# Using Statistical Models and Evolutionary Algorithms in Algorithmic Music Composition

Ritesh Ajoodha (School of Computer Science, University of the Witwatersrand, South Africa), Richard Klein (School of Computer Science, University of the Witwatersrand, South Africa) and Maria Jakovljevic (School of Computing, University of South Africa, Pretoria, South Africa)
DOI: 10.4018/978-1-4666-5888-2.ch597

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## Background

### The Statistical Model

Conklin (2004) reviewed the process of music generation and equated it with the problem of sampling from a statistical model. One can represent a piece of music as a chain of events, which consist of music objects (e.g. notes) together with a duration and an onset time. A statistical model captures the probabilities of different musical features in a piece, given data such the genre and style. For example, in a Rock song, one is likely to see a 4/4 time signature, 5th intervals and it is rare to see notes that aren’t in the current scale. In a Jazz song however, one is likely to see the notes appearing from various modes with a variety of different time-signatures and chromatic runs. To generate music from a statistical model, one samples these different features with frequencies appropriate to the desired style. Conklin (2004) pointed out that statistical models can be beneficial but only a few sampling methods have been explored in the music generation literature.

## Key Terms in this Chapter

Genetic Algorithm (GA): A genetic algorithm is a heuristical model of machine learning that is based on the process of natural selection.

Probability of Occurrence (PO): The probability of occurrence is a static constant assigned to every music object in the Statistical Phase to produce a sample.

Statistical Phase: The Statistical Phase is the first phase of a five phased model. The Statistical Phase presents a Context free grammar and statistical model that produces an initial population.

Statistical model: A statistical model is an interpretation that uses variables and equations to show mathematical relationships.

Gaussian Distribution: Gaussian distribution, sometimes referred to as normal distribution, is a mathematical function that defines the probability of a number in some context falling between any two real constants.

Fitness Function: A fitness function is an objective function that is used to evaluate how close a given construction is to achieving the pre-determined criteria.

Context-Free Grammar (CFG): A Context-free grammar is a formal grammar in which every production rule is in the form V ? u, where V is a single non-terminal symbol and u is a string of terminal and/or non-terminal symbols, u can also be empty.

Genetic Phase: The Genetic Phase is the second phase of a five phased model. The Genetic Phase presents a genetic algorithm that refines a statistical sample through a fitness function and genetic operators over a number of generations.

Music Representation: A notational portrayal of acoustic music.

Note Counting: Is a procedure where a scale counter for a corresponding scale counts the occurrences of each note in the sample that belong to the corresponding scale. The corresponding scale with the largest counter value is returned.

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