Quadrilles were a popular genre of group dancing in the nineteenth century. Existing melodies were normally used to accompany the dancing sessions, but the monotony of their repetition and the cost of a professional piano player capable of improvising were an issue. Thus, the idea of a “machine” that would be able to endlessly produce quadrille music at no cost was suggesting itself. The Quadrille Melodist, a paper-based system for the generation of piano pieces, was published in nineteenth-century Victorian London by John Clinton, a “professor in the Royal Academy of Music.” Already in 1650, Athanasius Kircher proposed in his Musurgia Universalis a device consisting of stripes with short snippets of music that could be used to create combinatorial pieces and variations. By the beginning of the nineteenth century, a whole genre of quasi-algorithmic compositions was emerging, spurred by the popularity of such works as the Musikalisches Würfelspiel, a piece attributed to Mozart. In this article, I analyze the Quadrille Melodist against the background of the history of combinatorial music. I contrast its unique features with other predigital, as well as later digital, music systems and discuss its design with respect to the phenomenon of predictability in dance music. Additionally, I discuss reasons for the circumstance that the historically advertised number of possible quadrilles, 428 million, is much smaller than the real number of combinations.