There are quite a number of piano compositions that require you to play one rhythm with one hand and another with your other hand. Most of the time, your left hand will usually be playing low, backing notes, whereas your right hand tends to pick out a higher melody. The technique is similar to that of patting your head while rubbing your stomach. It will require some time to pick up. You can begin practicing by playing a melody with your right hand, and at the same time, playing whole note harmonies with your left.
After you have practiced that and got the hang of it, you can then move on to practice moving your hands. By using this technique that requires you to move your hands, you will eventually have to leave the middle C area of the keyboard and venture out more towards the edges. You can get used to it by trying to play your practice drills an octave lower or higher than what you would usually play.
Do keep in mind that when you are using this technique, you should still be sitting as per normal and not scoot down the bench. In a concert, there is definitely not enough time to scoot from the low end all the way to the high end. Instead, you should lean your torso slightly sideways, but do not bend your back or perform any twisting action. Then, stretch or contract your arms so that you will be able to reach the notes.
Whenever possible, try changing positions on the fly. You can actually begin by playing something relatively simple, like a scale or arpeggio, from a lower position than normal. From there, you can then jump your hands up to continue it through to a second octave. Take note that if you begin with your left hand, let it cross lightly over your right and hold the position above the proper keys just before you need it for the second octave. As you continue to play those notes, draw your right hand back to its higher position as well.
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