double-coil (humbucker) - it is some way in between. It has more warmth than the Fender, so sings (feeds back) a little easier, but it also has more top end, or crispness, than a humbucker, and does not self-limit at high levels, because its inductance is smaller. We figure that the "fatness" which we like so much comes from the fact that a Tri-sonic seems to pick up vibrations from the string over a longer distance measured along the string than a normal single coil. Maybe this is because the casing is magnetic itself, and spreads the magnetic field. Well, whatever the reason is, they just have that sound, which thanks partly perhaps to me, and post Range Master treble boosters, and AC 30 amps, has become a sound that many guitarists enjoy having at their fingertips. The sound that makes chords keep their clarity, yet sound big, and makes single notes go into smooth distortion and sing like a bird.
The original Tri-Sonics were pretty unusual by today's standards - a coil wound loosely on a collapsible former, the former was then removed leaving just an "air" coil which was wrapped in tape. The whole coil was then slipped over the bar magnet (there are no polepieces as such). Brian Epoxied the casings on his to control microphonic squeal, but they are still pretty microphonic (because epoxy does not saturate the coil, only stops the cover from ringing). It's also worth noting that Brian's middle pickup is hotter than the other two and the switching system is pretty unique -
all of which add together for the characteristic but unique tone of his guitar.
The modern Tri-Sonics are not quite the same as the old ones (for accurate reproductions look at the Adeson copies), bit are still good pickups. Note that they don't fit into a Strat pickup route either.