Fingering for String Instruments with the Optimum Path Paradigm
Samir I Sayegh · Computer Music Journal · 1989
This paper introduces a new connectionist paradigm, the optimum path paradigm (OPP) and its application to the problem of string instrument fingering. The optimization approach on a Viterbi network is the feedforward phase that maps input to output once the values of the weights are known. The approach taken is a natural one that proceeds from the formulation of the problem, goes through the rule-based and the optimization approaches, and leads to the final learning phase. A discussion of how the optimum path paradigm relates to other connectionist paradigms is also presented. The paper will address the specific problem of fingering for string instruments (Yampolsky 1967; Gilardino 1975), in particular the fingering of homophonic music written for the classical guitar (Gilardino 1975; Sayegh 1987; 1988). The method presented is general, however, and can be used in a variety of musical applications, where the written transcription often carries only partial information about the sound to be rendered-the remaining information depending on context and/or interpretation. The reason for restricting the study to a particular application is the desire to introduce another level of generality, illustrating different approaches that can be taken. One such approach, the optimization approach, leads naturally to a new connectionist learning paradigm, the optimum path paradigm, whose generality goes beyond musical applications (Sayegh and Manzor-Coats 1988). The connectionist aspect of the problem is introduced in a very natural way. In the early phases of the treatment, it is present at the level of constraint propagation (Waltz 1975) or of connectionism (Feldman 1985) and is very closely tied to the nature of the problem. The most interesting aspect is that it then goes one step beyond, culminating in the learning aspect that is absent in similar treatments, although essential for a viable connectionist paradigm.