Music as a Symphony of Symmetry

Music is fundamentally about symmetry and playing with symmetry. The repetition of musical ideas is a form of symmetry that is widely appreciated, but transformational repetition, where musical ideas are repeated with variations, is where things get interesting. Composers intelligently deploy relationships and structures, even if listeners are not always directly sensitive to them. The mathematics of music points to the importance of symmetrical structures and how they can create a rich set of perceptual symmetries. This symmetrical play in music can transport us to otherworldly places and create deeply enjoyable and mysterious musical experiences.