What your students are experiencing is common especially on tenor. In addition on some makes of instruments the high G goes very easily to the high D overtone.
Here are some of the techniques that have worked with my students:
-Sing "AHH" on the lowest note they can sing and play with that feeling in the mouth and throat
-Make sure the mouthpiece goes straight into the mouth, not down (check neckstrap)
-Direct the airstream as though they are blowing at the R.H. thumb
-Make sure that the pitch on the mouthpiece and neck alone is no higher than D concert
-Practice going back and forth from high G to high D with G's fingering shaping the tongue as if saying AHH-EE-AHH-EE to learn to control the overtone.
If the problem is that high G drops to low G or plays both octaves (multiphonics) with the octave key open, try using faster air and check the mouthpiece+neck pitch. Sometimes in teaching I found the best technique was to demonstrate the note(s) for the student on my sax, and tell them to "make it sound like that". Often times they will figure out what to do inside the mouth without needing a detailed explanation.
Hope some of this helps. Good luck in your teaching.
John
Here are some of the techniques that have worked with my students:
-Sing "AHH" on the lowest note they can sing and play with that feeling in the mouth and throat
-Make sure the mouthpiece goes straight into the mouth, not down (check neckstrap)
-Direct the airstream as though they are blowing at the R.H. thumb
-Make sure that the pitch on the mouthpiece and neck alone is no higher than D concert
-Practice going back and forth from high G to high D with G's fingering shaping the tongue as if saying AHH-EE-AHH-EE to learn to control the overtone.
If the problem is that high G drops to low G or plays both octaves (multiphonics) with the octave key open, try using faster air and check the mouthpiece+neck pitch. Sometimes in teaching I found the best technique was to demonstrate the note(s) for the student on my sax, and tell them to "make it sound like that". Often times they will figure out what to do inside the mouth without needing a detailed explanation.
Hope some of this helps. Good luck in your teaching.
John