When a student is first learning extensions, I teach it as a multi-step movement that goes something like this, if we’re doing 1, 2, 4:
1st finger goes down like nothing’s different. (a lot of people prepare, pre-prepare, go insane pronating or other left hand freak out)
then, take 2nd, and stretch it to where 3rd would normally be, and as soon as you have that stretch, move 1 up into the new position. This is when you actually play the note…after all of that movement.
4th is as/is.
This is a technique that is good for slow scales and passages, and it makes the very important distinction between a shift and a stretch, while also etching in the mind of the student the absolutes of the cello: no matter what finger you use, the notes stay in the same place.
The next technique is one where we use 2 as a pivot, and maintain the “extended” shape of the hand. (so 1 never comes up next to 2) This is useful for faster passages like Brandenburgs and Mozart symphonies, and also for non-linear gestures where you might be moving between 1 and 4.
If it’s 1, 2, 4, the technique goes like this:
1 goes down, and 2nd is relaxed, and stretches to hit extended 2, where it remains throughout, or until you have to return to 1. As you go for 4, 2 stays planted, and the hand pivots forward. This motion comes from the top of the forearm, so the sanctity of the wrist/hand relationship remains. Some people leave 1 down, others allow it to come off the fingerboard. (NB: is is never pulled or held off of the fingerboard. This indicates additional tension and is never a part of good technique. If 1 sleepily drifts less than a centimeter above the string and the intonation is right on, I allow for that variation) Then if you return to 2, the pivot comes neutral, and for 1, the pivot swivels back only slightly. It is a stretched shape, and the thumb has to be taken care of to make sure it remains behind 2nd, and also that it is not jammed into the neck.
If it’s 1, 4, then I tend to straighten and release my 2nd and 3rd fingers (as opposed to holding them in the usual curved posture) to allow for a lot of distance without tension across the top of my hand. If a student comes to me with an unsuccessful extension technique or pain, I modify small elements of the practice until we have success. The only thing that I insist on is that the general shape of the hand remains the same: no huge pronations, no big bend in the wrist, and lastly no “sailing east to go west”, where the student pulls the hand backward to accomplish the stretch forward! Only move in the direction you intend to go! I try to instill this in my students from day 1: simple, singular movements that have no preamble. Are you extended or not extended? Are you on the D or the A? Be one or the other, and then the liaisons between the two become swift and confident.
These are my thoughts, and although they just scratch the surface of possibility, I figure it’s better to post this now and open up conversation than try to be ultimate and exhaustive. Words fail after a point!