MIT’s virtual violin offers luthiers a new design tool

麻省理工学院的虚拟小提琴为制琴师提供了新的设计工具

Violin makers, aka luthiers, traditionally learn from hands-on experience how to craft parts and select materials to shape an instrument’s final sound. MIT engineers hope to streamline that painstaking process with their new virtual violin. It’s a computer simulation tool that can capture the precise physics of the instrument and even reproduce a realistic sound of a plucked string, according to a paper published in the journal npj Acoustics.

小提琴制作师（又称制琴师）传统上通过实践经验来学习如何制作部件和选择材料，以塑造乐器的最终音色。麻省理工学院的工程师们希望通过他们研发的新型虚拟小提琴来简化这一艰苦的过程。根据发表在《npj 声学》（npj Acoustics）期刊上的一篇论文，这是一种计算机模拟工具，能够捕捉乐器的精确物理特性，甚至可以重现拨弦时逼真的声音。

Unlike more common software programs and plugins that simulate violin sounds via sampling, averaging the final sound from thousands of notes, the MIT model is based on the fundamental physics of the instrument. “We’re not saying that we can reproduce the artisan’s magic,” said co-author Nicholas Makris. “We’re just trying to understand the physics of violin sound, and perhaps help luthiers in the design process.”

与通过采样（对成千上万个音符的最终声音进行平均）来模拟小提琴声音的常见软件程序和插件不同，麻省理工学院的模型基于乐器的基本物理原理。“我们并不是说我们可以复制工匠的魔力，”合著者尼古拉斯·马克里斯（Nicholas Makris）说，“我们只是试图理解小提琴声音的物理原理，并希望能为制琴师的设计过程提供帮助。”

Violin acoustics has long been a hot topic of research among acousticians, particularly when it comes to unlocking the secret to the superior sounds of violins crafted during the so-called “Golden Age”—notably the instruments of famed Cremona luthier Antonio Stradivari, as well as those of the Amati family and Giuseppe Guarneri. There are plenty of variables to consider, given a violin’s acoustic complexity.

小提琴声学长期以来一直是声学家研究的热门课题，特别是在揭开所谓“黄金时代”所制小提琴卓越音质的秘密方面——尤其是著名的克雷莫纳制琴师安东尼奥·斯特拉迪瓦里（Antonio Stradivari），以及阿马蒂（Amati）家族和朱塞佩·瓜奈里（Giuseppe Guarneri）制作的乐器。考虑到小提琴声学的复杂性，有许多变量需要考量。

Per my 2021 article, the (perceived) unique sound can’t just be due to the instrument’s geometry, although Stradivari’s geometrical approach gave us the violin’s signature shape. It might be due to the wood; some researchers have hypothesized that Stradivari used Alpine spruce grown during a period of uncommonly cold weather for the region. The annual growth rings were closer together, making the wood unusually dense. Differences in wood density, they argue, would have an impact on the instrument’s vibrational efficiency and hence its sound.

根据我 2021 年的文章，这种（被感知的）独特声音不仅仅归因于乐器的几何形状，尽管斯特拉迪瓦里的几何设计方法赋予了小提琴标志性的外形。这可能与木材有关；一些研究人员推测，斯特拉迪瓦里使用了在当地异常寒冷时期生长的阿尔卑斯云杉。其年轮间距更紧密，使木材密度异常高。他们认为，木材密度的差异会影响乐器的振动效率，进而影响其音色。

Or perhaps it was the varnish Stradivari used: a cocktail of honey, egg whites, and gum arabic. A 2022 study involving nanoscale imaging of two such instruments revealed a protein-based layer at the interface of the wood and the varnish, which may influence the wood’s natural resonance. Biochemist Joseph Nagyvary has argued that it was the chemicals used to treat the wood that give Stradivari violins their unique sound, specifically salts of copper, iron, and chromium used to preserve the wood—all of which are excellent wood preservers but may also have altered the instruments’ acoustical properties. A 2021 study supported that argument, identifying borax, zinc, copper, alum, and lime water as the most likely chemicals affecting the sound.

又或许是斯特拉迪瓦里使用的清漆：一种由蜂蜜、蛋清和阿拉伯树胶混合而成的配方。2022 年一项涉及两件此类乐器纳米级成像的研究显示，在木材和清漆的界面处存在一层蛋白质层，这可能会影响木材的自然共振。生物化学家约瑟夫·纳吉瓦里（Joseph Nagyvary）认为，正是用于处理木材的化学物质赋予了斯特拉迪瓦里小提琴独特的音色，特别是用于防腐的铜、铁和铬盐——这些物质虽然是极好的木材防腐剂，但也可能改变了乐器的声学特性。2021 年的一项研究支持了这一观点，指出硼砂、锌、铜、明矾和石灰水是最有可能影响声音的化学物质。

CT scans have provided quite a bit of insight into the conundrum, since the technique can reveal wood density, size and shapes, volume measurements, and thickness graduation, as well as any damage or repairs to a given instrument. For instance, a 2009 study used CT scans to study the material properties of the wood. In 2011, Minnesota radiologist Steven Sirr took detailed CT scans of the 1704 “Betts” violin and then collaborated with two luthiers to make a replica. One of the most thorough investigations was the Strad3D project, spearheaded in 2006 by the late George Bissinger. That project used 3D scanning lasers to make detailed quantitative measurements of the acoustic properties of several Stradivarius violins, essentially mapping out precisely how the instruments vibrate and produce their distinctive sound.

CT 扫描为解决这一难题提供了不少见解，因为该技术可以揭示木材密度、尺寸和形状、体积测量值和厚度梯度，以及乐器上的任何损坏或维修痕迹。例如，2009 年的一项研究利用 CT 扫描来研究木材的材料特性。2011 年，明尼苏达州的放射科医生史蒂文·瑟尔（Steven Sirr）对 1704 年的“Betts”小提琴进行了详细的 CT 扫描，并与两名制琴师合作制作了一个复制品。最彻底的调查之一是 2006 年由已故的乔治·比辛格（George Bissinger）领导的 Strad3D 项目。该项目使用 3D 激光扫描对几把斯特拉迪瓦里小提琴的声学特性进行了详细的定量测量，本质上精确绘制了这些乐器如何振动并产生其独特声音的图谱。

MIT’s virtual violin is based on the Strad3D project’s scan of the 1715 “Titian” Stradivarius. Makris et al. imported that data into a modeling software program and generated a 3D model of the instrument. Then they ran a simulation that broke down the violin into millions of cubes, noting which materials were used in each cube—such as the kind of wood that makes up the back plate, or whether it had natural fiber or steel strings. Next, the team used physics equations to predict how those materials would move and interact relative to every other element in the violin. Those elements include the air surrounding the instrument, simulated using acoustic wave equations.

麻省理工学院的虚拟小提琴基于 Strad3D 项目对 1715 年“Titian”斯特拉迪瓦里小提琴的扫描数据。马克里斯等人将这些数据导入建模软件，生成了该乐器的 3D 模型。随后，他们运行了一项模拟，将小提琴分解为数百万个立方体，并记录每个立方体所使用的材料——例如构成背板的木材种类，或者它是天然纤维弦还是钢弦。接下来，团队利用物理方程来预测这些材料如何相对于小提琴中的其他每个元素进行移动和相互作用。这些元素包括乐器周围的空气，这是通过声波方程进行模拟的。

Having built their virtual violin, Makris et al. were able to simulate the sound of a single plucked string—a playing technique called “pizzicato”—and program it to pluck out several notes of Bach’s “Fugue in G Minor,” as well as “Daisy Bell (A Bicycle Built for Two).” They have not yet figured out how to simulate bowing, which is a much more complex interaction, but it is a focus of their future research. In the meantime, the team hopes their virtual violin will prove useful for luthiers in the early design process, enabling them to test the effects of various parameters, such as wood type or body thickness. “You can tweak the model to hear the effect on the sound,” said Makris. “Since everything obeys the laws of physics, including a violin and the music it makes, this approach can add an appreciation to what makes violin sound. But ultimately, we…”

在构建好虚拟小提琴后，马克里斯等人成功模拟了单根琴弦拨奏的声音——这是一种被称为“拨奏”（pizzicato）的演奏技巧——并对其进行编程，使其拨奏出巴赫《G小调赋格》以及《黛西·贝尔》（Daisy Bell）中的几个音符。他们尚未找到模拟拉弓的方法，因为这涉及更复杂的相互作用，但这将是他们未来研究的重点。与此同时，团队希望他们的虚拟小提琴能对制琴师的早期设计过程有所帮助，使他们能够测试各种参数（如木材类型或琴身厚度）的影响。“你可以调整模型来听取对声音的影响，”马克里斯说，“由于万物都遵循物理定律，包括小提琴及其发出的音乐，这种方法可以增加人们对小提琴发声原理的理解。但最终，我们……”