David Cope

A Musical Learning Algorithm

In this article I describe a computer program called Gradus (after Johann Joseph Fux’s 1725 treatise Gradus ad Parnassum) that initially analyzes a set of model two-voice, one-against-one, first-species counterpoints in order to produce a series of compositional goals. Gradus then attempts to compose goal-correct counterpoints similar to the models using a given fixed voice called a cantus firmus. Initial notes for the new lines of these counterpoints are drawn from pre-compositional seed notes, the choice of which are optimized by consulting the program’s previously saved successful compositions. The article then describes how Gradus, in order to compose more quickly and mistake-free, backtracks from the ‘‘dead ends’’ it encounters, catalogs the conditions that led to these dead ends as rules, and avoids these conditions on subsequent runs with the same cantus firmus until backtracking is no longer necessary. Gradus then uses the rules it collects when encountering new cantus firmi, applying its accumulated experiences to increase the chances that it will succeed. Ultimately, the program learns to compose first-species counterpoint quickly, accurately, and without any need for backtracking. I have based the processes used in Gradus on those that I use when learning or re-learning species counterpoint. This article includes a brief discussion of musical inference and a description of how the learning processes described may be seen as computationally inferring solutions to basic musical problems. The article then concludes with more elaborate examples created by the program, including a fugue exposition and counterpoint in a more dissonant, non-triadic style.

Recombinant music: using the computer to explore musical style

A research project called Experiments in Musical Intelligence (EMI) is discussed. One subprogram of EMI is an expert system that uses pattern recognition processes to create recombinant music, i.e. music written in the styles of various composers by means of a contextual recombination of elements in the music of those composers. This EMI subprogram separates and analyzes musical pitches and durations and then mixes and recombines the patterns of these pitches and durations so that while each new composition is different, it substantially conforms to the style of the original. The fundamental problems in building a program to produce effective recombinant music are identified. The three steps used by the EMI program are discussed. They are: pattern matching for characteristics of the composers style, analyzing each component for its deep hierarchical musical function, and reassembling the parts sensitively with a technique drawn from natural-language processing. Some examples of EMIs output are examined.<<ETX>>

Computer Analysis of Musical Allusions

Computer Music Journal, 27:1, pp. 11–28, Spring 2003 2003 Massachusetts Institute of Technology. In this article I describe a computer program called Sorcerer. Sorcerer provides analytical verification of the presence of musical allusions for what I call referential analysis, a semiotic approach roughly situated between hermeneutic (interpretive) analysis (e.g., Agawu 1991, 1996; Gjerdingen 1988; Nattiez 1990) and Retian (motivic) analysis (Reti 1962). Sorcerer associates patterns found in a target work— music under study—with several potential source works—music assumed to either influence or be influenced by the target work. Sorcerer then presents these patterns as possible references or allusions. The program lists its findings without regard for whether the composer of the target work consciously or subconsciously referenced the source work, only that the found allusions exist. I further describe the possible relevance and importance of this type of analysis as a complementary approach to more standard harmonic, melodic, and formal types of analysis, as a method for performers to better interpret the music they play, and as one possible approach to the deeper understanding of meaning in music.

Experiments in musical intelligence (EMI): Non‐linear linguistic‐based composition

Abstract EMI was founded in 1983 as a project for understanding musical style. The motive for establishing it was purely selfish: the authors desire to have help in finishing a commission. He focused on how to imitate musical styles, since nothing useful could be accomplished if the computer did not understand how to produce viable music in his style. One of the components of emulating style discovered during the years of research since EMIs inception includes non‐linear composition, the focal point of this article. Results of research have been presented at the International Computer Music Conference (1987, Champaign, IL) and its resultant proceedings, at the International Symposium: Charles Ives and the American Music Tradition up to the Present (Cologne, Germany, February, 1988), the American Association of Artificial Intelligence (St. Paul, August, 1988), AIM, First International Workshop on Al and Music (Bonn, Germany, September, 1988), as well as articles in the Computer Music Journal (Winter, 198...

The Composer's Underscoring Environment: CUE

There are virtually hundreds of computer music programs currently available that are related to composition. Synthesis programs, for example, offer composers opportunities to create and modify timbres and sonic space (Loy 1989). Sequencer and notation programs provide visual and aural control over orders and playback of note sequences (Puckette 1991; Yavelow 1992). Analysis programs reveal harmonic functions, pitch set relationships, and so on (Castine, Brinkman, and Harris 1990). Composition programs generate random techniques, Markov chains, fractal and chaotic algorithms, and so on, to produce new ideas that can be used or discarded (Buxton 1978; Winsor 1987; Rowe 1993). Important as these are to composers, however, they do not offer all of the potential that computational means can provide. Many composers seek algorithmic composition in a style more akin to their own. Composing programs that offer style replication, however, are rare, and often their poor ratio of success to failure greatly diminishes their usefulness. My own EMI (Experiments in Musical Intelligence) is just such an example (Cope 1991). Even its best efforts often achieve less than satisfactory results. The majority of its works-which generally go unheard by anyone but myself--fall much further from acceptability. As well, EMI is not interactive, but rather creates works of whole cloth or fragments that cannot relate stylistically to surrounding human-composed passages. This results in large part because EMI models its compositions on rules and structures found in music located in its database. With the exception of manipulating variables associated with pattern matching for stylistic signatures, EMI users simply load databases and wait for EMI to produce new compositions. There is, then, a need for a program that offers composers the opportunity, within the same environment, to compose using all of the standard tools (notation, analysis, MIDI playback, etc.), while at the same time providing any amount of new music-a note, measure, phrase, and so on-within the current works and the composers overall style. This new music would be available at any point during composition, and would be logical and relevant to the user-created music surrounding it. Creating such a program, however, requires a composing algorithm as good as, if not better than, the current offerings. This program would need to keep a running tabulation of the melodic, harmonic, motivic, and structural content of a current work, as well as maintain an accurate sense of a composers overall ongoing style. No mean feat, this; but an enviable goal, one that I, at least, feel would constitute a true composers assistant. Users could then request algorithmically composed music to present possible solutions to certain compositional problems, indicate alternative routes at musical pivot points, extend passages experimentally, develop the potentials of composer-created germ ideas, offer new ideas when inspiration temporarily wanes, and so on. It is with these requirements in mind that I created CUE (Composers Underscoring Environment). The main advantage of CUE is that it can compose as much relevant music as desired-from a single note to an entire piece-in a composers general style as evident in the previously composed music in its database, and in the style of a work currently being composed. In addition, CUE has the notational, sequencer, and analytical tools that I and others have found useful while composing. This article, then, describes some of the principles on which CUE is based, presents a brief tour of the resources that CUE makes available, and ends with a few thoughts on how programs like CUE may serve composers in the 21st century. Computer Music Journal, 21:3, pp. 20-37, Fall 1997 ? 1997 Massachusetts Institute of Technology

Facing the Music: Perspectives on Machine-Composed Music

The author describes some of the processes required in creating Experiments in Musical Intelligence, a computer program for the simulation of musical styles. He then outlines many of the problems listeners face when attempting to deal with successful output from such programs. These problems involve redefining terms, debating humanversus computer-creativity and, ultimately, grappling with the meaning of music. This discussion includes an example from the computer-composed opera Mahler. The author argues that such music should be considered integral to mainstream humancomposed music since it results from a collaboration between humans and the machines they have created.

Algorithmic Music Composition

David Cope describes how the use of computers in the composing process is a natural outgrowth and continuation of how composers have been using algorithms for composing since the very beginning of recorded time.

One approach to musical intelligence

The author began Experiments in Musical Intelligence in 1981 as the result of a composers block (D. Cope, 1991; 1996). His initial plan involved creating a computer program that would have a sense of his overall musical style. It would track the ideas of a current work such that at any given point the author could request a next note, next measure, next 10 measures, and so on. The author hoped that this new music would not just be interesting but relevant to his style and current work. Having very little cognitive information about his style, however, the author began creating computer programs that composed complete works in the styles of classical composers, about which he knew something more concrete.

Computational Creativity and Music

In this chapter, I first define the word ‘creativity’ for the purposes of my research and then compare this definition to others found in the literature. Following this, I present two simple examples of creativity involving games—words and chess—in which I invite readers to participate. I then describe two musical situations and subsequent computer programs that, following the discussion surrounding the examples, creatively provide output as tentative proof of their success. Finally, I describe ways this software can be improved to output more elegant results.

The well-programmed clavier: style in computer music composition

A look into the workings of the Emmy and Emily Howell programs, including musical examples with pointers to where they can be heard as well as seen.