Abstract

With the birth of the monastic schools, the religious education of the high clergy was amplified with the introduction of arithmetic of the proportions; and the two 'sister sciences', arithmetic and music, began to assume a primary role in the field of the four arts of the "quadrivium". This new method of devising learning ended up by also investing the field of games, through which the "ludus" inevitably began to be connected to discipline, seriousness and science. Beyond utilizing the abacus, the "monocordo", the "sphere of Armilla" and the "astrolabio", in fact, the students of the episcopal schools of the German empire of Otto the Great were practising with "rithmomachia" ('the battle of the consonances of numbers') or "ludus philosophorum": a table game whose purpose was that of researching, like the real musicians of boetian memory, the relationships that ruled musical consonances. It functioned by means of numbered pawns which, placed on a "tavoliere" (a kind of card-table), were moved with complicated and continuous mathematical calculations. The game spread rapidly also in France, England and Italy. It had its greatest diffusion in the Renaissance (with the revival of the entire "corpus" of classical works), as is evinced by the copious production of tracts on the "rithomachia" that flowered in that period. After the twelfth century information regarding this "ludus pythagoricus" is scarce, although almost contemporaneously other mathematical-musical games emerged and survived until the dawn of the twentieth century. Conceptually, these games can be defined as the heirs of the "rithomachia", not so much for their rules as for their didactic but simultaneously recreational aim. Notable examples include Antonio Calegari's "Gioco pitagorico musicale" and Hermann Hesse's "Il gioco delle perle di vetro".