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