High range is the 2000 pound elephant that refuses to leave the room. My personal philosophy is that my top (arpegiated, buttocks clinched, red face
) range should be a forth higher than the range I need to play any particular piece. So, if the literature that I'm playing requires a high c (2nd ledger line) I need to be able to play the f above that.
I use clark study #2 starting at the top of the staff g. I play this every day and stop at c. This takes me up to the octave g. By applying common sense practice and playing principles this routine has extended my "top range" to the 5th ledger line c (that I call "double high c"). Gigging range is g.
This is, however, only the start. You must also learn how to play the full range of the horn correctly (you guys know what I mean) so that when the music demands high notes you've still got them.
Oh well, my 2.1415926873 Cents on this subject.