Editing Computer music (section)

===Music composed and performed by computers===
{{Main|Algorithmic composition}}

{{See also|Generative music|Evolutionary music|Genetic algorithm}}
Later, composers such as [[Gottfried Michael Koenig]] and [[Iannis Xenakis]] had computers generate the sounds of the composition as well as the score. Koenig produced [[algorithmic composition]] programs which were a generalization 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]] in the 1970s.<ref>{{cite journal|last=Berg|first=Paul|author-link=Paul Berg (composer)|title= Abstracting the future: The Search for Musical Constructs |journal=[[Computer Music Journal]]|year=1996|volume=20|issue=3|pages=24–27 [11]|publisher=[[MIT Press]]|doi=10.2307/3680818|jstor=3680818}}</ref> In the 2000s, [[Andranik Tangian]] developed a computer algorithm to determine the time event structures for [[Canon (music)|rhythmic canons]] and rhythmic fugues, which were then "manually" worked out into harmonic compositions ''Eine kleine Mathmusik I'' and ''Eine kleine Mathmusik II'' performed by computer;<ref>{{Cite journal|last=Tangian|first=Andranik|author-link=Andranik Tangian|year=2003|title=Constructing rhythmic canons|journal=[[Perspectives of New Music]]|volume=41|issue=2|pages=64–92|url=http://repmus.ircam.fr/_media/mamux/papers/tangian-2003-pnmcanons.pdf|access-date=January 16, 2021|archive-date=24 January 2021|archive-url=https://web.archive.org/web/20210124090024/http://repmus.ircam.fr/_media/mamux/papers/tangian-2003-pnmcanons.pdf|url-status=dead}}</ref><ref>{{Cite book|last=Tangian|first=Andranik|author-link=Andranik Tangian|year=2010|title=IRCAM, Seminaire MaMuX, 9 February 2002, Mosaïques et pavages dans la musique|chapter=Constructing rhythmic fugues (unpublished addendum to ''Constructing rhythmic canons'')|url=http://repmus.ircam.fr/_media/mamux/saisons/saison01-2001-2002/tangian_2002-2003_einekleinemathmusik_1-2_with-articles.pdf|access-date=January 16, 2021|archive-date=22 January 2021|archive-url=https://web.archive.org/web/20210122043156/http://repmus.ircam.fr/_media/mamux/saisons/saison01-2001-2002/tangian_2002-2003_einekleinemathmusik_1-2_with-articles.pdf|url-status=dead}}</ref>
for scores and recordings see.<ref>{{Cite book|last=Tangian|first=Andranik|author-link=Andranik Tangian|year=2002–2003|title=IRCAM, Seminaire MaMuX, 9 February 2002, Mosaïques et pavages dans la musique|chapter=Eine kleine Mathmusik I and II|url=http://repmus.ircam.fr/mamux/saisons/saison01-2001-2002/2002-02-09|access-date=January 16, 2021|archive-date=21 January 2021|archive-url=https://web.archive.org/web/20210121042242/http://repmus.ircam.fr/mamux/saisons/saison01-2001-2002/2002-02-09|url-status=dead}}</ref>