Neural Networks. Vol. 5. pp. 551-564. 1992 0893-6080/92 $5.00 + .00 Printed in the USA. All rights reserved. Copyright ~c, 1992 Pergamon Press Ltd. ORIGINAL CONTRIBUTION Learning Syntactically Significant Temporal Patterns of Chords: A Masking Field Embedded in an ART 3 Architecture ROBERT O. GJERDINGEN State University of New York at Stony Brook (Received I0 June 1991 : revised and accepted 22 October 1991 ) Abstract--In the traditional harmonic s),nta.x of classical music, temporal patterns of chords vao, in length, they often nest one within another, and they may lack overt markers indicating pattern boundaries. Tire selJ:organized learning of such patterns can be accomplished by a maskingfwld embedded in an ART 3 architecture. A simulation of learning the chord patterns in the music of Handel uses a dynamic short-term memoo, store to transform sequential patterns of chords into network patterns of activation. A masking field develops distributed recognition codes for those patterns. Some suggestions are offered for implementing masking fields within the ART 3 architecture. Keywords--Neural network, Pattern recognition, Adaptive resonance theory, Masking field, Music theory, Music cognition, Music perception, Syntax, Harmony. 1. INTRODUCTION Musical patterns are patterns in time. They embody temporality directly and essentially. A neural network designed to recognize musical patterns must thus, at a minimum, be capable of processing temporal order, inasmuch as temporal order is central to the meaning of musical patterns. Moreover, the network must be capable of processing temporal order with great gen- erality, since real music presents temporal patterns that vary in length (temporal scale), in their rate of presen- tation (tempo), in their partitioning of time intervals between constituent events (relative duration), and in their placement of those events with respect to a tem- poral grid or schema (meter). Common musical pat- terns include, but are not limited to, temporal patterns of durations (rhythm), of individual pitches (melody), of pairs of pitches (counterpoint), and of groups of pitches (harmony). This article discusses harmony, in particular the learning of harmonic syntax. Syntax, of course, involves more than just temporal order. Sections 2-5 introduce some rudiments of harmonic syntax and Acknowledgments: An early stage of this research was supported in part by a Ford Cognitive Science Grant from Carleton College. I would like to thank Mike Page for clarifying some points about mask- ing-field parameters. Requests for reprints should be sent to Robert O. Gjerdingen, Department of Music, SUNY at Stony Brook, Stony Brook, NY I 1794-5475. 551 discuss a 535-chord series abstracted from works by George Frederick Handel, composer of the Messiah. Sections 6-10 show how, using a recency effect, a dy- namic short-term memory store transforms Handel's temporal patterns of chords into spatial patterns of ac- tivations. And Sections 11-20 discuss how a masking field, serving as the top layer of an ART 3 network, develops distributed representations of syntactically significant temporal patterns in Handel's harmony. 2. HARMONIC SYNTAX How might we best conceptualize the interactions be- tween, on the one hand, a temporal series of musical chords and, on the other, the moment-by-moment ac- tivities of a neural network as it works to interpret the harmonic significance of those chords? To begin, we might look to explanations of how humans interpret harmony. Musical scholars have, after all, been writing elaborate treatises on harmony since the early 18th century (Rameau, 1722). Yet these treatises typically assume a listener who has already internalized a knowledge of how harmony "works." Even today, when a listener's task of interpreting a series of chords is usu- ally explained as one of parsing a string of chords ac- cording to the rules of a harmonic grammar, whether a traditional grammar (Winograd, 1968), a generative grammar (Lerdahl & Jackendoff, 1983), or an aug- mented transition network (Pulkk6, 1988), there are few detailed explanations of how the listener obtained