Subjective Evaluation of Correlation of Melody Length and Melodic Similarity Based on a Music Theory

Abstract

This paper studies to measure similarity of melodies based on Implication-Realization Model (IRM), a music theory that abstracts music and then expresses music through symbol sequences based on information constituting the music such as pitch, rhythm, and rests and so on. The model employed in this paper is an extended one that is much more appropriate to measuring similarity of melodies. Compared with the symbols of the original IRM, the extended model employs finer grained symbols by simply distinguishing up and down of interval directions and by dividing each most symbols of the original IRM into two extended symbols. Based on such a fundamental framework of measuring similarity of melodies by an extended IRM, the major focus of this paper is to claim that the similarity measure studied in this paper has a certain correlation with subjective human judgments on melodic similarities. Furthermore, this paper examines the correlation between melody length and subjective human judgments on melodic similarities. It is quite remarkable to note the result of this analysis: i.e., the smaller the melody length is, the more similar the pair of melodies is judged to be by human subjects, even though their similarities based on the extended IRM are measured to be almost in the same range. Thus, we conclude that it is necessary to invent a much finer-grained similarity measure which is designed to be more sensitive to melody length and to be coincide with the results of subjective human judgments.