As the saxophone is the most modern of all of our woodwind instruments, it naturally follows that it has the most perfect mechanism. To that end, the technique on the saxophone is simple and easy. There are only a handful of trills that cannot be done, namely all trills on the low B-flat, the whole-tone trill on the low B, and the whole-tone trill on the low C-sharp. Aside from these small restrictions any and all technical passages should be playable on nearly any saxophone.
There are a few range variations among the different instruments. All modern Baritones and most Contrabasses possess a low A extension (in both cases sounding a C). Some older Sopraninos, Sopranos, and Basses are only keyed up to high E-flat, though players are able to produce higher notes through the use of harmonics.
All saxophones, with the possible exception of the Piccolo, are able to produce to so-called altissimo range. This range consists of notes above the top keyed note on the instrument (usually high F or F-sharp). A general rule of thumb goes: the larger the instrument, the easier it is to produce the altissimo register. Also, the larger instruments will have a larger range of altissimo. For instance, the Soprano may only be able to play a few notes into the altissimo range, while a Bass may be able to play well over an octave above its normal range.
In general, the altissimo range is somewhat inflexible. Technique up here is difficult, so sustained lines are best. Only the most advanced players will be able to produce the altissimo range, which is why it is often left as an option only for soloists.
“Holy Roller” for Saxophone and band by Libby Larsen. Check out the technique, and especially the use of altissimo.