A diffusion model for generating unknown Pinax data of Athanasius Kircher's Arca Musarithmica

Automatic music generation has a long history. One significant example from the 1600s is Athanasius Kircher's concept of a music-generating machine. Today, automatic music generation has advanced significantly thanks to the rapid growth of machine learning and AI techniques. While Kircher's machine was quite primitive, relying on direct combinatorial methods, the core idea shares similarities with modern AI algorithms for music composition. In this study, we focus on Kircher's music theory for automatic generation, specifically his set of musical arrays, Syntagma, and the creation of Kircher-style music not found in his original tables. The number of Pinax he provided is limited and insufficient for further training to generate more phrase blocks. To enhance training, we first transform the Pinax data into image form and apply a diffusion model. For this transformation, we use nearest-neighbour interpolation, paying special attention to boundary values in the images. By employing the diffusion model, we demonstrate that it is possible to generate new phrase blocks beyond Kircher's original set. This approach not only enables the creation of a wider variety of Kircher-style music but also potentially provides new insights through the generated compositions.