Towards Formalizing Jazz Piano Knowledge with a Deductive Object-Oriented Approach
The aim of this research is to provide a formalization method for the musical concepts and entities observed in scores and texts, that is, musical knowledge. As a first step, the knowledge domain of the research is restricted to a jazz piano solo performance, and the knowledge activities of a jazz pianist are represented using the deductive object-oriented (DOO) method. The advantages of the DOO method bring about that musical knowledge is systematized by a partial ordering, the flexible object representation makes it possible to manipulate musical knowledge incrementally, and the rules in a clausal form realizes useful and complicated functions, such as property inheritance, similarity and deductive inference. First, this paper shows a sample problem that the transcription of an actual solo performance by a jazz pianist is presented, explained, and analyzed. We are motivated to formalize the various musical knowledge appearing in the sample problem. From the sample problem, the observation that the piano performance analysis consists of abstraction and association is obtained. In the DOO framework, the abstraction relation can be naturally represented by a partial order $\sqsubseteq$, and the association by connecting different musical concepts to each other. Next, the DOO representation starts with a note, and the ordering of sets is discussed. To represent a chord, a new data structure, $\mu$ term, is introduced. Then, it is demonstrated that the abstraction in the sample problem is naturally translated to the $\sqsubseteq$-ordering. Next, a method of forming associations by attributes is introduced. Moreover, a new notation, called a dotted notation, useful for designating attribute values is introduced. The examples of voice leading and chord structure are presented. The author is prototyping a musical knowledge base system employing the formalization method presented in this paper. The prototype system is supposed to store actual performances, scores and their explanations as they are. Then, the music knowledge is managed along the $\sqsubseteq$-ordering. Thus, least abstraction upon storing avoids to lose necessary information. Last, sample queries to the system are shown.