We discuss how the modal response of violin plates changes as their shape varies. Starting with an accurate 3D scan of the top plate of a historic violin, we develop a parametric model that controls a smooth shaping of the interior of the plate, while guaranteeing that the boundary is the same as the original violin. This allows us to generate a family of violin tops whose shape can be smoothly controlled through various parameters that are meaningful to a violin maker: from the thickness in different areas of the top to the location, angle, and dimensions of the bass bar. We show that the interplay between the different parameters affects the eigenmodes of the plate frequencies in a nonlinear fashion. We also show that, depending on the parameters, the ratio between the fifth and the second eigenfrequencies can be set to match that used by celebrated violin makers of the Cremonese school. As the parameterisation that we define can be readily understood by violin makers, we believe that our findings can have a relevant impact on the violin making community, as they show how to steer geometric modifications of the violin to balance the eigenfrequencies of the free plates.
References
1.
Blahout
, V.
(2020
). “The violin making manual
,” http://www.makingtheviolin.com/ (Last viewed 3/2/2021).2.
Bretos
, J.
, Santamaria
, C.
, and Moral
, J. A.
(1999
). “Vibrational patterns and frequency responses of the free plates and box of a violin obtained by finite element analysis
,” J. Acoust. Soc. Am.
105
(3
), 1942
–1950
.3.
Buen
, A.
(2006
). “Can we hear the geometrical measures of a violin?
,” in Proceedings of the Joint Baltic-Nordic Acoustics Meeting (BNAM)
, Gothenburg, Sweden, pp. 1
–15
.4.
Buksnowitz
, C.
, Teischinger
, A.
, Müller
, U.
, Pahler
, A.
, and Evans
, R.
(2007
). “Resonance wood [Picea abies (L.) Karst.]—Evaluation and prediction of violin makers' quality-grading
,” J. Acoust. Soc. Am.
121
(4
), 2384
–2395
.5.
Cacciatori
, F.
(2016
). Antonio Stradivari. Disegni, Modelli, Forme. Catalogo Dei Reperti Delle Collezioni Civiche Liutarie Del Comune di Cremona. Con DVD. Ediz. italiana e Inglese
(MdV-Museo del Violino
, Cremona, Italy
).6.
Canclini
, A.
, Antonacci
, F.
, Tubaro
, S.
, and Sarti
, A.
(2020
). “A methodology for the robust estimation of the radiation pattern of acoustic sources
,” IEEE/ACM Trans. Audio Speech Lang. Process.
28
, 211
–224
.7.
Chatziioannou
, V.
(2019
). “Reconstruction of an early viola da gamba informed by physical modeling
,” J. Acoust. Soc. Am.
145
(6
), 3435
–3442
.8.
Curtin
, J.
(2005
). “Tap tones and weights of old Italian violin tops
,” J. Violin Soc. Am.
20
(2
), 161
–174
.9.
Davis
, E. B.
(2013
). “On the effective material properties of violin plates
,” in Proceedings of the Stockholm Music Acoustics Conference 2013
, July 30 to August 3, Stockholm, Sweden.10.
Edelsbrunner
, H.
, Kirkpatrick
, D.
, and Seidel
, R.
(1983
). “On the shape of a set of points in the plane
,” IEEE Trans. Inf. Theory
29
(4
), 551
–559
.11.
Fritz
, C.
, Curtin
, J.
, Poitevineau
, J.
, Borsarello
, H.
, Wollman
, I.
, Tao
, F.-C.
, and Ghasarossian
, T.
(2014
). “Soloist evaluations of six Old Italian and six new violins
,” Proc. Natl. Acad. Sci. U.S.A.
111
(20
), 7224
–7229
.12.
Fritz
, C.
, Curtin
, J.
, Poitevineau
, J.
, Morrel-Samuels
, P.
, and Tao
, F.-C.
(2012
). “Player preferences among new and old violins
,” Proc. Natl. Acad. Sci. U.S.A.
109
(3
), 760
–763
.13.
Fritz
, C.
, Woodhouse
, J.
, Cheng
, F. P.-H.
, Cross
, I.
, Blackwell
, A. F.
, and Moore
, B. C.
(2010
). “Perceptual studies of violin body damping and vibrato
,” J. Acoust. Soc. Am.
127
(1
), 513
–524
.14.
Gore
, T.
, and Gilet
, G.
(2016
). Contemporary Acoustic Guitar Design and Build
, 2nd ed., Vol. 1
(Trevor Gore
, Terrey Hills, Australia
).15.
Gough
, C.
(2015
). “Violin plate modes
,” J. Acoust. Soc. Am.
137
(1
), 139
–153
.16.
Harris
, N.
(2005
). “On graduating the thickness of violin plates to achieve tonal repeatability
,” VSA Papers
1
(1
), 111
–120
.17.
Hutchins
, C. M.
(1981
). “The acoustics of violin plates
,” Sci. Am.
245
(4
), 170
–187
.18.
Knott
, G.
, Shin
, Y.
, and Chargin
, M.
(1989
). “A modal analysis of the violin
,” Finite Elem. Anal. Des.
5
(3
), 269
–279
.19.
Molin
, N.-E.
, Lindgren
, L.-E.
, and Jansson
, E. V.
(1988
). “Parameters of violin plates and their influence on the plate modes
,” J. Acoust. Soc. Am.
83
(1
), 281
–291
.20.
Nia
, H. T.
, Jain
, A. D.
, Liu
, Y.
, Alam
, M.-R.
, Barnas
, R.
, and Makris
, N. C.
(2015
). “The evolution of air resonance power efficiency in the violin and its ancestors
,” Proc. Math. Phys. Eng. Sci.
471
(2175
), 20140905
.21.
Razeto
, M.
, Staforelli
, C.
, and Barrientos
, G.
(2006
). “Sensibility analysis of violin plates
,” in Computational Methods in Engineering and Science
(Springer
, Berlin
), pp. 333
–333
.22.
Ross
, R. J.
(2010
). Wood Handbook: Wood as an Engineering Material
, General Technical Report GTR-190 (United States Department of Agriculture, Forest Service, Forest Products Laboratory
, Madison, WI
).23.
Sacconi
, S.
, Dipper
, A.
, and Rivaroli
, C.
(1979
). The Secrets of Stradivari
(Libreria del Convegno
, Milan, Italy
).24.
Schelleng
, J. C.
(1968
). “Acoustical effects of violin varnish
,” J. Acoust. Soc. Am.
44
(5
), 1175
–1183
.25.
Schleske
, M.
(1996
). “Eigenmodes of vibration in the working process of a violin
,” Catgut Acoust. Soc. J.
3
(1
), 2
–8
.26.
Setragno
, F.
, Zanoni
, M.
, Antonacci
, F.
, Sarti
, A.
, Malagodi
, M.
, Rovetta
, T.
, and Invernizzi
, C.
(2017
). “Feature-based analysis of the impact of ground coat and varnish on violin tone qualities
,” Acta Acust. United Acust.
103
(1
), 80
–93
.27.
Staforelli
, C.
, Razeto
, M.
, and Pascual
, R.
(2002
). “Numerical and experimental analysis on the dynamic behaviour of the violin plates
,” in Proceedings of the 2002 International Conference on Noise and Vibration Engineering
, ISMA, September 16–18, Leuven, Belgium.28.
Stoel
, B. C.
, and Borman
, T. M.
(2008
). “A comparison of wood density between classical Cremonese and modern violins
,” PLoS One
3
(7
), e2554
.29.
Tai
, H.-C.
, Shen
, Y.-P.
, Lin
, J.-H.
, and Chung
, D.-T.
(2018
). “Acoustic evolution of old Italian violins from Amati to Stradivari
,” Proc. Natl. Acad. Sci. U.S.A.
115
(23
), 5926
–5931
.30.
Tinnsten
, M.
, and Carlsson
, P.
(2002
). “Numerical optimization of violin top plates
,” Acta Acust. United Acust.
88
(2
), 278
–285
.31.
Torres
, J. A.
, Soto
, C. A.
, and Torres-Torres
, D.
(2020
). “Exploring design variations of the Titian Stradivari violin using a finite element model
,” J. Acoust. Soc. Am.
148
(3
), 1496
–1506
.32.
Woodhouse
, J.
(2014
). “The acoustics of the violin: A review
,” Rep. Prog. Phys.
77
(11
), 115901
.33.
Yu
, Y.
, Jang
, I. G.
, Kim
, I. K.
, and Kwak
, B. M.
(2010
). “Nodal line optimization and its application to violin top plate design
,” J. Sound Vib.
329
(22
), 4785
–4796
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