Harmonics are notes that are higher than the designed capabilities of the instrument. In effect, they extend the range of your saxophone. The above ten fingerings are all I use myself, though it is entirely possible to go much higher. There are many alternate fingerings for the above notes; your reed/mouthpiece setup could drastically alter the situation one way or the other. It is not an exact science, so experimentation is the key. Using harmonics, however, does require a whole new practice regime - not to mention a whole new ⫘ embouchure ⫘ and are not for the faint-hearted!

Though I do use hermonics occasionally, I did not study their usage in any great depth. Had I heard the link at the other end of the picture below it might have been altogether different. Back in the day, Earl Bostic was just a guy who had a couple of "pop" hits to his name.  And let that be a lesson to us all!  I only recently unearthed the following recording (An Eb 16-bar blues sequence). Some one-minute and forty-eight seconds into the tune, Bostic takes his Alto up into the stratosphere...and he stays there for much of the remainder of the track.   Bostic was a man well ahead of his time, and - probably because of his brush with the "Pop music" charts - desperately under-rated as a jazz musician. (Jazz musicians and afficinados can be a bit precious about their preferences!)