ALGORITHMS IN MUSIC Algorithmic composition is defined as the creation of music by methodical procedures. Although algorithmic processes are not new to composition, computer processing has made many algorithms in musical contexts more sophisticated. Systematic processes are by their very nature algorithmic. From this perspective, algorithmic ideas can be found in music from as far back as the Middle Ages. For example, canons are a musical genre composed with recurring melodic patterns based on imitation. A traditional canon in two voices will consist of two superimposed melodies. The first melody provides a basic intervallic construct for the second melody. The algorithmic instructions for creating a canon might read as follows: take a melody, duplicate it, then superimpose the two melodies so that the melodies create a counterpoint; that is, the melodies are concurrent with each other, but not synchronized by the same starting time. Some canons are also unified by proportional rhythmic durations called mensuration canons (see Ockeghem's Missa Prolationem or Josquin des Pres' Agnus Dei from L'Homme Arme Mass). Other types of canons might be built on melodic variations from inversions and retrogrades (see J.S. Bach Musical Offering). Machaut's rondeau Ma fin est mon commencement uses a palindrome to illustrate how my end is (truly) my beginning. Through the ages, composers such as J.S. Bach, Mozart, F.J. Haydn, Debussy, Ravel, Messiaen, Cage, and Nancarrow are credited with using systematic operations. Since the 1950's, composers like Lejaren Hiller, James Tenney, and Iannis Xenakis designed algorithms with the help of computers and complex calculations to create a new and innovative music based on pre-compositional resources: stochastic formulas, aleatoric methods, genetic algorithms, fuzzy logic, pattern matching, spectral modeling, and artificial intelligence. Two primary algorithm classes prevail: deterministic and probabilistic. Deterministic procedures generate music by non-random selection. Probabilistic procedures integrate random choice in decision making. Sources: Cope, David. Techniques of the Contemporary Composer. U.S.: Schirmer, 1997. Roads, Curtis. The Computer Music Tutorial. Cambridge: MIT Press, 1996. AlgorithmHistory Links ----------------- Algorithms in Music ----------------- Algorithms in Math ----------------- Algorithms in Science ----------------- Algorithms and Computers