Mathemusical Conversations celebrates the understanding of music through mathematics, and vice versa. This volume is a compilation of the invited talks given at the workshop of the same name that took place in Singapore from 13-15 February 2015, organized by Elaine Chew in partnership with Gérard Assayag for the scientific program and with Bernard Lanskey for the artistic program. The contributors include world experts and leading scholars, all writing on the intersection of music and mathematics. They also focus on performance and composition, two topics which are foundational both to the understanding of human creativity and to the creation of tomorrow's music technologies. This book is essential reading for researchers in both music and mathematics. It should also appeal more broadly to scholars, students, musicians, and anyone interested in fresh perspectives on the intimate relationship between these two ubiquitous human activities.