Accepted Manuscript Elemental analysis as statistical preliminary study of historical musical instruments G.V. Fichera, T. Rovetta, G. Fiocco, G. Alberti, C. Invernizzi, M. Licchelli, M. Malagodi PII: DOI: Reference: S0026-265X(17)30832-9 doi:10.1016/j.microc.2017.11.004 MICROC 2947 To appear in: Microchemical Journal Received date: Revised date: Accepted date: 26 August 2017 31 October 2017 13 November 2017 Please cite this article as: G.V. Fichera, T. Rovetta, G. Fiocco, G. Alberti, C. Invernizzi, M. Licchelli, M. Malagodi , Elemental analysis as statistical preliminary study of historical musical instruments. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Microc(2017), doi:10.1016/ j.microc.2017.11.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. 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Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. ACCEPTED MANUSCRIPT Elemental analysis as statistical preliminary study of historical musical instruments Fichera G.V.(1), Rovetta T.(1), Fiocco G.(1), Alberti G.(2), Invernizzi C.(1), Licchelli M.(2), Malagodi M.(1,3)* PT (1) Laboratorio Arvedi di Diagnostica Non-Invasiva, Università di Pavia, via Bell'Aspa 3, Cremona 26100, Italy (2) Dipartimento di Chimica, Università di Pavia, Via Taramelli 12, Pavia 27100, Italy (3) Dipartimento di Musicologia e Beni Culturali, Corso Garibaldi 178, Cremona, 26100, Italy SC marco.malagodi@unipv.it; telephone 0039.0372567770 RI * Corresponding author Abstract The history of bowed string instruments includes centuries of experimentation performed by NU violin makers with different manufacturing processes and several natural materials. The characterization of the material components can therefore often help researchers to identify MA the construction period of an instrument, its geographical origins or, if possible, the name of the violin maker. In a few cases, musical instruments, especially bowed ones, that were played frequently over time suffered severe damage (e.g. cracks, woodworms), and some parts of D the instruments needed to be replaced to repair such damage. Gaetano Sgarabotto (1878- TE 1959) and his son Pietro (1903-1990), two of the most eminent violin makers and restorers of the 20th century, collected many replaced parts in a group of fragments from musical instruments manufactured between the 16th and the 19th century by some of the most AC CE P important Italian and European violin makers. In this work, non-invasive and micro-destructive analyses could be combined through portable X-ray fluorescence spectrometry (PXRF) and scanning electron microscopy (SEM) with an EDAX spectrometer (SEM-EDX) on 24 fragments of the Sgarabotto collection. Principal Component Analysis was applied to classify relics, highlighting the most relevant and particular elements in the dataset. The principle of transformation is the extraction of maximum variance for each successive new variable. This procedure leads to the separation of valuable information from noise and to the selection of a small number of influential and statistically significant variables. The application of this analytical procedure leads to (i) assessing the existence of elemental markers of specific historical periods and/or manufacturing areas; (ii) characterizing the materials that the layers of a selected group of fragments are composed of; (iii) identifying any correlations between different fragments. 1 ACCEPTED MANUSCRIPT Keywords XRF, multivariate statistical data analysis, musical instrument, pigment, SEM-EDX 1. Introduction Nowadays, historical documentation, materials and construction information about a work of art can be correlated through the joined work of art critics, conservators and conservation scientists. A certain number of recent examples can be mentioned, such as the study of canvas attributed to Jackson Pollock [1], the identification of particular pigments from Vincent PT van Gogh’s paintings [2], or the identification of inks in Antonio Stradivari’s handwritten texts [3]. Similarly to other fields of art, stylistic critical studies of historical musical instruments have RI also been supported by scientific analysis, mostly focused on the identification of varnishes, pigments and wood treatments [4-7]. Proteinaceous preparations and organic binders, like oil- SC resin mixtures including very small amounts of inorganic substances, such as earth pigments, lakes and residuals of wood treatments, have already been identified [8-10]. The NU characterization of material components and their methods of application led to many different speculations about their role in determining acoustic features, especially in violins [11]. In any way, it is fairly certain that each individual violin maker arbitrarily selected their own MA manufacturing materials [12], probably depending on their availability and their appearance according to the aesthetic trends of the time [13]. This means that, apart from sound, a musical instrument can be identified from its stylistic features and the materials applied onto the wood. D All these data pools allow to point out correlations and differences between the choices made more accurate way. TE by masters and their pupils [12], thus describing the lost modus operandi of violin makers in a AC CE P In this work, we had the opportunity to study a collection of fragments from historical instruments that underwent extraordinary restoration during the 19th and the 20th centuries, by applying non-invasive and micro-invasive techniques, such as X-ray fluorescence spectroscopy (XRF) and electron microscopy coupled with an energy dispersive X-ray spectrometer (SEM-EDX). The opportunity to collect many XRF spectra from several fragments of historical musical instruments allowed to define a characteristic “spectral pattern”, so that each fragment could be matched with other fragments of the same author. In order to match the elemental analysis of the fragments with the author of the instrument in a correct way, statistical methods were significantly useful, such as Principal Component Analysis [14,15], which allowed to identify relations between data through cluster analysis [16,17]. To confirm the results obtained by multivariate statistical analysis applied to the XRF data, some samples were collected from the recto side of the most well-matched fragments and observed in cross-sections. Microscopic data allowed to highlight similarities and to identify inorganic substances through punctual elemental analysis. Finally, to validate the statistical 2 ACCEPTED MANUSCRIPT PCA model, an XRF dataset collected from a Giovanni Paolo Maggini double-bass (1610) was used as a test set. The results allowed to detect a correlation with the other fragments by evaluating the reliability of the approach for the preliminary attribution of authorship. 2. Materials and Methods 2.1 Materials This work involved a group of 24 fragments from the Sgarabotto collection. The fragments are PT shown in Fig. 1a and described in Table 1. The collection consists of parts of historical bowed string instruments (i.e. violins, violas, double basses) restored during the 20th century by Gaetano (1878–1959) and his son Pietro Sgarabotto (1903–1990). They used the relics as RI original models for manufacturing their own instruments until 1983, when the whole collection SC was donated to the International Violin Making School of Cremona and exhibited for over thirty years. The 24 fragments are attributed to some of the most important Italian and European historical violin makers who worked between the 17th and the 19th century (i.e. Gasparo da NU Salò, Giovanni Paolo Maggini, Nicola Amati, Andrea Guarneri, Lorenzo Guadagnini, Luigi Baioni) [18,19]. MA The case study is focused on an original double bass from the Museo Civico of Brescia manufactured by Giovanni Paolo Maggini in 1610 (Fig. 1b). Originally manufactured as a bassviol, the instrument was then reconfigured by Stefano Scarampella into a double bass during D its first restoration in 1881 and repaired in 1960 by Gio Batta Morassi. Especially on the back, TE the instrument shows many repaired cracks, varnish touch-ups and filled-up woodworm holes. 2.2 Experimental methods AC CE P A preliminary study of the surface of the fragments was performed through the observation of images acquired by a Nikon D4 full-frame digital camera (Minato, Tokyo, Japan) equipped with a 50-mm f/1.4 Nikkor objective. Visible light illumination was obtained using a softbox LED lamp (camera setup: f/11, ISO 100), while UV-induced visible fluorescence was obtained using two Philips TL-D 36W BBL IPP (emission peak at 365 nm) low-pressure Hg tubes (camera setup: 30 s exposure time, f/11, ISO 400). Ultraviolet illumination was employed to detect the most well-preserved areas for the subsequent analyses. XRF spectra were acquired using the portable EDXRF spectrometer XGLab ELIO (Milan, Italy). The system was composed of a large-area silicon drift detector (25 mm2) with good throughput capability thanks to a new complementary metal-oxide semiconductor (CMOS) silicon drift detector readout (CUBE). The device was equipped with a low-power X-ray tube with Rh anode and a 1.2 mm analysis spot area. XRF measurements were performed operating at 40 kV, 80 µA and using an acquisition time of 300 s. From 4 to 8 XRF spectra (191 measures) were collected for each fragment, while the net area counts of each element 3 ACCEPTED MANUSCRIPT (Kα, except for Pb, for which Lα was used) were calculated and used for the subsequent multivariate statistical analysis (see 2.3). In addition, further measurements were carried out on the historical varnish of a double bass (G. P. Maggini, 1610). Although a full quantitative analysis was not feasible, by using the same geometry, voltage and current conditions for different specimens, reasonable comparisons could be achieved. Some micro-samples from selected fragments were collected using a scalpel; then, they were embedded into epoxy resin (Epofix Struers and Epofix Hardener with ratio 15:2) and polished PT with silicon carbide sandpaper (800–4000 mesh). The polished cross-sections were observed through a polarized light optical microscope Olympus BX51TF equipped with an Olympus RI TH4-200 lamp (visible light) and an Olympus U-RFL-T (UV radiation). The cross-sections were made conductive by applying a graphite coating (8 nm of surface SC deposit) with a Cressington sputter carbon-coater 208C, and then observed through Scanning Electron Microscopy SEM-EDX by using a Tescan FE-SEM (MIRA3 XMU series) apparatus high vacuum. MA 2.3 Multivariate statistical data analysis NU equipped with an EDAX spectrometer at an accelerating voltage of 15–20 kV, operating in For the multivariate statistical XRF data treatment, at first some outliers were removed applying Dixon’s Q test; then, the mean values of the net area counts of different D measurements on the same fragment were considered. PCA is a multivariate statistical TE technique [14,20] useful for displaying and analyzing the structure of multivariate data. It is based on the representation of the original dataset in a new reference system characterized AC CE P by new orthogonal variables called principal components (PCs). Cluster analysis techniques [21] investigate the relationships between objects or variables of a dataset with the aim of detecting the existence of groups. In this paper, the agglomerative hierarchical method was applied, and a dendrogram representing average Euclidean distances between data was created. PCA and cluster analysis were applied to the matrix of the dataset obtained from the XRF analysis of the 24 fragments and of a double bass (G. P. Maggini, 1610). The data matrix used was an n X v matrix, where n was the number of objects (number of fragments) and v was the number of variables (XRF mean net area counts). PCA and cluster analysis were performed using PAST3 ver. 1.0.0.0 freeware software. 3. Results 3.1 XRF data clustering 4 ACCEPTED MANUSCRIPT The non-invasive EDXRF analytical campaign performed on the varnished side of the historical fragments allowed to highlight similarities in their elemental composition. In most cases, characteristic peaks of S, K, Ca, Ti, Cr, Mn, Fe, Ni, Cu, Zn and Pb were identified. Si and Cl signals were also frequently recognized; however, due to their low atomic weight, their characteristic emissions were severely attenuated by the organic matrix. It is worth noting that very low peak intensity fluctuations could be noticed in the characteristic spectra of each fragment. This means that every fragment was represented by a distinctive “spectral pattern” PT differing from the others by its peak intensity variations (Fig. 2). From the qualitative point of view, in addition to the homogeneous essential composition RI mentioned above, very small amounts of other elements, i.e. Br and Hg (fragments F25 and F1, F2 respectively) and Sr (fragments F7, F14, F15, F16, F19), were also identified. In order SC to better compare data from different fragments, a new method was used by applying multivariate statistical analysis; in particular, PCA and hierarchical cluster analysis were NU considered. PCA was performed on the data matrix of dimensions 24 × 11, where the rows represented the studied fragments and the columns represented the variables. In particular, the variables included the XRF data, i.e. the mean net area counts for each significant element MA found. Before applying the multivariate analysis, non-significant elements, i.e. Si and Cl (concentrations underestimated due to the matrix effect), Br, Hg and Sr (significant markers D but present only in few fragments and at trace levels), were excluded from the dataset. TE Moreover, a first skimming of data was performed, with the aim of excluding possible outliers. Dixon's Q test was used for identifying and rejecting anomalous data. AC CE P The results of PCA are reported in Table 2 and Fig. 3. The first two principal components account for 85% of the variance of the dataset and they were therefore considered as significant. The following analysis was then performed based on the first two PCs. Fig. 3 shows the biplot of the first vs. the second component, resulting from the PCA computed on the XRF data. The biplot provides not only a plot of the observations, but also a plot of the relative positions of the variables in two dimensions. Moreover, the superimposition of the two types of graphs provides additional information about relationships between variables and observations not available in either individual plot. In the following biplot (Fig. 3), the observations (fragments) are represented as points, whereas variables are represented as vectors, with arrowheads at the ends of the vectors. The first component of the PCA (explained variance 54%) is characterized by a dominance of the most relevant elements, such as Pb, Ca, Fe and S, which have a positive sign and significant loading values in contrast to K, which has an opposite trend. Trace elements are all close to zero, since they are not generally present at high concentrations in the materials of the fragments. 5 ACCEPTED MANUSCRIPT In order to quantitatively describe the data distribution, hierarchical cluster analysis was applied to the first two PCs, while a dendrogram representing average Euclidean distances indicated the similarities between the considered fragments. Objects (or fragments, observations) in a specific cluster shared many characteristics, but were very dissimilar to objects not belonging to the same cluster. In order to determine the number of clusters that need to be kept in the data, and considering the only meaningful indicator related to the distances at which the objects are combined, a PT scree plot was created showing the number of clusters on the y-axis (starting with the onecluster solution at the very left) against the distance at which objects or clusters were RI considered on the x-axis. Using this plot, the distinctive break could be searched for (Fig. 4); the presence of four main groups of fragments in the dendrogram shown in Fig. 5 was SC suggested. These groups can be divided into nine subgroups consisting of: A) F14 and F16; B) F13; C) F17; D) F11 and F25; E) F24; F) F15, F2, F7 and F18; G) F4, F26, F5, F8 and F22; NU H) F9, F10, F12, F19, F20, F1 and F21; I) F3. 3.2 Micro-invasive analysis of selected fragments MA In order to validate the preliminary approach for gathering groups of fragments, further microinvasive investigations were performed, and both were then selected for their authorship attribution and for the cluster analysis results. Below, the optical microscopy and SEM-EDX D results collected on cross-sections are shown, describing the multilayered stratigraphy starting Gasparo da Salò fragments (cluster A, B and F) - The first fragments come from violin maker Gasparo Bertolotti “da Salò” (F13, F14, F15 and F16) (Table 1). The multivariate AC CE P - TE from the outer layer (layer 1) down to the wooden support (wood). analyses (Fig. 5) grouped F14 and F16 in cluster A, while F13 and F15 were placed in cluster B and F respectively. Qualitative observation by optical microscope of crosssections F14 and F16 showed similar stratigraphy, composed by two layers (Fig. 6). Layer 1 (~5 µm of thickness), characterized by white-yellowish UV fluorescence, embedded organic black particles and it seemed to be composed of calcium and magnesium carbonates (Ca, Mg) and feldspars (Si, Al, K, Na). The underlying layer 2 (~15-20 µm of thickness) instead, which showed light-blue UV fluorescence, included reddish particles (Fig. 6). Some of these particles (~5-10 µm) may be composed of Fe oxides and/or hydroxides, Pb and As (Fig. 7a), while others may consist of Pb oxides and/or Pb carbonates (~2 µm). Between layer 2 and the wood, spots of Ca, S and Pb and traces of Si, K, Al, P, Mg, Na and Fe were highlighted, probably attributable to calcium sulfates used for the wood sealing [22]. The P signal could also be correlated to the composition of proteinaceous binders, e.g. animal glues or caseinates [23]. 6 ACCEPTED MANUSCRIPT Fragment F13 (cluster B) showed a very complex stratigraphy with five alternating thick and thin (from ~2 µm to 10 µm of thickness) superimposed layers (Fig. 6). When subjected to UV radiation, layer 1 showed a high quantity of black organic and red inorganic particles, probably composed of Fe oxides and/or hydroxides. On the contrary, layer 2 was thicker and showed no presence of particles. Layer 3 showed brownish UVfluorescence and it embedded particles composed of Si, Al, Ca, K, S, Fe, P. Layer 4, revealed a white-pinkish color with the possible presence of calcium sulfates (S, Ca) (Fig. PT 7b). Moreover, signals of Al, Si and Fe attributable to iron oxides/hydroxides and aluminosilicates were detected in some particles. Finally, layer 5 was the closest layer to RI the wood surface and it showed UV-fluorescence very similar to layer 3; it embedded a considerable amount of Fe oxide particles. SC Fragment F15 (cluster F) was characterized by two layers with slight differences in UVfluorescence (from beige to white-pinkish) and thickness (~5 µm for the upper layer L1 NU and ~15 µm for L2) (Fig. 6). The matrix of both seemed to be mainly composed of organic materials (the sample degraded completely under the electron beam), showing no inclusion compounds. Weak signals of Ca, Fe, S and K were detected, but only in layer - MA 1. Amati fragments (cluster F) - The two fragments (F7 and F18) of violin maker Nicola Amati were grouped together in cluster F (Fig. 5). Microscopic observations highlighted the D presence of two layers in fragment F18 and one layer in fragment F7. Layer 1 (~8 µm of TE thickness) of fragment F18 was characterized by grey UV-fluorescence and by many inclusion compounds of calcium sulfates/carbonates, aluminosilicates and traces of AC CE P elements such as Na, Mg and P. The presence of these inorganic fractions can probably be attributed to residuals of gypsum molds used for restoration processes in the past. The underlying layer 2 (~8 µm of maximum thickness) showed whitish UV-fluorescence, no particles and an elemental composition mainly consisting of Na, Mg, S, Cl, K and Ca (Fig. 7c). The same features were found in the only layer of fragment F7 (Fig.6). - Baioni fragments (cluster G) - The two fragments of Luigi Baioni (F4 and F26) were grouped together in cluster G despite their differences in UV-fluorescence, and in the number and thickness of the layers (Fig. 6). The whitish UV-fluorescence of layer 1 (~7 µm of thickness) of fragment F4 was characterized by sub-micrometric particles attributable to aluminosilicates (Al, Si, Mg, Ca, S, K, Fe) and particles with high amounts of Zn, probably zinc oxide or metallic zinc. Higher concentrations of particles containing Zn, mixed with small amounts of iron oxides/hydroxides attributable to red ochres (Fe, Si, Al, Na, Mg, K) were detected in the thicker layer 2 (20 µm of thickness), which showed brown UV-fluorescence. Fragment F26 showed three different layers (~10 µm of thickness) (Fig. 6). Layer 1 was composed of only organic materials showing whitish UV7 ACCEPTED MANUSCRIPT fluorescence. On the interface between layers 1 and 2, a few particles of probably aluminosilicates were detected (Al, Si, Mg, Ca, S, K, Fe). Layer 2 embedded some particles containing high amounts of Zn (diameter <5µm), comparable with those identified in fragment F4. A few yellow particles containing Pb and Cr (Fig. 7d) (maybe attributable to lead chromate) [24], traces of Al, Si, Na and Mg, and black organic particles were detected. Moreover, rare red-colored Al-based inclusion compounds, sub-micrometric particles of Sn and Ca, and possibly calcium sulfates were also identified. Between layer PT 2 and the wooden support, a thin brownish layer (layer 3) included a few black particles attributable to iron oxides/hydroxides and red ochres (Na, Mg, Al, Si, K, Fe). Maggini fragments (cluster H) - Both fragments (F19 and F20) attributed to Giovanni Paolo RI - Maggini were grouped in cluster H (Fig. 5). Their cross-sections were fully comparable, SC composed of one layer (~30 µm of thickness) applied directly on the wooden support (Fig. 6). These layers were both made of an organic binder with yellow UV-fluorescence, and NU they embedded rare reddish particles, probably composed of iron oxides and aluminosilicates attributable to red ochres (Fe, Al, Si, Na, Mg), including traces of P, K, Ca and Ti. Fragment F19 showed traces of Ca and S upon its layer, probably related to MA gypsum molds of past restorations. 4. Discussion D Generally, the application of XRF to musical instruments has many hidden issues, strictly TE related to matrix effects due to the mainly organic composition of the instruments themselves, which causes intense Bremsstrahlung phenomena. This means that the very low amounts of detectable elements, which are heterogeneously distributed in the stratigraphy, could be, in AC CE P some cases, underestimated, since their characteristic emissions could be partially selfabsorbed. Therefore, the elemental concentration, represented by the net area counts, could be not fully reliable. In any case, linear correlation between these values is comparable with the spectra collected from the same artifact, which suggests that some of these ratios are highly specific of each work of art. The fragments which are the object of this research represent a set of historical models, each characterized by a particular “spectral pattern” that could be used for the attribution of undocumented relics. A detailed comparison between the XRF data of the fragments was made by using multivariate statistical data analyses, i.e. Principal Component Analysis and Cluster analysis. The clustering results confirmed the validity of the multivariate approach in gathering groups of fragments with similar characteristics, but they also showed some critical issues due to the limits of the XRF technique. In detail, 9 clusters were obtained (Fig. 5), and 5 of them were considered for the subsequent micro-invasive analyses for their association with their authors (Table 1). The first group selected was made up of fragments from Gasparo “da Salò”, one of 8 ACCEPTED MANUSCRIPT the most important violin makers in Brescia during the Venetian occupation [25]. The observation of fragments F14 and F16 (cluster A) by optical and SEM-EDX microscopy confirmed the presence of Fe oxides with small amounts of Pb and As particles (probably plumbic ochre rich in brown lead(IV) oxide PbO2, and Pb oxides/carbonates), perhaps associated to the same lead-rich ore deposit [24]. It is worth noting that a thin preparatory gypsum layer was also present. Even if Sr was excluded from PCA, it was probably strictly related to this gypsum layer and should be considered as a specific elemental marker for PT Gasparo da Salò instruments [26]. The presence of gypsum in the preparation layer, tied to the past traditional painting procedures, has a close correspondence with other instruments RI from the same period, such as the Venetian Magno Dieffopruchar theorbo (late 16th century), studied by Echard [22]. In any case, the position of these two fragments in the biplot (Fig.3) SC highlights that Pb is the most important element for discriminating these samples from the others (Fig. 7a). Conversely, micro-invasive analyses pointed out remarkable differences with NU the other two fragments F13 and F15 (Fig.5, cluster B and F respectively), showing variations in the layers and in the elemental composition. These changes could be related to many causes: Gasparo could have experimented new processes and materials during his life or the MA fragments could come from restored instruments and could have been erroneously attributed by Sgarabotto. Two Nicola Amati fragments (F7 and F18) and one Jacobus Stainer fragment (F2) were also grouped in the same cluster of F15 (cluster F). Even in this case, the two Amati D fragments shared a very simple and comparable stratigraphy, mainly composed of a thin TE organic layer without any pigments [12]. Their position in the biplot (Fig. 3) shows a higher contribution from K compared to Pb, Fe and S. As for other trace elements, Hg was excluded AC CE P from PCA; it is worth noting that this element was detected only in Stainer fragments (F1 and F2), and thus it should be considered a significant elemental marker for this author. Two fragments belonging to 19th century violin maker Luigi Baioni (F4 and F26) were grouped in cluster G. Although the analyzed cross-sections apparently did not show the same number of layers, particles with high amounts of Zn, probably zinc oxide or metallic zinc used as substrate for organic dyes [27], and red ochres (Fe, Si, Al, Na, Mg, K) were noticed in both fragments. Moreover, the presence of particles containing Pb and Cr (Fig. 7d) (probably attributable to chrome yellow pigment) is coherent with the fragment dating, since lead chromate (PbCrO4) was first synthesized around 1800 and suggested as potential pigment by Berthollet and Vauquelin in 1804 [24]. By reference to statistical analysis, it can be underlined that, despite its low loading value, chromium is also interesting, because it results to be a characteristic element of the fragments placed in that area of the biplot (Fig. 3). Cluster H, in which Maggini fragments (F19 and F20) were placed, also included Lorenzo Guadagnini fragments (F21). Maggini was a pupil of Gasparo’s from 1595 and he probably had a hand in making violin family instruments in Gasparo’s workshop. Three years before 9 ACCEPTED MANUSCRIPT Gasparo da Salò’s death, in 1609, Maggini left the workshop to start his own business in Brescia [19]. From this date, he experimented some independent stylistic changes, which probably also affected the materials selected, which reflected the production of the Cremonese makers of the time. The PCA could distinguish XRF results of Gasparo da Salò from those of G.P. Maggini and the differences between the two groups were also pointed out by the microinvasive analysis. Microscopic investigations revealed that both Maggini and Guadagnini are associated by the presence of rare iron-based particles dispersed in layer 1 of fragments F19 PT and F20 and in the thin preparatory layer of Guadagnini’s fragment (F21), in agreement with previous studies [12]. Ca and S signals, related to gypsum, were observed in all fragments, RI i.e. fragments of both violin makers, although gypsum seemed to be used for different purposes (Guadagnini used it as a filler for the wooden substrate, while in Maggini’s SC manufacturing it could be a material added posthumously, probably used a by restorers as plaster cast). However, Ca and S concentrations were lower and not much significant NU compared to K, which is clearly dominant in this area of the biplot (Fig. 3). 4.1 Case study: G.P. Maggini double bass (1610) MA In order to validate the efficiency of the treatment of statistical data proposed in this study, we planned an accurate analytical XRF investigation on a historical case study: the G.P. Maggini double bass (1610). Firstly, UV-induced fluorescence images were collected (Fig. 1); some D areas of interest were selected, excluding those with different fluorescence phenomena clearly TE related to restoration processes. A total of 24 measurements were carried out on the top plate, back plate, ribs and in the scroll fluting of the double bass. AC CE P The qualitative analysis showed the same elemental composition compared to those of the Maggini fragments (F19 and F20). The back plate of the instrument probably underwent many non-documented restoration processes, as can be seen by the many wood reinforcements. For these reasons, the XRF data collected on the top plate, ribs and scroll (M1) were considered separately from those of the back plate (M2). Dixon’s Q test was applied to both M1 and M2 XRF data, in order to remove any possible outliers. Therefore, the mean values of each variable were calculated, and the dataset obtained was used as a validation test set in the previous PCA model obtained with the data about the fragments. As it can be seen in Fig. 8, dataset M1 shows extraordinary similarities to the other Maggini fragments, i.e. those grouped in cluster H. Conversely, dataset M2, which summarizes the data about the back plate, which was probably restored in the past, does not belong to this cluster. This result suggests that the instruments from which G.P. Maggini fragments originate and the double bass were probably made with the same materials and emancipated craftsmanship, and therefore after 1607-1609, when Maggini left his master to start his own workshop. This 10 ACCEPTED MANUSCRIPT post-quem chronological reference is also confirmed by the manufacturing date of the double bass (1610). 5. Conclusions In this paper, we present the application of multivariate statistical analysis to an XRF dataset characteristic of historical fragments from several historical musical instruments. Principal Component Analysis (PCA) was used for a subsequent classification of the relics through PT cluster analysis. The latter procedure allowed to properly group fragments with similar elemental composition, although they were made by different violin makers in different periods RI of time. Micro-invasive analysis, performed only on selected fragments, allowed to identify some materials and to gather new information about the modus operandi of the past. The latter SC data were compared with the XRF results used as a dataset for the PCA, confirming the similarities in elemental composition in the same cluster and many variations between different NU groups. Finally, an additional validation test was performed on a double bass made by Giovanni Paolo Maggini (1610). The XRF dataset of this instrument was compared with the PCA training set, i.e. the dataset of XRF results obtained from the fragments. A significant MA result was obtained, since the measures collected on the most original part of the instrument collapsed in the cluster where the Maggini fragments were located (cluster H). This study, as far as we known, represents an accurate and reasonably rigorous application D of multivariate statistical methods, such as PCA and clustering, to an XRF dataset TE characteristic of the materials that musical instruments are made of. This approach could be considered as a key step for the creation of new protocols for the preliminary attribution of AC CE P unknown - or uncertainly attributed - musical instruments. Acknowledgments We would like to thanks the International Violin Making School of Cremona which furnished the historical fragments; Elisa Scrollavezza and Andrea Zanrè for allowing us the reading of Sgarabotto’s notes. A special thanks to the Museum of the Violin of Cremona for supporting analysis and results. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. 11 ACCEPTED MANUSCRIPT References [1] F. Rosi, C. Grazia, R. Fontana, F. Gabrieli, L. Pensabene Buemi, E. Pampaloni, A. 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Int. 49:1 (2010) 197–201 DOI: 10.1002/anie.200905131. [9] H.C. Tai, G.C. Li, S.J. Huang, C.R. Jhu, J.H. Chung, B.Y. Wang, C.S. Hsu, B. Brandmair, D.T. Chung, H.M. Chen, J.C. Chan, Chemical distinctions between Stradivari's maple and modern tonewood, Proc Natl Acad Sci USA 3 :114 (2017) 27-32 DOI: 10.1073/pnas.1611253114. [10] L. Bonizzoni, C. Canevari, A. Galli, M. Gargano, N. Ludwig, M. Malagodi, T. Rovetta, A multidisciplinary materials characterization of a Joannes Marcus viol (16th century), Heritage Science Journal, 2:15 (2014) DOI: 10.1186/2050-7445-2-15. 12 ACCEPTED MANUSCRIPT [11] F. Setragno, M. Zanoni, F. Antonacci, A. Sarti, M. Malagodi, T. Rovetta, C. Invernizzi, Feature-Based Analysis of the Impact of Ground Coat and Varnish on Violin Tone Qualities, Acta Acustica united with Acustica 103:1 (2017) 80-93 DOI: 10.3813/AAA.919035. [12] G. Fiocco, T. Rovetta, M. Gulmini, A. Piccirillo, M. Licchelli, M. Malagodi, Spectroscopic Analysis to Characterize Finishing Treatments of Ancient Bowed String Instruments, Appl Spectrosc (2017) 1-11 DOI: 10.1177/0003702817715622. PT [13] W. Fulton, S. Schmidt, Violin Varnish Now and Then, J. Violin Soc. Am. 9:3 (1988) 48– 70. RI [14] I.T. Jolliffe, Principal Component Analysis, Second Edition (Springer series in statistics); ed. Springer-Verlag, New York, 2002. SC [15] G. Gallello, M. Ramacciotti, M. Lezzerini, E. Hernandez, M. Calvo, A. Morales, A. Pastor, M. de la Guardia, Indirect chronology method employing rare earth elements to NU identify Sagunto Castle mortar construction periods, Microchemical Journal 132 (2017) 251–261 DOI:10.1016/j.microc.2017.02.009. [16] M. L. Amadori, C. Del Vais, P. Fermo, P. Pallante, Archaeometric researches on the MA provenance of Mediterranean Archaic Phoenician and Punic pottery, Environ Sci Pollut Res Int 24:16 (2017) 13921–13949 DOI: 10.1007/s11356-016-7065-7. [17] G. Capobianco, M. P. Bracciale, D. Sali, F. Sbardella, P. Belloni, G. Bonifazi, S. D Serranti, M. L. Santarelli, M.C. Guidi, Chemometrics approach to FT-IR hyperspectral TE imaging analysis of degradation products in artwork cross-section, Microchemical Journal 132 (2017) 69–76 DOI: 10.1016/j.microc.2017.01.007. AC CE P [18] K. Jalovec, Italian Violin Makers. Crown Publishers, New York, 1958. [19] S. Sadie, J. Tyrrell, The New Grove Dictionary of Music and Musicians. Macmillan Publishers Limited, London, 2001. [20] R. Bro and A.K. Smilde, Principal component analysis, Anal. Methods 6 (2014) 28122831 DOI: 10.1039/C3AY41907J. [21] P. Gemperline, practical guide to chemometrics, ed. Taylor & Francis Group, New York, 2006. [22] J.P. Echard, M. Cotte, E. Dooryhee, L. Bertrand, Insights into the varnishes of historical musical instruments using synchrotron micro-analytical methods, Appl. Phys. A 92:1 (2008) 77–81 DOI:10.1007/s00339-008-4449-7. [23] I.C.A. Sandu, S. Schäfer, D. Magrini, S. Bracci, C.A. Roque, Cross-Section and Staining-Based Techniques for Investigating Organic Materials in Painted and Polychrome Works of Art: A Review, Microsc. Microanal. 18 (2012) 860–875 DOI:10.1017/S1431927612000554. 13 ACCEPTED MANUSCRIPT [24] N. Eastaugh, V. Walsh, T. Chaplin, R. Siddall, Pigment Compendium, A Dictionary and Optical Microscopy of Historical Pigments, Elsevier, Oxford, 2008. [25] R.E. Andrews, Gasparo Bertolotti Da Salò, Berkeley California, 1953. [26] E. Franceschi, F. Locardi, Strontium, a new marker of the origin of gypsum in cultural heritage?, J Cult Herit 15:5 (2014) 522-527 DOI: 10.1016/j.culher.2013.10.010. AC CE P TE D MA NU SC RI PT [27] T. Bechtold, R. Mussak, Handbook of Natural Colorants, John Wiley & Sons, 2009. 14 ACCEPTED MANUSCRIPT Captions Fig. 1 Some of the fragments considered in this study from the Sgarabotto collection: Luigi Baioni (F4), Nicola Amati (F7), Gasparo Bertolotti “da Salò” (F13-F16) and Giovanni Paolo Maggini (F19, F20) (A); visible and ultraviolet images of two sides (front and back) of the double bass manufactured in 1610 by Giovanni Paolo Maggini (B). Fig. 2 XRF spectra representative of fragments attributed to Gasparo Bertolotti “da Salò” (F14), Giovanni Paolo Maggini (F19) and Luigi Baioni (F4). PT Fig. 3 Biplot of the first two components of XRF dataset of 24 fragments. Fig. 4 Scree plot useful to select the significant clusters in the dendrogram of Fig. 5. RI Fig. 5 Dendrogram showing the succession of clusters highlighted by cluster analysis along with the distances to which they occur; the clusters selected for micro-invasive analyses are SC circled. Fig. 6 Ultraviolet-light optical microscopy of 10 selected fragments’ cross sections with layers highlighted (red circles). Violin makers are grouped according to different clusters: Gasparo NU “da Salò” (cluster A: F14, F16; cluster B: F13; cluster F: F15), Nicola Amati (cluster F: F07, F18), Luigi Baioni (cluster G: F04, F26) and Giovanni Paolo Maggini (cluster H: F19, F20). MA Fig. 7 Energy dispersive X-ray spectroscopy analyses performed on some particles identified in the fragments’ stratigraphy: Gasparo “da Salò” F14 (a) and F13 (b); Nicola Amati F18 (c); Luigi Baioni F26 (d) D Fig. 8 Biplot of the first two components of XRF dataset of 24 fragments grouped after cluster AC CE P back plate). TE analysis (Fig. 4) and Maggini double bass samples (M1: top plate, ribs and scroll fluting; M2: 15 ACCEPTED MANUSCRIPT AC CE P TE D MA NU SC RI PT Figure 1 16 ACCEPTED MANUSCRIPT AC CE P TE D MA NU SC RI PT Figure 2 17 ACCEPTED MANUSCRIPT AC CE P TE D MA NU SC RI PT Figure 3 18 ACCEPTED MANUSCRIPT AC CE P TE D MA NU SC RI PT Figure 4 19 ACCEPTED MANUSCRIPT AC CE P TE D MA NU SC RI PT Figure 5 20 ACCEPTED MANUSCRIPT AC CE P TE D MA NU SC RI PT Figure 6 21 ACCEPTED MANUSCRIPT AC CE P TE D MA NU SC RI PT Figure 7 22 ACCEPTED MANUSCRIPT AC CE P TE D MA NU SC RI PT Figure 8 23 ACCEPTED MANUSCRIPT Violin Maker Period Area Instrument F1, F2 Jacob Stainer ?16171683 Absam, Austria Cello F3 Florentin ?1800 Mirecourt, France Violin F4, F26 Luigi Baioni 1838-1878 Milan, Italy Cello F5 Lorenzo and Tommaso Carcassi ?1750 Florence, Italy Cello F7, F18 Nicola Amati 1596-1684 Cremona. Italy Viola F8 Unknown ?1500 - Viola F9 Fisher ?1700 ? Violin F10 Müller ?1750 ? Cello F11 Andrea Guarneri 1623-1698 Cremona, Italy Cello F12 Antonio Bagatella 1755-1829 Padova, Italy Violin F13, F14, F15, F16 Gasparo Bertolotti “da Salò” 1540-1609 Brescia, Italy Cello F17 Unknown ?1600 - Cello F19, F20 Giovanni Paolo Maggini 1580-1631 Brescia, Italy Double bass 1685-1746 Piacenza, Italy Double bass 1687-1737 Mittenwald, Germany Cello ? - Viola, Cello F22 F24, F25 SC NU MA D TE AC CE P F21 Lorenzo Guadagnini George Klotz Unknown RI Inv. N° PT Table 1 List of the fragments of the Sgarabotto collection with inventory number of the fragments, name, life period and city of the violin makers and identification of the original bowed string instrument from which the relics were removed. 24 ACCEPTED MANUSCRIPT Table 2 (a) The percentage of variance cumulatively explained by the first four eigenvectors (the first two are considered as principal), (b) the score values of the fragments on PC1 and PC2, (c) the loadings of the variables on PC1 and PC2. PC2 PC1 PC2 PC 1 PC 2 S 0.1 976 0.1 102 85.09 94.01 99.66 F3 F4 F5 F7 4557.4 31465 15132 F12 11504 5259.2 25584 18887 F13 20614 22003 15081 F14 78145 5633.1 14458 F11 10361 25776 20.989 RI 14000 F8 PT F2 F15 10700 15502 13359 F16 61660 20474 30499 32022 F19 F20 F21 F22 F24 F25 23735 12968 8452.8 11849 8449.7 17226 3066.1 1093.7 47160 36599 3154.9 12306 K Ca Ti Cr Mn Fe Ni Cu Zn 0.5 0.0 0.4 0.017 0.006 0.11 731 047 0.0 0.0 435 0.000 1 4 82 049 019 9 0.09 0.8 0.0 0.023 0.013 25 179 0.0 0.0 045 0.2 0.003 3 6 050 071 834 5 AC CE P ( c ) 53.90 NU PC1 Env 4 MA PC2 7306.8 2466.5 F10 13678 4167.6 F18 519.52 17675 Env 3 D PC1 Env 2 TE ( b ) Explained variance, % F1 Env 1 SC ( a ) F9 18881 5861.8 F17 2369.4 13670 F26 27055 18974 Pb 0.649 2 0.478 7 25 ACCEPTED MANUSCRIPT Highlights 1. Non-invasive and micro-invasive techniques applied to a collection of 24 fragments replaced from historical instruments of the 19th and 20th centuries. 2. Multivariate statistical analyses (Principal component analysis and Cluster analysis) used to establish correlations and distribution of elemental markers in the fragments. 3. Observations in cross sections of the recto side of the most correlated fragments to PT confirm the results obtained by the multivariate statistical analysis. 4. New information about the modus operandi of the violin maker of the past obtained by micro-invasive analysis of the cross-sections identifying some characteristic materials. RI 5. Validation of the multivariate statistical PCA model by an external test-set, i.e. XRF AC CE P TE D MA NU SC dataset collected on a Giovanni Paolo Maggini double-bass (1610). 26