A A0–A1 Cavity Mode Model, 330–331 Accelerance Banjo, 71 Cellos

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Index

A body resonances, 105–108 A0–A1 cavity mode model, 330–331 drilling-enlarging technique, 113 Accelerance electronic TV holography, 105 banjo, 71 Estonia, kannel, 103 cellos, 247 Finland, kantele, 103 guitars, 49–52 history, 103–104 violin, 222 Latvia, kokle, 103 Acoustic guitars light construction, 112 force exerted, 20–21 Lithuania, kankles, 103 frequency response, 21–22 Northwestern Russia, gusli, 103 schematics, 20 playing techniques, 104–105, 114 Agraffe, 356 radical design, 114–115 Agren, C.H., 312 sound boxes, 102 Aizawa, H., 174 sound hole distribution, 111–112 Amati, Andrea, 245 sound quality, 103 Amati, Hieronymus, 265, 267 string coupling, 103, 109–111 Anderson, P., 225 traditional-style designs, 113–114 Ando, T., 191 without frets, 102 Ando, Y., 185, 190 modernized Andreas, 6 chromatic baltic psalteries, 118–121 Anomalous low frequencies (ALF), 287 diatonically tuned versions, 117–118 Antinodes, 13 Banerji, B., 347 Antonio, 265, 267 Banjo Appalachian dulcimers, 99 bridges Archtop mandolins acoustic anisotropy, 71 f-holes, 81 resonances, 71, 72 oval soundhole, 81 string vibrations, 72 Asian musical instruments, 173–176. See also total sound pressure vs. frequency, Plucked string instruments 72–73 Askenfelt, A., 6, 218, 253, 259, 282, 296, 347, classiﬁcations, 59 350, 351 features, 59–60 harmonics analysis, 67–68 head modes B Fourier analysis, 66 Bach, J.S., 6, 141, 142, 301, 354 head tension, 65–66 Backhaus, Hermann, 210 holographic interferometry, 65, 66 Baltic psalteries low-frequency response, 66–67 carved impedance matching, 74–75

T.D. Rossing (ed.), The Science of String Instruments, 457 DOI 10.1007/978-1-4419-7110-4, # Springer Science+Business Media, LLC 2010 458 Index

Banjo (cont.) Borman, T.M., 230 neck, 73–74 Boullosa, R.R., 53 parts, 60–61 Bouncing rate, 296–297 Raejusters, 60, 69 Boutillon, X., 203 resonator Boutin, H., 242 adjustments, 69 Bow cavity tuning, 69 camber effect, 279–281 Helmholtz resonator, 68–69 François Tourte, 281 maximum sound volume, 70 hair elasticity effect, 282 resonance measurement, 69 pernambuco, 281 total sound fraction vs. frequency, 70 rosin/friction, 282–283 rims, 73–74 snakewood, 281 sound radiation tonal quality, 281–282 vs. frequency response, 62–64 Bowed string instruments, 2–3 power spectrum, 62 cellos, 245 vibrations, 63–64 medieval (see Medieval bowed string structural dynamics model, 59 instruments) tone rings, 73–74 structural acoustics, 324–325 Barbera, Richard, 401 traditional and octet, 329 Barlow, C.Y., 229 violin (see Violin) Baroque viols, 310 viols (see Viols) acoustics Bowed strings bass viol, 313–314 anomalous low frequencies (ALF) tenor viol, 313 flattening effect, 203 treble viol, 312–313 musical terms, 204 development, 311–312 reflected torsional waves, 205 Barth, Paul, 396 sound spectra, 204 Bassbar, 234–235 synchronizing mechanism, 205 Ba Than, U., 168 timing mechanism, 203 Beauchamp, George, 396, 399 violin G string, 205 Beauchamp violin design, 399–400 waveforms, 206–207 Beck, Jeff, 398 dynamics, 202–203 Beebe, C., 123, 125 kinematics Beethoven, 78 bowing condition limits, 199 Bell, A.J., 158, 164 bowing force range, 199, 200 Benioff, Hugo, 400, 401, 410 bridge force waveform, 201, 202 Benioff violin design, 400–401 displacement and velocity, 197, 198 Bernoulli, Daniel, 2 friction force, 198 Besnainou, C., 37, 242 ingenious vibration microscope, 200 Bigsby, Paul, 395, 397 multiple-flyback motion, 201 Bissinger, G., 213–216, 221, 225, 231, 233, Raman model, 201 235, 240, 241, 306, 317, 336 string motion, 197, 198 Biwa. See Satsuma biwa velocity and displacement curves, 201 Boccherini, 4 vibration cycle, 198, 199 Body resonance Bowing techniques bi-directional interaction, 433–434 B5 harmonics, 290, 291 driving-point admittance, 432 bouncing rate, 296–297 filtering, 432–433 bow acceleration, 292 string-body scattering junction, 434–435 bow-hair ribbon, 293 Body resonator bowing parameters low-order filter, 449–450 corner rounding, 288 response and admittance, 447, 449 Helmholtz mode, 287 Bork, I., 6 pitch flattening, 289 Index 459

Schelleng diagram, 288, 289 Campbell, P., 301 sul ponticello, 290 Campbell, R., 77 de´tache´, 294–295 Castanet, Burmese, 167 double stops, 292 Causse´, R., 241 ﬂautando, 290 Cavity modes, 320 friction force, 293–294 C-bout rhomboid mode (CBR), 324 harmonics and intonation, 291–292 CBR. See C-bout rhomboid mode light bowing, 295 Cello martele´, 295 body modes spiccato/sautille´/ricochet, 295–296 A0, 251, 252 string spectrum, 297–298 A1, 251–252 thumb rule, 290 B1, 252 tone onsets, attacks, 292–294 C, 252, 253 Bowlback mandolin. See Neapolitan mandolin frequencies, 253 Bracing holographic interferograms, 251–252 asymmetrical and radial, guitars, 34–35 resonance (mode) frequencies, 254 hammered dulcimer, 376, 380 vs. double bass, 259 ladder, 88 exploded view, 245, 246 mandolin, 87 family, 256 patterns, 79 history, 245 X-bracing, 81 mobility, 255 Brant, Henry, 320 modal analysis Brauchli, B., 123, 136 frequency response, 247–248 Bretos, J., 225 labeling resonances, 249 Bridge hill, 264 mode observation, 249 Bridges vibration modes, 248–249 banjo, 71–73 sound spectra, 254–255 guitars and lutes, 33 vibration mode, component part hammered dulcimer, 389–390 air cavity modes, 250–251 impedance, 437–438 plate modes, 250 violin vs. violin dimensions, 246 force transfer function, 232 vs. violin resonances, 254 in-plane modes, 231–232 Chaigne, A., 347 mode frequency, 233 Christensen, O., 5, 26 resonance, 231–232 Christian, Charley, 395 schematics, 231 Cimbalom, 99, 117, 118. See also Hammered tuning, 232 dulcimer Broadwood, 6 Cittern, 47 Bucur, V., 131 Clapton, Eric, 397, 398 Burmese arched harp Classical guitar construction, 168–169 bracing, 34–35 history, 167–168 frequencies, principal modes, 25 intonations, 170 holographic interferograms, 28, 29 playing techniques, 168–169 sound quality, 32 plucked tone measurements, 170–171 sound spectrum, 22 scales and tunings, 169–170 top plate resonance, 28 Bynum, E., 245, 253 vibration modes, 23–24 Clavichord, 5–6 design C brass strings, 137 Cabral, P.C., 54 double-fretted, 136 Caldersmith, G.W., 5, 19, 26, 32, 35, 36 fretting, 137–138 Campbell, M., 301 Helmholtz resonance, 137 460 Index

Hubert clavichord, 137 bridge hill, 264 string lengths and diameters, 138 vs. cello, 259 keyboard tuning vs. Dalinger bass, 8–10 cycle of ﬁfths, 141 directional radiation, 275–276 harmonics, 140 player’s support, 269–270 inharmonicity, 142 scaling, 270–271 Pythagorean comma, 141 schematics, 260 quarter-comma meantone, 141 stage risers, 273–275 syntonic comma, 141 tone quality, 264–265 temperament, 141 vibration modes string excitation, 139–140 bowed instruments, 259 Cocchi, A., 255 mobility curves, 261–263 Cohen, D.J., 77, 87, 88 mode shapes, 260 Coincidence frequency, 239–240 in playing, 260–261 Colichon, Michel, 313 vs. violin and cello, 263–264 Complex spectral subtraction, 450 violin octet, 268 Conklin, H.A., 6 Dowland, John, 4 Conklin, H.A. Jr., 347, 365 Driving-point admittance, 432 Consorts, 4 DTC. See Directional tone color Convolution, 414 Ducornet, Marc, 138 Costa, Lorenzo, 307 Duhamel, Jean-Marie, 2 Courtney, P.E., 255 Dulcimer Cousineau, Jacques-Georges, 151 hammered, 117, 352 (see also Hammered Cremer, L., 3, 201, 210, 221, 225, 233, 240 dulcimer) Cremona, 265, 267 history, 5–6 Cremonese instruments, 414–415 Dunnewald,€ H., 214–217, 242, 306, 307, 413 Cristofori, Bartolomeo, 6, 353, 354, 360 Dunnwald-type€ bridge driver, 214 Cross, Eric, 413 Curtin, J., 209, 229, 241, 342, 414 Cylinderback mandolin, 81 E Cymbals, Burmese hand, 167 Eban, G., 35 Edge, Anthony, 310, 311, 313 EDR. See Energy decay relief D Eggers, F., 253 d’Alembert, J.I.R., 2, 11, 15, 423 Eldredge, N., 104 D’Alembert’s wave equation, 423–425 Electric guitar Dalinger double bass, 265–266 body vibrations and dead spots, 39 Dalinger, Sebastian, 263, 266 development, 395–396 David, Gerard, 304 electric bass, 39 Davis, T., 90 electromagnetic pickups, 38 Day, T., 394 features, 37–38 Dedilho, 47 frying pan, 396–397 de Forest, Lee, 393 future developments, 398–399 del Gesu, Giuseppe Guarneri, 2 history, 394–395 del Gesu, Guarneri, 217, 326 magnetic pickups, 38–39, 396–397 de Torres Jurado, Antonia, 4, 19 modern replicas, 397–398 Dickey, J., 59 optical pickups, 39 Digital waveguide model, 426–427 piezoelectric pickups, 39 Dimitru, Gabriel, 399 Electric violin, 240–241 Directional tone color (DTC), 215–216 Beauchamp design, 399–400 Dolmetsch, Arnold, 5 Benioff design, 400–401 Double bass Cremonese instruments, 414–415 body size and sound radiator, 271–273 development, 399 Index 461

hand-crafted design, 401–402 sound spectrum, 30–31 history, 394–395 vibrational motion, 27 multiresonant filter characteristics, Force hammer, 438 412–413 Ford, Henry, 372 pickups Fourier analysis, 14 acoustic, 402–403 Fourier, Jean Baptiste, 212 magnetic, 403–406 Frequency response function (FRF), 8, 213 optical pickups, 410 Friedlander, F.G., 220 piezoelectric, 407–410 Fritz, C., 242, 413 special sound effects, 406 Frying pan guitar, 396–397 signal path schematics, 411 Fryxell, Robert, 210 sound perception and acoustical properties, Fuller, Walter, 397 413–414 Elejabarrieta, M.J., 54, 55 Ellis, Bernard, 303, 305, 306 G Energy decay relief (EDR) Galilei, Vincenzo, 151 definition, 444 Galileo, 2 gain vs. frequency, 447, 448 Galluzzo, P.M., 217, 218 loop filter, 445 Gayageum, 190–193 plucked guitar note plot, 444–445 Gaydecki, P., 413 vs. time, 445–446 Geissler, P., 225 English guitar, 48 Geomungo, 192 Erard, Se´bastien, 6, 151 Gerle, Hans, 304 Errede, Steven, 403 Gervaise, Benoit, 308 Escapement, 356 Ghosh, R.N., 347 Estonia, kannel, 103, 119, 120 Gibson mandola, 96 Experimental modal analysis, 7–8, 319 Gibson, Orville, 78 Gifford, Paul, 371 Gill, D., 77 F Giordano, N., 17, 353 Fado, 47 Gore, Trevor, 35 Farina, A., 241 Gorrill, S., 241 Fast Fourier transform (FFT), 212 Gough, C.E., 393, 414 Fender, Clarence Leonidas, 5 Graesser, H., 399 Fender, Leo, 395, 397, 406 Grand piano, 355 Finger picking/strumming, 17 Gregorian, A., 221 Finger–string interaction, 17 Guarneri, Andrea, 263 Finite element analysis (FEA), 319 Guarneri del Gesu, Giuseppe, 230 Finland, kantele, 103, 120 Guarneri, Joseph, 2 Firth, I.M., 41, 157, 158, 164, 253 Guettler, K., 205, 279, 296 Fixed soundboard, 388 Guitars. See also Portuguese guitar Flangers, 406 acoustic guitars Flatback mandolins, 80–81 classical guitar (see Classical guitar) Fleming, John Ambrose, 393 folk guitar (see Folk guitar) Fletcher, H.A., 215 force exerted, 20–21 Fletcher, N.H., 5, 100, 123, 136, 201, 203 frequency response, 21–22 Floating soundboard, 388 schematics, 20 Folk guitar electric guitars (see also Electric guitar) air cavity modes, 24, 25 body vibrations and dead spots, 39 frequencies, principal modes, 25 electric bass, 39 low-frequency response curve, 26 electromagnetic pickups, 38 plate motion, 28 features, 37–38 sound radiation patterns, 31 magnetic pickups, 38–39 462 Index

optical pickups, 39 perfect fifth, 392 piezoelectric pickups, 39 pin blocks, 390–391 gypsy guitar, 37 soundboard vs. harp, 165 advantages, 388 quality back plates, 389 asymmetrical and radial bracing, 34–35 body modes, 387–388 bridge, 33 fixed and floating, 388 design and construction, 33 materials, 389 top plate and braces thickness, 33–34 sound holes, 391–392 scaled guitars, 35–36 sound radiation pattern, 391 sound radiation, 30–32 string coupling and resonance time string forces, 29–30 power spectrum, 385–386 synthetic materials, 37 vibrations, 386–387 telecaster, 5 tuning stability types, 4 humidity, 380–381 vibrations string-bridge friction, 382 low-frequency resonances, 27–28 temperature, 378–380 modal shapes, 28–29 Hammered strings normal modes, 22 dulcimer, hammered, 352 three-oscillator model, 27 dynamics two-oscillator model, 26 displacement and velocity, 348–349 vibration modes, component parts, spectrum, 348–349 23–25 striking string, 347–348 Guttler,€ K., 218 piano hammers (See Piano hammers) Gypsy guitar, 37 striking position, 351 Hammers compression characteristics, 360 H schematics, 360 Haas, A., 103, 113 spectral analysis, 361–362 Haines, D.W., 37, 174, 175, 229 string, 361 Hair scales, 282 tones, 362–363 Hall, D.E., 6, 347, 350 Hanson, R.J., 203–205 Hammered dulcimer, 117 Harmonic series, 358 basic instrument Harp. See also Burmese arched harp diatonic scales, 372–373 decay times, 163, 164 15 treble/bass courses, 372–373 vs. guitar, 165 treble bridge, 372–373 origins and development, 145–146 tuning scheme, 373–374 soundboard bridge caps and vibrations, 389–390 celtic seaboard, 156 course spacing, 384–385 cracking prevention, 157 history, 371–372 damping, 164 hitch pins, 391 resonance, 163 inharmonicity and scaling, 374–375 soundholes, 158 instrument warp sound output, 157 deflections, 377–378 vibrational behavior, 158, 159 horizontal bridge force, 376–377 soundbox simply supported beams, 376–377 acoustic velocities, 160, 162 lateral stability, 375–376 antinodes, 162 pegleg, 392 bending modes, 160 percussive sound Helmholtz and pipe resonances, hammer-to-bridge reflection, 382–383 158, 160 string-hammer interaction, 383–384 low-frequency behavior, 160 string velocity, 382–383 low modes of vibration, 160, 161 Index 463

sound radiation, 164–165 lute stop, 130 strings metal strings, 127–128 diatonic vs. chromatic stringing, 151 scaling parameters, 128 empirical dependencies, 153 string composition and diameter history, 150–151 variation, 128, 129 inharmonicity, 152 tone quality, 129 pitch dependencies, 153 pull-down mechanism, 135 sharping mechanisms, 151–152 soundboard and radiation sound spectrum influence, 153, 155–156 acoustic and vibrational properties, 131 and sound temporal development, 156, exploded view, 131 157 internal damping, 132 spacing, 152 sound quality, 130 47-string Salvi Aurora, 153, 154 vibrational mode shapes, 131 string-soundboard interaction, 164 string scaling, 123 structure Harpsichords, 5–6 configuration, 148 Harris, N., 229 erard double-action sharping Heat diffusivity, 378 mechanism, 149, 150 Hebenstreit, Pantaleon, 354 geometry and coordinate system, 146, Helmholtz motion, 218–219 147 Hendrix, Jimi, 397, 398 mechanical connection, 149 Henrique, L., 54, 55 Salvi Aurora, 146, 148, 149 Hill, T.J.W., 53 soundboard, 146, 147 Hitch pins, 391 soundbox, 148 Hochbrucker, Jacob, 151 Harpsichord, 16–17 Holliman, A., 399 acoustic balance Holographic interferometry Baroque pitch, 134 banjo, 66, 68 components, 132 cello, 251–252 decay time, 133 cellos, 250–253 Ruckers instrument, 133 guitar, 27–29, 35 sound level, 134 mandolin, 83–84 buff stop, 134 modal analysis, 9 design psalteries and zithers, 107, 108 construction, 125, 126 violin, 224–225 extensions, 134–136 Horiuchi, R., 189 hitchpins, 126 Horton, N.G., 38 jack, 126, 127 Hubbard, F., 123, 136 operation basis, 124 Hubert, Christian Gottlob, 136, 138 pedal mechanism, 127 Humbucking coil systems, 405–406 string tension, 124 Hutchins, C.M., 1–3, 36, 210, 222, 227–229, Flemish instruments, 135 256, 268, 317–323, 326–330, 332, keyboard tuning 337–339, 341–343 cycle of fifths, 141 Hutchins-Schelleng violin octet harmonics, 140 A1 radiation in B1 region, 326–327 inharmonicity, 142 development Pythagorean comma, 141 evolution, 321–323 quarter-comma meantone, 141 signature modes, 323–324 syntonic comma, 141 direct radiation mechanisms, 321 temperament, 141 history, 319–320 lute stop, 135 material properties, 325 plucked strings modal and acoustical analyses fundamental vibration frequency, 127 A0 and A1 coupling, 336–337 harmonics, 129 A1 mode status, 338–340 464 Index

A1 radiation, 340 Kirnberger III, 141 averaged corpus vibration, 333–335 Kishi, K., 185 force hammer impact excitation, Knott, G.A., 225, 322 333–334 Kohut, J., 7, 215, 241, 412, 413 lower/upper bout pressure ratio, Kondo, M., 201 340–341 Koto relative strength, 341 harmonic structure, 191 rib height and pressure ratio, 338 pentatonic scale, 190 tests, 332–333 sound holes, 190 wall compliance and cavity mode transfer function, 192 frequencies, 337–338 tuning, 192 mode, 317 vibrato effects, 192 nomenclature, 319 Kottick, E.L., 123, 136 radiation mechanisms, 324–325 Koussevitzky, Serge, 265, 267 resonance, 320–321 Krigar-Menzel, O., 201 scaling Kubata, H., 201 A0 equation, 330–331 Kuus, Alfred, 117, 118 assumptions, 327–328 Ky, Lovikka, 118 flat plate equations, 329–330 practicality, 328–329 shape similarity, 331–332 L shape/size, 318 Lang, 266 signature modes, 318 Langhoff, A., 214, 235, 253 Langmuir, Irving, 393 Latvia, kokle, 103, 119 I Lauterborn, W., 241 Impulsive waves, 12 Lawergren, B., 201 Inaćio, O., 53 Le Carrou, J.-L., 17 Inverse filtering, 450 Lee, N., 417 Leoncavallo, 78 Linarol, Francesco, 308–310 J Linear superposition principle, 12 Jahnel, F., 4, 19 Linear system, 319 Jansson, E.V., 5, 6, 21, 32, 33, 53, 223, Lithuania, kankles, 103 225, 228, 231, 305, 321, 322, Loar, Lloyd, 78, 395, 399 339, 347, 351 Loos, U., 217 Japanese instruments Lover, Seth, 405 koto, 190–192 Lundberg, R., 40 Satsuma biwa (see Satsuma biwa) Lutes shamisen, 187–190 European short lute, 41, 42 Johnson, Ieva Sijats, 112 long-necked lute, 41–44 Johnson, J.R., 78 mechanical admittance, 41 Jones, Richard, 308–310 plectrum, 4 Renaissance, 40 Turkish tanbur, 41–44 K uses, 4 Karplus, K., 431 Lynn, Bert, 395, 400 Kasha, M., 35 Kasil, King, 192 Keller, J.B., 220 M Kennedy, Nigel, 401 Maala, V€aino, 120 Khin May, Daw, 168, 170 Magnitude spectrum smoothing method Kimura, M., 204, 205 (MSS), 441–442 Index 465

Mandocello, 82–83, 96 C holes, 303 Mandola, 82–83 construction, 302, 303 Mandolin rebecs (see Rebecs) archtop mandolins Meinel, H.F., 210, 214 f-holes, 81 Mellody, M., 215 oval soundhole, 81 Memling, Hans, 302 cylinderback mandolins, 81 Mersenne, M., 2, 210, 314 family, 77–78 Meyer, Erwin, 210 flatback mandolins, 80–81 Meyer, J., 5, 6, 21, 53, 92 F5 mandolin, 78 Mobility curves general similarity law, 95 cello and violin, 248 Gibson mandola, 96 double bass Helmholtz air resonance frequency, 95 Dalinger bass, 266 mandocello, 82–83, 96 definition, 261–262 mandola, 82–83 double bass bridge, 265 Neapolitan mandolin, 79–80 double bass vs. violin and cello, normal mode frequencies 263–264 asymmetric radial bracing pattern, 79, measurement, 262, 265 91–92 mode shapes, 261, 262 firmer bass response, 91 player’s support, 269–270 modal analysis, 87 quality, 264, 266 (0,0) mode, 91 small and large bass, 269 (1,0) mode, 92 Mockel,€ O., 229 plate/air phase relationships, 88, 90 Modal analysis normal mode shapes and acoustical analysis, Hutchins-Schelleng Helmholtz air resonance, 86–87 violin octet ODS, 84–85 A0 and A1 coupling, 336–337 two-oscillator and three oscillator A1 mode status, 338–340 model, 86 A1 radiation, 340 normal vibration modes and holographic averaged corpus vibration, 333–335 interferometry, 83–84 force hammer imapct excitation, octave mandolin, 82–83 333–334 operating deflection shape (ODS), 83 lower/upper bout pressure ratio, popularity, 78 340–341 sustainability, 89, 92–94 relative strength, 341 Mandoline. See Neapolitan mandolin rib height and pressure ratio, 338 Marie Antoinette, Queen, 151 tests, 332–333 Marshall, K.D., 225, 322 wall compliance and cavity mode Marty, Simon, 35 frequencies, 337–338 Mascagni, 78 cellos, 247–249 Masino, T.R., 233 experimental modal testing, 7–8, 319 Mathematical modal analysis, 8 holographic modal analysis, 9 Mathews, M.V., 7, 215, 241, 401, 410, 412, 413 mathematical modal analysis, 8 Matrix-pencil inverse-filtering (MPIF) sound field analysis, 9 method, 440 violin, 225 Maung Maung Gyi, U., 168 Molin, N-E., 225, 260 Ma, Yo-Yo, 401 Monochord, 357 May, Vanessa, 401 Monroe, Bill, 78 McIntyre, M.E., 201, 214, 216–218, 410 Moore, Brian, 413 Mechanical admittance, 222 Moore, T.R., 38, 59 Medieval bowed string instruments Moral, J.A., 228, 229 fiddles Moseley, Semie, 398 acoustical properties, 305–306 Mozart, Leopold, 6, 78, 284–285 466 Index

Muhling,€ Kristi, 120 Peekna, A., 99, 115 Muller,€ G., 241 Pegleg, 392 Muller,€ H.A., 225, 232 Percussive sound, 382–384 Multiresonant filter characteristics, 412–413 Peterson, D., 371 Musical acoustics, 1 Pfeil, Victor, 399 Myall, Norman, 309, 311–313 Phaser effect, 406 Myint Maung, U., 168, 170, 171 Philp, Eugene, 36 Piano, 6 Piano acoustics N design, 355–356 Nakamura, I., 6 hammers (see Piano hammers) Neapolitan mandolin, 79–80 history, 353–355 Neupert, H., 123, 136 modeling, 368–369 Nodes, 13 soundboard Northwestern Russia, gusli, 103 mechanical response, 366 patterns, 365–366 second partial behavior, 363–364 O sound production, 363 Octave mandolins, 82–83 speaker, 363 Octave stretching, 359–360 vibrational modes, 364–365 ODS. See Operating deflection shape tones, 367 Operating deflection shape (ODS) vibrating strings baltic psalteries, 105–108 arrangement, 356–357 cello, 248 harmonic frequencies, 358–359 guitars, 22 monochord, 357 Hutchins-Schelleng violin octet, 325 octave stretching, 359–360 mandolin, 83 schematics, 355 violin, 222 standing waves, 357–358 Oppenheim, A.V., 420 Young’s modulus, 359 Ordu$$$a-Bustamante, F., 53, 55 Pianoforte, 354 Piano hammers acoustics P compression characteristics, 360 Parameter estimation, virtual string schematics, 360 instruments spectral analysis, 361–362 body resonator (see Body resonator) string, 361 excitation tones, 362–363 MPIF, 440 hardness, 349–350 MSS, 441–442 string excitation, 350–351 SPNIF, 440–441 Pickering, N.C., 218 SSI, 442–444 Pickups, electric violin radiated sound pressure acoustic, 402–403 low-order filter, 451–452 magnetic measurement, 452 humbucking systems, 405–406 radiation response measure, 450–451 resonant frequency, 404 STFT, 439–440 sensitivity dependence, 404–405 string loop filter estimation steel string vibrations, 403–404 digital waveguide model, 445 optical pickups, 410 EDR (see Energy decay relief) piezoelectric Partials, 358 bowed string instruments, 407–408 Patch near-field acoustical holography frequency response, 408–409 (pNAH), 323 heavy bridge, 409–410 Paul, Les, 5, 395, 397, 398 material, 407 Index 467

mounting position, 408 Lisbon guitar, 48–49 special sound effects, 406 origin, 47–48 Pin block, 390–391 Porto guitar, 48 Pipa, 186 subjective acoustical quality evaluation Pitteroff, R., 201 listening tests, 54 Plectrum, 354 objective parameters, 53–54 Plucked string instruments test procedure, 55–56 classification tests conditions, 54–55 abscissa, 175 timbre, 56 acoustical properties, 176 vibroacoustic behavior hachion, 173 accelerance FRF, 50–51 soundboard, 174 Helmholtz resonance, 50–52 sound board wood, 176 modal characteristics, 49 sound-hole structure, 174 monopole and dipole modes, 52–53 transmission characteristics, 175 vibroacoustic transfer functions, 49 wood properties, 174 Powell, R.L., 225 force, transverse and longitudinal, 15–16 Praetorius, M., 311 frequency analysis, 14 Psalteries Japanese koto and Korean gayageum baltic (see Baltic psalteries) geomungo, 192 plucking stiffness and strength, 100–101 harmonic structure, 191 string pentatonic scale, 190 materials, 101–102 sound holes, 190 stress, 100 transfer function, 192 zither family, 99 tuning, 192 Puccini, 78 vibrato effects, 192 Pythagoras, 1, 357 Japanese Satsuma biwa vs Chinese pipa, 186 fundamental structure, 176, 177 Q sawari mechanisms, 180–184 Quiescent camber (QC), 280 sound characteristics, 185–186 string tension, 176 structural response, 178–180 R Japanese shamisen Radiation efficiency, 240 sawari mechanism, 189–190 Radiation ratio, 229 string-bridge-membrane system, Radiativity, 319 187–189 Rae, J., 59 plucking Raejusters, 60, 69 finger picking/strumming, 17 Raman, C.V., 3, 201, 210, 220, 347 plectrum, harpsichord, 16–17 Raphael, 308 rest and free strokes, 17 Raps, A., 201 spectrum, 14–15 Rayleigh, L., 3 time analysis, 14, 16 Rebecs transverse waves acoustical properties, 306–307 impulsive waves, reflection and sound characteristics, 303, 304 interference, 12 structural features, 304 standing waves, 12–13 Reinecke, W., 225, 265 pNAH. See Patch near-field acoustical Reinel, 266 holography Reinhardt, Django, 37 Polkki,€ J., 114 Renaissance viols Portuguese guitar acoustics, 309–310 Coimbra guitar, 48–49 development, 307–309 frequency response vs. resonance, 56–57 Richardson, B.E., 5, 21, 23, 26, 33, 34, 92 468 Index

Rickenbacher, Adolph, 5 Second harmonics. See Standing waves Roberts, G.W., 24, 26, 33 Senda, T., 184 Roberts, M., 224 Sethares, W.A., 142 Rodgers, O.E., 214, 225, 228, 233 Shaker, 438 Rossing, T.D., 1, 11, 19, 21, 26, 59, 60, 77, Shamisen 83, 86–88, 92, 99, 100, 123, sawari mechanism, 189–190 197, 201, 203, 209, 221, 224, string-bridge-membrane system, 245, 260, 347 187–189 Rossini, 19 Shaw, E.A.G., 322 Ross, R.E., 21, 26 Short-time-Fourier-transform (STFT), Rubio, David, 305, 313 439–440 Ruckers, Andreas, 125 Silbermann, Gottfried, 6, 354 Ruckers, Hans, 5 Sines-plus-noise inverse-ﬁltering method Ruggieri, Francesco, 263 (SPNIF), 440–441 Russell, R., 123, 136 Sizzle, 215 Smallman, Greg, 34, 36 Smith, J.O., 417, 427, 436 S Smith, R.R., 398, 400 Sachs, C., 145 Sor, Fernando, 4, 19 Saldner, H.O., 235 Sound ﬁeld analysis, 9 Sampling rate, 419 Sound holes, 391–392 Sanders, L.C., 215 Sound radiation Satsuma biwa banjo, 62–64 vs. Chinese pipa, 186 guitars, 30–32 fundamental structure, 176, 177 hammered dulcimer, 391 sawari mechanisms harp, 164–165 collision process, 184 harpsichord, 130–132 degree of reverberation, 181 violin, 235–238 Kyushu type, 181, 182 Spanish-style harp, 157 numerical simulations, 184 Sparks, P., 77 plucked string vibration (Doubt), 183 Spear, R., 342, 343 Runge-Kutta method, 182 Standing waves tori-kuchi or shohgen, 180 piano, 357–358 sound characteristics, 185–186 plucked strings, 12–13 string tension, 176 Statistical spectral interpolation method (SSI), structural response, 178–180 442–444 Saunders, F., 3, 210, 216, 319–322 Stein, Nannette, 6 Sau`ng gauk. See Burmese arched harp Steinway, Henry, 6 Savage, W.R., 131, 132 Stephey, L.A., 59 Savart, Felix, 2, 3, 210, 228 Stetson, K.A., 225 Scattering junction, 434 STFT. See Short-time-Fourier-transform Schelleng, J.C., 36, 175, 197, 201, 203, 210, Stradivari, Antonio, 2 218, 219, 229, 289, 298, 317, 318, Strings 320, 321, 324, 326, 328–330, 332, damping, 285 337, 339, 340 tension, 284–286 Schelleng’s ratio, 340–341 torsion, 287 Scherer, 410 wave resistance/impedance, 283–284 Schleske, M., 212, 229, 234, 235, 322, 328, Strong, A., 431 330, 342 Structural acoustics, 324–325 Schmitz, H.-E., 178, 185 Strutt, J.W., 3 Schneider, Richard, 35 Sulis, Doriano, 185 Schubert, 19 Sundin, H., 322 Schumacher, R.T., 203, 218 Suzuki, H., 6 Index 469

T ribs, 233 Taguti, T., 88, 180, 184, 185 tap tones (see Tap tones) Takasawa, Y., 187 top and back plates, 227 Tangent, 354 vs. double bass, 263–264 Tap tones electric (see Electric violin) Chladni patterns, 227 electric and virtual, 241–242 Italian violins, 228 evaluation, 211–212 plate tuning, 228–229 frequency response, 213 radiation ratio, 229 high-frequency radiation, 239–240 Tarrega, Francisco, 4, 19 history, 209–210 Taskin, Paul, 5 low-frequency radiation Taylor, Brook, 2 monopole radiation, 237, 239 Te¨mkin, I., 104 total radiation, 239 Thwaites, S., 123, 136 volume ﬂuctuation, 237, 239 Tiideberg, Ilmar, 118, 119 naming modes, 221 Tohnai, K., 178, 180, 184, 185 playability Tolonen, T., 436 bow force limits, 219–220 Toshikawa, 184 damping, 220 Tourte, Francois, 2, 210, 279, 281, 282 Helmholtz motion, 218–219 Transverse waves mobility, 218 plucked strings, 12–13 radiation damping, 240–241 Tronchin, L., 255 research, 210–211 Tsuruta, Kinshi, 182 sound analysis, 212–213 Tuning stability, hammered dulcimer sound radiation measurement humidity, 380–381 experimental setup, 236 string-bridge friction, 382 microphone position, 235–238 temperature radiativity, 235 vs. frequency, 378–379 single microphone measurement, tension, 379–380 237 thermal expansion, 379 single response curves, 237–238 Tureck, Rosalyn, 401 spikiness, 237 Turkish tanbur, 41 tone quality Turnbull, H., 4, 19 acoustical measurement, 213–214 Tyler, J., 77 DTC, 215–216 Dunnwald-type€ bridge driver, 214 echoes, 214–215 V projection/carrying power, 216–217 Valette, C., 285 sizzle, 215 V€alim€aki, V., 436 timbre, 214 Ventapane, Lorenzo, 263 vibrations Verdi, 19 modal analysis, 225 Vermeij, K., 123, 136 modal overlap, 226 Vihuela, 19 normal modes, 222–223 VIOCADEAS analysis, 319 statistical overlap, 226 Viola, 47 three-dimensional model, 224–225 Violin two-dimensional model, 223–224 vs. cello, 254 Violin octet, 268 component parts Viols bassbar and soundpost, 234–235 baroque viols (see Baroque viols) bridge (see Bridge) family, 301 enclosed air, 230 medieval bowed string instruments ﬁngerboard, 234 (see Medieval bowed string mass, 229–230 instruments) 470 Index

Viols (cont.) Vivaldi, 78 renaissance viols von Helmholtz, H.L.F., 3, 197, 200, 201, acoustics, 309–310 210, 218, 347, 367 development, 307–309 von Hornbostel, E.M., 145 Virtual string instruments, 7 von Weber, 19 applications, 417 Vuillaume, Jean Baptiste, 2, 210 body resonance bi-directional interaction, 433–434 driving-point admittance, 432 W filtering, 432–433 Wah-wah effect, 406 string-body scattering junction, Wakefield, G., 215 434–435 Waltham, C., 145 decomposition abstraction block diagram, Way, D.J., 138 422 Weinreich, G., 6, 215, 216, 235, 239, 241, 414 digital nomenclature Werckmeister III, 141 filtering, 422 Wien, 263 sampling, 419–420 Wilfer, 266 sum of sinusoids, 420–422 Wilkins, R.A., 250 measurements Williams, J., 34 body vibration, 438–439 Williamson, M.C., 168, 170 bridge impedance, 437–438 Williamson, R.M., 167, 170 pressure signal, 439 Willsky, A.S., 420 string vibration, 436–437 Winans, J.P., 17 old recordings, 417–418 Wogram, K., 6 parameter estimation Wolf note, 220 body resonator, 447–450 Wolf tones, 284 excitation, 440–444 Woodfield, I., 307 radiated sound pressure, 450–452 Woodhouse, J., 214, 216–219, 226, 231, 255, short-time-Fourier-transform, 439–440 305, 413 string, 444–447 Wungyi, Myawadi, 168 plucking string complexities, 431 theoretical, 430–431 Y pressure radiation, 435–436 Yako, M., 190 vibration string Yamanaka, K., 88 D’Alembert’s wave equation, 423–425 Yoshikawa, S., 173, 174, 176 delay line, 425–426 Young’s modulus, 359 digital waveguide model, 426–427 natural decay, 427–428 plane vibration, 428–429 Z varying digital waveguides, 429–430 Zithers Virtual violin fretted (alpine), 116 digital bow, 241 without fretboard, 115 reciprocal bow, 241–242 Zuckermann, W.J., 123 Vistasen, R.B., 26 Zwicker, T., 5