There are two basic fingerings a clarinetist can use for B4:
But there are some other possibilities, such as adding either of the pinky C keys. Doing this doesn’t open or close any additional toneholes, so the note isn’t affected at all:
While the extra pinky finger is technically unnecessary, it is sometimes convenient and conducive to smoother technique. For example, option 4 is frequently taught as a “standard” B fingering in beginning band method books. That is probably because it works well in a C major scale:
When moving from A to B, this only adds one extra finger, the right hand pinky, to the B. Since there are already several fingers of the right hand moving in the same direction (down onto keys), this is only a minimal issue. And the movement from B to C is very simple: just release the left pinky.
The same sequence can be played without the extra key:
This is very slightly advantageous for A to B, since there is one fewer finger to move. But it introduces a more significant complication for B to C, since there is a “flip-flop:” the left pinky is lifting up as the right pinky is pressing down. A good clarinetist can execute this successfully, but it’s a little risky, since fingers on different hands are moving in different directions. There’s a possibility of finger mistiming that can result in an audible blip—a moment when both fingers are up together, producing a brief D5.
So there are advantages to using “extra” pinky fingers in some cases, but it doesn’t make sense in others. Some of my students stumble over sequences like this:
The right-hand pinky isn’t needed for the B, but some of my students use it out of habit whenever they see that note. Then they run into trouble when they have to slide the pinky to a different key for the E-flat. Advancing clarinetists should be aware of the fingerings they are using, and make each choice purposeful. Careful, consistent scale and arpeggio practice can help reinforce and habituate good fingering choices.
By the way, for the sake of completeness, you can add the opposite-hand C/F key for any of these written notes on the clarinet:
Adding pinky keys to any other pinky note will affect pitch.