Sequential Association Rules in Atonal Music

Abstract

This paper describes a preliminary study on the structure of atonal music. In the same way as sequential association rules of chords can be found in tonal music, sequential association rules of pitch class set categories can be found in atonal music. It has been noted before that certain pitch class sets can be grouped into 6 different categories . In this paper we calculate those categories in a different way and show that virtually all possible pitch class sets can be grouped into these categories. Each piece in a corpus of atonal music was segmented at the bar level and of each segment it was calculated to which category it belongs. The percentages of occurrence of the different categories in the corpus were tabulated, and it turns out that these statistics may be useful for distinguishing tonal from atonal music. Furthermore, sequential association rules were sought within the sequence of categories. The category transition matrix shows how many times it happens that one specific category is followed by another. The statistical significance of each progression can be calculated, and we present the significant progressions as sequential association rules for atonal music.