- 234 -Mazzola, Guerino / Noll, Thomas / Lluis-Puebla, Emilio: Perspectives in Mathematical and Computational Music Theory 
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concerned with notation, as well notation of the result (a musical score) as of the process leading to this result (visual program).
  • Programming languages provide composers with a great freedom of decision, in exchange of a certain effort in formalization and design. Visual programs, implementing a formal music calculation, are good candidates to denote compositional procedures, insofar as they exhibit their logical components.
  • Building structures to express calculations is useful for composers if the results can be interpreted and represented in significant music dimensions such as pitch, duration or intensity. Providing visual interfaces which materialize this interpretation is therefore an imperative necessity. We use traditional music notation to visualize musical structures. In a CAC context, music notation acts ideally not only like materialization of a calculus but is also a support of formal inventiveness. For this reason, the notation should be equipped with the same flexibility and the same opening (in terms of extensibility and programmability) as the language.

The fact of representing compositional processes by visual programs and visualizing musical material as scores, seems to be a good compromise between representation and expressiveness. However, in practice the boundaries between musical material and process are not well-defined. The roles of material and process are often inverted. In addition, material and processes can be explicit or implicit in the composition. As mentioned in (Balaban and Elhadad1999), composition environments must offer the possibility of dealing with this ambiguity between material and process to composers. This paper describes different strategies to mix and unify visual programs and music scores. Section 2 presents the OpenMusic language. We will focus on visual programs and score descriptions. Section 3 details two ways of combining visual programs and scores. In Section 4 we explain the concept of maquette which aims at unifying visual programs and scores in a homogenous way.

2 OpenMusic description

OpenMusic is based and implemented on CLOS. It was implemented by sub-classing the Meta Object Protocol (G. Kiczales and Bobrow1991). We have extended meta-objects (e.g. methods, classes, generic functions) by adding visual counterparts. Visually meta-objects are represented either as composed frames or simple frames. Simple frames which represent an object are called views and generally appear as icons. Composed frames representing objects are called editors. Several frames (i.e. different points of view) may be produced for the same object. Figure 1 shows the view and the editor for a given class.


PIC
Figure 1: View and editor of the class note.


2.1 Patches

The main concept of our language is the patch. It reifies the concept of program. A patch is the place where objects will be interconnected in order to specify musical algorithms. Patches consist of boxes (icons) and connections between them.


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- 234 -Mazzola, Guerino / Noll, Thomas / Lluis-Puebla, Emilio: Perspectives in Mathematical and Computational Music Theory