ARCA MUSARITHMICA

a device for automatic music composition from 1650

Arca musarithmica Athanasii Kircherii MDCL

This site presents a digital implentation of device for automatic music composition invented by Athanasius Kircher in 1650. Based on the specifications in Kircher’s Musurgia universalis (Rome, 1650), Book VIII, the core program was written in Haskell (2021), with a simple web interface in Javascript and PHP.

Image: The original print illustration of Kircher’s Arca
                      musarithmica, a large box containing many sets of ruler-like
                      rods and adorned with images of historic musical instruments.

An Ark of Musical Knowledge in Infinite Permutations

The Arca musarithmica Athanasii Kircherii MDCL is an ark or box for music-arithmetic, or musical calculation. The ark holds a set of data tables, which together with a list of rules for how to use the tables, amounts to a computation device for composing music. Given input in the form of a marked text in Latin and a small set of simple choices about the musical setting, a user who knows nothing about music can use the ark to generate unique, never-before-heard musical settings of that text for four-voice (SATB) chorus.

Kircher presented this as an embodiment of mathematical permutations. Like many of his seventeenth-century contemporaries, he understood music as sounding number, an embodiment of the mathematical order inherent in God’s created universe, and a reflection of the perfection of God himself. Out of the infinite variety of possible combinations of notes and rhythms, the user of the ark selects a specific set of permutations and thus imitates God in his original act of creation.

The combination of structured data and completely prescribed algorithms makes Kircher’s device a computational system, with some of the characteristics that would later characterize modern computers, though of course Kircher had no way to automate his system and certainly did not theorize it fully. This implementation, written in the pure-functional programming language Haskell, models the entire ark as a single mathematical function: it takes one series of symbols, representing an input text and the choice of musical parameters, and transforms those into another set of symbols that represents musical notation. Though others have implemented portions of the ark and related systems (see the bibliography), to my knowledge this is the version to be fully automatic and to be capable of setting texts of any length and type.

Kircher intended his device for the total musical novice, a Tyro who knew nothing about music except the rules he provided. Kircher did not know it, but he was describing an automatic computer. All we have done is create a digital version of his ark that an electronic computer, the ultimate know-nothing, can use to generate music.

The program and its output make it possible to reflect on what Kircher’s project meant: What does his artificial system of composition tell us about his and his contemporaries’ concepts of both music and computation? How much musical knowledge is embodied in this device? What is missing? And what purposes would such a device have served in its time?

Run the ark as many times as you like and create ever-new, unique musical combinations!

Next Steps

Learn how to use the ark and dig into the details of this digital implementation.

Read the documentation and the code

Compose new music using the ark!