Principles of radiation of bowed instruments and challenges for modelling. FAMA 2017 Berlin

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1 1 / 9 Principles of radiation of bowed instruments and challenges for modelling Robert Mores University of Applied Sciences Hamburg 1

2 Plate modes f mn Frequencies in plane wooden plates: 2 m 1 2 n 1 0,453 h cl cw L W for mode m across length L and mode n across width W of the plate plate strength h, speed of sound cl and cw Mode superposition on frequency coincidence (0,0) (1,2) (0,2) (2,0) (0,2) (2,0) H (0,2) (2,0) H For Sitka spruce: W / L ca. 1.9 Fletcher and Rossing, / 9

3 Body modes breathing superposition bending () breathing superposition bending () Signature modes B1 B1, but also CBR Gough, / 9

4 Helmholtz and cavity modes Helmholtz resonance A0 volume V of the cavity, speed of sound c area A of the fholes for neckless cavities correction factor a = Hz Cavity modes at A1 500 f0 A c 2 A A h a A V A Hz Bissinger, 1992 and 1992b 4 4 / 9

5 Tuning Plates Signature modes Helmholtz Cavity modes Example: spacing between A1 and B1 > 100Hz Hz Hz Hz by h by rib strength and height by volume and fhole area by fhole position, cavity height 5 / 9 unplayable violin edgy tone, for skilled soloists only fine ton and projection for soloists gentle tone for chamber music and easy playing Hutchins,

6 Radiation versus mobility measurements radiated sound Bridge admittance Y in db (65 db) / SPL in db / 9 90 CBR B1 A1 B plate modes plate modes A0 C1 bridge admittance Schleske, Frequency in Hz Schreiber Stradivari 6

7 Critical frequency n= n=2 90 n=3 90 n=4 d > λ /2! d = f (E) fcrit 1/Dicke fbend Dicke d=¾ 90 Summe = null n=6 e m al m / 9 Su a7xim m 0 n= e m al m Su axim m Reihe gegenphasiger Einzelquellen Erst bei hohen Frequenzen wird der kritische Wert von d = λ/2 erreicht, da der Abstand im Gegentakt schwingender Bereiche mit dem Kehrwert der Wurzel aus der Frequenz fällt, während die Luftwellenlänge mit dem Kehrwert der Frequenz fällt. 7

8 1712 Schreiber Stradivari radiation 360 one axis 8 / 9 8

9 Challenge for modelling: nonstationary radiation (1) Vibrato > frequency modulation Combined with resonance profile amplitude modulation 9 / 9 Stegadmittanzpegel in db Teilton 35 ct ct f in Hz Meyer: Zur klanglichen Wirkung des StreicherVibratos, Acustica 76, Weinreich: Directional tone color, JASA 101,

10 Sampled instruments RWTH Aachen 10 / 9 10

11 Sampled instruments Brigham Young University 37 mics semicircular, 5 steps some slides from Leishmans presentation 11 / 9 Leishman: Highresolution directivities of several played musical instruments, ACOUSTICS 17, Boston,

12 Numerical modelling Early FEM/FDM: Marshall Recent FEM/FDM: Bader Problems: 12 / 9 Inaccuracy (edges, plate thickness, anisotropic material) Radiation? Computational effort Marshall, Modal analysis of a violin, JASA 77(2), Bader, Whole geometry FiniteDifference modeling of the violin, ForumAcusticum, Budapest,

13 Inverse modelling Rolf Bader solved the inverse problem of formulating plate vibrational modes from microphone array recordings 13 / 9 early: 100 mics, plucked, bowed, percussive now: 1000 mic positions, grand Bader: Reconstruction of radiating sound fields using minimum energy method JASA 127, Bader, Fischer, Abel: Minimum Energy Method (MEM) microphone array backpropagation for measuring musical wind instruments sound hole radiation, JASA 141,

14 Trend modelling General predictions from empirical data translated into an auralized (mono) trend model parameters: plate strength & bridge rocking frequency 14 / 9 O X Bissinger & Mores, JASA 137,

15 Challenge for modelling: nonstationary radiation (2) Instruments in motion during performance: directional tone colour = f(time) Spatial acuity improves with source in motion (and head in motion) E.g. distance acuity 15 / 9 Real violinist in natural motion Stationary sound sources Mores, AES convention, Piteo, Kerkmann & Mores, DAGA, Darmstadt,

16 Sampling rooms E.g. concert halls Sampling individual seats Sampling of performer space mapping in the hall 16 / 9 Amengual, S. V., Pätynen, J., and Lokki, T., "Physical and perceptual comparison of real and focused sound sources in a concert hall," Journal of the Audio Engineering Society, vol. 64, no. 12, pp ,

17 Modelling rooms Virtual acoustics, eg. with UNITY 17 / 9 Vorländer: Auralization: fundamentals of acoustics, modelling, simulation, algorithms and acoustic reality Springer, Behler, Pollow, Vorländer, M.: Measurements of musical instruments with surrounding spherical arrays. Acoustics

18 Virtual violin capturing in a familiar environment 18 / 9 Türckheim: Die virtuelle Violine, Dissertation

19 Virtual violin playing various violins 19 / 9 piezo transfer function H EQ: H1 minimumphase filter design minimumphase filter design convolution convolution 19

20 Thank you References Amengual et al.: Physical and perceptual comparison of real and focused sound sources in a concert hall, J. AES 64, Bader, R.: Whole geometry FiniteDifference modeling of the violin. In Proceedings of the Forum Acusticum, Bader, R. : Reconstruction of radiating sound fields using minimum energy method. JASA 127(1), , Bader, R.: Microphone array. In Springer Handbook of Acoustics (pp ). Springer New York, / 9 Bader, Fischer, Abel: Minimum Energy Method (MEM) microphone array backpropagation for measuring musical wind instruments sound hole radiation, JASA 141, Behler, Pollow, Vorländer, M.: Measurements of musical instruments with surrounding spherical arrays. Acoustics Bissinger, Mores (2015). Modelbased auralizations of violin sound trends accompanying platebridge tuning or holding. JASA 137(4). Cremer, Lothar: Physik der Geige, Hirzel, Kerkmann, Mores: Precision and Shifting Effects of Distance Hearing in Listening Tests, 38. DAGA Darmstadt, Marshall, K. D.: Modal analysis of a violin. The Journal of the Acoustical Society of America, 77(2), , Meyer: Zur klanglichen Wirkung des StreicherVibratos, Acustica 76, Loomis & Klatzky & Golledge: Mixed Reality Merging, Real and Virtual Worlds, Springer, Berlin, Leishman: Highresolution directivities of several played musical instruments, ACOUSTICS 17, Boston, Mores, R.: Measuring Perceived Distance of Violins A Direct Scaling Test. 38th AES Conference in Piteo, Schleske, Martin: Empirical Tools in Contemporary Violin Making: Part I. CAS Journal Vol. 4, No.5 (Series II), May Vorländer: Auralization: fundamentals of acoustics, modelling, simulation, algorithms and acoustic reality Springer, Weinreich, G.: Directional tone color. The Journal of the Acoustical Society of America, 101(4), , Türckheim: die virtuelle Violine, Dissertation, HSU Hamburg,