Left Hand as maker of beauty

For Frankie, his left hand symbolizes his ability to bring true beauty into the world. El Maestro tells him the left hand creates the beauty because it's the hand that creates chords on a guitar. When Frankie mutilates his left hand as a self-imposed punishment for ruining his family, he is symbolically destroying his one true purpose: his ability to bring great beauty into the world. Frankie's left hand stays injured the rest of his life, but he manages to still practice the guitar. This represents the power to transcend one's trauma and still create art.