Here’s an exercise on harmonics, from Earl Bostic’s alto playing, bars 9-11 of ‘Bugle Call Rag’ (1956). Alternate upper register G with normal fingering and the same note produced as a harmonic of low C (no octave key). Start slow, then see if you can match Bostic’s virtuosity. This is a way of making repeated notes more interesting and a useful exercise to build up altissimo technique.
Bostic hits a super high B near the end of this recording, which is really a little over the top for most players.