Index
k − ε model, 244turbulence, 245
1/f noise, 393spectrum, 393
absolute, 407admittance, 177, 239
violin, 200ADSR, 333aesthetics, 370, 406, 407air, 172, 174, 220
coupled oscillator, 158damping, 125forced oscillation, 159microphone array, 52opto-acoustics, 53physical modeling, 117violin, 204
air column, 220air flow, 220air jet, 221, 237
impulse pattern formulation, 310aksak, 381
Ligeti musica ricercata, 427amadinda, 326, 381analogy, 319, 323, 410ANOVA, 344, 348arithmetics, 320, 321articulation, 195, 341, 355, 427
bow, 355bowing, 202guitar, 193information structure, 90, 93Lyapunov exponent, 107timbre, 332, 355violin, 200, 215, 355
attack, 240, 333–337, 341, 342, 344,346, 348, 349, 353, 360, 439
attractor, 63, 64
capacity dimension, 77clarinet, 231efficient coding, 364hard, 190information structure, 90neurological correlates, 359, 360perception, 333, 334saxophone, 229soft, 190spectral entropy, 40timbre, 333violin, 215wavelet, 14
attack-decay-sustain-release, 333attenuation, 359, 360
neurological correlates, 360attractor, 60
correlation dimension, 99Lyapunov exponent, 103
attractorssinging voice, 263tonality, 417
auditory time scale, 323autocorrelation, 16
correlogram, 17entropy from autocorrelation matrix,
102global fractal dimension, 101Karhunen-Loeve decomposition, 46rhythm, 382
autocorrelation matrixKarhunen-Loeve decomposition, 46
back plate, 171–173physical modeling, 113violin, 204
bar, 163, 275, 330, 364, 372, 381basilar membrane, 323, 324, 356bass drum, 396
444 Index
attractor, 63bassoon, 340, 341, 346, 348
perception, 333, 340physical modeling, 114timbre, 332
Bayes, 370, 408tonality model, 425
beats, 381, 382bell, 394, 420, 421
contact problem, 147Lyapunov exponent, 106physical modeling, 114, 126radiation, 125, 126
bending stiffness, 175, 330violin string, 207
Bessel horn, 126bifurcation, 263, 264, 266, 267, 278, 441
bowing, 208Hopf, 263, 278impulse pattern formulation, 293information structure, 93Lyapunov exponent, 104multiphonics, 226singing voice, 261, 262violin bowing, 203, 212, 213
bimanual, 388blowing pressure, 220, 229, 238, 239,
247dizi, 228multiphonics, 226
bos-counting dimension, 76boundary condition
finite-element method, 140bow, 157, 160, 203, 341
attractor, 63, 64coupled oscillator, 159impulse pattern formulation, 304information structure, 93physical modeling, 114velocity, 201violin, 198, 204width, 207
bow-string interaction, 160, 198, 198,353
finite-difference model, 207model, 200self-organization, 202transients, 200
bowing
force, 198initial transient, 202motion, 200point, 204point on string, 200pressure, 201violin, 198
bowing pressure, 198, 203, 208physical modeling, 114violin, 207
bowing velocity, 207, 210, 211brass instruments, 353
perception, 333bridge, 143, 160, 170, 171, 174–177,
182, 354, 355, 440finite-element solution, 140hill, 204, 355mobility, 204plate, 204resonance, 204spectrum, 204tambura, 176violin, 200, 204
brightness, 171–173, 319, 322, 325, 335,336, 338, 339, 341, 346, 347, 351,355, 355, 362, 373, 403
centroid, 355enhanced with guitar back plates,
172guitar, 171impulse pattern formulation, 313material properties, 372neurological correlates, 359perception, 333physical modeling, 113spectral centroid, 27, 28spectral entropy, 40spectrum, 356temporal integration path, 29timbre, 332
CALSCAL, 346capacity dimension, 76, 81cello, 340, 341, 354, 430
attractor, 64information structure, 91multi-fractal spectrum, 89perception, 333, 340timbre, 332
Index 445
cembalo, 335, 337centroid, 319, 321, 322, 337, 338, 343,
344, 346, 349, 353, 360capacity dimension, 78correlogram similarity function, 26entropy gestalt pattern, 45gestalt pattern, 33, 34, 37material properties, 372neurological correlates, 359, 360spectral entropy, 38, 40temporal integration path, 29, 41, 42wavelet, 15
chaotic motion, 278chiff, 253, 337
initial transient, 355chord sequence, 417, 422clapper, 394
contact problem, 147clarinet, 160, 220, 230, 330, 335, 340,
341, 351, 354, 440articulation, 230correlogram, 234impulse pattern formulation, 306initial transient, 354mouthpiece, 222multiphonics, 226perception, 333, 340performance, 232physical modeling, 114radiation, 125timbre, 332tone transition, 230wavelet, 236
cluster analysis, 340contact problem, 147
equation system, 148node point, 148
correlation dimension, 11, 94attractor, 63centroid similarity function, 26event density, 427multiphonics, 227phase plot, 71saxophone, 229transients, 98violin, 216
correlogram, 11, 16clarinet, 234harmonic series, 17
harmonic spectra, 17Ligeti galamb borong, 431Ligeti musica ricercata, 429saxophone, 230similarity function, 21sinusodial, 18violin, 212
correlogram similarity function, 26cortex, 323, 324, 326, 327, 360, 362, 397
posterior paretal, 382sensorimotor, 382supplementary motorial, 382
cutaways, 140cymbals, 276
density, 150, 251, 275, 281, 372air, 221attractor, 67capacity dimension, 77correlation dimension, 94fractal dimension, 57linear, 177, 180, 198, 207opto-acoustics, 53spectral centroid, 27spectral entropy, 38temporal integration path, 45
dialectics, 407dimensionality, 58dipole, 157, 237, 238
edge tone, 237microphone array, 52
directivityguitar, 189minimum energy method, 54physical modeling, 114
discrete, 333, 382attractor, 60, 62, 65fractals, 59
discrete integration, 139dispersion
Karhunen-Loeve decomposition, 46,49
distance, 331, 337, 344, 352, 353global fractal dimension, 101Karhunen-Loeve decomposition, 49rhythm, 394
dizi, 228, 439fractal dimension, 228information structure, 92
446 Index
mirliton, 227noise, 228roughness, 228
dopamine, 327, 398drum, 277, 282, 283, 329, 381
microphone array, 53minimum energy method, 54physical modeling, 114
drummer, 381
edge tone, 237, 237, 238–240, 242–244attack, 239bifurcation, 237flute, 242initial transient, 237, 240mode coupling, 238Navier-Stokes, 238onset, 237self-organization, 252spectrum, 242turbulence, 240
efficient auditory coding, 361, 362, 363,364
equation system, 364noise, 364solver, 364timbre, 364transient, 364
efficient codingtonality, 417
eigenvalue analysismodes, 145
eigenvalue solution, 120, 145emotion, 327, 328, 362, 395, 396, 398
neurophysiological correlates, 362end correction, 330energy transfer, 171, 176, 276
correlation dimension, 98membranes, 283shells, 283temporal integration path, 43
entropy, 366, 369, 370entropy gestalt pattern, 45free-energy model, 369from autocorrelation matrix, 102information dimension, 81, 84spectral centroid, 27temporal integration path, 41, 43wavelet, 15
entropy from autocorrelation matrix,102
entropy gestalt pattern, 45equation system, 149
attractor, 61, 65differential, 11efficient coding, 363finite-element method, 135linear, 119, 149, 150Lyapunov exponent, 103microphone array, 52minimum energy method, 54noninear, 150physical modeling, 119
equidistant scale, 430event density
fractal dimension, 426, 427initial transient, 428Ligeti galamb borong, 431Ligeti musica ricercata, 427, 428loudness, 432melody, 426
event denstiycorrelation dimension, 428
event-related potentials, 359external damping, 124, 166EXTREE, 346, 347, 350
fan bracingphysical modeling, 113
filter bank, 363, 366pitch, 415
filter constant, 165, 324, 325finger movements, 383finite-difference method
mouthpiece, 220violin bow, 204violin transient, 204
finite-elementstress-strain model, 134
finite-element method, 133bridge, 140contact problem, 147eigenvalue analysis, 145Gauss integration, 139mass matrix, 145moving mesh, 146node point, 135nonlinear solver, 148
Index 447
Poisson contraction, 137potential energy, 138shape function, 135stiffness matrix, 139time-dependent solution, 146turbulence, 247
fix pointimpulse pattern formulation, 289
flattening effect, 210Floquet exponent, 104flute, 221, 237, 238, 238, 239, 240, 244,
247, 248, 250–252, 324, 340, 341,347, 354
attractor, 62finite-element method, 247impedance, 239, 244initial transient, 251labium-lip distance, 238minimum energy method, 54mirliton, 227perception, 333, 340radiation, 126timbre, 332
forced oscillation, 158, 164, 181, 182guitar, 184microphone array, 51minimum energy method, 54radiation patterns, 181
formants, 353Fourier analysis
attractor, 68fractal correlation dimension, 94fractal dimension, 57, 75, 79
dizi, 228Even Parker, 433event density, 426guitar, 189multiphonics, 227saxophone, 227, 229singing voice, 270violin, 202, 215
fractals, 75free-energy model, 366
entropy, 369larynx, 370noise, 370variational principle, 370
freedom, 406french horn, 340, 341
perception, 340friction, 124
bowing, 207, 208violin bow, 200
friction instruments, 282self-organization, 283
frontal lobe, 382
gammatone, 363–368, 415Gauss impulse, 165, 201, 312, 439, 440generator, 159Gestalt, 404
melody, 414proximity, 414rhythm, 414
Gestalt pattern, 418gestalt pattern, 33
entropy gestalt pattern, 45gesture
rhythm, 383, 395global fractal dimension, 100glottis, 266GMRES, 148gongs, 278good continuation
tonality, 414graininess, 337groove, 324, 327, 396guitar, 158, 164, 166, 167, 171, 173,
181, 182, 335, 345, 352, 421, 431,440
air, 164articulation, 189, 194attack, 190attractor, 63back plate, 164body, 164bridge, 164, 182capacity dimension, 77correlation dimension, 189correlogram, 19correlogram similarity function, 23coupled oscillator, 158directivity, 189eigenmodes, 168entropy gestalt pattern, 44forced oscillation, 165, 184fractal dimension, 189gestalt pattern, 36
448 Index
Helmholtz resonance, 168information dimension, 83information structure, 90inharmonic components, 190initial transient, 164, 164, 189loudness, 190microphone array, 51–53minimum energy method, 54modes, 164monopole, 189multi-fractal spectrum, 85, 88noise, 189phase plot, 72physical modeling, 113pitch, 189radiation, 182radiation patterns, 181ribs, 164spectral centroid, 29, 30spectral integration path, 30string, 164string-body coupling, 170temporal integration path, 43top plate, 164, 189wavelet, 15, 168
hammer, 337contact problem, 147piano, 259
harmonic spectral components, 338harmony, 404, 408, 409, 416, 431harp, 347
phase plot, 72harpsichord, 175, 179hearing threshold, 323, 325Helmholtz motion, 200, 355
irregular, 201regular, 201violin, 198
hidden layer, 353hollowness, 337, 372horn, 125, 160, 330, 341, 346, 348
perception, 333radiation, 125shock waves, 254timbre, 332
hybrid instruments, 335, 337, 348hysteresis
bow, 201
rhythm, 387violin, 200, 212, 214violin bowing, 201, 212
identification task, 350, 361identification threshold, 339idiophone, 282impedance, 238
flute, 238violin, 198
impulse pattern, 157, 289, 291, 439violin, 201
impulse pattern formulation, 285air, 293air jet, 309attack, 299back plate, 291bell, 306bifurcation, 288, 293, 295, 299, 305,
307blowing pressure, 289, 294, 306bow, 304bowing pressure, 305brightness, 313changing control parameter, 294chaotic motion, 310clarinet, 306constant control parameter, 294delayed interaction, 288external damping, 297fix point, 289flute, 309Gauss impulse, 313, 314guitar, 291, 297
air, 300back plate, 299ribs, 300top plate, 299
high-speed camera, 294initial transient, 299, 302, 311instantaneous interaction, 287instrument family, 288labium, 309material properties, 291, 302method, 286multi delayed interaction, 290multiphonics, 306noise, 289, 294, 303, 310pipe, 310
Index 449
pitch, 288, 299radiation, 298, 314reed, 286, 287, 306reed instruments, 306, 313ribs, 291sawtooth motion, 314saxophone, 287, 288self-organization, 303self-sustained oscillation, 309sound production, 311stability analysis, 310strain, 291string, 291string-body motion, 293synchronization, 310top plate, 291transient, 288, 294trombone, 314trumpet, 313violin, 303, 314
air, 303bow, 304ribs, 303string, 304top plate, 303
INDSCAL, 331infinity
fractal dimension, 76fractals, 59
information dimension, 81information structure, 88
information dimension, 82phase plot, 71
inharmonic components, 11, 193, 330,333, 349
attractor, 63correlation dimension, 96, 98correlogram, 17correlogram similarity function, 26guitar, 170information dimension, 83Karhunen-Loeve decomposition, 46violin, 217
initial transient, 302initial transient, 157, 173, 176, 253,
325, 334, 335, 337, 344, 347, 351,353, 354, 364, 366, 373
attractor, 63capacity dimension, 77
clarinet, 230, 354correlation dimension, 94correlogram, 20correlogram similarity function, 23edge tone, 240entropy gestalt pattern, 44flute, 354formants, 354fractal dimension, 57gestalt pattern, 37guitar, 174, 189horn, 354identification task, 354impulse pattern formulation, 299,
313information dimension, 83, 84information structure, 89, 90instrument identification, 351Karhunen-Loeve decomposition, 46loudness, 354Lyapunov exponent, 107oboe, 354onset perception, 394perception, 334phase plot, 72, 75physical modeling, 114piano, 259reed, 354saxophone, 229, 354self-organization, 202singing voice, 354spectral centroid, 27spectral entropy, 40temporal integration path, 29, 30, 42,
43timbre, 341violin, 198, 202, 213, 215wavelet, 13, 14
instrument family, 173, 214perception, 333
instrument identification, 235, 335, 339,341, 348, 351, 351, 373
integration pathspectral entropy, 38
intensity, 358interlocking, 381internal damping, 124
Jacobian matrix, 140
450 Index
Jetztpunkte, 327
Karhunen-Loeve decomposition, 45definition, 46
keyboard, 351, 396Kohonen maps, 352, 414, 419
labium, 237, 237, 238–243, 248–252,309
impulse pattern formulation, 309physical modeling, 113
limit cycle, 63, 263, 264, 268attractor, 63information structure, 90Lyapunov exponent, 104, 107singing voice, 262
line segment, 333, 334log-log plot, 58logic, 319–321, 323, 404, 409
fractals, 60rhythm, 394semantic, 409
long-term correlationrhythm, 392
longitudinal waves, 172, 174, 175coupling, 171guitar, 172physical modeling, 117piano, 260
loudness, 323, 338, 360, 361bowing, 202, 207event density, 432guitar, 189information structure, 93initial transient, 354violin, 215
Lyapunov exponent, 103, 277
malletattractor, 63
Mark VI, 338mass matrix
eigenvalue analysis, 145mass-spring system
Lyapunov exponent, 106material properties, 372
brightness, 373spectrum, 372
melody, 327, 344, 404, 405, 423, 424,430, 431
event density, 426Gestalt, 414
membrane, 279, 282, 329, 439attractor, 63, 64contact problem, 147information structure, 92mirliton, 227physical modeling, 114
membranesenergy transfer, 283
microphone array, 51, 181minimum energy method, 54mirliton, 227, 439
fractal dimension, 228mode coupling, 160, 172, 173, 176, 177,
179, 274bar, 275bifurcation, 274chaotic motion, 275energy transfer, 274longitudinal waves, 274Lyapunov exponent, 107percussion, 274
mode shapesdamping, 124
modes, 162, 172, 174, 177, 280, 282, 372correlation dimension, 98microphone array, 53piano, 259shock waves, 254temporal integration path, 43
monopole, 157, 237edge tone, 237microphone array, 52minimum energy method, 54
mouthpiece, 221, 248, 252, 440equilibrium, 221moving mesh, 147pressure, 222turbulent flow, 221
moving mesh, 146, 439air, 147mouthpiece, 147reed, 147saxophone, 146solver, 147
MPEG 7, 353multi-fractal spectrum, 85multidimensional, 359, 361, 372, 373
Index 451
perceptional space, 329phase plot, 71
multidimensional scalingspectral centroid, 28
Multidimensional Scaling Method, 331multidimensional space, 330multiphonics
fingering, 306fractal dimension, 227impulse pattern formulation, 306,
307reed instruments, 226valve, 306, 307
Music Information Retrieval, 11, 353music therapy, 382musical flow, 382musical form, 324, 327, 428
event density, 427
Navier-Stokes, 252, 440k − ε model, 244edge tone, 240incompressible, 223moving mesh, 147nonlinear solver, 148Raynolds-Averaged, 243saxophone, 223turbulence, 243
nearest neighbour, 101, 416nerve cells, 323–325
pitch, 416neural maps, 351neural nets
tonality, 414Newton-Raphson method, 149, 150node point, 119, 146, 150
contat problem, 148finite-element method, 135
noema, 405noise, 179, 320, 325, 353, 358, 362, 363,
370, 427, 432, 433attractor, 63bowing, 203capacity dimension, 77clarinet, 232correlation dimension, 96correlogram, 18correlogram similarity function, 22entropy gestalt pattern, 44
gestalt pattern, 36information dimension, 83information structure, 90Karhunen-Loeve decomposition, 50microphone array, 52minimum energy method, 54mirliton, 228motor, 382phase plot, 72spectral centroid, 29spectral entropy, 39temporal integration path, 31, 42violin, 216
nonlinearacoustics, 157bells, 274bowing control parameter, 210coefficients, 162coupling, 162, 252cymbal, 274damping, 157detection, 106differential equation, 106driving curves, 220driving force, 161, 179driving mechanism, 157Duffing equation, 181energy transfer, 15, 274, 283equation system, 111forced radiation patterns of guitar,
181friction, 274generator, 160generator model, 239geometry, 124gongs, 274guitar, 171guitar mode coupling, 174harmonic series, 160Lyapunov exponent, 107mode coupling, 177modes, 274multiphonics, 220musicality, 157Navier-Stokes, 252Navier-Stokes term, 149Newton-Raphson method, 150percussion instruments, 274piano pre-stress, 259
452 Index
pitch glides, 274radiation, 114reaction to small system deviations,
105restoring force, 122, 181, 276scaling effects, 173shock waves, 254singing voice, 263solver, 148solving equation systems, 120stick-slip, 210string displacement, 179string-bow interaction, 200subharmonics percussion, 276sudden phase changes, 237synchronization, 231tension, 177timbre, 176turbulence, 251violin bowing, 214violin modes, 200vortex shedding, 237
nonlinear solver, 148algorithm, 148GMRES, 148transient, 148
notion, 320, 361, 362, 406, 407, 410, 411fractals, 59
nous poeticos, 407nut
microphone array, 53violin, 200
oboe, 220, 335, 340, 341, 354perception, 333, 340timbre, 332
offsetorgan, 254
onset, 327detection, 418organ, 254perception, 394
optimum processor, 408, 421opto-acoustics, 53organ, 237, 238, 240, 251–254, 302, 325,
337coupled oscillator, 158initial transient, 355synchronization, 253
orthotopy, 324
pacemaker-accumulator model, 324,327, 398
PARDISO, 120, 150Parkinson disease, 382participatory discrepancies, 396perception
categorial, 406perceptron, 353percussion, 274
mode coupling, 274nonlinear, 274subharmonics, 276
performance, 150, 160, 324, 326, 352,373, 383, 421, 432
clarinet, 231dance, 394fractal dimension, 57rhythm, 383, 395
phase-plot, 63, 71attractor, 63, 64capacity dimension, 77clarinet, 232information structure, 93Lyapunov exponent, 107violin bowing, 209
physical Modeling, 111physical modeling
eigenvalue solution, 120external damping, 124implicit formulation, 119internal damping, 124solver, 120static solution, 119stiffness matrix, 118time dependent solution, 122
piano, 166, 171, 175, 259, 325, 335,347, 354, 403, 420, 421, 427, 431,440
admittance, 260brightness, 259hammer, 259, 260initial transient, 259longitudinal waves, 260mode shapes, 259modes, 259neurophysiological correlates, 362physical modeling, 113
Index 453
pre-stress, 259radiation, 259rhythm production, 383soundboard, 259spectrum, 259
pipe, 220, 237, 238, 240, 241, 252–254,325, 337
impulse pattern formulation, 311pitch, 11, 159, 171, 190, 302, 319, 320,
323, 325, 326, 329, 403, 420–422,432
autocorrelation, 416basilar membrane, 403Bayes model, 425brightness, 404chroma, 403class, 403, 406, 412, 419correlogram, 19coupled oscillator, 159extraction, 415flattening effect, 209fractal dimension, 57harmonic spectrum, 408harmony, 405impulse pattern formulation, 289interlocking, 403log-log plot, 58loudness, 405melody, 405musical score, 404nerve cells, 403neurological, 404optimum processor, 408, 419perception, 329roughness, 405spectrum, 403threshold, 324timbre, 404tonal fusion, 405, 419tonality, 405, 413violin, 204, 213violin string, 209virtual, 403, 415wavelets, 13
pitch glidedrums, 282energy transfer, 282percussion, 278
pitch glides
gongs, 278pitch threshold, 324plate bridge, 204plates, 171, 172, 278Poisson constant, 281Poisson contraction, 137potential energy
finite-element method, 138pre-stress
piano, 259profile analysis, 357, 358
density, 358filter bank, 357, 358intensity, 357, 358logic, 358noise, 357, 358onset, 358spectrum, 358
proximitytonality, 414
pseudo phase plot, 71psyche, 405, 407psychoacoustics, 319–323
confound dimensions, 360logic, 319
radiation, 157, 160, 172, 181, 182, 237,282
edge tone, 237gestalt pattern, 33guitar, 189horn, 125Karhunen-Loeve decomposition, 46material properties, 372microphone array, 52minimum energy method, 54physical modeling, 124
radiation pattern, 164, 182guitar, 189minimum energy method, 54
radiation patterns, 181radius of gyration, 275recorder, 239reed, 158, 220, 354, 440
characteristics, 223, 223clarinet, 222flow, 223forced oscillation, 159geometry, 223
454 Index
impulse pattern formulation, 288moving mesh, 147spring, 221tip, 221, 224
reed instruments, 220, 222, 248resonance, 160, 167, 168, 171, 176, 182,
355, 390attractor, 63–65
resonator, 159reverberant, 337rhythm, 160, 326, 327, 363, 381, 428,
430additive, 427aksak, 381autocorrelation, 382, 392Bayes model, 425beats, 396bifurcation, 389bimanual, 383, 388chaotic motion, 389circadian, 397continuous movements, 393cortex, 398detection, 418deviation, 396discrete events, 390discrete movements, 393distance, 394divisive, 381dopamine, 397, 398drum, 383drummer, 389event density, 427event-related potentials, 397Farey sequence, 391filter constant, 394finger movements, 383Fourier analysis, 397fractal dimension, 57Gauss impulse, 394Gaussian random process, 393gesture, 395groove, 396Haken-Kelso-Bunz model, 384hysteresis, 385infinite, 383information structure, 94isochrone, 382Ligeti musica ricercata, 427
long-term correlation, 392, 393, 395loudness, 397musical form, 398neuronal representation, 397noise, 383, 393, 395onset, 382, 393, 397, 398oscillatory detection, 397oscillatory model, 395participatory discrepancies, 396perception, 326, 363, 396, 397performance, 383, 389, 393pitch, 397polyrhythm, 388, 389, 430production, 324resonance model, 397rhythmogram, 397semantic, 396spectrum, 392, 395striatal beat-frequency, 398subdivision, 381, 396sudden phase change, 383swing, 396synchronization, 388, 397tapping, 383, 392, 393timbre, 396time-keeper model, 382, 392, 395tonality, 413
ribs, 171, 172microphone array, 53violin, 204
rims, 171, 278physical modeling, 113
room acousticslog-log plot, 58
rosin, 200roughness, 356
information structure, 93mirliton, 228temporal dimension, 357timbre, 357
sawtooth motion, 202bowing, 198finite-difference method, 203impulse pattern formulation, 305regular, 201
saxophone, 220, 330, 346, 348, 354, 432,439, 440
attack, 230
Index 455
attractor, 62correlation dimension, 97correlogram, 230coupled oscillator, 158forced oscillation, 159, 220fractal dimension, 229information structure, 91, 92initial transient, 354multiphonics, 226perception, 333physical modeling, 114radiation, 125reed, 223synchronization, 253timbre, 332
self-organization, 57, 202adaptive resonance theory, 414Bayes tonality model, 425bow-string interaction, 202damping, 158edge tone, 252filter bank, 415free-energy model, 369friction instruments, 283guitar, 190hidden layer, 419impulse pattern formulation, 285,
303Kohonen maps, 422maps, 415musical instruments, 157neural maps, 351percussion, 274pitch, 415rhythm, 415timbre, 352, 415tonal system, 418tonality, 414violin, 198, 214violin bowing, 210
self-sustained oscillation, 237, 309impulse pattern formulation, 309
semantic, 341, 363, 382instrument family, 347material properties, 347self-organization, 352
shape functionBessel horn, 130finite-element method, 135
linear, 135physical modeling, 122
shells, 278, 279, 281, 282energy transfer, 283
shock waves, 254horn, 254modes, 254trombone, 254trumpet, 254
similarity judgements, 331, 340, 342,346, 351, 353, 354, 360, 361, 373
spectral centroid, 28singing voice, 261
attractors, 270bifurcation, 261chaotic motion, 266equation system, 263fractal dimension, 270Hopf bifurcation, 263hysteresis, 267, 268information structure, 94inharmonic components, 261internal damping, 261, 263, 265limit cycle, 263noise, 261, 265onset, 261, 267stability analysis, 263subharmonics, 261, 266tone onset, 263, 267turbulence, 262two-mass model, 265
snare drum, 396solver
microphone array, 52minimum energy method, 54physical modeling, 120
SOM, 414–419sound pressure level
correlogram, 20soundboard, 171, 179, 260
piano, 259spatial dimension, 362, 373
Karhunen-Loeve decomposition, 48spectral centroid, 27
definition, 27spectral entropy, 38
definition, 38spectral fluctuation
information structure, 92
456 Index
spectral flux, 337, 346, 347spectrum, 121, 166, 251, 322, 330, 344,
346, 349, 353, 358, 364, 4211/f noise, 393attractor, 63correlogram, 17guitar, 190harmonic, 419initial transient, 355material properties, 372microphone array, 51multiphonics, 226reed, 224, 225violin, 214
stability analysis, 310impulse pattern formulation, 310Lyapunov exponent, 103
static solution, 119stiffness matrix, 118, 119, 149
eigenvalue analysis, 145finite element method, 133moving mesh, 147physical modeling, 122
stimulus, 359, 361, 382strain, 134striatal beat-frequency, 324, 327string, 146, 164, 166, 167, 329, 330, 335,
341, 353, 355, 394, 420, 440attractor, 63bridge coupling, 165correlogram, 19information structure, 91microphone array, 53perception, 333physical modeling, 114, 121, 122tension, 165
string-bow interactionfinite-difference model, 203
string-bridge coupling, 180subharmonics, 277, 441
percussion, 276singing voice, 266violin, 211, 214
sudden phase changerhythm, 383violin bowing, 210
syllogistics, 319synchronicity, 344
perception, 335
Synchronization, 1synchronization, 145, 253, 254, 325,
327, 330, 398edge tone, 252impulse pattern formulation, 285,
310labium, 253neural maps, 351organ, 231, 253rhythm, 388, 397violin bowing, 214
synergeticsfinger movements, 383violin, 198
synthesizer, 339, 351attractor, 62
tapping, 327, 382, 388–390rhythm, 392
tempo, 324, 327, 382, 383, 389, 394temporal dimension, 333, 373temporal integration path, 29, 41timbre, 176, 323–329, 329, 330, 331,
335, 341, 343, 344, 346–351, 360,362, 373, 408, 420, 427
attack, 333bassoon, 332, 333categorial perception, 347clarinet, 332event density, 426features, 347flute, 332, 333fractal dimension, 57horn, 332information structure, 92instrument identification, 351Lyapunov exponent, 107material properties, 372multidimensional space, 330neural maps, 351neurological correlates, 359, 359, 360neurophysiological correlates, 362oboe, 332pitch, 404reed, 223rhythm, 396roughness, 357saxophone, 332self-organization, 352
Index 457
semantic, 362spectral centroid, 27, 28string, 332, 333trombone, 332, 333trumpet, 332
time-dependent solution, 122, 146equation system, 146solver, 146
tonal fusion, 404, 405, 407, 419, 420,427
fractal dimension, 57information dimension, 85
tonal system, 328, 408, 412consonance, 409logic, 408
tonality, 360–362, 404, 405, 411,416–418
Gestalt, 414neural nets, 414pitch counting, 413Riemann, 369self-organized, 414
tonotopy, 324top plate, 166, 167, 170, 172, 173, 182,
190, 364, 365forced oscillation, 182microphone array, 52physical modeling, 113violin, 204, 205
transformationguitar, 172longitudinal waves, 164perception, 406wave types, 164
transient, 16, 173, 294, 301, 302, 314,334, 348, 351, 354, 394, 449
capacity dimension, 77clarinet, 230information structure, 89microphone array, 52, 53physical modeling, 114saxophone, 229violin, 199, 202, 203
transversal waves, 171, 172guitar, 172
triad comparison, 337trombone, 160, 314, 335, 340, 341, 344,
345, 354perception, 340
shock waves, 254timbre, 332
trumpet, 160, 313, 326, 335, 340, 341,346–348, 354, 439, 440
coupled oscillator, 158impulse pattern formulation, 313neurophysiological correlates, 362perception, 333, 340radiation, 125shock waves, 254timbre, 332
turbulence, 150, 221, 243, 244, 246–248,251
finite-element method, 221mouthpiece dissipation, 220physical modeling, 113
turbulent, 439two-mass model, 266
UMFPAK, 120, 150Urmelodie, 408, 424Ursatz, 404, 408, 424
valve, 158, 220clarinet, 222forced oscillation, 159impulse pattern formulation, 307mouthpiece, 221multiphonics, 226reed, 223
variational principle, 366, 370Verstand, 406vibrato, 330, 341, 344, 346, 354, 373
attractor, 68information structure, 90
violin, 157, 160, 171, 175, 198, 330,340, 341, 352, 354, 364, 365, 373,439
articulation, 355bridge, 204correlation dimension, 216correlogram, 20coupled oscillator, 158fractal dimension, 214initial transient, 198, 200, 354loudness, 198microphone array, 53minimum energy method, 54neurophysiological correlates, 362
458 Index
perception, 340pitch, 205radiation, 198, 205radiation pattern, 198sawtooth motion, 198top plate, 204, 205wood, 205
violin bridgefinite-element solution, 140
violin family, 173viscosity, 243, 245, 246vocal folds, 261–266, 270
bifurcation, 261vocal tract, 267, 268
walking, 324, 327wave coupling, 171wave equation
attractor, 67bending, 170Lyapunov exponent, 104
physical modeling, 117violin string, 207, 208Webster equation, 128
wavelet, 13attractor, 68definition, 13, 14kernel, 14
Webster equation, 127, 160wind instruments, 220
bifurcation, 220multiphonics, 220noise, 220
wood, 341, 353damping, 124Karhunen-Loeve decomposition, 49
xylophone, 326, 329, 364, 366–368, 381,394, 426, 430
Young’s modulus, 67, 171, 177, 275, 281