Algorithm

An algorithm informally refers to a series of steps or instructions that can be followed for solving a problem. The formal definition of an algorithm arises from its origins in computer science. According to the formal definition, there are five main characteristics of an algorithm. Algorithms (1) are well ordered, (2) consist of unambiguous operations, and (3) consist of computable operations. In other words, there is a correct order in which the steps or instructions for solving a problem need to be followed. These instructions are clear enough such that they need not be further simplified. They are doable and not impossible to compute. Additionally, algorithms (4) produce a result (5) in a finite amount number of steps. These characteristics allow an algorithm to be implemented as a computer program for carrying out a process with a specific solution or goal in mind. One of the main advantages an algorithm offers is the ability to automate an activity. Given this advantage, algorithms are widely used in music composition.

Algorithms for music composition differ in several ways. They may differ with respect to the domain in which they compose. Some algorithms compose music and output the composition in the form of music notation or another symbolic format, whereas other algorithms output their compositions as audio. Algorithms may range from simple to complex. A simpler algorithm might compose melodies based on a set of pitch classes restricted to a specific scale. A more complex algorithm might compose melodies based on constraints imposed by music theory regarding melodic structure and harmony. In such a case, the rule-set to be followed by the algorithm will be larger and more complex.

Algorithms may differ in terms of the purpose they serve in composition. They may be used to replicate only certain aspects of composition and aid a person in the composition of a larger piece of music. For instance, an algorithm's task might involve ensuring that a composition adheres to a specific style or genre of music. In such a case, the algorithm might compare all the pitch classes and pitch class intervals in a melody composed by a person against a set of prior occurrence probabilities of pitches and intervals for that specific musical style based on a database of music. Then it could flag pitch classes and intervals that fall below a certain threshold and thus assist the composer by imposing constraints. Another example might involve an algorithm generating the composition entirely on its own by replicating the style of a specific composer, based on analysis of a selected data set of examples.