Altissimo is a funny word that is best defined as the high notes on the saxophone that start when the regular fingering scale ends. The saxophone normally goes up to a high F or F# (sometimes even high G) and the fingering chart ends there.
These Altissimo notes are the high notes you hear pro sax players hitting that go way above the normal fingering charts. The goal for jazz and classical range extension is a full octave above high F. Usually up to altissimo D is common, and altissimo F and above is more common on tenor sax. Some pro players have mastered the 4th octave on sax and even ventured off into a 5th octave. The obvious example would be Lenny Pickett from Saturday Night Live; blasting up so high we all want to shout and holler.
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