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 Franc¸ois 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,