The pentatonic scale is a great place to start improvising on the piano. My students first introduction to improvisation is the pentatonic scale in F# major, which consists of only black keys.
So you can play any black key at all, in any way you wish!
I think improvisation is very liberating and also can go a huge way to improving a student’s sense of musicality. In fact after introducing this improvisation technique to an adult student of mine today she actually said she was “on a high!” – it doesn’t get much better than that for me as a teacher!
As a starting point, try playing two notes simultaneously in the left hand, repeating the same two notes throughout and coming in every 4 beats.
Then try this the other way around, with the right hand sustaining two notes for 4 beats, and the left hand doing the improvisation.
If you’re having trouble keeping steady beats, try using a metronome to accompany you for a while.
Just have fun with it! Don’t worry about playing wrong notes or it sounding bad, power on through and enjoy being freed from the confines of sheet music.
Also check out the fantastic ted talk below about the pentatonic scale, really can’t recommend this one enough! Makes me smile every time!