Athanasius Kircher's Arca musarithmica (1650) as a Computational System

Abstract

In Book Eight of Athanasius Kircher’s Musurgia universalis (Rome, 1650), this Jesuit polymath describes a computing device for automated music composition, called the Arca musarithmica. A new software implementation of Kircher’s device in Haskell, a pure-functional programming language, demonstrates that the Arca can be made into a completely automatic computational system. Moreover, the project also demonstrates that the Arca in its original form already constituted a computational system that almost completely automatic though designed to be operated by a human user: as Kircher advertised, a completely “amusical” user could generate music simply by using the device according to his rules. The device itself served as a microcosm of Kircher’s goal in the Musurgia to encapsulate and codify all musical knowledge, and demonstrate that music manifested the underlying mathematical order of the Creation and its Creator. This article analyses the concepts and methods of computation in Kircher’s original system, in dialogue with the interpretation of his system in software. The Arca musarithmica, now available on the web, makes it possible actually to hear how well Kircher was able to reduce seventeenth-century music to algorithmic rules. The successes of the system are inseparable from many paradoxical elements that raises broader questions about how Kircher and his contemporaries understood the links between composition and computation, mathematics and rhetoric, traditional harmonic theory and emerging tonal practice, and concepts of “invention” and authorship.