scientific metalanguage is another aspect of a shifting scientific interest. One should mention that Mazzola’s metalanguage goes beyond a mere descriptive framework. It includes classification methods, that apply to a large class of possible models and it supports the construction of complex models from given simpler ones.

Music-theoretical knowledge is based on denotation and predication. Denotators identify discourse subjects, while predicates load them with meaning in various ways. We give a short portrait⁹

of the Denotator system. Its design has been motivated by two main ingrediences as shown below:

The upper left corner represents denotative aspects in the systematic investigation of generalized musical parameter spaces as proposed in [5] and [6]. The upper right side labels denotative aspects of general concept analysis and construction which gained Mazzola’s interest in connection with data modeling for RUBATO. It seems useful not to directly enter Mazzola’s system. For the most part of this section we restrict our considerations to a simplified “dollhouse”-ontology corresponding only to the upper right corner. In order to avoid confusion we mark the “dollhouse”-Denotators with the prefix , with the idea in mind that these are built upon simple acts of pointing at (arbitrary) objects. At the end of this portait we comment on the refinements which come into play in Mazzola’s ontology together with the integration of the upper left corner.

The accessability of Denotators is controlled though Forms. A Form basically consists of an AmbientSet having Denotators as its elements. Extensionally, the AmbientSet serves as a Denotator-container. In addition, a Form includes the definition of its construction relative to other Forms. This attributes a formal intension to the Denotators in addition to the mere elementship.

We now adopt Mazzola’s definition to our narrowed pointing-ontology. A Denotator is constituted by its name, its Form and its Coordinates. This can be written as

The coordinates identify the Denotator as an element of its AmbientSet. How is this related to the corresponding Form F?. The AmbientSet AS(F) is the core of the Form. It is embedded into the FrameSet FS(F) by an injective set-map which is called the Identifier: