Beginning cellists are often confused about the various "positions" of the left hand. It CAN be confusing, especially when one expert says there are 32 positions, and another tells you that there are an infinite number of positions! What's a poor beginner to think? Here is a very simple explanation of four basic positions for the left hand. (You may like to print this page, and put it on your music stand, and play along as you read.)
First Position--After learning to play the open strings, without any left-hand at all, every cellist begins learning first position. As you can see in the illustration below, the first finger (index finger, the one you point with) of the left hand plays D, A, E or B, depending on which string is depressed.
Second Position--Shift your left hand on the finger board a little bit toward the bridge, and you move from first position into second position. Here your first finger will play either an E, B, F or C as it depresses the strings.
Third Position--From second position, move your left hand a little bit more toward the bridge, and you will find yourself in third position. Your first finger depressing the strings, will play either an F, C, G or D.
Fourth Position--From third position, shift your left hand a bit more toward the bridge, and you will be in fourth position. Here your first finger will be depressing a G, D, A or E.
Complications!--All above is basically true, and a good place to start, but there are a few complications that must be kept in mind:
All scales are a mixture of half-step intervals, and whole-step intervals between notes. Take a look at a cello-fingered scale in the key of C:
When the perfomance of a scale requires a whole-step between the first and second fingers, then the cellist must stretch those fingers apart to a greater than normal interval. For example, look at this scale in F major:
A similar extension takes place in the other direction in some scales, for example, E Major. Look at this illustration:
Now here is where the "infinite number of positions" comes into the picture. Suppose, instead of trying to stay in first position, and extending the first finger back to a B flat (see the F Major illustration above), the cellist simply shifts his entire hand backward, so his first finger falls naturally on the B flat, then just allows his other fingers to fall naturally on the string. Then the fingering would look like this:
Conclusion: In order to avoid confusion, the beginning cellist should concentrate on the four basic positions, and learn to do extensions as called for by each key. The most useful and common are stretching the first finger back to flatten the D, A, E or B, depending on which string is in question. Or to stretch to an F sharp, C sharp, G sharp or D sharp with the fourth finger, as called for. The advanced cellist no longer thinks about positions, simply which finger placement lends itself best to technical accomplishment and artistic expression. Any note can be played by any finger, including the thumb, and the virtuoso just does whatever works best and sounds right from the infinite possibilities at his command.
If you are a beginner struggling to figure out fingerings for various positions on all cello strings, you may find help from Per Stromgren's Fingering Chart.
You will also enjoy reading the Cello Chat Archive thread about playing in positions.