the one thing I feel we're not considering here, is mouthpiece shank length:
- try extending your soprano sax mpc shank (i.e. increasing the sounding-length) with a - say - 0.5 cm cardboard cylinder, and suddenly you've lowered the upper pitch limit of the reed+tube by a tone or more.
I have a different view about the
mouthpiece shank length and mouthpiece pitch.
On a saxophone the length of the "tube" for any given note has a "natural resonant frequency". It is this "natural resonant frequency" that couples with the reed's vibrations to produce that particular pitch. Of course the player has a bit of leeway to "lip" the pitch of the note slightly sharper or flatter, but that note is for the most part "locked in".
By the time the tube becomes quite short as when playing palm D, the "resonant frequency" is weak enough that it allows the resonance inside the player's oral cavity to take over the reed's vibrations and the pitch can be lowered as much as 3 or 4 half steps. When the "tube" becomes
extremely short like the mouthpiece shank when playing the mouthpiece alone, the "resonant frequency" of this very short tube is too weak to have much of an effect upon the reed's vibrations. This is why a skilled player can play an octave scale on the mouthpiece alone.
Adding to the length of the mouthpiece shank can have a slight effect upon the mouthpiece pitch, but the voicing and lip pressure are still mostly in charge of the pitch that sounds. In my teaching, I use the mouthpiece pitch test as an
embouchure tightness test. I know from experience that a pitch higher than A=880 on an alto mouthpiece usually means the player is "biting" and the resultant tone is going to sound pinched and the upper register is going to be sharp.
One can experiment and tighten the embouchure on an alto mouthpiece to the point that the reed closes off, and then relax just enough to make a sound and see what note is at the "top of the mouthpiece pitch. I haven't tried this, but I suspect that the A Concert is at least 2 or 3 steps below this note. Alternately on a clarinet mouthpiece I suspect the reed closes off not too far above the recommended C Concert.