Hermann von Helmholtz-Zentrum für Kulturtechnik

Zentralinstitut der Humboldt-Universität zu Berlin

Music and Mathematics

Friedrich Kittler, Philip v. Hilgers, Ana Ofak

The aim of the »Image–Script–Number« research group was and is to study the three elementary cultural techniques of showing, writing and counting, examining their historical combinations and transformations in order to arrive at a cultural history from below.

As with Brüning’s subproject, it is therefore imperative to investigate the foundations of the European sciences in ancient Greece. It was Pythagoras of Samos and his students in Southern Italy who took the basic concepts of music theory (harmony, octave, interval) and created mathematics as a science of general laws. The conceptual pair even/odd made it possible to conceive consonance per se, in other words, without actual numbers. The science thereby emerged as a generally practised cultural technique in the form it still has today in schools, academies and universities.

Taking elementary cultural techniques as our starting point promises to generate new, synthesising findings because this approach enables interactions between image, script and number to be identified. According to a new thesis (Powell, 1991), the Greek alphabet itself, the first and only alphabetic script in history, appears to be the reason why singing and music became the object of a new kind of writing and counting. They both employed the same cultural technique because Greek numbers were a superset of the alphabet.

Conversely, geometry emerged as a scientific image of objects distinct from arithmetics from one of the fundamental Pythagorean discoveries, namely that not all intervals or geometric lines are rational. But when arithmetics and geometry in this complementarity of theirs seek to capture »what« essentially »is«, then image, script and number combine to form an ontology – for the first time, as far as I can see.