The piano is an amazing instrument. So many notes, so many keys! That's why the crossover or arpeggio technique is employed frequently. It allows the pianist to use much of the keyboard and the left hand.

The trick to using this technique is in the crossover itself. Usually, the left hand's initial position will span an octave and then the index or ring finger will be used to crossover the thumb to continue playing more notes of the chord.

A good example of this is the piece "Thanksgiving" by George Winston. Here, a whole harmonic background is created by the left-hand crossover technique while the right improvises a melody line. And the results are a beautiful piece of music! Nothing complicated here. He just gets his left hand down using a few chords. This creates the backdrop for the entire piece - and the mood.
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