Arca musarithmica Athanasii Kircherii MDCL
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)
Kircher presented this as an embodiment of mathematical permutations.
Like many of his seventeenth-century contemporaries, he understood music
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
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
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!
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!