Actually we should try and relax as much of our bodies as possible when playing music. Muscular tension is at the heart of most bad technique and often leads to unmusical and ungraceful playing. It is also the principle cause of musician’s injuries. But having relaxed and free wrists is particularly important for good piano playing.
It is helpful to know a little about how the wrist works. The forearm contains two large bones. The radius and the ulna. The ulnar does not rotate and when we turn our wrists the radius moves over the ulna which remains stationary. One end of the ulna meets the elbow, the other meets the wrist at the pinky side. So, when we turn our wrists they actually rotate around the pinky. This is surprising, most of us imagine that our wrists rotate around the 1st finger, but actually they rotate around the 5th finger. Try it! Point out your 1st finger and try rotating your wrist around it; it quickly becomes impossible without contorting your whole upper body! Now try pointing your fifth finger and rotating your wrist around it, and things become much easier.
"Muscular tension is at the heart of most bad technique and often leads to unmusical and ungraceful playing."
What does this have to do with scales? Well, unless we play scales with only five notes we are going to have to rotate our wrists to play more notes. Try playing a scale in contrary motion. Notice how the wrist moves when the hands are moving apart and the thumb needs to move under the third finger. Now notice how the wrist moves when the third finger crosses over the thumb when the hands are coming together. Now shake out your wrists and relax them as much as possible. See if this makes that movement of the thumb and third finger easier. Think back to pointing the fingers and rotating the wrist. Does knowing how the wrist turns most naturally help you to get a smooth movement of the fingers?
One of the biggest problems in scale playing, and the playing of scale passages in repertoire is that we can often hear a little bump in the sound when the thumb moves under, or the third finger moves over. This is really problematic, with the music being interrupted every three or four notes, and should be avoided. I have found that relaxed and free wrists help get rid of this problem forever.