So you "start" from C or G (depending on embouchure), then the middle valve drops you one half step, first valve drops you one step, and the third valve a step and a half? Then in the upper octaves, you can also start with E?
I always figured the amazingly rich tone of a French horn comes from basically "always playing in the upper register" (relative to trumpet, that is) but mellowed by about a mile and a half of tubing. Obviously that's an exaggeration, and I don't know all the proper terms, but that's how it seems to me, a humble woodwind player.