These proceedings comprise 26 refereed research papers that were presented at theSecondInternationalConferenceonMathematicsandComputationinMusic (MCM 2009), which met in conjunction with the John Clough Memorial C- ference during June 19-22, 2009, at Yale University in New Haven, Connecticut, USA. The International Conference on Mathematics and Computation in Music (MCM) is the ?agship conference of the Society for Mathematics and Com- tation in Music. The inaugural conference of the society took place in 2007 in Berlin.Thestudyofmathematicsandmusicdatesbacktothetimeoftheancient Greeks.The riseof computing andthe digitalagehas addedcomputationto this august tradition. MCM aims to provide a dedicated platform for the commu- cation and exchange of ideas amongst researchers in mathematics, informatics, music theory, composition, musicology, and related disciplines. TheJohnCloughMemorialConferencehonorsamathematicalmusictheorist whose research modeled the virtues of collaborative work across the disciplines, and who generously fostered a cooperative attitude with and among younger researchers. The quadrennial conferences that Clough ?rst organized at Bu?alo in 1993 positioned neo-Riemannian theory on the map of musical scholarship. TheJohnCloughMemorialConferencecarriesthespiritofthosesessionsbeyond his passing in 2003, while embracing the entire domain of mathematical music theory. High-quality contributions — including research papers, invited sessions or panels,tutorials,andexhibits — were solicitedin allareasrelatedto the mission of the society.