The NEXTPITCH Learning Classifier System: Representation, Information Theory and Performance

Abstract

NEXTPITCH, a learning classifier system (LCS) using genetic algorithms, inductively learns to predict the next note in a musical melody. NEXTPITCH models human music learning by developing the rules that represent actual pitch transitions in the melody. In this article, the author addresses the issues of (1) the impact of the representation of a domain (the encoding of the characteristics of the field of study) on the performance of an LCS and (2) the classification of the input (the melodies to be learned) to an LCS in order to determine the highest percentage of correct next-note predictions.

The focal point of this article is to summarize my work with the domain of music within the construct of a learning classifier system (LCS) [1]. The program I have developed, called NEXTPITCH, models the inductive learning of Western tonal melodies, such as occurs naturally in human listeners, using an LCS that employs a genetic algorithm (GA) as the optimization mechanism. NEXTPITCH adapts D.E. Goldberg's simple classifier system (SCS) [2], a subset of LCSs, to the domain of music.

This article presents three findings: (1) the way in which notes are represented will affect the performance of the system; (2) varying the classifier format will also affect the performance of the system and (3) the classification of the input (using information theory and the musical expectancy of a note) to an LCS will lead to an understanding by the human user of the behavior of the system. Comparing findings from previous studies—which used the melodies from nursery rhymes as input—to others using Bach chorale melodies as the input has produced similar results with the two types of melodies [3].

Each musical note has multiple features, among them dynamics, timbre, duration and pitch. Pitch consists of the note name, octave and accidental. Since notes are grouped into phrases and motives, the relationship between notes (i.e. contour, duration and interval) is important. In developing the LCS, I found the following issues to be critical: which features should be represented, how they should be represented, how the principal feature of pitch should be joined to the relational properties and how the features affect the performance of the system. Information theory is used by the operator to partition melodies into classes in order to examine the effect of the structure of the area of concern, Western tonal music, on performance. This research uses four representations of pitch and three representations of the relational properties, which I carefully selected based on concepts from LCS theory and music psychology.

An Overview—Music Learning

The specific music-learning task modeled by the system is how a listener learns to develop expectations of future musical events based on what he or she has heard so far. A listener has expectations, at any point in a piece, about what is to follow. That is, based on the notes just heard, there is a limited set of notes that can reasonably be expected to follow [4]. The NEXTPITCH model predicts each note in a sequence of notes (all notes are presented; the prediction, based on two consecutive notes, starts with the second note) and maintains a set of rules that represent the melody being learned.

Nursery Melodies and Chorales

The attributes of nursery melodies are completely organized, making them highly predetermined music. By using basic repetitive rhythmic patterns, nursery melodies demonstrate perfect rhythmic clarity. They are generally short in length and are constructed with stepwise motion with few skips. Because of these inherent qualities, nursery melodies are useful candidates for study.

I chose to study chorales both because of their higher level of complexity and their similarities to nursery melodies [5]. I selected the chorale melodies from the 371 Four-Part Chorales of J.S. Bach, edition Brietkopf. Chorales involve orderly and sustained melodic development under the control of harmonic progression. Similar to nursery songs, chorales possess clarity of rhythmic structure and, generally, a single motive or melody based on a leading voice. Rhythmic continuity is achieved through repetition of rhythmic and melodic patterns and a consistent overlapping of each motive statement...