All saxophone/mouthpiece/player combinations are different with respect to which overtones are strongest and how closely matched they are with the harmonic series. That's why some sound "bright," "dark", "focused," "spread," etc.
I see. So do you mean that every note has different overtones but for all players that group of overtones is the same? I think not. You are saying that even if we keep the same actual instrument in mind each player will generate a different sequence of overtones. Yes? I understand that if we change the mouthpiece we change the overtone sequence but I'm surprised that if we keep everything the same and only change the player we get a dufferent result. Is this result due to having different mouth and throat resonances when we change players?
I see. That's very interesting. I'll give it several tries to see for myself but I'm sure you are right. I'm only a beginner myself. It looks as if my quest to tabulate the harmonics and overtones versus each note may be a hopeless job, in view of what you've told me. Thanks for your input, anyway.