I'm new to the sax, just a couple of months. I live on a small Island and all of my music information is online. There are no other sax players here. Lately, during my practice routine, I'm finding that I'm able to blow upper octave notes when fingering the lower register and not depressing the octave key. Is this what is refered to as harmonics or do I have a leak somewhere?
If you are able to produce the fundamentals (the intended low-range pitches) without too much trouble, then it's likely that you are overblowing and/or applying too much mouth pressure on the mouthpiece and reed. As Cherryplaysroblox suggests, you might as well check for leaks around the octave holes (both of them) as well as other holes high up on the body of the sax. Personally I abhor smoke-testing and recommend inserting a white LED into the main bore and looking for light leaks at each pad (use a dark room, of course).
Once you've taken care of leaks, time to work on your embouchure -- keep it a bit looser than one would on a clarinet (if that helps!), and maintain lots of breath control.