By Gerhard Nierhaus

Algorithmic composition – composing through formalizable tools – has a century previous culture not just in occidental song background. this can be the 1st publication to supply a close evaluation of popular methods of algorithmic composition in a practical manner instead of by way of treating formalizable elements in unmarried works. as well as an old assessment, every one bankruptcy provides a particular type of set of rules in a compositional context by means of offering a basic creation to its improvement and theoretical foundation and describes varied musical functions. every one bankruptcy outlines the strengths, weaknesses and attainable aesthetical implications as a result of the appliance of the handled methods. issues coated are: markov versions, generative grammars, transition networks, chaos and self-similarity, genetic algorithms, mobile automata, neural networks and synthetic intelligence are lined. the great bibliography makes this paintings excellent for the musician and the researcher alike.

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Leibniz, an admirer of Chinese culture and striving for an intellectual exchange, described his system in 1701 in a letter addressed to Jesuit padres Joachim Bouvet and Claudio Filipo Grimaldi, who worked as mathematicians for the Chinese emperor. In November of the same year, Bouvet answered Leibniz with reference to the binary structure of the “I Ching,” 5 whose different hexagrams (in this context, a symbol consisting of six lines) are only represented by two symbols. Although all hexagrams in the “I Ching” are made of only two symbols, they cannot be used for representing information outside of the concrete context.

12 From the Loom to the “Analytical Engine” Leibniz’ idea of applying the binary numeral system to an automaton was realized by an invention in the textile industry. In the year 1725, Basile Bouchon developed the first system for an automatic control of looms. Information about raising and lowering the warp threads is transmitted via punched holes in paper tapes. In 1728, Jean Baptiste Falcon replaced the fragile paper tapes with punched wooden boards. The boards, like the paper tapes, must be fed manually; an automatic control mechanism was only developed by the automata constructor Jacques de Vaucanson in 1745.

15 shows this principle with the help of the multiplication of 2357 * 7. ” The result comes from the addition of the digits within the diagonals. For multi-digit multiplications, the partial products are added. In division, the quotient is obtained stepwise by indicating all products of the respective divisor. Caspar Schott (1608–1666), Jesuit padre and professor of mathematics at W¨urzburg University, described in his “Organum Mathematicum” of 1668, containing a detailed description of the “mathematical organ” of his teacher Kircher, a mechanical arrangement of Napier’s bones.

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