Generative Grammar Based on Arithmetic Operations for Realtime Composition

Mathematical sequences in \(\mathbb {N}_0\) are regarded as time series. By repeatedly applying arithmetic operations to each of their elements, the sequences are metamorphised and finally transformed into sounds by an interpretation algorithm. The efficiency of this method as a composition method is demonstrated by explicit examples. In principle, this method also offers laypersons the possibility of composing. In this context it will be discussed how well and under what kind of conditions the compositional results can be predicted and thus can be deliberately planned by the user. On the way to assessing this, Edmund Husserl’s concept of “fulfillment chains” provides a good starting point. Finally, the computer-based board game MODULO is presented. Based on the here introduced generative grammar, MODULO converts the respective game situation directly into sound events. In MODULO, the players behave consistent to the gaming-rules and do not care about the evolving musical structure. In this respect, MODULO represents an alternative draft to a reasonable and common use of the symbols of the grammar in which the user anticipates the musical result.