Figure 1.
Shape differences between violin family members and close relatives.
A) Outlines of instruments that likely contributed to violin design (the rebec, vielle, and lira da braccio) and the related viola da gamba family. Outlines of experimental instruments, the Savart violin and Pellegrina viola, are also shown. B) Outlines of violin family members. On the left, the upper, center, and lower bout regions are indicated. C) Eigenviolins for the violin family morphospace. For Principal Components (PCs) 1–4, violin outlines -5 standard deviations (blue) and +5 standard deviations (orange) along each axis are shown, as well as the mean (gray). Together, the four PCs explain 77.6% of shape variance. Percent variance explained by all PCs and PC values for each instrument can be found in supplemental information. D–E) Scatter plots of D) PCs 1 and 2 and E) PCs 3 and 4. Plots on the left display all instruments and middle plots overlay instrument type by color. Right plots indicate the distribution of each instrument type as a contour plot, upon which is overlayed 95% confidence ellipses. Violins, teal; violas, magenta; cellos, burnt orange; double bases, lavender.
Figure 2.
Linear discriminant analysis of violin family members and comparison of outlines using thin plate splines.
A) Scatterplot of the separation by linear discriminants (LDs) 1 and 2, providing 66.4% and 30.8% of total instrument separation, respectively. Vertical line indicates the LD1 values separating all double basses from other instrument types. B) Histogram of LD2 values (30.8% of separation), which largely separate violins and cellos. No cellos have LD1 values less than the LD1 value of the left line, and no violins have LD1 values greater than the LD1 value of the right line. C) Histogram of LD3 values (2.8% of separation), which differentiate some violas from violins and cellos. The indicated tail of the viola LD3 distribution does not include violins or cellos. Note: for both panels B) and C), double basses are not shown to better focus on violin, viola, and cello distributions. D) Pairwise thin plate splines, using grids to show the deformations necessary to transform reference instrument outlines (vertical) into targets (horizontal). Mean outlines of instruments are overlaid and colored to indicate type. Violins, teal; violas, magenta; cellos, burnt orange; double bases, lavender.
Table 1.
Reassignment of instrument types.
Figure 3.
The historical and geographic context of luthiers and their violins.
A) Geography of violin production in Europe. Overlaid on a map, circle color and location indicates cities of production and size is proportional to the violin output represented in this dataset. B) Stacked histrogram of violin production by year. Colors indicate city of manufacture. C) Same data as in B), but scaled to show the proportional output of each city by year. D) Output of prolific luthiers (with>45 violins in the dataset) over historical time. Points correspond to violins and the year of production, colored by the city of production. Luthiers are organized temporally, by the mean year of their violins represented in the dataset. Cremona, red; Naples, blue; Milan, green; Paris, purple; Venice, orange; Turin, yellow; Mantua, brown; Florence, pink; London, grey; other cities, black.
Table 2.
MANOVA results for violin outlines by luthier and year.
Figure 4.
Linear discriminants of luthier correlated with time.
A) Percent separation contributed by linear discriminants (LDs) 1–85, separating violin outlines by luthier. Averaged LDs by luthier were correlated with the mean year of manufacture for luthiers. Those LDs significantly correlated with time are indicated in red. B) Scatterplot of Spearman's rho (x-axis) and -log10 p-values (y-axis) for averaged LD values by luthier correlated with mean year of luthier production. Circles, labels, and red indicate significant LD correlation with time. Note that LD1 (9.4% separation) is exceptionally correlated with time. C) Scatterplot showing correlation of averaged LD1 values for luthiers with average year of luthier violin production. rho and p values and indicated. All p values shown in this figure are multiple test adjusted across LDs to control false discovery rate (FDR) using the Benjamini-Hochberg (BH) method.
Figure 5.
The contributions of luthiers to the correlation of violin shape attributes with time.
A) Scatterplot showing individual violins with LD1 values (9.4%) plotted against year. Colors indicate violins produced by select luthiers. B) Similar to A), showing boxplots of LD1 values of violins produced by prolithic luthiers. Luthiers are arranged temporally along the x-axis by the average year of the violins they produced. See text for details for the relationships of luthiers to each other and known copying of violin design. Purple, Giovanni Maggini; red, Antonio Stradivari; yellow, Nicolas Lupot; orange, Jean-Baptiste Vuillaume; blue, Eugenio Degani; green, Giulio Degani; black, other.
Table 3.
Reassignment of luthier identity.
Figure 6.
Hierarchical clustering of violin shape.
Clustering based on averaged harmonic coefficients by prolific luthier (>45 violins). Four main clusters, named by prominent luthiers they contain, are indicated by color. As discussed in the text, know copyists of Antonio Stradivari cluster with the Stradivari cluster, and often members of the same family cluster together. Members of family houses that cluster together are indicated. Blue, Maggini cluster; red, Stradivari cluster; purple, Amati cluster; green, Stainer cluster.
Figure 7.
Thin plate splines of major violin clusters.
Thin plate splines, deforming grids to transform violins from members of reference clusters (vertical) with those of targets (horizontal), are provided. Averaged violin outlines from prolific luthiers (>45 violins) from each cluster are superimposed and indicated by color. Differences between reference and target outlines have been amplified by a factor of four to better visualize subtle details. Blue, Maggini cluster; red, Stradivari cluster; purple, Amati cluster; green, Stainer cluster.
Table 4.
MANOVA results for violin outlines by familial identity and year.