Rather than thinking of a tone that is good or bad, try thinking in terms of a "characteristic" tone. In other words does it sound the way a saxophone should sound. The tone is full bodied and rich without being pinched or flabby sounding. It is well controlled at different dynamic levels and during crescendos and diminuendos. It is even with a constant pitch on long tones.
A lot of what we think of as "tone quality" when we listen to different jazz players is really their style of playing which involves inflections, embellishments like vibrato and articulation. Any held long tone with the entrance and ending of the note removed will sound surprisingly the same among very different jazz players.
Try to avoid falling into the common trap of trying to "buy" a particular sound by changing equipment. Instead work on establishing the concept in your mind of how you want to sound when you play. Then practice moving toward that sound by adapting your embouchure, airstream, and the shape inside your mouth.
However, I believe it is important to develop a well controlled "characteristic" sound first before branching out into different jazz styles. Put another way, learn to play the saxophone well first and then work to add different styles to your repertoire. And yes this means learning to play with a classical sound to begin your journey.
Should I go back to the roots and chase the classical sound first then? I am thinking right that classical sound will be more mellow without "sharp edges" or almost any overtones in the tone?
