The note b is very often been skipped on the saxophone when improvising, strange but true. While improvising with students, I repeatedly noticed that they hardly use the b. I’ve come to call this the b-syndrome. And I found the following explanation for that: our fingers don’t like it, especially when playing down, and also have to play a b between the c and the a.
Just take your sax in your hands and, first time without blowing, play slowly with your fingers e-d-c-a-g. And now play e-d-c-b-a-g, so the same notes but now with the b in between. Can you feel the difference? The first run goes ‘motorically seen’ more smoothly. Your fingers don’t have to make the artificial switch from c to b. If you play a little faster, you feel the difference even better.
Playing upwards you feel that difference a little less, but still; play one after the other: g-a-b-c-d-e then g-a-c-d-e. First play slowly and portato (slightly on) and then a bit faster and legato (bound). Do you feel the difference?
The biggest problem is that most people are not aware of it. While it is quite limiting in your melodic possibilities. Just try to observe when others are soloing (for instance at a workshop); look good at those fingers playing around the a, b and c. If you start seeing it happen, you will start hearing it as well.
In case you still find this story interesting, we also have the f/f#–syndrome. What I said above about the note between a and c also applies to a lesser extent to the note between e and g (depending on the key, the f or f#). This is also a ‘motoric thing’ but much less logical than the story about the b. And yet that note is also regularly skipped unconsciously and unjustly. Pay attention to that as well. It feels like the right index finger and middle finger like to move at the same time; like they are stuck together.
,Tip:
By regularly thinking about it while improvising (you can’t do that all the time) and using the b ‘consciously’ as well, your fingers will also start finding that more normal. So first, become well aware of it, and then slowly start using that note in a natural way.