Correlation Between Anatomical Grading and Acoustic–Elastic Properties of Resonant Spruce Wood Used for Musical Instruments

Article Correlation between Anatomical Grading and Acoustic–Elastic Properties of Resonant Spruce Wood Used for Musical Instruments Florin Dinulică 1 , Mariana Domnica Stanciu 2,3,* and Adriana Savin 4 1 Department of Forest Engineering, Forest Management Planning and Terrestrial Measurements, Transilvania University of Brasov, 500123 Brasov, Romania; [email protected] 2 Department of Mechanical Engineering, Transilvania University of Brasov, B-dul Eroilor 29, 500360 Brasov, Romania 3 Russian Academy of Natural Sciences Sivtsev Vrazhek, 29/16, Moscow 119002, Russia 4 Institute of Research and Development for Technical Physics, B-dul Mangeron 47, 700050 Iasi, Romania; [email protected] * Correspondence: [email protected] Abstract: This paper deals with the acoustic and elastic properties of resonant wood, classified into four classes, according to the classification of wood quality by the manufacturers of musical instruments. Traditionally, the quality grades of resonant wood are determined on the basis of the visual inspections of the macroscopic characteristics of the wood (annual ring width, regularity, proportion of early and late wood, absence of defects, etc.). Therefore, in this research, we studied whether there are correlations between the acoustic and elastic properties and the anatomical char- Citation: Dinulic˘a,F.; Stanciu, M.D.; acteristics of wood used for the construction of violins. The results regarding the identification of Savin, A. Correlation between the anatomical properties of resonant spruce, the wood color, and the acoustic/elastic properties, Anatomical Grading and Acoustic–Elastic Properties of determined by ultrasonic measurements, were statistically analyzed to highlight the connection Resonant Spruce Wood Used for between the determined properties. From the statistical analysis, it can be seen that the only variables Musical Instruments. Forests 2021, 12, with the power to separate the quality classes are (in descending order of importance) the speed of 1122. https://doi.org/10.3390/ sound propagation in the radial direction, Poisson’s ratio in the longitudinal–radial direction, and f12081122 the speed of propagation of sounds in the longitudinal direction. Academic Editors: Michele Brunetti, Keywords: anatomical patterns; resonant spruce; acoustic properties; elastic properties; Discriminant Michela Nocetti and Function Analysis; Principal Components Analysis Alexander Petutschnigg Received: 22 July 2021 Accepted: 20 August 2021 1. Introduction Published: 22 August 2021 Numerous studies concerning the acoustical behavior of violins refer to the similarities Publisher’s Note: MDPI stays neutral and differences in the tonal qualities, produced by good and bad, and old and new instru- with regard to jurisdictional claims in ments, depending on various factors [1–4]. Wood with anatomical and acoustic properties published maps and institutional affil- used in the construction of stringed musical instruments is also known as resonant wood, iations. tonewood, or music wood. The acoustical characteristics of wood species are criteria for the selection of the most appropriate raw material for making violins [4–6]. The behavior of wood in the acoustic field is conditioned by its elastic properties, which are characterized by the longitudinal modulus of elasticity, the shear modulus, and Poisson’s ratio, according to the three planes of the anisotropy of wood (longitudinal, radial, tangential). The size of Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. these constants is critical in the selection of resonant wood. Numerous studies have shown This article is an open access article the existence of close correlations between the physical properties of the resonant wood distributed under the terms and structure and the elastic ones [7–9]. conditions of the Creative Commons In the past, luthiers did not have the knowledge and techniques necessary for deter- Attribution (CC BY) license (https:// mining the acoustic and elastic properties of wood as they do today, with the recognition of creativecommons.org/licenses/by/ resonant wood being based on the macroscopic analysis of the structure of softwood. Thus, 4.0/). the need for the material to have narrow and regular rings was established; the contribution Forests 2021, 12, 1122. https://doi.org/10.3390/f12081122 https://www.mdpi.com/journal/forests Forests 2021, 12, 1122 2 of 18 of a few late wood to this is modest [10–13]. The relevance of the annual ring structure as an acoustic marker remains debatable. Some have opined that the vibrational properties of Forests 2021, 12, x FOR PEER REVIEW 3 of 18 wood are determined on the scale of the cell wall rather than on the macroscopic scale of the growth rings [12–14]. In the stringed instruments industry, musical instruments are classified according to the anatomical quality of the wood used in their construction, with 2.this Materials aspect being and Methods revealed in the final price of the instrument [15–17]. The classification of quality raw materials for the manufacture of stringed instruments is discussed in detail 2.1. Materials elsewhere [16–18]. Resonant wood is divided into four quality grades: A, high anatomical quality;The B,samples average of quality; Norway C, spruce low anatomical (Picea Abies quality; L. Karst D, common)), 40 mm wood, in size without and oriented defects. towardsThe main the anatomical symmetry parameters planes, were of resonantdelivered wood by Gliga are the Musical totalring Instruments, width, the Reghin, proportion Ro- maniaof late wood(https://gliga.ro/ within the annual(accessed ring, on the 20 widthJanuary difference 2021)). betweenThe samples two consecutivewere cut from growth the samerings, batch and the of regularitytonewood ofraw the material ring widths. from Thewhich longitudinal the violin and boards transverse were cut. propagation The raw materialspeeds in had the been wood, sorted in the since three the directions, primary andcutting the of elastic the spruce characteristics, logs according complete to the qualityicon of class resonant of the wood violins, [18 –taking20]. Knowing into account this, the as well anatomical as the density characteristics of the wood, of the one spruce can woodestimate (Figure a number 1a). Before of acoustic entering parameters the violin of resonant manufacturing wood [17 flow,–21]. the Wegst, wooden 2006, parts noted were that driedthe Young naturally and shearfor at modulileast 3 years parallel (for and school perpendicular violins) and to up the to wood 10 years fibers for are maestro important violins.parameters From the for stage musical of the plate radial vibration cutting in of the the structure logs, the of semi chordophone-finished products instruments were [ 20se-]. lectedTherefore, according the static to their and quality dynamic class, moduli paired of tonewoodfor future violin related boards, to anatomical and stored parameters for nat- uralinfluence drying the [11 acoustic–14]. To qualitymeasure of the wood. acoustic The properties vibration in of the flat three orthotropic main directions plates, such of the as wood,violin the plates, samples involves were the accurately flexural cut plate perpendicular modes, which to arethe two-dimensional,principal direction while(longitu- the dinalfrequency L, radial depends R, tangential on several T) elastic along parameterswhich the ultrasonic of anisotropic waves media, propagate as noted (Figure by [21 –1b).23]. ThisIn regard is a mandatory to the orthotropic requirement anisotropy when determining of wood, the acoustic following parameters ratios should using the be ultra- taken soundinto consideration: method. Being the extracted ratio of from Young’s the semi moduli-finished EL/E Rproducts:EL/ET; theprepared ratio of for shear the entry moduli on theGLR technological/GRT:GLT/GRT flow; and of Poisson’s the violins, ratios the [moisture20–24], where content L, R, of and the Twood are the was main checked directions and foundin wood to (L,be around longitudinal 6–8%. (along Being fibers); a high R,quality radial; wood and T,and tangential) carefully and selected LR, RT, from and the LT pri- are marythe planes processing formed phase, according the number to the main of samples directions, analyzed as can bewas seen relatively in Figure small1b. In compared addition toto the the number values for of thesamples elastic used and physicalfor other properties,determinations. research The has physical shown characteristics that the value of of thethe resonant specific modulus spruce samples in the radial are portrayed direction in (E TableR/r;G 1.LR /r)[25]. (a) (b) Figure 1. TypesTypes of samples analyzed:analyzed: ((aa)) correspondencecorrespondence between between the the quality quality class class of of the the wood wood depending depending on on the the anatomical anatom- icalcharacteristics characteristics and and the qualitythe quality classes classes of the of violins; the violins; (b) the (b main) the main sections sections of wood of wood (L: longitudinal; (L: longitudinal; R: radial; R: radial; T: tangential). T: tangential). Table 1. The physical features of the spruce wood samples. Grade/Average Value/STDV Physical Features A STDV B STDV C STDV D STDV Longitudinal 40.508 0.187 40.304 0.706 40.116 0.120 39.957 0.157 Radial 40.326 0.137 40.291 0.159 40.136 0.099 40.259 0.112 Forests 2021, 12, 1122 3 of 18 In previous research, the propagation of waves in isotropic and anisotropic materials and the determination of the elastic properties

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