In fast passages going from mid D to C or C# ( and back): is it common to leave the right hand down while also leaving the RH pinky off the D# key for D? Will it flatten those C`s too much?

Also fast passages from mid D to E: can the pinkey be left off?

Michelle
(A saxophonist learning flute)

My flute teacher believes very strongly in right hand down for C#, but if it is in very fast passages, the pinky will do fine because it is so fast you won`t be able to hear a difference. I believe the same goes for the E.