"The famous man who has the greatest praise in our town in music, and the greatest admiration of connoisseurs, does not get into condition, as the expression goes, to delight others with the mingling of his tones until he has played something from the printed or written page, and has thus set his powers of imagination in motion... The able man... usually has to play something from a page which is inferior to his own ideas. And yet his superior ideas are the consequences of those inferior ones." (Quoted in Christoph Wolff's landmark book).
It's an interesting approach first to warm up with the music which has been composed before and then try to improvise based on the themes or style of that music.
Leaving the concept of inferior and superior aside, it's like a musical sermon when a priest or a pastor first reads the excerpt from the Scripture and later elaborates on it's main themes.
You can try it for yourself. It really works. It gives you the starting point from which you can build your own ideas.
You can even take it one step further, by playing a piece that you are currently working on and later put the score further from you (not too far for you to lose the general feel of the music and not too close to really see the notes). When you only see the general shape and texture of a composition, you can elaborate on it with your own improvisations. My professor Pamela Ruiter-Feenstra used to ask this from me during lessons.
PS So far more than 20 people have sent me their answers about why they like Bach and his art. If you like Bach but haven't written a few sentences about it, you can do it here until tonight. After today I will share all of the answers in a special article.