Most of the papers in this collection are from the journal Connection Science. The aim of these researchers is “to make computer models based on `brain-style computation’ to see if we can accurately capture human musical behavior in an artificial system.” Most of their work uses parallel distributed processing. Their procedures attempt to mimic the way that neurons in the brain process information. The word “connectionist” is often used to describe the methods used, and one reads of “connectionist perspective,” “modern connectionist cognitive modeling,” “the connectionist algorithm,” and “a connectionist model of the perception of musical sequences,” to list a few uses of the term.

The theoretical study of music has often concentrated on a single component of music, such as melody, rhythm, or structure. The editors hearken to this tradition by grouping the essays as follows.

Part 1 addresses “Pitch and Tonality.” Ian Taylor and Mike Greenhough, in “Modeling Pitch Perception with Adaptive Resonance Theory Artificial Networks,” describe their technique for extracting the perceived pitch of a tone (as played on various instruments) using a series of steps that begin with a Fourier transform. Co-editor Niall Griffith’s chapter, “Development of Tonal Centres and Abstract Pitch as Categorizations of Pitch Use,” describes his efforts to determine how listeners comprehend the tonality of a melody. In “Understanding Musical Sound with Forward Models and Physical Models,” Peter Desain and Henkjan Honing describe their work on a challenging problem. Trained musicians (and many lay listeners) recognize the physical conditions that produce a particular tone (or pitch) on a musical instrument. Using techniques of forward modeling and distal teaching, these researchers probe this problem as it relates to a sounding violin string. They plan to extend their work to the study of brass and woodwind instruments.

Part 2 discusses “Rhythm and Meter.” Edward W.Large and John F. Kolen’s paper on “Resonance and the Perception of Musical Meter” tackles a problem that seems simple to a trained musician--to recognize the meter of a melody--but is difficult to model mathematically. The pitch, timing, and hammer velocity of a computer-monitored Yamaha Disklavier acoustic upright piano are collected. A bank of oscillators is then exposed to this “performance,” after which, through a series of steps too complicated to summarize here, the authors are able to make limited observations on the perception of meter. They conclude, as do many of the papers in this book, with plans for future research to arrive at more definitive conclusions. The next two papers are rather unusual. The first, Stephen Smolier’s “Modeling Musical Perception: A Critical View,” which questions the conclusions of an earlier paper by Peter Desain, is followed by a reply by Desain and Henkjam Honing. The issue in this spirited debate is the validity of the efforts to deal with the “quantization problem,” that is, the assignment of note values to the performance of a melody.

Part 3, “Melodic Memory, Structure, and Completion,” deals with the subtle and complex problem of determining how we perceive a string of musical notes as a coherent and expressive melody, and how we can recognize separate melodies simultaneously in a polyphonic structure. Stephen Grossberg writes on “Pitch-Based Streaming in Auditory Perception.” He points out that the problem of separating overlapping harmonic components emitted by several instruments in a symphony parallels the well-known “cocktail party problem,” in which we keep track of a particular conversation amid the hubbub of a noisy room. Using adaptive resonance theory, he has developed a model of pitch streaming that uses sophisticated techniques to separate meaningful tones from surrounding noise. “Apparent Motion in Music?” is the provocative title of a paper in which Robert O.  Gjerdingen  describes research exploring the well-known fact that “a great deal of the motion perceived in music is more apparent than real.” Gjerdingen’s work, including interesting use of computer graphics, seems to indicate that analogies between apparent motion in vision and music are weak in high-level cognition, but “gain considerable strength when cast in terms of low-level neural processes.” In the second paper in this section, Michael P. A. Page writes on “Modelling the Perception of Musical Sequences with Self-Organizing Neural Networks.” His SONNET model aggregates a melody into a hierarchy of phrases culminating in a single cell “which can be thought of as that sequence’s plan cell. This plan cell will be strongly activated only by the presentation of its associated sequence: such activation constitutes recognition of the sequence.” This leads to sequence recall. The last chapter in this group ventures into the area of music aesthetics. Bruce F. Katz explores the principle of unity in diversity as it is experienced in the well-known musical form theme and variations. The successive steps of his model seem to point to the prominence of stepwise movement in pleasing melodies.

Part 4 is about “Composition.” Michael C. Mozer’s paper, “Neural Network Music Composition: Exploring the Benefits of Psychoacoustic Constraints and Multi-scale Processing,” explores a connectionist network called CONCERT that is first trained on sets of pieces by J. S. Bach and traditional European folk melodies and then allowed to “compose” novel melodies. While the results are interesting and impressive, no trained musician would attribute them to a human composer. The author readily acknowledges this and outlines desiderata for further work. Mathew I. Bellgard and C. P. Sang describe their neural system for chorale harmonization in “Harmonizing Music the Boltzmann Way.” Their Boltzmann machine harmonizes a chorale melody quite effectively but, as the authors indicate, is not yet trained to deal with meter and rhythm. Edward W. Large, Caroline Palmer, and Jordan B. Pollack, in their chapter on “Reduced Memory Representation for Music,” describe their work on determining the structurally important elements in improvised melodies using a recursive auto-associative memory network. “Frankensteinian Methods for Evolutionary Music Composition” is the intriguing title of the article in which Peter M. Todd and Gregory M. Werner explore the evident fact that the more constraints built into an algorithmic composition program, the less creative the output will be, but the less structure built into the system, the greater the risk of ugly results. They conclude a survey of work done by others to date with a description of their “preliminary model of coevolved ‘males’ who produce rhythmic songs along with picky ‘females’ who judge these songs.” They ran “populations of 1000 individuals for 1000 generations in six different conditions.” They candidly admit that the results are mixed and cite parallels to the experience of  Victor  Frankenstein. The only non-musical chapter in the book is “Towards Automated Artificial Evolution for Computer-Generated Images,” by Shumeet Baluja, Dean Pomerleau, and Todd Jochem. They apply a union of learning and evolutionary methods to creating new visual images. The final chapter is an amusing one-page spoof of all this work, “The Connectionist Air Guitar: A Dream Come True,” by Garrison W. Cottrel.