Abstract
The first violins appeared in late 16th-century Italy. Over the next 200 years, they spread across Europe and luthiers of various royal courts, eager to experiment with new techniques, created a highly diverse family of instruments. Around 1750, size standards were introduced to unify violin making for orchestras and conservatories. Instruments that fell between two standards were then reduced to a smaller size by luthiers. These reductions have an impact on several characteristics of violins, in particular on the contour lines, i.e. lines of constant altitude, which look more like a U for non reduced instruments and a V for reduced ones. While such differences are observed by experts, they have not been studied quantitatively. This paper presents a method for classifying violins as reduced or non-reduced based on their contour lines. We study a corpus of 25 instruments whose 3D geometric meshes were acquired via photogrammetry. For each instrument, we extract 10-20 contour lines regularly spaced every millimetre. Each line is fitted with a parabola-like curve (with an equation of the type y = alpha*abs(x)**beta) depending on two parameters, describing how open (beta) and how vertically stretched (alpha) the curve is. We compute additional features from those parameters, using regressions and counting how many values fall under some threshold. We also deal with outliers and non equal numbers of levels, and eventually obtain a numerical profile for each instrument. We then apply classification methods to assess whether geometry alone can predict size reduction. We find that distinguishing between reduced and non reduced instruments is feasible to some degree, taking into account that a whole spectrum of more or less transformed violins exists, for which it is more difficult to quantify the reduction. We also find the opening parameter beta to be the most predictive.
Abstract (translated)
第一把小提琴出现在16世纪晚期的意大利。在接下来的200年里，它们传播到了整个欧洲，各个宫廷里的制琴师们热衷于尝试新技术，从而创造出了一个高度多样化的乐器家族。大约到1750年，为使乐团和音乐学院中的小提琴制作标准化，制定了尺寸标准。那些介于两种标准之间的小提琴则被制琴师缩小尺寸。这些缩减影响了小提琴的多个特性，尤其是在轮廓线方面：对于未被缩减的小提琴而言，轮廓线看上去更像一个“U”形；而对于已被缩减的小提琴，则更像是一个“V”形。尽管专家们观察到了这样的差异，但这些变化尚未得到定量研究。 本文介绍了一种基于小提琴的轮廓线来分类其是否为缩减型的方法。我们研究了一个包含25把乐器的数据集，其中每把乐器的3D几何网格是通过摄影测量技术获得的。对于每个乐器，我们会提取出10-20条间隔一毫米等距分布的轮廓线，并使用一个类似抛物线的曲线（方程形式为y = alpha * abs(x)**beta）来拟合每一根线条，这条曲线由两个参数描述，即开放程度(beta)和垂直拉伸度(alpha)。根据这些参数，我们计算出额外的特征值，包括回归分析以及统计哪些数值低于某个阈值的数量等，并处理异常值及不同数量级的问题，最终为每把乐器获得一个数值轮廓。之后，我们将应用分类方法来评估仅凭几何形状是否能够预测尺寸缩减。 我们的研究发现，在一定程度上可以区分出被缩减与未被缩减的小提琴，尽管考虑到存在一系列程度不同的变形小提琴，这种区分更加困难。此外，我们还发现开放性参数(beta)具有最强的预测能力。
URL
https://arxiv.org/abs/2507.07743
