This chapter traces philosophy of music from the end of the ancient world until 1500. Following Boethius, medieval Latin writers regarded music as having three parts: musica mundana (Boethius’ cosmic music), musica humana (the harmony found in human souls) and musica instrumentalis (instrumental music). Music was usually regarded as a mathematical science more than a fine art. Only limited attention was paid to music as an aesthetic object or something able to arouse emotion. Medieval Islamic and Jewish philosophers were also heirs of ancient philosophy and contributed to the Western philosophical tradition. Authors in both the Latin and Arabic traditions debated whether music can promote religious experience. Figures discussed include Jacques of Liège, Hugh of Saint Victor, Al-Kindī, Avicenna, Al-Ghazali, Al-Fārābī, Johannes de Grocheo, Aurelian of Réôme, Bonaventure, Roger Bacon, Alan of Lille, Maimonides, Johannes Tinctoris, Aquinas, Johannes de Muris, Guy of Saint-Denis, Peter of Auvergne, Albertus Magnus and Marsilio Ficino.