A discussion about violin reduction: geometric analysis of contour lines and channel of minima

TL;DR

The paper tackles the problem of distinguishing reduced from unreduced violins by leveraging 3D geometric analysis of contour lines and the channel of minima derived from photogrammetric meshes. It extends prior work from two instruments to 38, introducing an improved plane-of-symmetry alignment and a grid-based minima-channel method that is faster and more robust. The results show a spectrum of transformations—including reductions, twisting, and cracking—that affect contour and channel features, highlighting interpretation challenges. The authors propose future quantitative modeling of contours and channels and machine-learning classification to corroborate qualitative assessments and enable more objective attribution of reductions.

Abstract

Some early violins have been reduced during their history to fit imposed morphological standards, while more recent ones have been built directly to these standards. We can observe differences between reduced and unreduced instruments, particularly in their contour lines and channel of minima. In a recent preliminary work, we computed and highlighted those two features for two instruments using triangular 3D meshes acquired by photogrammetry, whose fidelity has been assessed and validated with sub-millimetre accuracy. We propose here an extension to a corpus of 38 violins, violas and cellos, and introduce improved procedures, leading to a stronger discussion of the geometric analysis. We first recall the material we are working with. We then discuss how to derive the best reference plane for the violin alignment, which is crucial for the computation of contour lines and channel of minima. Finally, we show how to compute efficiently both characteristics and we illustrate our results with a few examples.

Figures (8)

• Figure 1: Impact of the reduction of the length of the sound box on the channel of minima (left) and impact of the reduction of the width of the sound box on the contour lines (right)
• Figure 2: Four scale bars are used during the data acquisition process. Examples for a violin (left) and a cello (right)
• Figure 3: Planes of the sound board and back before (top) and after (bottom) the plane of symmetry has been matched with the plane $z=0$, i.e. after a 3D rotation (which does not correspond to a 2D rotation of the yellow angle) and the offset adjustment
• Figure 4: Distribution of the dihedral angles between the planes of the sound board and the back (top-left, red), the plane of symmetry and the horizontal plane (top-right, yellow), the sound board and the horizontal plane (bottom-left, blue), and the back and the horizontal plane (bottom-right, green)
• Figure 5: Plane of symmetry and successive parallel horizontal planes