Algorithmic Composition: Paradigms of Automated Music by Gerhard Nierhaus

By Gerhard Nierhaus

Algorithmic composition – composing via formalizable tools – has a century outdated culture not just in occidental tune background. this can be the 1st ebook to supply an in depth evaluation of trendy strategies of algorithmic composition in a practical means instead of through treating formalizable elements in unmarried works. as well as an ancient assessment, every one bankruptcy offers a selected type of set of rules in a compositional context through offering a common advent to its improvement and theoretical foundation and describes various musical functions. each one bankruptcy outlines the strengths, weaknesses and attainable aesthetical implications caused by the appliance of the handled techniques. themes coated are: markov versions, generative grammars, transition networks, chaos and self-similarity, genetic algorithms, mobile automata, neural networks and synthetic intelligence are lined. the excellent bibliography makes this paintings perfect for the musician and the researcher alike.

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9 A New Numeral System for Automated Calculations 33 The first mass-produced calculating machine was the “Arithmom`etre” of Xavier Thomas de Colmar (1785–1870) patented in 1820 and built in a run of over 18,000 pieces. ” This handy four operations Fig. ” Photo Herbert Matis. With kind permission of Herbert Matis. machine (all basic arithmetic operations can be carried out) was developed by the Austrian producer of calculating machines Curt Herzstark from 1935 on and is the last mechanical competitor of the pocket calculators, appearing in the 1970s.

Napier’s abacus, also known as Napier’s bones, or Napier’s rods, consists of rods with product rows printed on each side where the digits of the numbers are separated by diagonal lines. 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.

The predicate refers to the name of characteristics, relations and classes, such as verbs, adjectives or similar. For objects unknown at the moment, variables are introduced. Symbols telling how many objects the predicate is asserted are known as quantifiers. The universal quantifier refers to all objects, whereas the existential quantifier refers to at least one object in the domain of discourse. Through further development by Bertrand Arthur William Russell (1872–1970) and Alfred North Whitehead (1861–1947), the predicate calculus becomes an instrument of fundamental mathematical research, whose objectives lead to polarizations among scientists.

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