Editing Algorithmic composition (section)

===Hybrid systems===
Programs based on a single algorithmic model rarely succeed in creating aesthetically satisfying results. For that reason algorithms of different type are often used together to combine the strengths and diminish the weaknesses of these algorithms. Creating hybrid systems for music composition has opened up the field of algorithmic composition and created also many brand new ways to construct compositions algorithmically. The only major problem with hybrid systems is their growing complexity and the need of resources to combine and test these algorithms.<ref>{{Cite book |last=Harenberg |first=Michael |url=https://www.worldcat.org/oclc/21132772 |title=Neue Musik durch neue Technik? : Musikcomputer als qualitative Herausforderung für ein neues Denken in der Musik |date=1989 |publisher=Bärenreiter |isbn=3-7618-0941-7 |location=Kassel |oclc=21132772}}</ref>

Another approach, which can be called ''computer-assisted composition'', is to algorithmically create certain structures for finally "hand-made" compositions. As early as in the 1960s, [[Gottfried Michael Koenig]] developed computer programs ''Project 1'' and ''Project 2'' for [[aleatoric music]], the output of which was sensibly structured "manually" by means of performance instructions. In the 2000s, [[Andranik Tangian]] developed a computer algorithm to determine the time event structures for [[Canon (music)|rhythmic canons]] and rhythmic fugues,<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}}</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|chapter=Constructing rhythmic fugues (unpublished addendum to ''Constructing rhythmic canons'')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}}</ref>
which were then worked out into harmonic compositions ''Eine kleine Mathmusik I'' and ''Eine kleine Mathmusik II''; 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}}</ref>