In the early 1970s, Martin Gutzwiller and Roger Balian and Claude Bloch described quantum spectra in terms of classical periodic orbits, and in the mid 1970s it became clear that the random matrix theory devised for nuclear physics would also describe the statistics of quantum energy levels in classically chaotic systems. It seemed obvious even then that these two great ideas would find application in acoustics, but it has taken more than three decades for this insight to be fully implemented. The chapters in this fine collection provide abundant demonstration of the continuing fertility, in the understanding of acoustic spectra, of periodic orbit theory and the statistical approach. The editors' kind invitation to me to write this foreword provides an opportunity to make a remark about each of these two themes.

First, here is a simple argument for periodic orbit theory being the uniquely appropriate tool for describing the acoustics of rooms. The reason for confining music and speech within auditoriums – at least in climates where there is no need to protect listeners from the weather – is to prevent sound from being attentuated by radiating into the open air. But if the confinement were perfect, that is, if the walls of the room were completely reflecting, sounds would reverberate forever and get confused. To avoid these extremes, the walls in a real room must be partially absorbing.