| Arban mentioned the trick that the Germans used -- pulling the third slide so that the extended third valve alone sounded the same as second and third valves together so as to play a low F (sounding Eb) on the Bb trumpet. This is as low as I've ever seen anything written in the orchestra -- a pedal c in Heldenleben for example. Written Ebs pop up often for F trumpet (Enigma Variations for example) and are much more frightening to read than to play. I've found it a help to think of such transpositions like this: figure out what the first note is (low Eb, uh, that's, oh yeah, Ab on this horn!) and then transpose the intervals from there. If the second note is notated as F, rather than go through the process again (low F, uh, that's, oh yeah, Bb!) I'll look at the interval (in this case a whole step from the first note to the second) and pretty much play a Bb automatically (because of all those scales they made me practice in band) because that is the second note in an Ab major scale.
Transposition exercises are designed to make our brains hurt, and if you want to inflict even more pain on yourself try transposing Bass Cleff pieces up a major third or a tritone, or something like that.
If the transposition is real hard, 23 is more often than not the correct valve combination (unless you pulled your third slide out for the low Ebs)
If you want to hurt your brain without making noise try the following:
8+2=?
6/3=?
and any other beginner math flash card exercises, but "transposing" the math symbols so that (for example) "+" means divide, "x" means minus, and do them as fast as you can.
Ouch!
Have fun!
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