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Modeling Mersenne's Clavichord

Mason Malone<br>June 20, 2026<br>view source

Introduction

I recently took part in a CAD contest hosted by Zoo, a very interesting CAD program intended for hardware design.<br>My submission, Mersenne&rsquo;s Clavichord, won first place.<br>It&rsquo;s a reconstruction of a 17th-century clavichord described by Marin Mersenne. This post will describe my experiences with Zoo and how I approached the model.

If you want to hear what this would sound like, check out the excellent album Mersenne&rsquo;s Clavichord: Keyboard Music in 16th & 17th Century France, which was performed on a reconstruction of this same instrument built by Peter Bavington.

Mersenne&rsquo;s Clavichord (Spotify link)

Background and History

What&rsquo;s a Clavichord?

The clavichord is a keyboard instrument that was invented at some point before 1404, and flourished for centuries in Europe.1<br>It was a highly expressive instrument, but too quiet for concert use, and gradually faded away with the rise of the piano.2<br>Despite its weak sound, it was the preferred instrument for many composers, notably C.P.E. Bach, who considered it superior to the piano in many respects.3

I&rsquo;ve been listening to classical music for over 20 years, but I was only vaguely aware of the clavichord until last year, when I randomly stumbled on the album Clavichord Recital by Gustav Leonhardt.<br>I immediately fell in love with that album, but I began to wonder: why is this my first time hearing a clavichord?<br>I had heard Bach played on the piano countless times, yet never the clavichord, despite it being the instrument on which he likely wrote many of his keyboard works.

At first, I thought the answer was that the piano was simply a superior instrument, so there was no reason to perform Bach on the clavichord anymore.<br>But then in Leonhardt&rsquo;s performance of the Sonata in B Minor, I heard what sounded like vibrato.<br>&ldquo;Surely that&rsquo;s a recording error&rdquo;, I thought, &ldquo;everyone knows you can&rsquo;t do vibrato on a keyboard instrument.&rdquo;<br>But I was wrong: unlike virtually every other keyboard instrument, you absolutely can perform vibrato on a clavichord, and it&rsquo;s a consequence of how the action works.

Clavichord Action

A clavichord action is a simple class 1 lever, where one end of each key has a piece of metal called a &ldquo;tangent&rdquo;.<br>When the other end of the key is pressed, the tangent rises and strikes the string. The distance between where the tangent strikes the string and the bridge is called the &ldquo;sounding length&rdquo; for that string.

Balance pin

Tangent

String

Bridge

Key lever

Clavichord action (source code)

By rocking the key slightly, the player can alter the tension of the string for the duration of the note, which changes the pitch.<br>This is a form of vibrato unique to the clavichord, and is sometimes called &ldquo;bebung&rdquo;.4

Why Model a Clavichord?

Even though there are still instrument makers keeping the art of clavichord building alive, many aspects of their construction have been lost to time.<br>Several modern clavichord builders, such as Peter Bavington and Pierre Verbeek, have done extensive work to rediscover these lost techniques.

Verbeek is an engineer and physicist who turned to clavichord construction in 2004. In 2011, he published a paper titled &ldquo;The Urbino Clavichord Revisited&rdquo;, in which he reverse-engineered how a 15th-century clavichord was built by analyzing an intarsia depicting it.

Verbeek&rsquo;s paper fascinated me, partly because it treated clavichord reconstruction as a puzzle to be solved, and partly from his creative use of math and physics.<br>Unlike every other paper I&rsquo;ve read, Verbeek included a plethora of measurements and technical drawings.<br>Still, even with all these details, I had trouble visualizing certain aspects of the instrument.<br>It&rsquo;s very difficult to accurately describe something as complex as a clavichord using only prose and technical drawings.

These days, engineers have largely migrated from technical drawings to CAD software. CAD software has many advantages for describing the kind of objects engineers typically work with:

Accuracy. CAD models can express measurements to an arbitrary level of precision.

Easy modification. The clavichord action diagram shown above is a simplified version of the one shown below.

Error checking. Most CAD software lets you express the different parts of an object in terms of constraints and equations, which it will check for you automatically.

Visualization. Nearly all CAD programs let you quickly render a 3D model, which allows quick verification.

Although clavichords are clearly not the kind of objects engineers typically work with, all these advantages are just as applicable to the work of people like Verbeek and Bavington.<br>I couldn&rsquo;t find any published CAD models of a clavichord, so I took it upon...