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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 , 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 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 , 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 , 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 , 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 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 , 69 Dantzig, Tobias, 10 , 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 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 , 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 , 227 First draft of a report on the EDVAC, 61 Diophantus of Alexandria, 8 first-order predicate logic, 245 Director Musices, 243–244 first , 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 Gogins, Michael, 146 Frege, Ludwig G., 45 GoL, see Game of Life Freytag-Loringhoff,¨ Bruno Freiherr von, 30 Goldberg, David E., 157, 159, 164–165 Friberg, Anders, 243–244 golden ratio, 15 Fry, Christopher, 229 Goldstine, Herman, 54 Fryden,´ Lars, 243–244 Gosper, William, 188 Fuenffache Denckring der Teutschen Sprache, GPMusic, 175 36 grammatical , 4, 91, 112–116 functional music, 262 Grassmann, Hermann G., 44 , 235–236 Grassmann, Robert, 44 fuzzy set, 178, 255 Greek, 131 Greek number system, 12 Godel,¨ Kurt, 47, 58 Griffeath, David, 197 Gorz,¨ Gunther,¨ 228, 229 Grilo, Carlos, 250 Galilei, Galileo, 8 Grimaldi, Claudio F., 34 Game of Life, 188–189, 191–192, 197 Groove, 63 game theory, 35 Grossberg, Stephen, 208 Gamelan, 100 Gudwin, Ricardo, 178–179 Gartland-Jones, Andrew, 165–166 Guido of Arezzo, 1, 21 GAT, see generate-and-test Gunter, Edmund, 29 gate component of an LSTM, 220 Gutenberg, Johannes, 7 Gates, Bill, 56 printing press, 7 Gena, Peter, 182 Gwalior, inscription from Gwalior, 13 generalization capability, 215 generate-and-test, 238, 261 Henon´ attractor, 134 generative capacity, 87, 117 Habsburg, Carl J., 26 generative grammar, 4, 148, 153, 222, 241, Hahn, Philipp M., 32 265, 266, 270 HAL 9000, 264, 273 applications in algorithmic composition, half-logarithmic notation, 50 91–112 halting problem, 47, 60 Chomsky hierarchy, 87–90 Hamilton, William, 44 historical, 83 HarmAn, 94 theory of , 84–86 HARMONET, 213–214 genetic algorithm, 5, 157, 201, 266 HARMONY, 98 applications in algorithmic composition, Harsdorffer,¨ Georg P., 36 164–165, 176–182 Harter, William, 141 in comparison to rule-based system, Harter-Heighway Dragon, 141 171–172 Hauer, Joseph M., 24, 261, 272 280 Index

Haus, Goffredo, 128–129 Illiac Suite, 4, 63, 64, 72, 238–239, 261 Hausser, Roland, 84 immediate constituent analysis, 84 Haydn, Joseph, 38 incompleteness theorem, 58, 60 head-note, 93 IndagoSonus, 166 Hebb, Donald O., 207 indeterminacy relation, 35 Hebbian , 207 India Heighway, John, 141 mathematics and number system, 13–14 Heisenberg, Werner, 35 philosophy, 13 Henz, Martin, 237 Indo-Arabic number system, 13, 14 Herbrand, Jacques, 47 induction, 16 heredity concept, 27 by enumeration, 16 Herzstark, Curt, 33 imperfect, 16 Hesper, Ben, 138 inductive , 245 , 232, 254 infinitesimal calculus, 7 hidden layer, 209 information continuum, 187 hidden Markov model, 4, 69–71, 81 Information Mechanics Group, 188 applications in algorithmic composition, initial probabilities, 70 77–80 initial state distribution, 70 stylistic classification, 80 Inochuki, Seiji, 244 hierarchical grammars, 148 input layer, 212 hieratic, 9, 12 Institut de Recherche et Coordination hieroglyphs, 9, 24 Acoustique/Musique, see IRCAM higher programming language, 62 integrated circuit, 56 Hilbert, David, 45 Integrated Electronics, see Intel Hild, Hermann, 213–214 Intel, 56 Hiller, Lejaren, 56, 63, 64, 72, 238–239, 261 Intel 4004, 56 Hintergrund, 93 intelligence Hinton, Geoffrey, 208 etymology and definitions, 227–228 Hirzel, Martin, 77 intelligence quotient, 227 HMM, see hidden Markov model intelligence test, 228 Hobbes, Thomas, 9 International Business Machines Corporation, Hoff, Marcian E., 208 see IBM Hofstadter, Douglas R., 123, 127, 255 Introductio in analysin infinitorum, 7 Hogeweg, Paulien, 138 intuitionists, 46 Holland, John H., 157 IRCAM, 229, 240 Hollerith, Hermann, 8, 48 Isaacson, Leonard, 56, 63, 64, 72, 238–239, Hopfield net, 209, 212, 219 261 Hopfield, John, 208 Ishango bone, 10 Hopkins, A. L., 72–74 Ising, Ernst, 187 Hopper, Grace M., 54 Ising model, 187 Horner, Andrew, 164–165 isorhythm, 23 Horowitz, Damon, 173 iteration depth, 140 Hughes, David W., 99–101 Hume, David, 9 Jackendoff, Ray, 83, 93–94, 146, 251 Hunt, Andy, 197 Jacob, Bruce L., 165–166 hyperbolic function, 206 Jacoboni, Carlo, 98–100 hypertext system, 38 Jacquard, Joseph-Marie, 8, 39 Jacquet-Droz, Henri, 8 IAS, 56 Jacquet-Droz, Pierre, 8 IBM, 49 Jeppesen, Knud, 77, 115 IC, see integrated circuit Jerse, Thomas A., 145 I Ching, 34, 38, 39 Jevons, William S., 44 ideogram, 9 Jobs, Stephen P., 56 ILLIAC computer, 56, 63, 72 Johanson, Brad, 172, 175–176 Index 281

Johnson, Margret, 241 law of excluded middle, 16, 235 Johnson-Laird, Philip N., 107–109 law of identity, 16 Jones, Kevin, 75 law of non-, see law of Jordan net, 211, 215 contradiction Julia, Gaston M., 136 laws of gravitation, 8 laws of planetary motion, 8 Konig,¨ Gottfried M., 1 Leach, Jeremy, 146–147 Kaleidacousticon System, 262 Lebedev, Sergey A., 57 Kanji, 9 Le Corbusier, 64 Kansei Music System, 244 left-linear, 89 Kant, Immanuel, 9 Leibniz, Gottfried, 7, 9, 16, 26–28, 30, 33–35 Kaplan, Robert, 13 Lemombo bone, 10 Kasparov, Garry, 57, 272 Lempel-Ziv encoding, 110, 111 Katayose, Haruhiro, 244 Lempel-Ziv tree, 110–111 Keefe, Douglas H., 218 Lenz, Wilhelm, 187 Kempelen, Wolfgang von, 8 Leonardo da Pisa, 15 Kepler, Johannes, 8, 30 Leonardo da Vinci, 8, 28 key words, 226 Leonin, 21 al-Khwarizmi, 2, 13 Lerdahl, Fred, 83, 93–94, 146, 251 Kilby, Jack St.C., 56 Lesniewski, Stanislaw, 84 Kippen, Jim, 101–106, 228 Leupold, Jakob, 32 Kircher, Athanasius, 24, 29 Levitt, David, 241 Kirnberger, Philipp, 36 lexical categories, 85 Kleene, Stephen C., 58 lexical insertion rules, 85 Kleene closure, 84 lexicon, 84 Knab, Bernhard, 70 Li, Tien-Yien, 131 knowledge , 229 Liber Abaci, 15 knowledge-based system, 91, 237, 270, 271 limit cycle, 134 context-dependent, 233 Lindblom, Bjorn,¨ 96–99 Knuth, Donald, 10 Lindenmayer, Aristid, 137–138 Koch, Helge von, 136, 140 Lindenmayer system, 5, 112, 131, 153, Koch curve, 140 264–265 Kohonen, Teuvo, 113–115, 208 0L, 140 Kohonen feature map, 208, 212 1L-system, 140 Kohonen’s self-organizing maps, 221 2L-system, 140 Kopfnote, 93 applications in algorithmic composition, Kreutzer, Wolfgang, 228 148–149 Kubrick, Stanley, 264 axiom, 139 2001: A Space Odyssey, 264 context-free, 140–141, 148 Kyburz, Hanspeter, 154 context-sensitive, 140–141 D0L, 140, 141 Lammel,¨ Uwe, 228, 252 deterministic, 142–143 Laden, Bernice, 218 history, 137–138 lambda calculus, 58 IL-system, 140 Lang, Bernhard, 265 k, l-system, 140 Langton, Chris, 195 non-parametric, 142–144 Langton’s Lambda parameter, 195 parametric, 142–144 language predecessor, 139 artificial, 84 production rule, 139 natural, 84 stochastic, 142–143 Laplace, Pierre S. de, 35, 67 successor, 139 Lasswitz, Kurd, 38 theory, 138–144 Lavoisier, Antoine L., 8 linear associator, 208 law of contradiction, 16 linear-bounded automaton, 88 282 Index lipogram, 38 Malt, Mikhail, 252–254 LIQUIPRISM, 200 Mandelbrot, Benoit, 131, 135, 154, 264 Lisp, 63 Mandelbrot set, 136–137 Lloyd, Charles, 77 Manhattan project, 188 Llull, Ramon,´ see Lullus, Raimundus Manzolli, Jonatas, 178–180, 236 Locke, John, 9 map layer, 212 Loebner Prize, 227 mapping, 267–268 logarithm, 7 mapping of a mapping, 268 Loggi, Laura W., 177 Margolus, Norman, 188 logic, 15–16 Mark I, 50 conclusion, 15, 16 Mark I Perceptron, 207 copula, 45 Mark I to Mark IV, 54 existential quantifier, 45 Markov, Andrey A., 67 judgment, 44 Markov chain, 68 juncture, 17 Markov model, 4, 91, 129, 148, 216, 222, 265, major premise, 16 266 minor premise, 16 applications in algorithmic composition, predicate, 16, 44, 45 71–77 subject, 16, 44 historical, 67–68 term, 45 theory, 68–69 terminus medius, 16 materialistic-mechanistic , 9 universal quantifier, 45 mathematical music theory, 1 logical piano, 44 mathematical organ, 26, 29 Logic Theorist, 48 Mathews, Max, 63, 64 logistic equation, 132–133, 146 Mauchly, John W., 54 logogram, 9 MAX, 130 logos, 15 Maya, 12 long short-term memory recurrent neural Mazzola, Guerino, 1, 240 network, 220–221 McCarthy, John, 228 loom, 39 McClelland, James, 208 loop, 43 McCormack, John, 148–149 Lorenz, Edward N., 131, 133, 264 McCulloch, Warren St., 207 Lorenz attractor, 134 McCulloch-Pitts neuron, 207, 208 Lorenz equations, 133 Mcel, 190 Lovelace, Ada, 4, 43, 54 Mc Intyre, Ryan, 167–168, 183 LS, see Lindenmayer system Mealy machine, 59 Luger, George, 228, 229, 252 mechanistic determinism, 35 Lullus, Raimundus, 17, 24, 26, 36 Meehan, James, 93, 94 Lyon, Douglas, 129 Mellish, Chris, 76–77 LZ-encoding, see Lempel–Ziv encoding MELOS 2, 98 LZ-tree, see Lempel-Ziv tree memory block component of an LSTM, 220 Menabrea, Luigi F., 43 Muller,¨ Johann H., 32, 40 mensural notation, 23–24 Mantaras,` Ramon L. de, 251–252 Menzel, Wolfram, 213–214 Macedo, Lu`ıs, 250 Metaphysics, by Aristotle, 15 Machaut, Guillaume de, 23 Micro Instrumentation and Telemetry Systems, machine languages, 62 see MITS machine learning, 237, 244–252, 255 Micrologus de disciplina artis musicae, 1, 21 symbol-based, 245 micro processor, 56–58 Madaline, 208 Microsoft, 56, 57 Magnus liber organi de gradali et antiphonario, MIDI, 260 21 Midi Lisp, 63 major premise, 16 Mill, John S., 44 Mallarme,´ Stephane,´ 38 Millen, Dale, 195–197 Index 283 minor premise, 16 neuron Minsky, Marvin, 208, 210 artificial, 206 Miranda, Eduardo R., 197–199 biological, 205 Mirifici logarithmorum canonis descriptio, 29 Nevill-Manning, Craig, 112–113 MITS, 56 Newell, Allen, 48 Mittelgrund, 93 Newton, Isaac, 7, 8 model-based system, 250 NFA, see non-deterministic finite automaton, monotonicity of entailment, 235 89–90 Moonlight Serenade, 272 non-deterministic finite automaton, 89 Moore, Gordon E., 56 non-knowledge-based system, 91, 270, 271 Moore, Richard F., 63 non-linear dynamical system, 153 Moore machine, 59 non-linear equation system, 146 Moore School of Electrical Engineering, 54 non-linear maps, see non-linear equation Morgan, Augustus de, 44 system Morgenstern, Oskar, 35 non-linear separable functions, 210, 211 Moroni, Artemis, 178–179, 236 non-monotonic reasoning, 235, 255 Moscow mathematical papyrus, 12 non-terminal symbol, 85 motet, 21 Nordahl, Matts, 180–182 Motus, 21 Noyce, Robert N., 56 Mozart, Wolfgang A., 38 number system, development of, 9–13 Mozer, Michael C., 183, 217–222, 270 number theory, 7, 8 MS-DOS, 57 multi-agent system, 252, 253, 255 objective score, 158 multi-level perceptron, 209 object-oriented programming multi-valued logic, 235 class, 63 Multiple Adaline, see Madaline heredity, 63 multiple-viewpoint systems, 254 method, 63 MusaCazUza, 250–251 object, 63 MUSE, 245–246 observable output, 69 musical analysis, 80, 93–96, 259 occidental art music, 1 musical analysis by resynthesis, 259, 262 Olson, Harry F., 71 musical dice game, 4, 36–38, 261 OM, see OpenMusic MusicBox, 166 On Formally Undecidable Propositions...,see MusicN Uber¨ formal unentscheidbare Satze.¨ . . languages, 64 OpenMusic, 63, 130, 229 Musicomp, 63 Oppenheimer, Robert, 55 Musikalische Gestalt, 250 orbit, 146 Musurgia Universalis, 25–26 Organon, 15 mutation, 157 Organum Mathematicum, 29 in genetic programming, 162 Orlando di Lassus, 23 in the cell, 158 Orton, Richard, 197 in the genetic algorithm, 159 Oughtred, William, 30 Oulipo, 38 Napier, John, 7, 29 output function, 206 Napier’s abacus, see Napier’s bones Ouvroir de Litterature´ Potentielle, see Oulipo Napier’s bones, 26, 29, 30 over-generation, 81, 92 Napier’s rods, see Napier’s bones Naur, Peter, 84 Perotin,´ 21 Nearest Neighbor Heuristic, 233 Pachet, Franc¸ois, 108–112, 237 neighborhood, 189 Palestrina, Giovanni P., 23, 115 Neumann, John von, 35, 55, 187–189 palindrome, 38 Neumann, Peter G., 72–74 Pantano, Pietro, 200–201 neumes, 23 Papadopoulos, George, 167 neurocomputer, 207 Papert, Seymor, 208, 210 284 Index parallel rewriting system, 138 calculus, 7, 35 Pardo, Bryan, 94 production system, 236–237 parsing, 85 programming, 62–63 partially decidable language, 87 programming language Pascal, Blaise, 30 functional, 58 Pascal, programming language, 63 imperative, 58 Pascaline, 30 procedural, 58 Patch Work, 63 Prolog, 62 Pazos, Alejandro, 173, 221 propagation function, 206 Peano, Giuseppe, 46 propositional logic, 44 Pearce, Marcus, 173–174, 269 Prusinkiewicz, Przemyslaw, 138, 148 Peirce, Charles, 44 punched card, 39 Pelinski, Ramon,` 101–102 punched card computer, 8 perceptron, 207, 209–210 PureData, 64, 130 Perec, Georges, 38 pushdown automaton, 88 Pereira, Francisco, 250–251 Pythagorean abacus, 29 Petri net, 5 Pythagorean School, 14 applications in algorithmic composition, 128 marking, 127 qa’ida, 102 place, 127 QAVAID, 103–104 theory, 127 Queneau, Raymond, 38, 39 token, 127 Quipu, 10 transition, 127 Petrus de Cruce, 21 Rossler¨ attractor, 134 Petrus Hispanus, 17 Rabdologiae, 29 phase space, 134, 153 Rader, Gary, 96 phenotype, 158 radius, 189 Philips pavilion, 64 Ramirez, Rafael, 237 Phon-Amnuaisuk, Somnuk, 170–171, 183, random walk, 219 229, 241 Rank Xerox, 56 phonogram, 9 rationalism, 9 phrase structure grammar, 85 reasoning, 235–236 pictogram, 9 reasoning in uncertain situations, 235 Pigg, Paul, 172 Rechenberg, Ingo, 157 pin cylinder, 8 recognize-act cycle, 237 pink noise, 144 recognizer, 59 pitch class, 26 recombinancy, 123–127 Pitts, Walter, 207 recurrent network, 214 plan unit, 215 recursion depth, 141 Plankalkul,¨ 62 recursively defined geometric objects, 188 Plato, 15 recursively enumerable language, 87 Poeme` Electronique, 65 recursive transition network, 121 Poincare,´ Jules H., 132 regular grammar, see type-3 grammar Poleni, Giovanni, 32 regular language, 89 Poli, Ricardo, 175–176 reinforcement learning, 244 Ponsford, Dan, 76–77 Rennard, Jean-Philippe, 194 populations, 158 representation, 266–267 positional number system, 11 absolute, 182–183, 215, 221 Post, Emil, 84 distributed, 215, 221, 267 predicate calculus, 255 local, 215, 220, 221, 267 Pressing, Jeff, 146 multi-dimensional, 183, 217–219, 221 principal component analysis, 170 relative, 182–183, 215, 221 , 46 rewriting rules, 85, 142 principle of sufficient , 16 Reynolds, Craig, 253 Index 285

Rhind mathematical papyrus, 12 goal-driven, 231 Ribeiro, Paulo, 250–251 goal-oriented, 237 Riecken, Douglas, 244 heuristic, 232 Riego, A. Santos del, 173, 221 uninformed, 231 right-linear, 89 second premise, see minor premise ring tones, 262 Seife, Charles, 13 Roads, Curtis, 83, 93, 262 self-associative net, see Hopfield net Roberts, Edward, 56 Self-Learning Musical Grammar, 113–115 Roman number system, 12 self-organizing map, 208, 212 Romero-Cardalda, J.J., 173, 221 Self-Reproducing Automata, 188 Rosenblatt, Frank, 207 self-similarity, 5, 135, 138, 264 Rosetta Stone, 25 semantic networks, 233, 235 Ross, Kirk, 197 , 117, 124 Rozenberg, Grzegorz, 138 semi-decidability, 48, 88 rule, 237–238, 271 SEQUITUR, 112–113 rule-based expert system, 237 serialism, 39 rule-based system, 123, 174, 236–238, 241, sexagesimal system, 11 260–261 Shannon, Claude E., 44, 62 in comparison to genetic algorithm, 171–172 Shaw, Cliff, 48 Rumelhart, David, 208 Shyreswood, William, 17 Russell, Bertrand A.W., 45 SICOM, 269 Russell, Stuart, 228 Sierpinski triangle, 152, 191 sieves, 45 Sabater, Jordi, 251–252 sigmoid function, 206 Sametti, Alberto, 128–129 Simon, Herbert A., 48 SaxEx, 251–252, 268 simulated annealing, 219 scale invariance, see self-similarity Skolem, Thoralf, 47 Schutz,¨ Heinrich, 23 Sleator, Daniel, 94 Schonberg,¨ Arnold, 260 slide rule, 30 Schenker, Heinrich, 93, 94, 117, 125, 240 Smaill, Alan, 229, 241 Scheutz, Edvard, 41 Smalltalk, 63 Scheutz, Pehr G., 40 Smith, Alvy R., 138 Schickard, Wilhelm, 30 Smoliar, Stephen, 93, 94 Schickard’s calculator, 30 smoothed n-grams, 69, 77, 81 Schillinger, Josef, 24, 45, 272 Socrates, 15, 16 Schmidhuber, Jurgen,¨ 220–221 SOM, see self-organizing map Schockley, William B., 56 sonification, 182, 268–269 , 17 Soroban, 28 Schoner, Bernd, 77 Soukup, Daniela, 77 Schott, Caspar, 29 Spangler, Randall, 232 Schott’s counting box, 29 SPEAC, 124–126 Schottstaedt, Bill, 64 Spector, Lee, 172, 174–175 Schroder,¨ Ernst, 44 spectral density, 144 Schubert, Franz, 99 sprocket wheel, 32 Schwanauer, Stephan, 245–246 stability-plasticity dilemma, 212 Schwefel, Hans-Paul, 157 Stadler, Maximilian, 36 ScoreSynth, 128–129 state space, 231–233, 254 script, 234–235 state space search, 228 search state transition graph, 68 breadth-first, 232 Stchoty, 28 brute-force, 233 Steedman, Mark, 83, 84, 106–107 data-driven, 231 step reckoner, 30 data-oriented, 237 Stern, William, 227 depth-first, 232 stoa, 16 286 Index stochastic chain, 68 Traveling Salesman Problem, 233 Stockhausen, Karlheinz, 39 Tsang, Lawrence P., 219–220 strange attractor, 134 Turing machine, 58–60 Stubblefield, W., 229, 252 non-deterministic, 87 style imitation, 270 Turing test, 123, 227, 269 Suan Pan, 28 Turing, Alan M., 5, 58, 226–227 subroutine, 43, 54 turtle graphics, 139–148 system, 81, 201 Tuson, Andrew, 170–171 Summulae Logicales, 17 twelve tone technique, 39 Sundberg, Johan, 83, 96–99, 243–244 type-0 grammar, 87–88, 129 sunya, 13 type-1 grammar, 88 SuperCollider, 64 type-2 grammar, 84, 88–89 super computer, 57 type-3 grammar, 89–91 supervised learning, 244 surface structures, 90 Uber¨ formal unentscheidbare Satze¨ ...,47 survival of the fittest, 157, 158 Ulam, Stanislav M., 187–189 , 16 Unemi, Tatsuo, 253 Buddhist, 16 unfolding, 98 Sylvester II, see Gerbert of Aurillac universal language, 26–28, 35 symbol, development of, 9 unrestricted grammar, see type-0 grammar Symbolic Composer, 63 unsupervised learning, 91, 245 synapse, 205 Uomo Universalis, 8 syntagma, 25–26 Urlinie, 93, 98 syntax, 84–85 Ursatz, 93 definition by Chomsky, 85 Varese,` Edgar, 65 tabla, 101 Variations, 166, 228 Tabulating Machine Company, 49 Vaucanson, Jacques de, 8, 39 Talarico, Valerio, 201 Venn, John, 44 talea, 23 Vercoe, Barry, 64, 80 Temperley, David, 94 Verhulst, Pierre-Franc¸ois, 132–133 terminal symbol, 85 Verhulst equation, see logistic equation Texas Instruments, 56 vigesimal system, 11 theatre machines, 8 Virtual Laboratory, 139 thematic bridging, 164 Visser, Harm, 106 Thom, Belinda, 245 Viterbi algorithm, 71, 77, 80, 81 Thomas Aqinas, 14, 17 Viterbi path, 71 Thue, Axel, 84 Vitry, Philippe de, 21, 23 TN, see transition network von Neumann architecture, 55, 61–62 Todd, Peter M., 180–182, 214–217 Vordergrund, 93 Toffoli, Tomaso, 188 Voss, Richard F., 145 torus, 181, 190, 192, 197, 201, 202 Vox Populi, 176, 178–179, 236 Towsey, Michael, 168–170 Tractatus Logicae, 17 Wachowski, Andy and Larry, 264 TRADIC, 56 The Matrix, 264 trajectory, see phase space waiting loops, 262 transition matrix, 68 Wechsler, David, 228 transition network, 4 Weizenbaum, Joseph, 225–227 applications in algorithmic composition, well-formedness, 84, 92, 124 122–129 Well-Tempered Clavier, 241 augmented, 122 Werbos, Paul, 208 recursive, 121 Werner, Gregory, 180–182 theory, 121 white noise, 144 transition probability, 68 Whitehead, Alfred N., 45 Index 287

Widmer, Gerhard, 245–247 writing system, development of, 9 Widrow, Bernard, 208 Wiggins, Geraint, 76–77, 167, 170–171, 183, Xenakis, Iannis, 1, 45, 64, 72 229, 241, 269 wild card, 104 Yorke, James, 131 Wilkes, Maurice V., 56 winner neuron, 212 Z1 computer by Zuse, 50 Winston, Patrick H., 228 Z2 computer by Zuse, 50 Witten, Ian, 112–113 Z3 computer by Zuse, 50–53 Wojtowicz, Mirek, 190 Z4 computer by Zuse, 53 Wolff, Christian, 9 Zenon’s paradoxon, 14 WOLFGANG, 244 zero, development of, 13–15 Wolfram, Stephen, 189, 264 Zouhar, Vit, 65 Wozniac, Stephen, 56 Zuben, Ferdinando von, 178–179 Wright, Susan, 168–170 Zuse, Konrad, 4, 50–54, 62, 187–189 Wright, William V., 72–74 Zwolftonspiel,¨ 24, 272