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Index
University Press Scholarship Online
Oxford Scholarship Online Tonal Pitch Space Fred Lerdahl
Print publication date: 2005 Print ISBN-13: 9780195178296 Published to Oxford Scholarship Online: May 2008 DOI: 10.1093/acprof:oso/9780195178296.001.0001
(p.405)
Index
Abrams, R. M., and K. K. Gerhardt, 82 Acoustic scale, 267 African (sub‐Saharan) music, 287 Agmon, Etyan, 51, 270 Aldwell, E., and C. Schachter, 97, 99, 227 Anchoring principle, 52, 161, 317 Anchoring strength, 162 Anchoring/reduction rule, 320 Antokoletz, E., 337 Archangeli, D., and D. T. Langendoen, 7 Associational structure, 5–6, 346 Asymmetrical attractions, 167–170, 174 Asymmetrical distances, 79, 161, 283 Atonal branching well‐formedness condition, 346 Atonal function rule, 347 Atonal prolongations, 348–350 Attention band, 81, 165, 317 Attractions denied, 172, 174 melodic, 161–169, 274–277 metrical, 288–296 virtual, realized, and expected, 170–176 voice‐leading and harmonic, 173–176, 277–278 Attractional context, 176–179 statement of rule, 176, 178–179 Attractor, 162 Axis of symmetry, 336–337 Page 1 of 13
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Index Babbitt, M., 297 Bach, J. S., 110 Chorale, “Christus, der ist mein Leben,” 7–11, 18–25, 28–29, 31–32, 75– 77, 201–202, 219–221 Chorale, “Ich bin's, ich sollte büssen,” 35 Prelude in C major (WTC I), 36–37 Bailey, R., 108, 176 Balance constraint, 26, 28 Balkan dance music, 286 Balzano, G., 44, 50–51, 269, 288 Bartók, B., 264, 333–341, 343, 344, 351 String Quartet no. 4, V, 336–341, 349 String Quartet no. 5, I, 334; V, 334 String Quartet no. 6, III, 334–335; IV, 334–336 Basic space, 47–48 constraints on, 268–274 (p.406) Beach, D., 24–25, 227 Beethoven, L. van, 110, 313 Sonata, Op. 2, no. 1, I, 232, 234 Sonata, Op. 2, no. 2, I, 232, 234 Sonata, Op. 2, no. 3, I, 232, 234 Sonata, Op. 31, no. 3, I, 241 Sonata, Op. 53 (Waldstein), I, 37–40, 91, 202–207, 232–233, 235 Sonata, Op. 111, I, 241 Symphony no. 3 (Eroica, I, 53, 290 Symphony no. 9, I, 53; IV, 290 Berg, A., 336 Berger, A., 264, 313 Berger, K., 167 Berlioz, H., 110 Bernstein, D., 71 Berry, W., 205, 369 Bharucha, J. J., 41, 52, 81, 86–87, 161, 170, 172, 190–191 Bigand, E., R. Parncutt, and F. Lerdahl, 82, 86 Boretz, B., 184 Borrowing, 62–63, 218 Boss, J., 351 Boulez, P., 138, 297, 350, 373 Brahms, J., 82, 346 Intermezzo, Op. 76, no. 4, 311 Intermezzo, Op. 117, no. 2, 311 Branching left and right, 10–11, 14–15 strict, 29–32 Bregman, A., 32, 81, 350
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Index and S. McAdams, 33 Brown, H., and D. Butler, 194 Brown, M., 315–316 Browne, R., 50, 194 Bruckner, A., 58 Bruner, C., 285 Burns, E. M., and W. D. Ward, 80 Butler, D., 193 Cadential treatment, 12, 25, 218–219 Burgundian cadence, 317–318, 336 in nontriadic contexts, 325–326, 340 Callender, C., 323 Caplin, W., 232, 242 Carpenter, P., 91 Categorical perception, 80, 269 Chomsky, N., 4, 351 Chopin, F., 110 Ballade no. 2, 198 Prelude in E major, 89–104, 109 Prelude in E minor, 104–109 Chord distance rule, 55, 60 generality of, 263–264 Chord/region distance rule, 70 Chordal circle‐of‐fifths rule, 54 Chordal core, 56 Chordal space, 53–59 Christensen, T., 58, 166, 219, 318 Chromatic inflection, 63, 113, 218, 249 Churchland, P., 87 Closure and global prolongation, 227–229 Clough, J., and J. Douthett, 51, 269 Clough, J., N. Engebretsen, and J. Kochavi, 274 Coding theory, 45 Cognitive opacity of pitch‐meter analogies, 297 of tone rows, 375–380 Cognitive reference points, 161, 190 Coherence criterion, 50–51, 270–271 Cohn, R., 44, 83–84, 115, 264, 269, 271, 277, 298, 301 and D. Dempster, 31, 35 Compositional implications, 136–139, 297, 381 Computational modeling, 86–88, 152, 190, 381 Conceptual structure, 140 Conditioning, prenatal, 82 Consonance/dissonance, sensory, 81, 190, 269, 318–320, 349, 379–380 Constraints on basic space, 272–273 Cook, N., 227 Cooke, D., 167, 188
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Index Cooper, G., and L. B. Meyer, 293 Cowell, H., 297 Critical band, 81, 321 Cuddy, L., 348 Damasio, A., 192 de la Motte, D., 84 Debussy, C., 108, 265, 285, 313, 318 Prelude, “La terrasse des audiences du clair de lune” (Book II, no. 7), 305–312, 350 (p.407)
Prélude à l'après‐midi d'un faune, 315–316 Deliège, I., 80 Deutsch, D., 6, 7, 41, 45, 87, 378 and J. Feroe, 45–47, 379 Developmental learning, 41, 82, 190–191 Diatonic space, 47–73, 77–80 Dibben, N., 348 Distinctive (noncommon) pcs, 55 Dogantan, M., 167 Douthett, J., and P. Steinbach, 83 Dowling, W. J., 378 Drobisch, M. W., 43 Dubiel, J., 223 Elaboration, 15 Emancipation of dissonance, 349, 380 Emotion and expression, 188–192 Epstein, D., 53 Euclidean distances, 79 Euler, L., 43 Event governance, 177 Expectation rhythmic, 289 tonal, 170–173, 301 Experienced listener, 5, 143 Expressive timing, 7, 294, 296 Family resemblance, 361, 372 Fétis, F.‐J., 167 Feynman, R., 74 Fifth/leading‐tone space, 336–338 Final‐state idealization, 5 Fineberg, J., 349 Flat pitch space, 344 Flat‐space distance rule, 345 Fodor, J., 4, 172 Forte, A., 223, 281, 352, 372 and S. Gilbert, 24–25, 104 Francès, R., 378 Function rule, 215–216
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Index Functionality, 214–215, 227–231 in biology, 215, 227 and tension, 229–231 Fusion, 12, 33, 349–350 transformation rule, 350 Fyk, J., 170 Gestalt theory, 32–33, 161, 190 principle of Prägnanz, 74, 152 Gjerdingen, R., 31, 172, 190, 233–241 Gravitational analogy, 163, 166, 171, 296 Graybill, R., 293–296 Grouping structure, 3, 8 effect on metrical attractions, 294 polyphonic groupings, 6, 32–34, 368 Haimo, E., 373 Halle, J., and F. Lerdahl, 278, 350 Halving (almost‐halving) criterion, 269–270, 286–287 Handel, S., 7 Harmonic attraction rule, 175 Harmonic template, 80 Harrison, D., 196 Hasty, C., 285, 348 Haydn, J., 110 Hayes, B., 278 Heider, F., and M. Simmel, 192 Heinichen, J. D., 42 Heimholte, H. von, 44, 81, 85 Hexachordal combinatoriality, 71, 261, 375 Hexatonic rules chord distance rule and corollary, 260 intraregional chord‐cycle rule, 259 region‐cycle rule, 260 Hexatonic space, 249–251, 258–263 Hierarchical structure, 3, 5–6, 35 event hierarchy, 41 representational and inclusional hierarchies, 35 tonal hierarchy, 41 Hierarchical tension rule, 146–151 Hindemith, P., 81, 167, 346, 349 Hoffman, M., 138 Huron, D., 33 Hutchinson, W., and L. Knopoff, 321 Hyer, B., 44, 83, 176 Hypermeter, 8 Hypermodulation, 280 Idealizations, 5–6 Imig, R., 44 Implication/realization theory, 170, 190–191
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Index Indian (raga) music, 287, 375 (p.408) Inertia melodic, 171 metrical, 279 Inherited value (tension), 146 Innate structures, 190 Interaction principle, 16–17, 19–20, 157–161 revised statement of, 158–159 Interspatial distances, 280–285 statement of rule, 283–284 Interval‐class vectors, 281 Interval cycles, 43–45, 54, 56, 72, 110, 128, 249–252, 271 Intervallic scale generators, 271 Intonation, 170, 286 just intonation, 43–44, 269 Ito, J., 292 Jackendoff, R., 3–5, 7, 79, 140, 172–173, 202, 232 Japanese koto music, 375 Jazz, 292, 311, 361, 375 Johnson, M., 191 Jones, M. R., and M. Boltz, 315 Keiler, A., 220 Kellner, D., 42, 61, 71 Kerman, J., 223 Koffka, K., 74 Kolisch, R., 375 Komar, A., 138 Kopp, D., 44, 83, 215 Kramer, J. D., 7 Krumhansl, C. L., 6, 45, 78–79, 82–86, 193, 196, 200, 263 and J. J. Bharucha and E. Kessler, 82 and Edward Kessler, 82, 88, 91 Kurth, E., 167 Lake, W., 191 Lakoff, G., and M. Johnson, 191 Larson, S., 30, 163, 171, 191, 351 Leading‐tone formations, 333–343 Least action, principle of, 74 Lecanuet, J. P., 82, 190 Leman, M., 88 Lendvai, E., 264 Lester, J., 42, 219, 318 Lewin, D., 42, 44, 71, 83, 108, 215, 298, 352 Liberman, M., and A. Prince, 278 Linear completion, 52–53, 171, 173 Liszt, F., 280, 287 Litterick, L., 311 Lobe, J. C., 138
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Index Locke, D., 287 Logier, J. B., 138 London, J., and R. Rodman, 104 Longuet‐Higgins, C., 44, 84 and M. Steedman, 193 Lubin, S., 91 Lussy, M., 167 Lydian/Phrygian polymode, 333–334 Machaut, G. de, 319 Mahler, G. Lieder eines fahrenden Gesellen, “Die zwei blauen Augen,” 228–229 Symphony no. 4, IV, 198 Marr, D., 7, 88 Martino, D., 261 Marvin, E., and A. Brinkman, 227 Marx, A. B., 24 Mattheson, J., 42 Maximal evenness, 50, 269–271, 286–287 McCreless, P., 108 Mehra, J., 74 Melodic attraction rule, 163 Mendelssohn, F. Gondollied, Op. 30, no. 6 (from “Songs without Words”), 242–248 Italian Symphony, 245 Messiaen, O., 51 Metrical structure, 3, 8–9, 285–297 parallelism with basic spaces, 278–279, 282–288 Meyer, L. B., 5, 45, 52–53, 170, 172, 188, 190–191, 235 Mickelson, W., 59 Miller, G., 378 and E. Galanter and K. Pribram, 6 Minor scale harmonic, 50, 164, 273 natural, 61, 111 Mitchell, W., 184, 211, 214 Mixture, 62–63, 110–114 Momigny, J.‐J. de, 166–167 Mooney, M. K., 44, 83, 215 Morris, R, 281, 372, 375 (p.409) Morrison, C., 333, 336, 340 Mozart, W. A., 110 Piano Concerto no. 19, K. 459, III, 292–296 Sonata, K. 281, III, 241 Sonata, K. 282, I, 142–157, 176–183, 187–188, 237–241 Sonata, K. 333, I, 33–34 Symphony no. 40 in G minor, I, 30–31, 36 Musical surface, 3, 5 Mysterium space, 267, 273, 323–324
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Index Mystic space, 267–269, 322–324 Narmour, E., 52, 170, 190–191, 289, 296 Narrativity, 115, 119–139, 188 Nattiez, J.‐J., 184 Neisser, U., 6 Network representation, 31 Neo‐Riemannian theory, 83–86, 115, 264, 277, 298 Neural‐net (connectionist) modeling, 7, 86–88 Neumeyer, D., 24–25 Nontriadic spaces, 264–268 Normalization, 40 Normative prolongational structure, 25–26 Octatonic rules, statements of chord distance rule and corollary, 254, 258 intraregional chord‐cycle rule, 252 region‐cycle rule, 254 Octatonic space, 51, 249–258 Oettingen, A. von, 44 Ogdon, W., 366 Optimality theory, 7 Palmer, C., 296 Parncutt, R., 86 and W. Thompson, 81 Paths in chordal/regional space, 96–98 in pc/chordal space, 102–103 in regional space, 91–95 in scale‐degree space, 97–101 Pattern matching, 278–279, 285 Pentatonic space, 51–52 Perle, G., 192, 324, 336, 372, 379 Phenomenal accent, 8 Phonology, generative, 278 Pinker, S., 192 Pitch‐class space, 48–50 Pitch‐class set theory, 80, 281, 348, 361, 380 Pitch event (unit of analysis), 33, 97, 108–109, 227, 248, 345, 350, 373 Pitch space in evolution, 110–112, 249– 252, 350–351, 380–381 Pivot chord, 64, 97, 147 function, 147 region, 67–69, 82 Plomp, R., and W. J. M. Levelt, 81 Pople, A., 324 Position‐finding, 50, 269–270 Povel, D., 163 Preference rules, 6–7, 268–273 Pressing, J., 287
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Index Pressnitzer, D., et al., 349 Processing, real‐time, 5, 202 Prolongation, use of term, 15, 350–351 Prolongational connection rule, 74 Prolongational paths, 89–91 Prolongational reduction abstraction and transformations, 35–40 basic form, 25 construction of, 18–21 principles of, 14–18 prolongational functions, 228–229 prolongational good form, 25–29, 40, 77, 161 prolongational region, 15 and tone rows, 373–375 underlying transformations of, 35–40 vertical reduction, 14, 35–36, 340, 343 Prospective and retrospective hearing, 17, 157, 202 Prototypes, 40, 78–79, 110, 232 Psychoacoustics, 32–33, 80–81, 85–86, 150, 313–321, 349, 381 Rahn, J., 287 Rameau, J.‐P., 57–58, 166, 217, 318 corps sonore, 57 double emploi, 57 fundamental bass, 42, 145 supposition, 219 (p.410) Rare‐interval criterion, 194 Ratios of asymmetry, 167–169 Recursion constraint, 27–28 Regional circle‐of‐fifths rule, 59 Regional distance rule, 68 Regional prolongations, 104–109 Regional space, 63–70 collapsed regional space, 110–112 Reise, J., 323 Renaissance music, 317–318, 336, 381 Resile, F., 45 Riemann, H., 42, 45, 83–84, 91, 217, 222, 289 function theory, 59, 63, 196, 214–215, 218, 235 Klang, 53, 145, 215 Tonnetz (Riemann space), 44–45, 84–85, 110 Riepel, J., 233 Rosch, E., 78, 232 and C. Mervis, 78 Rothstein, W., 24, 40, 53, 242 Roughness, sensory, 81 Rumelhart, D., and J. McClelland, 7 Sadai, Y., 215 Salience, structural role of, 313–316
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Index Salience conditions, 320 Salzer, F., 315–316 Scale‐degree space, 97–101 Schachter, C., 40, 89, 104, 242 Scharf, B., 81 Schellenberg, G., 190 Schemas, 40, 231–242, 248 antecedent‐consequent period, 242, 245 Bar form, 233 cadential schema, 235, 238 changing‐note schema, 172, 235, 238 double period, 242, 245 Fonte, 237, 239 Prinner Riposte, 237, 239 Romanesca, 237–238 schematic ordering, 241 sentence (Satz), 231–234 T‐S‐D‐T progression, 215, 222 Schenker, H, 10, 37, 52–53, 164, 222–223, 361 Schenkerian analysis, 14, 15, 40, 89, 104, 138, 350 Stufen, 58–59 Urlinie, 24, 52, 104 Ursatz, 10, 25, 40, 235 will of the tones, 167, 173, 379 Zug, 52–53 Schoenberg, A, 71, 73, 91, 164, 205, 264, 336, 351, 372, 375 Book of the Hanging Gardens, Op. 15, 361 Erwartung, 351 First Chamber Symphony, Op. 9, 319, 334 Five Orchestra Pieces, Op. 16, 361 Klavierstuck, Op. 11, no. 1, 349, 353–361, 372–373 Klavierstuck, Op. 19, no. 6, 352–355 Klavierstuck, Op. 33a, 373–378 Orchestral song, “Seraphita,” Op. 22, no. 1, 351–352 Pelleas und Melisande, Op. 5, 336 Second String Quartet, Op. 10, 319, 334 Schubert, E, 285, 311, 351 Die schöne Müllerin, 139–140 Quartet in G major, 110 Quintet in C major, 110 Sonata in Bb, Op. posth., I, 114–115; IV, 241 Winterreise, 139 Schumann, R., 138 Dichterliebe, 138–139; “Aus meinen Tränen sprießen,” 222–223; “Ich hab' im Traum geweinet,” 138; “Im wunderschönen Monat Mai,” 138
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Index Frauenliebe und Leben, 138–139 Scriabin, A, 265, 267–268, 287, 336 Prelude, Op. 48, no. 4, 311 Prelude, Op. 67, no. 1, 316–317, 321–333 Sechter, S., 58, 217 Semantic paths, 140–141 Sensory consonance rule, 321 Sequential tension rule, 143, 151 Shepard, R., 43–45 and L. Cooper, 78 Shortest path, principle of, 73–77, 128, 159, 193–194 Similarity, pitch and pitch‐class, 281–282, 345 (p.411) Simon, H., 6 and R. K. Sumner, 45 Simplicity criterion, 51 Six‐four chord, interpretation of, 97, 119, 227 Sloboda, J., 4 Spectral music, 349 Sports, F., 137 Stability conditions, 4, 41, 74, 313–316, 348 Steps and skips, 48, 50, 57–58, 95, 379 Stockhausen, K., 297 Straus, J. N., 351 Strauss, R. Elektra, 351 Tod und Verklärung, 188–189 Stravinsky, I., 265, 281, 312–314, 343, 344 Le sacre du printemps, 342–343 Les noces, 341, 343 Symphony of Psalms, 313–314 Streaming (psychoacoustic), 32–33, 190, 316 Strict‐branching criterion, 29–32 Structural beginning, 12 Stumpf, C., 85 Subevents, 350 Surface dissonance, 150–151 Surface tension rule, 150 Swain, J., 188 Tactus, 9, 285–286, 289–291 Taruskin, R., 184, 265, 323, 343 Temperley, D., 193, 196, 201, 280 and D. Sleator, 143, 152, 286 Tension and attractions, 186–188 and pitch space, 142 relation to stability and instability, 142 schematic, 242–247 sequential vs. hierarchical, 143, 152–153
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Index tonal, 14–15, 143–152 Terhardt, E., 80, 86, 265, 321 and G. Stoll and M. Seewann, 81, 321 Time‐span reduction, 10–14 Time‐span segmentation, 4, 9–10 Time‐span stability, 74 Tone durations, 82, 200 Tonic‐finding, 193–201 statement of rule, 198–200 Toroidal structure, 42, 57–58, 64, 66 Transformational rules, 6, 14, 37, 218 Travis, R., 351 Tversky, A., and J. W. Hutchinson, 31 Twelve‐tone theory, 71, 80, 261, 375 Unaccompanied melody, 200–201 Underlying phrasal form, 248 Uniqueness criterion, 50, 270, 286–287 Universals, 4–5 van den Toorn, P., 264, 313, 343 Väisälä, O., 345 Varèse, E., 336 Vial, F.‐G., 42 Virtual pitch theory, 80–81, 86 Voice‐leading attraction rule, 173 Wagner, R., 82, 108, 110, 138, 176, 265, 280, 318 Parsifal, 119–138, 298–302 Tristan und Isolde: Prelude to Act I, 183–186, 205–214, 223–225, 233, 236–237, 308; Sehnen motive (Act II), 302–305; Transfiguration (Liebestod), 115–119, 186, 224–226 Wagner, W., 137–138 Wason, R., 58, 184 Weber, G., 42, 91, 138 Weber space, 43, 45, 64, 71, 73, 136–139 Webern, A., 372 Piece for violin and piano, Op. 7, no. 1, 349, 368–372 Weinberger, N., 87 Well‐formedness conditions, 6, 268–269, 272, 285–286 Werts, D., 91, 111, 138 Whole‐tone space, 251, 266–268 Wittlich, G., 372 Xenakis, I., 373 Youmans, G., 31 Zuckerkandl, V., 167 (p.412)
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Index
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Index
University Press Scholarship Online
Oxford Scholarship Online Tonal Pitch Space Fred Lerdahl
Print publication date: 2005 Print ISBN-13: 9780195178296 Published to Oxford Scholarship Online: May 2008 DOI: 10.1093/acprof:oso/9780195178296.001.0001
(p.405)
Index
Abrams, R. M., and K. K. Gerhardt, 82 Acoustic scale, 267 African (sub‐Saharan) music, 287 Agmon, Etyan, 51, 270 Aldwell, E., and C. Schachter, 97, 99, 227 Anchoring principle, 52, 161, 317 Anchoring strength, 162 Anchoring/reduction rule, 320 Antokoletz, E., 337 Archangeli, D., and D. T. Langendoen, 7 Associational structure, 5–6, 346 Asymmetrical attractions, 167–170, 174 Asymmetrical distances, 79, 161, 283 Atonal branching well‐formedness condition, 346 Atonal function rule, 347 Atonal prolongations, 348–350 Attention band, 81, 165, 317 Attractions denied, 172, 174 melodic, 161–169, 274–277 metrical, 288–296 virtual, realized, and expected, 170–176 voice‐leading and harmonic, 173–176, 277–278 Attractional context, 176–179 statement of rule, 176, 178–179 Attractor, 162 Axis of symmetry, 336–337 Page 1 of 13
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Index Babbitt, M., 297 Bach, J. S., 110 Chorale, “Christus, der ist mein Leben,” 7–11, 18–25, 28–29, 31–32, 75– 77, 201–202, 219–221 Chorale, “Ich bin's, ich sollte büssen,” 35 Prelude in C major (WTC I), 36–37 Bailey, R., 108, 176 Balance constraint, 26, 28 Balkan dance music, 286 Balzano, G., 44, 50–51, 269, 288 Bartók, B., 264, 333–341, 343, 344, 351 String Quartet no. 4, V, 336–341, 349 String Quartet no. 5, I, 334; V, 334 String Quartet no. 6, III, 334–335; IV, 334–336 Basic space, 47–48 constraints on, 268–274 (p.406) Beach, D., 24–25, 227 Beethoven, L. van, 110, 313 Sonata, Op. 2, no. 1, I, 232, 234 Sonata, Op. 2, no. 2, I, 232, 234 Sonata, Op. 2, no. 3, I, 232, 234 Sonata, Op. 31, no. 3, I, 241 Sonata, Op. 53 (Waldstein), I, 37–40, 91, 202–207, 232–233, 235 Sonata, Op. 111, I, 241 Symphony no. 3 (Eroica, I, 53, 290 Symphony no. 9, I, 53; IV, 290 Berg, A., 336 Berger, A., 264, 313 Berger, K., 167 Berlioz, H., 110 Bernstein, D., 71 Berry, W., 205, 369 Bharucha, J. J., 41, 52, 81, 86–87, 161, 170, 172, 190–191 Bigand, E., R. Parncutt, and F. Lerdahl, 82, 86 Boretz, B., 184 Borrowing, 62–63, 218 Boss, J., 351 Boulez, P., 138, 297, 350, 373 Brahms, J., 82, 346 Intermezzo, Op. 76, no. 4, 311 Intermezzo, Op. 117, no. 2, 311 Branching left and right, 10–11, 14–15 strict, 29–32 Bregman, A., 32, 81, 350
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Index and S. McAdams, 33 Brown, H., and D. Butler, 194 Brown, M., 315–316 Browne, R., 50, 194 Bruckner, A., 58 Bruner, C., 285 Burns, E. M., and W. D. Ward, 80 Butler, D., 193 Cadential treatment, 12, 25, 218–219 Burgundian cadence, 317–318, 336 in nontriadic contexts, 325–326, 340 Callender, C., 323 Caplin, W., 232, 242 Carpenter, P., 91 Categorical perception, 80, 269 Chomsky, N., 4, 351 Chopin, F., 110 Ballade no. 2, 198 Prelude in E major, 89–104, 109 Prelude in E minor, 104–109 Chord distance rule, 55, 60 generality of, 263–264 Chord/region distance rule, 70 Chordal circle‐of‐fifths rule, 54 Chordal core, 56 Chordal space, 53–59 Christensen, T., 58, 166, 219, 318 Chromatic inflection, 63, 113, 218, 249 Churchland, P., 87 Closure and global prolongation, 227–229 Clough, J., and J. Douthett, 51, 269 Clough, J., N. Engebretsen, and J. Kochavi, 274 Coding theory, 45 Cognitive opacity of pitch‐meter analogies, 297 of tone rows, 375–380 Cognitive reference points, 161, 190 Coherence criterion, 50–51, 270–271 Cohn, R., 44, 83–84, 115, 264, 269, 271, 277, 298, 301 and D. Dempster, 31, 35 Compositional implications, 136–139, 297, 381 Computational modeling, 86–88, 152, 190, 381 Conceptual structure, 140 Conditioning, prenatal, 82 Consonance/dissonance, sensory, 81, 190, 269, 318–320, 349, 379–380 Constraints on basic space, 272–273 Cook, N., 227 Cooke, D., 167, 188
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Index Cooper, G., and L. B. Meyer, 293 Cowell, H., 297 Critical band, 81, 321 Cuddy, L., 348 Damasio, A., 192 de la Motte, D., 84 Debussy, C., 108, 265, 285, 313, 318 Prelude, “La terrasse des audiences du clair de lune” (Book II, no. 7), 305–312, 350 (p.407)
Prélude à l'après‐midi d'un faune, 315–316 Deliège, I., 80 Deutsch, D., 6, 7, 41, 45, 87, 378 and J. Feroe, 45–47, 379 Developmental learning, 41, 82, 190–191 Diatonic space, 47–73, 77–80 Dibben, N., 348 Distinctive (noncommon) pcs, 55 Dogantan, M., 167 Douthett, J., and P. Steinbach, 83 Dowling, W. J., 378 Drobisch, M. W., 43 Dubiel, J., 223 Elaboration, 15 Emancipation of dissonance, 349, 380 Emotion and expression, 188–192 Epstein, D., 53 Euclidean distances, 79 Euler, L., 43 Event governance, 177 Expectation rhythmic, 289 tonal, 170–173, 301 Experienced listener, 5, 143 Expressive timing, 7, 294, 296 Family resemblance, 361, 372 Fétis, F.‐J., 167 Feynman, R., 74 Fifth/leading‐tone space, 336–338 Final‐state idealization, 5 Fineberg, J., 349 Flat pitch space, 344 Flat‐space distance rule, 345 Fodor, J., 4, 172 Forte, A., 223, 281, 352, 372 and S. Gilbert, 24–25, 104 Francès, R., 378 Function rule, 215–216
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Index Functionality, 214–215, 227–231 in biology, 215, 227 and tension, 229–231 Fusion, 12, 33, 349–350 transformation rule, 350 Fyk, J., 170 Gestalt theory, 32–33, 161, 190 principle of Prägnanz, 74, 152 Gjerdingen, R., 31, 172, 190, 233–241 Gravitational analogy, 163, 166, 171, 296 Graybill, R., 293–296 Grouping structure, 3, 8 effect on metrical attractions, 294 polyphonic groupings, 6, 32–34, 368 Haimo, E., 373 Halle, J., and F. Lerdahl, 278, 350 Halving (almost‐halving) criterion, 269–270, 286–287 Handel, S., 7 Harmonic attraction rule, 175 Harmonic template, 80 Harrison, D., 196 Hasty, C., 285, 348 Haydn, J., 110 Hayes, B., 278 Heider, F., and M. Simmel, 192 Heinichen, J. D., 42 Heimholte, H. von, 44, 81, 85 Hexachordal combinatoriality, 71, 261, 375 Hexatonic rules chord distance rule and corollary, 260 intraregional chord‐cycle rule, 259 region‐cycle rule, 260 Hexatonic space, 249–251, 258–263 Hierarchical structure, 3, 5–6, 35 event hierarchy, 41 representational and inclusional hierarchies, 35 tonal hierarchy, 41 Hierarchical tension rule, 146–151 Hindemith, P., 81, 167, 346, 349 Hoffman, M., 138 Huron, D., 33 Hutchinson, W., and L. Knopoff, 321 Hyer, B., 44, 83, 176 Hypermeter, 8 Hypermodulation, 280 Idealizations, 5–6 Imig, R., 44 Implication/realization theory, 170, 190–191
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Index Indian (raga) music, 287, 375 (p.408) Inertia melodic, 171 metrical, 279 Inherited value (tension), 146 Innate structures, 190 Interaction principle, 16–17, 19–20, 157–161 revised statement of, 158–159 Interspatial distances, 280–285 statement of rule, 283–284 Interval‐class vectors, 281 Interval cycles, 43–45, 54, 56, 72, 110, 128, 249–252, 271 Intervallic scale generators, 271 Intonation, 170, 286 just intonation, 43–44, 269 Ito, J., 292 Jackendoff, R., 3–5, 7, 79, 140, 172–173, 202, 232 Japanese koto music, 375 Jazz, 292, 311, 361, 375 Johnson, M., 191 Jones, M. R., and M. Boltz, 315 Keiler, A., 220 Kellner, D., 42, 61, 71 Kerman, J., 223 Koffka, K., 74 Kolisch, R., 375 Komar, A., 138 Kopp, D., 44, 83, 215 Kramer, J. D., 7 Krumhansl, C. L., 6, 45, 78–79, 82–86, 193, 196, 200, 263 and J. J. Bharucha and E. Kessler, 82 and Edward Kessler, 82, 88, 91 Kurth, E., 167 Lake, W., 191 Lakoff, G., and M. Johnson, 191 Larson, S., 30, 163, 171, 191, 351 Leading‐tone formations, 333–343 Least action, principle of, 74 Lecanuet, J. P., 82, 190 Leman, M., 88 Lendvai, E., 264 Lester, J., 42, 219, 318 Lewin, D., 42, 44, 71, 83, 108, 215, 298, 352 Liberman, M., and A. Prince, 278 Linear completion, 52–53, 171, 173 Liszt, F., 280, 287 Litterick, L., 311 Lobe, J. C., 138
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Index Locke, D., 287 Logier, J. B., 138 London, J., and R. Rodman, 104 Longuet‐Higgins, C., 44, 84 and M. Steedman, 193 Lubin, S., 91 Lussy, M., 167 Lydian/Phrygian polymode, 333–334 Machaut, G. de, 319 Mahler, G. Lieder eines fahrenden Gesellen, “Die zwei blauen Augen,” 228–229 Symphony no. 4, IV, 198 Marr, D., 7, 88 Martino, D., 261 Marvin, E., and A. Brinkman, 227 Marx, A. B., 24 Mattheson, J., 42 Maximal evenness, 50, 269–271, 286–287 McCreless, P., 108 Mehra, J., 74 Melodic attraction rule, 163 Mendelssohn, F. Gondollied, Op. 30, no. 6 (from “Songs without Words”), 242–248 Italian Symphony, 245 Messiaen, O., 51 Metrical structure, 3, 8–9, 285–297 parallelism with basic spaces, 278–279, 282–288 Meyer, L. B., 5, 45, 52–53, 170, 172, 188, 190–191, 235 Mickelson, W., 59 Miller, G., 378 and E. Galanter and K. Pribram, 6 Minor scale harmonic, 50, 164, 273 natural, 61, 111 Mitchell, W., 184, 211, 214 Mixture, 62–63, 110–114 Momigny, J.‐J. de, 166–167 Mooney, M. K., 44, 83, 215 Morris, R, 281, 372, 375 (p.409) Morrison, C., 333, 336, 340 Mozart, W. A., 110 Piano Concerto no. 19, K. 459, III, 292–296 Sonata, K. 281, III, 241 Sonata, K. 282, I, 142–157, 176–183, 187–188, 237–241 Sonata, K. 333, I, 33–34 Symphony no. 40 in G minor, I, 30–31, 36 Musical surface, 3, 5 Mysterium space, 267, 273, 323–324
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Index Mystic space, 267–269, 322–324 Narmour, E., 52, 170, 190–191, 289, 296 Narrativity, 115, 119–139, 188 Nattiez, J.‐J., 184 Neisser, U., 6 Network representation, 31 Neo‐Riemannian theory, 83–86, 115, 264, 277, 298 Neural‐net (connectionist) modeling, 7, 86–88 Neumeyer, D., 24–25 Nontriadic spaces, 264–268 Normalization, 40 Normative prolongational structure, 25–26 Octatonic rules, statements of chord distance rule and corollary, 254, 258 intraregional chord‐cycle rule, 252 region‐cycle rule, 254 Octatonic space, 51, 249–258 Oettingen, A. von, 44 Ogdon, W., 366 Optimality theory, 7 Palmer, C., 296 Parncutt, R., 86 and W. Thompson, 81 Paths in chordal/regional space, 96–98 in pc/chordal space, 102–103 in regional space, 91–95 in scale‐degree space, 97–101 Pattern matching, 278–279, 285 Pentatonic space, 51–52 Perle, G., 192, 324, 336, 372, 379 Phenomenal accent, 8 Phonology, generative, 278 Pinker, S., 192 Pitch‐class space, 48–50 Pitch‐class set theory, 80, 281, 348, 361, 380 Pitch event (unit of analysis), 33, 97, 108–109, 227, 248, 345, 350, 373 Pitch space in evolution, 110–112, 249– 252, 350–351, 380–381 Pivot chord, 64, 97, 147 function, 147 region, 67–69, 82 Plomp, R., and W. J. M. Levelt, 81 Pople, A., 324 Position‐finding, 50, 269–270 Povel, D., 163 Preference rules, 6–7, 268–273 Pressing, J., 287
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Index Pressnitzer, D., et al., 349 Processing, real‐time, 5, 202 Prolongation, use of term, 15, 350–351 Prolongational connection rule, 74 Prolongational paths, 89–91 Prolongational reduction abstraction and transformations, 35–40 basic form, 25 construction of, 18–21 principles of, 14–18 prolongational functions, 228–229 prolongational good form, 25–29, 40, 77, 161 prolongational region, 15 and tone rows, 373–375 underlying transformations of, 35–40 vertical reduction, 14, 35–36, 340, 343 Prospective and retrospective hearing, 17, 157, 202 Prototypes, 40, 78–79, 110, 232 Psychoacoustics, 32–33, 80–81, 85–86, 150, 313–321, 349, 381 Rahn, J., 287 Rameau, J.‐P., 57–58, 166, 217, 318 corps sonore, 57 double emploi, 57 fundamental bass, 42, 145 supposition, 219 (p.410) Rare‐interval criterion, 194 Ratios of asymmetry, 167–169 Recursion constraint, 27–28 Regional circle‐of‐fifths rule, 59 Regional distance rule, 68 Regional prolongations, 104–109 Regional space, 63–70 collapsed regional space, 110–112 Reise, J., 323 Renaissance music, 317–318, 336, 381 Resile, F., 45 Riemann, H., 42, 45, 83–84, 91, 217, 222, 289 function theory, 59, 63, 196, 214–215, 218, 235 Klang, 53, 145, 215 Tonnetz (Riemann space), 44–45, 84–85, 110 Riepel, J., 233 Rosch, E., 78, 232 and C. Mervis, 78 Rothstein, W., 24, 40, 53, 242 Roughness, sensory, 81 Rumelhart, D., and J. McClelland, 7 Sadai, Y., 215 Salience, structural role of, 313–316
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Index Salience conditions, 320 Salzer, F., 315–316 Scale‐degree space, 97–101 Schachter, C., 40, 89, 104, 242 Scharf, B., 81 Schellenberg, G., 190 Schemas, 40, 231–242, 248 antecedent‐consequent period, 242, 245 Bar form, 233 cadential schema, 235, 238 changing‐note schema, 172, 235, 238 double period, 242, 245 Fonte, 237, 239 Prinner Riposte, 237, 239 Romanesca, 237–238 schematic ordering, 241 sentence (Satz), 231–234 T‐S‐D‐T progression, 215, 222 Schenker, H, 10, 37, 52–53, 164, 222–223, 361 Schenkerian analysis, 14, 15, 40, 89, 104, 138, 350 Stufen, 58–59 Urlinie, 24, 52, 104 Ursatz, 10, 25, 40, 235 will of the tones, 167, 173, 379 Zug, 52–53 Schoenberg, A, 71, 73, 91, 164, 205, 264, 336, 351, 372, 375 Book of the Hanging Gardens, Op. 15, 361 Erwartung, 351 First Chamber Symphony, Op. 9, 319, 334 Five Orchestra Pieces, Op. 16, 361 Klavierstuck, Op. 11, no. 1, 349, 353–361, 372–373 Klavierstuck, Op. 19, no. 6, 352–355 Klavierstuck, Op. 33a, 373–378 Orchestral song, “Seraphita,” Op. 22, no. 1, 351–352 Pelleas und Melisande, Op. 5, 336 Second String Quartet, Op. 10, 319, 334 Schubert, E, 285, 311, 351 Die schöne Müllerin, 139–140 Quartet in G major, 110 Quintet in C major, 110 Sonata in Bb, Op. posth., I, 114–115; IV, 241 Winterreise, 139 Schumann, R., 138 Dichterliebe, 138–139; “Aus meinen Tränen sprießen,” 222–223; “Ich hab' im Traum geweinet,” 138; “Im wunderschönen Monat Mai,” 138
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Index Frauenliebe und Leben, 138–139 Scriabin, A, 265, 267–268, 287, 336 Prelude, Op. 48, no. 4, 311 Prelude, Op. 67, no. 1, 316–317, 321–333 Sechter, S., 58, 217 Semantic paths, 140–141 Sensory consonance rule, 321 Sequential tension rule, 143, 151 Shepard, R., 43–45 and L. Cooper, 78 Shortest path, principle of, 73–77, 128, 159, 193–194 Similarity, pitch and pitch‐class, 281–282, 345 (p.411) Simon, H., 6 and R. K. Sumner, 45 Simplicity criterion, 51 Six‐four chord, interpretation of, 97, 119, 227 Sloboda, J., 4 Spectral music, 349 Sports, F., 137 Stability conditions, 4, 41, 74, 313–316, 348 Steps and skips, 48, 50, 57–58, 95, 379 Stockhausen, K., 297 Straus, J. N., 351 Strauss, R. Elektra, 351 Tod und Verklärung, 188–189 Stravinsky, I., 265, 281, 312–314, 343, 344 Le sacre du printemps, 342–343 Les noces, 341, 343 Symphony of Psalms, 313–314 Streaming (psychoacoustic), 32–33, 190, 316 Strict‐branching criterion, 29–32 Structural beginning, 12 Stumpf, C., 85 Subevents, 350 Surface dissonance, 150–151 Surface tension rule, 150 Swain, J., 188 Tactus, 9, 285–286, 289–291 Taruskin, R., 184, 265, 323, 343 Temperley, D., 193, 196, 201, 280 and D. Sleator, 143, 152, 286 Tension and attractions, 186–188 and pitch space, 142 relation to stability and instability, 142 schematic, 242–247 sequential vs. hierarchical, 143, 152–153
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Index tonal, 14–15, 143–152 Terhardt, E., 80, 86, 265, 321 and G. Stoll and M. Seewann, 81, 321 Time‐span reduction, 10–14 Time‐span segmentation, 4, 9–10 Time‐span stability, 74 Tone durations, 82, 200 Tonic‐finding, 193–201 statement of rule, 198–200 Toroidal structure, 42, 57–58, 64, 66 Transformational rules, 6, 14, 37, 218 Travis, R., 351 Tversky, A., and J. W. Hutchinson, 31 Twelve‐tone theory, 71, 80, 261, 375 Unaccompanied melody, 200–201 Underlying phrasal form, 248 Uniqueness criterion, 50, 270, 286–287 Universals, 4–5 van den Toorn, P., 264, 313, 343 Väisälä, O., 345 Varèse, E., 336 Vial, F.‐G., 42 Virtual pitch theory, 80–81, 86 Voice‐leading attraction rule, 173 Wagner, R., 82, 108, 110, 138, 176, 265, 280, 318 Parsifal, 119–138, 298–302 Tristan und Isolde: Prelude to Act I, 183–186, 205–214, 223–225, 233, 236–237, 308; Sehnen motive (Act II), 302–305; Transfiguration (Liebestod), 115–119, 186, 224–226 Wagner, W., 137–138 Wason, R., 58, 184 Weber, G., 42, 91, 138 Weber space, 43, 45, 64, 71, 73, 136–139 Webern, A., 372 Piece for violin and piano, Op. 7, no. 1, 349, 368–372 Weinberger, N., 87 Well‐formedness conditions, 6, 268–269, 272, 285–286 Werts, D., 91, 111, 138 Whole‐tone space, 251, 266–268 Wittlich, G., 372 Xenakis, I., 373 Youmans, G., 31 Zuckerkandl, V., 167 (p.412)
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Index
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