Abstract In the framework of the Distributed RUBATO platform, we propose an improved version MeloTopRUBETTE of RUBATO’s successful module MeloRUBETTE for motivic analysis. It fits with computational steering interaction and implements topological and sheaf-theoretical aspects of motive theory, such as motivic evolution trees (MET) and stalk dimensions for weight function sheaves. We present the theory and the algorithm flow chart of our topological model of motivic analysis following Rudolph Reti’s approach.

1 Introduction

We propose an improved version of the module MeloRUBETTE of the software platform RUBATO for musical analysis and performance (Mazzola and Zahorka, 1994; Mazzola and Garbers, 2001). This module of the now developed Distributed RUBATO platform (Mazzola, 2002, chapter 40) is called MeloTopRUBETTE¹

and implements our mathematical motive theory. Its design follows the requirements of computational steering, i.e. with interactive control of the computational process during its execution

The motivic analysis of a score has always been a main subject in musicology, but the very complexity of the motivic concepts and configurations made it impossible to ’traditional’ musicologists to transcend pure intuition. Nonetheless, crucial ideas about motivic analysis were proposed by Reti and Kopfermann (1982). In order to find out which motives are the germs and motors in the evolution of the motivic content, they suggested an immanent approach: One should not impose the germinal motives from outside, but construct the germs from a thorough analysis of all possible motif structures and relations within a given composition. So musicology is facing two main problems: To formalize the concept framework dealing with motives, and to establish a formally valid model of motivic germs.

We propose a solution to these two problems: In Buteau (1998), we introduced a model which formally conceptualizes Reti’s and Kopfermann’s approach. The