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Want to learn about jazz piano in more detail? Check out my series of easy but in-depth tutorials for beginners: http://goo.gl/wgd3Zl
The point of this tutorial is to show you how easy piano improv can be.
There's a lot of mystique surrounding jazz piano, blues and other keyboard improvisation styles. And it's true that to improvise at a high level takes a great deal of skill and practice. However, getting started with piano improvisation is dead easy. The trick is just to realise that you don't have to use the whole keyboard at once. You can start with just one note.
The way I get started here is by improvising different rhythms on middle C. I then add a single note at a time, working my way up the blues scale. If you take this approach it allows you to start improvising with something very, very easy and push your boundaries gradually.
In the whole tutorial I only cover five notes in the right-hand. But you can do an enormous amount with those five. For example, you don't have to play just one note at a time -- you can form simple chords and use them to create rhythmic effects and jazzy licks. It's important to remember that the piano is a percussion instrument, so you should really explore what you can do with rhythm and the quality of sound you get from hitting the keys in different ways.
So far, so easy. Piano improvisation needs left-hand work as well, though. What I do in this tutorial is used a simple repeating left-hand pattern. There's quite a good lesson here: you can achieve an awful lot with a very simple left hand. As long as it provides some harmonic context and perhaps a little bit of rhythm, you don't need to go overboard.
So there we go -- blues and jazz piano and other forms of piano improvisation don't need to be difficult, at least when you're getting started. If you want to become a competent improviser at the keyboard, you will of course have to do a lot of practice, and in the end the amount of effort you put in will determine how successful you are. But you shouldn't imagine that improvisation is some sort of magical skill that's only accessible to elite pianists. Anyone can do it!