I got such a poor response to the following post in the Pianist Corner, I'm going to try here where I think more readers will be interested.

I know that two common techniques are practicing in rhythms and changing fingers on repeated notes and turns(or even trills). I am not trying to connect these two ideas except to ask the same question about both. Exactly why are these helpful(not for everyone but for many people, I think)?

When I was taught these techniques almost 45 years ago, my teachers just told me to do them and never explained why they were good!

changing fingers may be useful for long repeated notes (for eveness or finger relexations perhaps), but for some repeated notes it doesn't seem always to be a good choice, as in playing Bach's music for example. the reason i am saying this is that i am learning Bach's sinfonia no.2 now and there are several places, where one phrase ends and another begins on the same note, which is better played by the same finger or else risks awkward fingering for the following notes.

Changing fingers for repeated notes is sometimes necessary when things are going really fast - you can play faster using different fingers than using the same one. That's because you have one finger coming down as the previous one is going up/getting out of the way. Takes practice to get the hang of it though. There's a Hanon exercise devoted to it somewhere... When you can use the same finger it often makes sense to do so, one mustn't get too pedantic about these things. Sometimes changing fingers helps phrasing too.

I have heard two explanations for the varied rhythm exercise. The first is that by adding an extra difficulty to a passage and working on it, it actually becomes easier when the difficulty is removed. The second, which I like better is a bit harder to explain, but basically the idea is that by varying the rhythm, you are working different bits of the passage harder. For instance, if you have three notes XYZ that are giving you a problem, you are working the XY part more if you play XY fast and YZ slow. Then you are working the YZ part harder when you play XY slow and YZ fast. This forces you to focus on the XY motion and then the YZ motion as two separate things, which must also help.

-Mark