How do I relax my right pinky when playing black keys with fingers 3 and 4, according to the Taubman technique.
I had the same problem for a very very long time, and I managed to get rid of it. What worked for me may not work for you I can still sugest a few things:
Usualy the pinky pointing straight forward (either in the right hand or the left hand, most often when playing black keys with fingers 3 or 4, but not exclusively) has to do with tension in your playing.
The problem arise because you may be acustomed to play in such a way that tension feels normal, and playing without tension feels weird, particularly if you have been playing like this for a long time, as I did.
So the first thing you may try to do is playing a scale slowly (F major for instance), while keeping the shoulders loose and a naturaly curved hand to experiment what it is like to play without tension. Notice that in this position the pinky stays curved even when you play the B flat with your 4th finger.
You may try to play the scale more quickly, and see if you can keep the motion 100% tension free, and maybe increase the difficulty every day, try with arpeggios or more complicated motions once you are confortable. Always try to consciously keep the naturaly curved shape of your hand, particularly for the pinky.
If you are working on a passage on a particular piece and want to speed things up, you may want to try to 4-3-2-1 technique:
Start by repeating each note of the passage 4 times before going to the next one. Then repeat the passage repeating the note only 3 times, then 2, the play normaly. Basicaly by forcing yourself to spend more time on each indivudal note, you give yourself the opportunity to watch for any tension to arise and then to correct it. For instance the first time you strike that Bflat with your 4th finger in the Fmajor scale, your pinky may want to come up, but as you are still on that note, you can strike it again while correcting the shape of your hand to make it tension free. It will give you a sence of what playing tension free feels like on the passage you are working on, and progressively, by going to 3 repetition, then 2, you internalize the whole thing and hopefuly when you come to one repetition, aka normal playing, the problems are gone.
Note that this 4-3-2-1 exercice can also be applied for other reasons as you might see in this video but I found it particularly usefull to lower tension in my playing.
When I tried those tricks, in a few weeks the problem was gone! Sometimes I still need to make a conscious effort to prevent my pinky from raising up for no reason, but it is no longer a big deal as I can correct it easely :)
Again what worked for me might not work as well for you, but I hope that you will find these ideas helpfull.