Index abacus, 28 as a compositional language, 261–262 abductive reasoning, 235 conditions and classes, 2 Accadians, 11 definitions, 2 Ackermann, Wilhelm, 46 etymology, 2 action potential, 205 algorithmic composition activation function, 206 as style imitation or as a genuine method of Adaline, 208 composition, 259–264 Ada programming language, 43 aspects of creativity, 261–263, 272 adaptive linear element, see Adaline evaluation of results, 269–270 adaptive network architecture, 209 Allan, Moray, 78 adaptive resonance theory, see self-organizing Allen, Paul, 56 map Alpern, Adam, 172, 174–175 additive number system, 11 alphabet, 59, 84 additive rhythmic, 45 Altair 8800, 56 Adjukiewicz, Kasimierz, 84 Alto, 56 Afghan lute, 101 Ames, Charles, 241 agent, 252–254 anagram, 38 autonomous, 252 analysis, 7 continuous, 252 Analytical Engine, 41–43 interactional, 252 analytical geometry, 7 personality, 252 Anderson, Peter G., 177 situated, 252 Andronicus of Rhodes, 15 agogic, 221, 251 ANN, see artificial neural network Agon, Carlos, 240 Anselm of Canterbury, 17 Agostini, Philippe, 64 Apple I, 57 Ahlback,¨ Sven, 96 Apple Man, 136–138 Aiken, Howard H., 4, 50, 54 applicative programming languages, 62 A ja jait, 101 Aquinas, Thomas, see Thomas Aquinas al Khowarizmi, see al-Khwarizmi Arca Musarithmica, 25 Alamos National Laboratory, 55 Arca Musurgia, 25 Albertus Magnus, 17 Archimedes, 8 aleatorics, 39 Arcos, Joseph L., 251–252 Alexander de Villa Dei, 2 Ardeen, John, 56 Alexander the Great, 13 Aristotle, 14–17, 28 Algol 60, 84 Arithmometre,` 33 Algorismi de numero Indorum, 2 Ars Antiqua, 23 algorithm Ars Cantus Mensurabilis, 23 275 276 Index Ars conjectandi, 7 BandInABox, 262 Ars Magna, 17, 24, 272 Banks, Bruce, 141 Ars Nova, 23 Baroni, Mario, 98–100 ART, see self-organizing map Barr, Avron, 228 articulation, 241 Basic, 63 artificial intelligence, 5, 225–228, 264, 265 bass arpeggiation, 93 applications in algorithmic composition, 228 Bassbrechung, 93 artificial life-forms by genetic algorithm, Baum-Welch algorithm, 71, 80 180–182 bayesian network, 236 artificial neural network, 5, 264, 265 bayesian reasoning, 236 applications in algorithmic composition, Bays, Carter, 188 213–221 Becker, Alton, 100 architecture, 208–213 Becker, Judith, 100 as fitness evaluator, 172, 175, 177 Begriffsschrift, 45 history, 207–208 Bel, Bernard, 101–106, 228 theory, 205–207 Belar, Henry, 71 ARTMAP, see self-organizing map belief network, see bayesian network assembly languages, 62 Bellgrad, Matthew, 219–220 Atanasoff, John V., 54 Berkeley, George, 9 Atanasoff–Berry Computer, 54 Bernoulli, Daniel, 67 Atari, 57 Bernoulli, Jakob, 7 ATN, see augmented transition network Bernstein, Sergey N., 68 atomists, 14 Berry, Clifford Edward, 54 attractor, 134 Beyls, Peter, 195 dimension, 134 bias, 208 augmented transition network, 129 Bidlack, Rick, 146, 153 Ausfaltung, 93 Biles, Al, 172, 176–177 Auskomponierung, 93 Billings, John Shaw, 48 automaton Bilotta, Eleonora, 200–201 android, 8–9 binary system, 33–34 computability theory, 58–61, 87 Birmingham, William, 94 etymology, 58 Bisig, Daniel, 253 state, 58 Blacking, John, 92, 101 axiom, 15, 21 Bloomfield, Leonard, 84 axon, 205 BM, see Boltzmann machine Bod, Rens, 250 Burgi,¨ Jost, 7, 29 Boethius, 17 Babbage, Charles, 4, 40–43 BOIDS, 253 Babylonian number system, 11, 13 bol, 102 Bach, Carl P. E., 36 Bol Processor, 63, 101–106 Bach, Johann S., 1, 23, 28 Boltzmann machine, 219–220 cadences, 241 Boole, George, 44 chorales, 78, 99, 112, 123, 213, 217, 219, Boolean algebra, 44 239 Boolean lattice, 44 fugues, 241 Boolean network, 200 Bach in a Box, 167 Boolean Sequencer, 200 back-propagation algorithm, 208, 211, 221 Borges, Jorge L., 38 back-propagation net, 209, 211 Bouchon, Basile, 39, 48 backtracking system, 171 Bouvet, Joachim, 34 Backus, John, 84 BP2, 106 Backus-Naur form, 84 Braun, Antonius, 32 backward chaining, 237 Braunschweig, Johann F., 26 Baily, John, 101 Brittain, Walter H., 56 Baker, Robert, 63, 239 Brooks, Frederik P., 72–74 Index 277 Brouwer, Luitzen E.J., 46 CHANSON, 98 Brown, Andrew, 168–170 chaos, 5 brownian noise, 144 chaos theory, 264 Brunetti, Rosella, 98–100 applications in algorithmic composition, brute-force, 254 144–148 Buddhist logic, 16 history and theory, 131–137 Burks, Arthur W., 188 chaos, etymology, 131 Burton, Anthony R., 173 chaotic system, 153, 264 Bush, Vannevar, 38, 50 applications in algorithmic composition, butterfly effect, 133, 264 146–148 characteristic numbers, 27 CAC, see Computer Assisted Composition Chebyshev, Pafnuty, 67 CA Explorer, 195 Chemellier, Mark, 107 Cage, John, 39, 261 Chomsky hierarchy, 87–90 calculating machine, 28–33 Chomsky, Noam, 83, 85 Calculating Space, 187 CHORAL, 239–241 calculi, 28 chromosome calculus ratiocinator, 27 in the cell, 157 calibration, see bias in the genetic algorithm, 158 Callegari, Laura, 98–100 Church, Alonso, 58 Camillieri, Lelio, 99 circular reasoning, see circular statement Campo, Alberto de, 115 circular statement, 21, 24 CAMUS, 197–199 circulus vitiosus, see circular statement CAMUS 3D, 199 Clarke, John, 145 Cantor, Georg, 46, 135 classification, 221 Cantor set, 135 Cleve, Jurgen,¨ 228 cantus firmus, 93 Closed World Assumption, 270 Cardew, Cornelius, 253 Colmar, Xavier T. de, 33 Cardoso, Amilcar, 250–251 Colombo, Vittorio, 243–244 CARLA, 235 color, 23 Carmen de Algorismo, 2 Commodore, 57 Carpenter, Gail, 208 Common Lisp Music, 64 case-based reasoning, 250–252 Common Music, 63 categorical grammar, 84 compiler, 54 CDC 6600, 57 complexity, 87 Cellular Automata Music, 195, 196 computer Cellular Automata Workstation, 197 analogue, 50 cellular automaton, 5, 152, 264–266 digital, 50 1-dimensional, 189–191 etymology, 50 2-dimensional, 191–193, 201 Computer Assisted Composition, 260 3-dimensional, 193 Computing Tabulating Recording Company, applications in algorithmic composition, 49 195–201 concept graph, 234, 235 classes of 1-dimensional automata, 190 concept relation, 234 continuous, 194 CONCERT, 217–221, 267 extended types, 194 condition net, 127 history and theory, 187–195 conditional jump, 43 puffer, 193 conflict set, 237 rule, 190 constituent, 85 sonification, 200–201 constraint, 237–238, 271 space ship, 193 context depth, 216 C-Grammar, see categorical grammar context-free grammar, see type-2 grammar Chai, Wei, 80 context-free language, 88 Champollion, Jean F., 25 context neuron, 211 278 Index context-sensitive grammar, see type-1 grammar Dum calculat Deus, fit mundus, 28 context-sensitive language, 88 Dunn, John, 182 Context Snake, 115–116 dyadic, see binary system context unit, 215 Control Data Corporation, 57 Ebcioglu, Kemal, 229, 239–241 Conway, John H., 188, 191–192 Eck, Douglas, 220–221 Cope, David, 4, 116, 122–127, 227 Eckert, John P., 54 Courtot, Francis, 235 EDSAC, 56 Cray, Seymour R., 57 EDVAC, 50, 55 credo ut intelligam, 17 Egyptian number system, 12 crossover Ehrenfels, Christian, 250 in genetic programming, 162 Electronic Music Synthesizer, 71 in the genetic algorithm, 159 electron tube, 56 Csound, 64 ELIZA, 5, 225–228, 264 Curta, 33 Elman net, 211 Cybernetic Composer, 241 Elsea, Peter, 236 emergence, 252, 255 Dahlstedt, Palle, 180–182 EMI, see Experiments in Musical Intelligence Dannenberg, Roger, 232 emission probabilities, 69 Dantzig, Tobias, 10 empiricism, 9 Dartmouth Conference, 228 encoding, 266–267 Darwin, Charles, 5, 157 ENIAC, 50, 54 Davis, Martin, 48 Escher, Maurits C., 135 decadic wheel, 30 Essay d’une nouvelle science des nombres, 33 decidability problem, 47 Euler, Leonhard, 7 decidable languages, 88 event net, 127 deduction, 16 evolutionary algorithms, 157 Deep Blue, 57, 272 Experiments in Musical Intelligence, 122–127, deep structure, 90, 117 129, 227, 267 Deliege,` Celestin,´ 93, 94 expert system, 237 Democritus, 16 Demon Cyclic Space, 197–198 Fairchild, 56 demotic, 9, 12 Falcon, Jean B., 39 dendrites, 205 Farbood, Mary, 77 derivation, 85 feedforward network, 209 Descartes, Rene,´ 7, 8, 28 Feigenbaum, Edward A., 228 Desprez, Josquin, 23 Feigenbaum diagram, 133 deterministic finite automaton, 89–90 Fels, Sidney, 179–180 DFA, see deterministic finite automaton Fermat, Pierre de, 7, 8 Diederich, Joachim, 168–170 Ferrand, Miguel, 250–251 difference engine, 40 Feulner, Johannes, 213–214 difference engine no 1, 40 Fibonacci series, 15 difference engine no 2, 40 finite automaton, 59, 88–90, 121 differential psychology, 227 First draft of a report on the EDVAC, 61 Diophantus of Alexandria, 8 first-order predicate logic, 245 Director Musices, 243–244 first premise, see major premise Dodge, Charles, 145–146 Fitch, John, 146–147 Domino, Michael, 241 fitness evaluation, 255 Donaueschinger Musiktage, 64 fitness function, 159, 183, 269–270 Dorado, Julian, 173, 221 algorithmic, 172, 184 Dorin, Alan, 200, 202 human, 159, 167 dragon curve, 141 multi-dimensional, 168 DuBois, Roger L., 149–153, 265 multi-stage, 168 Dufay, Guillaume, 23 rule-based, 255 Index 279 fitness-bottleneck, 167 multi-stage model, 172 flocking agents, 253 scheme, 159 flow relation, 127 theory, 157–161 Fonseka, Joseph R., 253 genetic programming, 5 formal languages, 87 applications in algorithmic composition, Fortran, 63 174–176 forward algorithm, 70 genetic variability, 158 forward chaining, 237 GenJam, 176–177, 269 Foster, Stephen, 71 genome, 158 fractal, 135–137 genotype, 158 fractal dimension, 136 geometrical square, 26 fractional noise, applications in algorithmic Gerbert of Aurillac, 14–15 composition, 144–146 Glashoff, Klaus, 28 frames, 233–235, 245 Gleick, James, 131, 264 Franco of Cologne, 23 glider gun, 188 Fredkin, Ed, 188 Glushkov, Viktor M., 57 free monoid, see Kleene closure