Our research concerns the development of biocomputers using electronic components grown out of biological material. This article reports the development of a novel biological memristor and an approach to using such biomemristors to build interactive generative music systems. The memristor is an electronic component regarded as a resistor with memory. After an introduction to harnessing the Physarum polycephalum organism to implement biomemristors, the article presents PhyBox, a biocomputer that uses four biomemristors to generate music interactively. The resistance of a biomemristor varies as a function of the voltage that has passed through it. Music input is represented in terms of voltage transitions and music output is encoded as measurements of the current yielded by the system's memristive behavior. An example of a musical composition using PhyBox is detailed. The article concludes with a short discussion of how the combination between artificial machines and biological organisms is paving the way for the development of new technologies for music based on living processors.