Typically the lowest notes on a saxophone have a tendency to jump an octave when played softly or without the needed adjustments in the oral cavity due to the fact that the fundamental is weaker than the 2nd and 3rd harmonics. That is true not just on saxophones, but on all conical woodwinds. It is unusual that this tendency would go as high as the note F. It would be interesting to see the "harmonic footprint" of each of these notes on a spectrum analyzer to see what that reveals. "Split tones" can be caused when the vent that forces the fundamental to go to the second mode does not disrupt the vibration of the fundamental enough to let the second mode to take over completely, hence both frequencies can sound at the same time. The embouchure and voicing used by the player can also have an influence as well.
In my repair experience I have found that small leaks that are not apparent when using a leak light in a well lit area such as a typical shop become visible when checked in a pitch dark room. I always check my pad work in these conditions which is possible since I work in a one man shop.
In my repair experience I have found that small leaks that are not apparent when using a leak light in a well lit area such as a typical shop become visible when checked in a pitch dark room. I always check my pad work in these conditions which is possible since I work in a one man shop.