BUT! If you are a genius of the highly analytic kind - very very rare - you'll be able to teach yourself how to play at the level of the virtuosos. You'll make so many mistakes that don't seem like mistakes to begin with over the years but you'll analyze every correction to arrive at the "final" technique that seems to work the best for certain things. But this requires critical analyzation at every step and lots and lots of expiramenting - most people, almost all, will never do so much expiramenting on anything and will settle with just being adequate.
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So having a teacher is a very good tool for your goals as he will have the collective knowledge of three centuries worth of keyboard playing.
This is not to say you need one, though. There is this one pianist who has composed pieces for popular movies and other things and has never taken one lesson. She can play jazz and classical on the piano and can improvise like crazy. Her technique is horrible, though, and she will never play classical music in any aurally pleasing manner but she can improvise like crazy. I have her video on how to play the piano. No notes to read and her style of teaching seems to work! You'll be able to improvise something on your own almost immediately after a day or so of practicing what she tells you to do. What's great about her style is that you will learn the notes on the keyboard, as in you'll know the sound of the keys on the board after consistent practice.
Mind you, her playing sucks but this is my highly critical opinion comparing her to the virtuosos of our time. One of the reason she sucks? She improvises everything. Is this a good thing that she sucks? I'm comparing apples to oranges here. She can definitely play and she knows the piano keys much more than I know them and can pull a jazzy improv out of her... fingers... or a classical run.
In fact, you'll be able to improvise classical music and jazz if you follow her method! She provides the basics of music structure (harmonic chord progressions, mainly) and does not focus on technique at all. If you have the fingers, you can play. I should have continued practicing her methodoly 3 years ago because I know I would be able to pull a complete sonata out of my butt today. I made significant gains in just the first hour of following her method. I was actualy improvising! I gotta pull that video out of the book case and watch it again.
She has curly dark brown hair and was wearing a blue blouse sitting at the piano in the cover of teh video cassette.
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