3.1 Probabilities

The idea of devising systems for composing music using randomness has always fascinated composers, especially after the invention of the computer. But the raw outcome of a random process seldom fulfils of the expectations of exigent composers: they often prefer to assess its suitability for inclusion in their music according to their aesthetic preferences and musical aims. The conditions under which the randomly generated elements are used are therefore crucial for a composition.

The reason that randomness has gained so much popularity in the computer age is probably because computers can actually do better than just throwing a die or tossing a coin: they can be programmed to perform testing on the randomly produced material in order to assess its suitability for the piece in question. Moreover, as an alternative to the random-and-test process, musicians can design programs that embed compositional constraints within the random process itself. One way to do this is to use probabilities.

Chapter 2 introduced the fundamentals of probabilities and the concept of a fair trial, that is, the case in which the chances for obtaining a specific outcome are the same for all possible outcomes. There is no favouritism in a fair trial; for example, whilst the prediction of the outcome from rolling a die is fair, the same is not true for a football match between a strong and a weak team. Note that in this case the information about the past performance of the two teams is taken into account...