Diffusion model for unknown Pinax generation of Arca Musarithmica

Abstract

Automatic music generation has a long history dating back to probably the early 1600s, such as Athanasius Kircher’s idea for an automatic music generation machine. Nowadays, automatic music generation has significantly advanced with the rapid growth of machine learning and AI methodologies. Although Kircher’s machine is quite primitive, based on direct combinatorial approaches, the idea bears re- semblance to modern machine learning algorithms for AI music composition. In this study, we focus on Kircher’s music theory for automatic music generation, particularly on the set of music arrays, Syntagma, and the creation of Kircher-style music not found in his tables. The number of Pinax he provided is limited and insufficient for further training to create more Pinax data. To improve training, we first transform the Pinax data into image data and apply the diffusion model. For the transform, we utilize monotone cubic spline interpolation with special attention to boundary values of the images. By using the diffusion model, we verify that it is possible to generate more Pinax data not found in the original Kircher’s set. We demonstrate that this approach yields a method capable of creating a greater variety of Kircher music and possibly provides new insights through the generated music.