As mentioned earlier, many young jazz saxophonists who are struggling with their sound play higher on the mouthpiece than the prescribed classical mouthpiece pitch level. It is also very common for a beginning jazz student to not be able to hold a steady pitch when playing the mouthpiece alone. The inability to hold a steady pitch on the mouthpiece alone translates to an uneven tone and intonation problems on the saxophone. For this reason, all saxophone students, both jazz and classical, would benefit from practicing playing all pitches available on the mouthpiece. By doing so, they gain an understanding of the muscles required to both change pitch and maintain a steady pitch.
Playing higher on the mouthpiece requires less air, and that air is more constricted, or focused. Similarly, playing lower on the mouthpiece requires more air and produces a sound that is richer in harmonic content. If the desired jazz tone quality were in fact richer in harmonic content, playing a lower mouthpiece pitch would then produce a more characteristic jazz tone quality. Generating a higher mouthpiece pitch for a jazz tone quality would therefore be counterproductive.