Algorithmic Composition (eBook)

Acknowledgements 5
Contents 7
Introduction 11
References 16
Historical Development of Algorithmic Procedures 17
2.1 Interdependencies 17
2.2 Development of Symbol, Writing System and Numeral System 19
2.3 Much Ado About Nothing – The Development of the Zero 23
2.4 The Formalization of Thinking Processes 25
2.5 A Truth Machine from the 13th Century 27
2.6 Early Approaches to Algorithmic Composition 31
2.7 A Utopia of an All-Embracing Representation of Knowledge 36
2.8 Calculating Machines 38
2.9 A New Numeral System for Automated Calculations 43
2.10 Replacing the Mechanistic Determinism 44
2.11 Language and Music Generators – A Book of Books 46
2.12 From the Loom to the Analytical Engine” 49
2.13 The Implementation of Logical Operations 54
2.14 On Formally Undecidable Propositions 55
2.15 From Census Collector to ChessWorld Champion 58
2.16 Automata and Computability 68
2.17 The Model of a Universal Computer 71
2.18 Programming 72
2.19 The Computer in Algorithmic Composition 73
References 75
Markov Models 77
3.1 Theoretical Basis 78
3.2 Hidden Markov Models 79
3.3 Markov Models in Algorithmic Composition 81
3.4 Hidden Markov Models in Algorithmic Composition 87
3.5 Synopsis 91
References 92
Generative Grammars 93
4.1 Generative Grammars as a Model of the Theory of Syntax 94
4.2 Generative Grammars in Algorithmic Composition 101
4.3 Synopsis 127
References 128
Transition Networks 131
5.1 Experiments in Musical Intelligence 132
5.2 Petri Nets 137
5.3 Synopsis 139
References 140
Chaos and Self-Similarity 141
6.1 Chaos Theory 141
6.2 Strange Attractors 144
6.3 Fractals 145
6.4 Lindenmayer Systems 147
6.5 Chaos and Self-Similarity in Algorithmic Composition 154
6.6 Lindenmayer Systems in Algorithmic Composition 158
6.7 Synopsis 163
References 165
Genetic Algorithms 167
7.1 The Biological Model 167
7.2 Genetic Algorithms as Stochastic Search Techniques 168
7.3 Genetic Programming 171
7.4 Genetic Algorithms in Algorithmic Composition 174
7.5 Synopsis 192
References 194
Cellular Automata 197
8.1 Historical Framework and Theoretical Basics 197
8.2 Types of Cellular Automata 199
8.3 Cellular Automata in Algorithmic Composition 205
8.4 Synopsis 211
References 213
Artificial Neural Networks 215
9.1 Theoretical Basis 216
9.2 Historical Development of Neural Networks 217
9.3 The Architecture of Neural Networks 218
9.4 Artificial Neural Networks in Algorithmic Composition 223
9.5 Synopsis 231
References 232
Artificial Intelligence 235
10.1 Algorithmic Composition in AI 238
10.2 Synopsis 264
References 265
Final Synopsis 269
11.1 Algorithmic composition as a genuine method of composition 269
11.2 The dominance of style imitation in algorithmic composition 272
11.3 Origins and characteristics of the treated procedures 274
11.4 Strategies of encoding, representation and musical mapping 276
11.5 The evaluation of generated material 279
11.6 Limits of algorithmic composition 280
11.7 Transpersonalization and systems of universal” validity 282
11.8 Concluding remark 282
References 283
Index 285

Chapter 7 Genetic Algorithms (p. 157-158)

Genetic algorithms as a particular class of evolutionary algorithms, i.e. strategies modeled on natural systems, are stochastic search techniques. The basic models were inspired by Darwin’s theory of evolution. Problem solving strategies result from the application of quasi-biological procedures in evolutionary processes. The terminology of genetic algorithms including “selection,” “mutation,” “survival of the fittest,” etc. illustrates the principles of these algorithms as well as their conceptual proximity to biological selection processes.

In the initial stages of their development, these principles took shape in two different models: From the 1960s on, Ingo Rechenberg and Hans-Paul Schwefel introduced the evolution strategies at the Technical University of Berlin, and in the 1970s, the Americans John H. Holland and David E. Goldberg developed genetic algorithms. Rechenberg and Schwefel’s models are based upon a graphic notation and were modeled on biological procedures for the development of technical optimization techniques. Holland and Goldberg’s genetic algorithms use the principles of coding and transmission of data in biological systems for modeling search strategies. These two approaches developed, to a great extent, separately from each other. For application in music, the problem solving strategies of the “American school” are applied, and for this reason, Rechenberg’s model will not be explained here in detail.

7.1 The Biological Model

DNA in a cell consists of chromosomes that are made up of genes. Genes describe amino acid sequences of proteins and are responsible for the development of different traits that become manifest in different ways by transferring genetic information. The total complement of genes is referred to as a genome. The entirety of an individual’s hereditary information is known by the term genotype and the specific manifestation of his or her features called a phenotype. Genetic variability is ensured by a population with differing genetic characteristics as well as a continuous adaptation to changing environmental conditions. Genetic variations are caused by a process called meiosis, by which the hereditary disposition of the parents is allocated differently to the cells off the offspring, as well as by mutation of the genes, chromosomes or the whole genome. According to Darwin’s theory of evolution, the competing behavior of living organisms promotes the passing on of the genetic information of the fittest, meaning those organisms best able to survive in a particular environment. Consequently, this leads to the survival of the fittest, a term which can also be found in the terminology of genetic algorithms as the fitness function.

7.2 Genetic Algorithms as Stochastic Search Techniques

Genetic algorithms, which model the evolutionary processes in computer simulation, are methods that are used to solve search and optimization problems. For the application of a genetic algorithm, domain-specific knowledge of the problem to be solved is not necessary. Therefore, this class of algorithms is especially suitable for tasks that are difficult to model mathematically or for problem domains that do not have an explicit superior rule system.

By analogy to the biological model, the respective computer program serves as the habitat that provides particular conditions for surviving and heredity. In this artificial living space, populations of individuals, or chromosomes, are produced whose adaptation to an objective, referred to as objective score, is examined by means of a fitness function.