Trills between C5 and D5 are awkward using standard fingerings, and young saxophonists are surprised the first time they encounter this. They assume there is no other fingering option beyond the fingerings they know and use these to play a trill with an uneven and heavy-handed sound that will always be lacking to the ear, no matter how much a young student works.
Unfortunately, the proper trill fingering is rarely shown in charts. It makes use of the saxophone’s side keys, as can be seen below. The trill can be executed by leaving the C key depressed while trilling the middle side key in the left hand.
This works equally well trilling between C#5 and D5, as well. Again, simply trill the middle side key.
When tremolos to D#, Eb, or En are written, similar alternate trill fingerings can also be used. Figure 3 represents the proper trill fingering to be used for D#/Eb5.
Figure 4 is the trill fingering for E5. Both of these work equally well with the C key depressed (when trilling from C5) or without (when trilling from C#5).
Figures 2, 3, and 4 also make excellent special effects fingerings for D, D#/Eb, and E. In extremely soft passages, they make passages from C to these notes much easier.
These fingerings, whether they are used in ensemble music, an honor band etude, or solo literature, will ease the way for any saxophonist.