I can get an OK sound out of soprano and alto, and can almost play the full tenor range. I had trouble when playing on my fiend's narrow (tenor) jazz mouthpiece - I could only go down to the first E! I know it was my embouchure, although I think it was mainly that the mouthpiece was completely diffeent to anything I've played before - I can play bcl perfectly well so must have an OK embouchure; I think it was just because it was so narrow.
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The difference between an amateur and a professional: the amateur practises until it's right; the professional practises until it never goes wrong.