to apply them to the computational field. These ... making an aesthetic evaluation of each theme in the ... elements, such as musical sequences or themes.
Evolutionary Computation Systems for Musical Composition Antonino Santos, Bernardino Arcay, Julián Dorado, Juan Romero, Jose Rodriguez Information and Communications Technology Dept. University of A Coruña Faculty of Computer Science- CP15071 A Coruña. Spain
Abstract: - This work shows a perspective of the different researches on musical composition using evolutionary techniques. It is made a classification based on the critic element of the different compositions. Four types of works are analyzed: Interactive, based on examples, rule-based and autonomous ones. Finally it is proposed the integration of the several works in a common frame, where different approaches can compete and/or collaborate to create global compositions that can be adapted to different types of music, and so include the advantages of the different techniques. Key-Words: - Evolutionary Computation, Adaptive Systems, Artificial Neural Networks, Artificial Intelligence, Musical Composition.
1 Introduction Musical composition has been studied for a long time using every kind of computational techniques, including Expert Systems, Artificial Neural Networks (ANNs), statistic and stochastic methods for musical composition. However, many researches have been carried out in recent years which suggest the creation of artificial systems of musical composition, from different approaches, using evolutionary techniques.
2 Interactive Systems The first category to be dealt with in this classification is that of Interactive Systems.
Fig. 1 The user acts as critic of the system’s compositions
Evolutionary computation is inspired by nature, taking some features of the evolution process in order to apply them to the computational field. These techniques started with Holland’s work  in 1975. These techniques offer different solutions to a given problem, and the most highly adapted ones give rise to new generations of solutions through crossover, mutation and selection genetic operators. Evolutionary Computational Systems have proved to be very accurate in those fields which require a certain degree of creativity . Such is the case of the tasks related to visual        and musical art, as it will be explained in this paper. Two roles may be distinguished in a musical composition system, as in any system of artistic creation: Creator and Critic (Author and Audience). The works presented in this article have been organized according to the critic’s role, while the creator’s role has always been played by an evolutionary computational system. For a deep analysis of some of these implementations, see Burton  and Todd .
In this kind of system, the critic is a human being, making an aesthetic evaluation of each theme in the system and thus conducting its evolution. The system takes these evaluations into account for the creation of the next compositions. The user’s conducting role can be played by a single person or by a group, in the latter case, a group of people assesses the cybernetic composer’s works simultaneously. These systems, in their simplest form, pose the problem of time cost  (or bottleneck ) due to human participation. This problem may also tire the user, who has to evaluate a great number of musical examples. Besides, many researches think that these systems also have a high degree of subjectivity. On the other hand, the direct incorporation of the user allows to compose works with the right aesthetic conception for the individual or group with whom the system interacts.
Within this group, we may distinguish a whole set of systems which extract from a series of previous elements, such as musical sequences or themes.
one instrument, and it can only use the crossover operator with musicians which have the same instrument. The user evaluates each work as a whole.
Ralley’s works  can fit within this category, in which a genetic algorithm generates tunes which are variations of a melody given by the user. In this work, the melodies are limited to 12 notes of one octave. The representation is divided into two parts, the first one comprises information about the Key signature and the starting note of the phrase, the second one comprises integers which define intervals between consecutive pitches.
GaMusic is a system using a simple genetic algorithm in order to develop melodies. The user may configure the frequency of mutation and crossover, and he/she may also apply different scores to the melodies in order to conduct their evolution. The information representation is directly done using two octave notes, with a maximum duration of 30 notes.
Jacob’s works   can also be included within this category. There are several layers in this work. In the first place, an evolutionary critic is interactively adjusted by the critic’s and user’s evaluation of musical pieces. Next, the critic selects fragments generated by a stochastic process (or given by the user) as input to another module which unites them into phrases. This second evolutionary model also entails the user’s adjustment. In Biles’s work , the system, named GenJam, generates a series of musical motives from the user’s evaluation, who acts as a censor, and some genetic operators adapted to the musical field (transposition, etc.) Based on these motives, and from Jazz solos played by another user who acts as interpreter, new solos are generated. There is a version of this system called GenJam Populi  in which a group of people judges the solos generated by the system.
Other similar examples in the field of sound synthesis are the works by Johnson  , where genetic algorithms are used to develop sounds from the granular synthesis method incorporated by Csound. The user marks the results obtained, and the system adjusts the parameters of this synthesis technique. This technique is complex and difficult to adjust.
3 Systems based on examples The possibility of registering the user’s tastes within a subsystem was suggested in some instances, with a double purpose. The first would be facilitating the system’s learning rate, and using the present musical works to conduct it. The second would be solving the problems of interactive systems related to slowness and specialization.
There are other types of works which do not use initial musical information. Some of these works approach the problem of the composition of rhythmic themes. Horowitz  presents in his work several approaches to the generation of rhythmical textures with genetic algorithms. Each generated theme can be evaluated in the system, or the selected theme can be defined according to high-ranked musical parameters (sincopation, density, etc.) or else a group of themes, representing rhythmical clusters formed according to the aforementioned parameters, can be evaluated. The implementation also tests direct rhythm representations or through a series of intermediate parameters. Another implementation framed within the rhythmic dominion is Tribu   , which is a system inspired by the most primitive music, creating tribes of musicians. Each musician in the tribe is linked to
Fig.2 The user introduces a series of examples in order to train the ANN, which will work as a critic of the evolutionary system’s compositions.
This subsystem is usually integrated by an ANN trained from musical themes. These themes are examples of some musical style or author, or else they stem from some interactive system. We may quote Burton’s and Vladimirova’s   works as examples of this type of system which uses an ARTMAP  network that classifies rhythmical songs made with rhythm boxes. This network creates a cluster of rhythmical sequences, adding new
categories if the theme does not fall into one of the already-existing categories. Other examples of this type in which Multi Layer perceptrons are used, are Spector’s and Alpern’s works   which incorporated genetic programming. In this system, the individuals are functions which generate a new fragment from the previous one. Extracts from Charlie Parker’s compositions were used for training the ANN. A version of Biles’s system  was also implemented, which includes a Multi Layer Perceptron with three layers for the evaluation . This system includes a series of high 1evel musical parameters extracted from the sequences generated to train the ANN. Another example, is the one developed by Gibson et al. , where a system which generates small compositions using diatonic, four-part Western harmony is described. The system works in two steps. In the first one, rhythmical patterns are created and, in the second one, tonal information is added. In the first step, the system uses an ANN as evaluation function for the rhythmical patterns generated by a GA. Two ANNs are used in the second step in order to generate the pitches associated with each stroke of the rhythmical pattern.
A similar system is the one shown by McIntyre . This system harmonizes voices according to 4 voice Baroque harmony, using a voice given by the user. The evaluation function has three layers, the first one examines the correction of the chord, the second one analyzes the harmonic movement between notes, and the third one the smoothness of chord changes. Wiggin’s article   also includes a system which generates Jazz solo instrumentals. The evaluation function rules are extracted from music books and informal statistic analysis of Jazz solos, and from the authors’intuitive ideas. Golberg’s work , offers a system for composing minimalist music. This system stems from a source theme and a target theme given by the user. The system carries out a series of transitions between the two themes using an evolutionary procedure and following a series of rules which define the musical links between two sequences.
5 Autonomous Systems The radical change in the separation between system and user occurs in those systems which have their own autonomous aesthetics. In this case, musical works evolve following their own path, which may have nothing to do with human aesthetics. They are usually regarded as models of social evolution.
4 Rule-based Systems In rule-based systems, the critic is built from a set of rules which conduct the system. This set of rules is built by the system’s author from his/her musical knowledge or from musicological studies.
Fig.3 The user defines a set of rules used to evaluate the system’s compositions.
Examples of this kind of system can be found in Wiggin’s work   , which harmonizes choirs, using as reference the soprano tune given by the user. The system creates the three other voices. The notes are represented according to scale degrees, and the octaves are distinguished by associated integers. It uses musical-field adapted operators. The evaluation rules are given by the authors from classical harmony.
Fig.4 In this case, composer and critic are part of the system, and they evolve simultaneously.
As an example of this kind of system, we may quote the work by Peter M. Todd  , who developed a system based on Co-evolution, where a group of elements work as evaluators and others work as composition creators, while both evolve simultaneously. The synergy of both groups creates musical evolution. Other works use techniques related to evolutionary systems, such as artificial life and cellular automatons. This is the case of McAlpine’s work , which consists of a system called CAMUS3D, based on Conway’s Game of Life in 3D, for generating compositions according to the positions occupied by the elements in the virtual world. The user may define a series of probabilities of different musical parameters such as pitch, duration, etc.
In other work which uses these techniques, Eduardo Miranda’s , shows a system of granular synthesis in which the user defines a series of parameters such as the waves to be used, the number of oscillators, etc.
6 Hybrid systems Finally, it is relevant to comment on the possibility of using more than one approach in one system simultaneously. In this way, some of the problems independently solved by the different approaches could be efficiently solved by compensating them with features from another approach.
Fig.5 This figure shows, on the left, the use of different paradigms in a single system. On the right, the integration of systems from different approaches within a common environment is represented.
The left part of Fig.5 shows this possible integration in which a given system could implement some the different types of critics seen up to this point. As an example of this approach, we could quote the GeNotator system , a system which creates musical compositions using genetic algorithms. The user may define a set of rules in order to reduce the searching space previous to the user’s evaluation. In this case, there are two critics of the system: the user and the rules. Another kind of integration would consist of the creation of environments in which the various types of systems could exist. This is shown on the right part of Fig.5, in which each shape inside the rectangle represents a system with some of the features of the left square. In this environment, the different systems would collaborate and/or compete in the elaboration of compositions.
7 Conclusions The state of the Art shown in this paper reflects the thriving moment that this research field is going through. There is a promising diversity, quantity and quality of works.
Therefore, presently we are able to tackle the construction of global musical composition systems capable of creating different types of music according to different musical styles. But it would be desirable that these systems could adapt themselves dynamically to the tastes of the users interacting with them. One of the problems in this field is the high degree of dispersion of these works, given that there are few conferences on this specific area. This makes the spread of field-work difficult. But this situation is beginning to change, thanks to conferences such as the “Musical Creativity” Symposium, which is part of AISB’99, and GAVAM, which is part of GECCO’2000. These events will also enable a closer collaboration among researchers. In order to facilitate this common work, at RNASA lab (Artificial Neural Networks and Adaptive Systems Laboratory) we are currently working on a  environment based on an artificial life philosophy, in which various evolutionary musical composition works and various human users can be integrated via the Internet.
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