a simple warm up exercise i’ve recently tried out, before connecting the neck to sax.
Get the tuner out, connect the Alto mouthpiece to the sax neck, do not connect to the sax, just blow the mouthpiece attached to the neck, you should be blowing an f# on the tuner.
blow a steady f# for about 50 seconds non stop, trying to get the best tone possible, relax the rib cage and let the air slowly out for about 50 seconds, beyond that, you might faint.
Do this about 5 times, control the steadyness, pitch and spit build up in the mouthpiece. to start out you may only achieve 20 seconds, over time you can get up to 50 seconds.
now attach the neck to the sax, and hear how you pitch and tone sounds better …