What does it mean for music to be emotional? How can these mysterious feelings be understood and validated?Some modern thinkers, unable to find an answer, have gone so far as to declare that music must be pure form, without emotion. Yet philosophers from Confucius to Plato and Aristotle, religious traditions from Hinduism and Buddhism to Christianity, all regarded music as a profound form of moral-emotional training.Can we link the ancient spiritual purposes of music to our modern secular and scientific understanding of man?This book argues we can, presenting a new theory that music produces the *psychological signature* of emotion-a motion of the mind with a distinctive set of mathematical characteristics. This theory provides a new way of making sense of musical emotion, a rational framework for understanding and validating it. It thus holds the promise of restoring the importance of music as a humanistic art form, and a vehicle for rewarding the good.