Sensitivity analysis

Abstract

The goal of this chapter is to present a systematic analysis of audio key-finding to determine the factors important to system design, and the selecting and evaluating of solutions. First, we present a basic audio key-finding system consisting of a Fuzzy Analysis technique and the Spiral Array Center of Effect Generator algorithm, with three key determination policies: the nearest-neighbor, the relative distance, and the average distance policy. An evaluation on 15-second excerpts of 410 classical pieces from a variety of stylistic periods shows that the average-distance key determination policy achieves a 79% correct key identification rate, at least 8% higher than the systems employing other key determination policies. Two examples are given to illustrate why audio key-finding could outperform symbolic key-finding, where precise pitch information is known. An analysis of the results by period shows that pieces from the romantic period may be the most challenging for key-finding. We next propose three extensions to the basic key-finding system—the modified Spiral Array approach, fundamental frequency identification, and post-weight balancing— to improve the performance at different stages of the system. The three extensions are evaluated using 15-second excerpts of recordings of Chopin’s Preludes for piano. Quantitative analyses of the results show that fundamental frequency identification provides the greatest system improvement in the first 8s, while modifying the representation model using audio frequency features leads to the best performance after 8s. Two case studies show detailed analyses of an example where all extended systems give the correct answer, and another where all systems were incorrect.