![]() ![]() ![]() This book presents a novel viewpoint on automatic sequences, and more generally on combinatorics on words, by introducing a decision method through which many new results in combinatorics and number theory can be automatically proved or disproved with little or no human intervention. Clearly not all composers have such a carefree attitude about choosing “the actural notes,” but the use of algorithms as a composer’s assistant is gaining acceptance in many musical circles.Īutomatic sequences are sequences over a finite alphabet generated by a finite-state machine. Part of the appeal of algorithmic techniques is the possibility that the composer can focus on the essence of a piece, its form and deep structure, while the algorithm takes care of surface details like the actual notes. In the twentieth century, serial composers have openly employed algorithmic techniques, and many composers, for example Cage and Xenakis, have composed aleatoric or “chance” music using random number generators. Mozart, whose parlor game Musikalisches Würfelspiele allows players to compose minuets with the aid of a pair of dice, is a slightly more recent example of a composer who was a least intrigued by the idea of algorithmic composition. In the 1400’s Guillaume Dufay experimented with “formal processes” and even composed a piece using the golden mean. Algorithmic composition dates to around 1026, when Guido d’Arezzo used vowels in the text of a choral piece to determine the pitches in the melody. ![]()
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