First of all, Tuning on a saxophone is a nightmare. It doesn't play in tune like a piano or strings. It needs player input across the range.
Also tuning isn't a rigid thing. The tuner uses equal temperament. ie it splits the octave in to 12 equal intervals.
Natural harmonies are a little different. They sound great but the tuner tells you you're off pitch.
As for mouthpiece position, the best advice I have had, on here, is to tune the horn to itself using harmonics.
Finger low Bb1 and overblow to Bb2. Check this against normal Bb2 fingering.
You can use the tuner for this but only to get them to match.
Then overblow to F2 and do the same.
Repeat this procedure for B1, B2 and F#2 and C1, C2 and G.
When they all match up as close as you can get them, that's the natural position for the mouthpiece.
Playing there, once used to it, will improve intonation when playing.
The next step is to put the tuner in a drawer and leave it there, before it drives you mad.
Only take it out again if you change your gear.
Once the gear technicalities are sorted it's a matter of learning to listen while you're playing, which will come over time, with practice.
(bottom of page)
