Music composed and performed by computers

Later, composers such as Gottfried Michael Koenig had computers generate the sounds of the composition as well as the score. Koenig produced algorithmic composition programs which were a generalisation of his own serial composition practice. This is not exactly similar to Xenakis' work as he used mathematical abstractions and examined how far he could explore these musically. Koenig's software translated the calculation of mathematical equations into codes which represented musical notation. This could be converted into musical notation by hand and then performed by human players. His programs Project 1 and Project 2 are examples of this kind of software. Later, he extended the same kind of principles into the realm of synthesis, enabling the computer to produce the sound directly. SSP is an example of a program which performs this kind of function. All of these programs were produced by Koenig at the Institute of Sonology in Utrecht, Holland in the 1970s.
Procedures such as those used by Koenig and Xenakis are still in use today. Since the invention of the MIDI system in the early 1980s, for example, some people have worked on programs which map MIDI notes to an algorithm and then can either output sounds or music through the computer's sound card or write an audio file for other programs to play.
Some of these simple programs are based on fractal geometry, and can map midi notes to specific fractals, or fractal equations. Although such programs are widely available and are sometimes seen as clever toys for the non-musician, some professional musicians have given them attention also. The resulting 'music' can be more like noise, or can sound quite familiar and pleasant. As with much algorithmic music, and algorithmic art in general, more depends on the way in which the parameters are mapped to aspects of these equations than on the equations themselves. Thus, for example, the same equation can be made to produce both a lyrical and melodic piece of music in the style of the mid-nineteenth century, and a fantastically dissonant cacophony more reminiscent of the avant-garde music of the 1950s and 1960s.
Other programs can map mathematical formulae and constants to produce sequences of notes. In this manner, an irrational number can give an infinite sequence of notes where each note is a digit in the decimal expression of that number. This sequence can in turn be a composition in itself, or simply the basis for further elaboration.
Operations such as these, and even more elaborate operations can also be performed in computer music programming languages such as Max/MSP, SuperCollider, Csound, Pure Data (Pd), Keykit, and ChucK. These programs now easily run on most personal computers, and are often capable of more complex functions than those which would have necessitated the most powerful mainframe computers several decades ago.

Diagram illustrating the position of CAAC in relation to other Generative music Systems

There exist programs that generate "human-sounding" melodies by using a vast database of phrases. One example is Band-in-a-Box, which is capable of creating jazz, blues and rock instrumental solos with almost no user interaction. Another is Impro-Visor, which uses a stochastic context-free grammar to generate phrases and complete solos.
Another 'cybernetic' approach to computer composition uses specialized hardware to detect external stimuli which are then mapped by the computer to realize the performance. Examples of this style of computer music can be found in the middle-80's work of David Rokeby (Very Nervous System) where audience/performer motions are 'translated' to MIDI segments. Computer controlled music is also found in the performance pieces by the Canadian composer Udo Kasemets (1919-) such as the Marce(ntennia)l Circus C(ag)elebrating Duchamp (1987), a realization of the Marcel Duchamp process piece Music Errata using an electric model train to collect a hopper-car of stones to be deposited on a drum wired to an Analog:Digital converter, mapping the stone impacts to a score display (performed in Toronto by pianist Gordon Monahan during the 1987 Duchamp Centennial), or his installations and performance works (e.g. Spectrascapes) based on his Geo(sono)scope (1986) 15x4-channel computer-controlled audio mixer. In these latter works, the computer generates sound-scapes from tape-loop sound samples, live shortwave or sine-wave generators.