The vertical arrows denote shifts of interest between ideosyncratic structures and theoretical problems. The horizontal arrows denote mathematical modeling (left to right) and music-theoretical interpretation of mathematical facts (right to left). Mazzola’s earlier investigations (e.g., on modulation and counterpoint) started from theoretical problems and are hence located on the top side of the square. The analytical applicability of these approaches is limited to very special musical structures. As a consequence, Mazzola’s later investigations within the context of the RUBATO-project aimed at reaching the bottom side of the square as well. The analytical RUBETTEs are software tools to be used within the RUBATO frame application. They provide methods for the analysis of scores (given in MIDI-format) through the transformation of empirically given sets of tones (in the onset-pitch space) into highly structured mathematical objects and finally encoding them in analytical weigths. These transformations are motivated by general ideas on paradigmatics and syntagmatics, but they are not comparable to grammars. There is no normative distinction between well-formed and ill-formed musical structures. The RUBETTEs work on any set of tones. As a consequence, there is a division of labour involved between

1. RUBETTE-authors who offer analytical transformations of musical input data into mathematical structures and analytical weights,
2. and RUBETTE-users who interpret these structures and weights in the context of other analytical methods and/or by means of experimental performance.

In the case of the existing RUBETTES⁶

it is interesting to characterize this division of labour from a scientific point of view. To call RUBETTE-authorship a mere service would certainly miss the point. The transformations from musical input data into the analytical data include (in the given cases) a lot of theoretical ideas – including music-theoretical and semiotical ones. On the other hand, these approaches start from the left bottom corner of the square and end up at the top right one. There is not a strong music-theoretical hypothesis behind each RUBETTE to be falsified. The user is invited to find out what is interesting in given ideosycratic structures under the specific perspective – provided by the RUBETTE. The creative scientific work as well as the responsibility are hence distributed among both: authors and users.

We recall the remark about the engagement of a modelist in his model resulting in a shifting focus of scientific interest. Once a mathematical model of a specific music-theoretical situation is established, it asks for separate attention. What distinguishes a model from a mere description is its metaphorical mechanism. The more knowledge about the model can be transferred into the music-theoretical domain, the richer its explanatory power. Hence, gaining knowledge about the model is a necessary prerequisite for the metaphorical transfer. It is essential that the researcher moves with the focus of his interest from the object domain to the model and back.