As I stated in my last post on the subject the Saxophone is not an instrument known for alternate fingerings, not like the oboe - where it seems every phrase has a different optimal fingering. There are however several very useful alternate fingerings that we often overlook, or outright ignore for various reason.
One does not normally think of alternate fingerings for the C key, but there are several possible fingerings, the normal middle finger, the B + the side key, and the low C fingering using an octave overtone.
The guideline for using alternate fingerings for C is the same basic guideline that applies to all alternate fingerings. You want to choose the fingering that sounds the best, and minimizes the amount of movement you have to make between notes. The quicker the passage the more you want to favor the minimization of movement, the longer the note the more you want to emphasize the note that sounds best.
So for C, in general
On passage that go between C and B, the first and side -- whether ascending or descending.
For sustained notes or passages that leap from C to any other notes, or from any other notes, the second finger.
For rapid passages that start on middle C and go up, the overtone of the low C fingering is available, if your intonation allows it.
First finger and side key
Usage of the second finger C
The overtone fingering
Once again, the most important exercise is the tone matching exercise.
An important note about the Tone Matching exercise, is that you can get the intonation to match, but the actual tone will come close, but will never precisely match. This is due to the physics of the saxophone. The awareness of the tonal differences will allow you to add color and shade to your performance, and help you make the best choices of which fingerings to use. Just so you don't think this is unique to the saxophone, string players (even guitar players) deal with this kind of choice constantly , "does an open A sound better or does the fingered A on the adjacent string work better for this passage?"
Here we see how to put together the various fingerings for C and Bb
Do you have any phrases or passages that you have found where the fingerings you are used to may have been awkward? Did a change in fingering help?