I know about true or false harmonics tones on various
instruments but I do not understand what an altissimo is. Just
very high notes? Can you produce them on every kind of
saxophone? Can you play a melody with them? Altissimo is just a
name for notes above what is (or used to be, at least)
considered higher than the "normal" range of the instrument.
Most saxophones can play up to written F or F-sharp above the
treble staff normally just by using side keys that open tone
holes farther up the saxophone to make the air column shorter
along with the octave vent opening. The notes higher than that
are considered "altissimo." Altissimo can be played on any
saxophone (of sufficient quality), and it's still called
altissimo regardless of whether it is being played on alto,
soprano, tenor, etc. Generally speaking, the lower saxophones
have more altissimo notes available than the higher ones, and it
is easier to play altissimo on lower saxophones than higher
ones. The fingerings for altissimo notes are not the same on