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Physical Modeling in Eurorack: an Introduction

Plonks, Pings, Rings, Strings, and Twangs Explained

Matt Biancardi · 12/24/24

Wherever you’re sitting, rap your knuckles against the table or desk. Don’t hurt yourself, but give it a good enough knock that you feel the space taken up by the sound. We often think of sound as a separate kingdom from the physical world, but as articulated in this wonderful Radiolab episode you should absolutely check out, psychologist Anne Fernald describes sound as “touch at a distance.” Whether you’re hitting the head of a drum, the string of a guitar, or just a plastic five-gallon bucket, you’re creating a temporary physical presence that touches everyone within audible distance.

The straightforward act of striking one object with another to elicit a sonic response is the bedrock of one of my favorite arenas of synthesis: physical modeling. While more techniques exist under the general umbrella of physical modeling, the essential idea here is simulating an exciter (mallet, stick, pick, breath, etc.) striking a resonator (drum, cymbal, guitar string, etc.). Simple enough on paper, physical modeling is a complex and fascinating process that has a number of means at its disposal to achieve the desired ends.

I was first entranced by physical modeling while living in Paris and listening to The Knife’s Silent Shout ad nauseam, specifically the intro of “Marble House”. While not technically physical modeling (I’m pretty sure Olof Dreijer used an FM synth with some nice reverb), the sound of a synth behaving like raindrops gripped my imagination and never let go. Now, what if those raindrops could turn into a marimba, then into a gong, then into a violin, then back into raindrops? Creating impossible spaces/objects, sometimes referred to as “Superphysical Modeling” (which sounds like an Armed song title) is where this type of synthesis shines, but we’re getting ahead of ourselves.

As a complex process with a number of variables weighing on the finished product, physical modeling is ideal for the modular environment. We’re going to do a quick history lesson on the origins of physical modeling synthesis, then dive straight into our favorite modules that use different techniques like Karplus-Strong and digital waveguide synthesis to achieve the organic, surreal, and enchanting sounds of physical modeling.

Origins of Physical Modeling

Recreating sounds in the physical world through artificial means stretches all the way back to the 19th century and includes speech synthesis, the creation of “talking machines”, and a wild contraption named “Voder” developed by Bell Labs in the first half of the 20th century. If you’d like to parse a detailed history, we have an excellent article examining physical modeling writ large, but for our purposes, we’re starting in 1982 with the advent of Karplus-Strong string synthesis.

Before we examine the Karplus-Strong method, it’s important to understand one of the main challenges to physical modeling: the continually-evolving relationship between multiple variables of the sound. Think about when you pluck a string on a guitar: you press the string at a given fret, you strike the string with your finger or pick, and the guitar responds to the physical excitation within the confines of its current space. And that’s just one pluck. While actively strumming, all of these variables are in flux, changing from one second to the next. It’s not dissimilar to Jeff Goldblum dripping water on Laura Dern’s hand while explaining chaos theory in Jurassic Park: we don’t know which way those droplets are going.

Synthesizers were designed to be constant and reliable: it wouldn’t do to press down on Middle C and hear an ox belching. To create the required parameter variance for physical modeling, algorithms are necessary. While “algorithm” is very much a buzzword in 2024, an algorithm is simply a set of rigidly-defined rules or steps followed by a digital brain like a computer during an operation. “Rigidly-defined rules” doesn’t exactly smack of the required variation we mentioned earlier, but it’s exactly because of algorithms that brilliant minds were able to devise artificial means to recreate the physicality of sound.

With that primer in tow, let’s take a look at Karplus-Strong. Created by Alexander Strong and first tested by Kevin Karplus, both Stanford students who were exploring wavetable synthesis, this method revolves around a delay line with a filter in its feedback loop to achieve its ends. A short burst of sound like white noise is output and concurrently fed into the delay line, then the filter, then back into the original signal. Factors like delay length and feedback as well as filter cutoff and resonance are vital in establishing the harmonic content of the end product and are niftily handled in the context of an algorithm.

Karplus-Strong became the first and most rudimentary instance of digital waveguide synthesis, a technique in which the acoustic waves are processed through a computational model of a physical medium, or the waveguide. Some real-world examples include loudspeaker enclosures, stethoscopes, and the human ear canal. Personally, I like to think of waveguides like that old Japanese game show Brain Wall where contestants play human Tetris to fit through an odd-shaped hole in an oncoming wall. Sure, they may not look exactly like an “X” with a head on it, but the facsimile is enough to fascinate and amaze, not unlike how an ersatz marimba or timpani fascinates the person behind the synth.

Physical Modeling in Eurorack

It’s nigh impossible to talk about physical modeling in eurorack and not start with Mutable Instruments. The brainchild of French designer Émilie Gillet, Mutable Instruments (often shortened to simply “Mutable”) was one of the standout names throughout the 2010s in creating new, exciting modules and enticing musicians to dip their toes in the modular world. Though now defunct, the company remains influential thanks to the originality of Gillet’s designs and her decision to make all of her designs open-source, hence the enormous market for Mutable clones (thanks Émilie!), as well as ports of her code in other formats. Her implementations of physical modeling went beyond Karplus-Strong synthesis alone, and into the realm of modal synthesis: allowing for the modeling of more complex types of resonators.

Mutable Instruments: Elements + Rings

Now onto the fun part: modules capable of physical modeling synthesis. Both Elements and its smaller counterpart Rings operate on modal synthesis, which uses a number of resonant bandpass filters to mimic the sonic structure of an object (or mode). So the same exciter and resonator principle applies, but the resonator is made out of filters instead of a delay line. Plus it can morph into different objects with the twist of a dial. Not bad at all.

Elements is divided into two sections: the exciter and the resonator. The exciter section gives you three options: a Bow sound, a Blow sound, and a percussive Strike. Each has a Timbre control with CV and the Blow/Strike excitations can be texturally altered via the Flow/Mallet knobs. Finally, a Contour knob grants you an envelope for tailoring the Bow and Blow sound sources to taste.

While the expansive exciter section is novel, the resonator is what persists in the imaginations of modular enthusiasts to this day (the resonator section of Elements is also what constitutes the core of Rings). Coarse, Fine, and Frequency Modulation (FM) knobs provide control over the fundamental frequency response; Geometry alters the frequencies, gains, and Q, or feedback, of the resonator’s filters to simulate different objects and materials; Brightness and Damping adjust high frequencies and reduce simulated object vibration respectively; Position moves the strike point of the resonator from the middle outward; and Space not only adds reverb, but mixes the exciter output on the left and the resonator output on the right into a stereo image.

Rings streamlines this section into what is one of my desert island modules. I love Rings and have spent countless hours frolicking in its intuitive layout and sonic capabilities. Coarse and Fine tuning are collapsed into a single Frequency knob and there’s no onboard reverb, but in their absence, you get three different resonator types and up to four-note polyphony accessible via the small buttons at the top of the module. Combined with both an internal exciter activated by the Strum input and the In input which allows you to choose your own sound source, Rings has earned its place as one of modular synth’s GOATs.

Intellijel Designs Plonk

For those who want the possibilities of physical modeling with an expanded set of sounds and fewer parameters to control, the Intellijel Plonk could be an attractive option. Created in partnership with plugin experts Applied Acoustics Systems, the Plonk employs the same exciter-resonator structure as Elements and Rings with a wider array of modes and digital screen for diving into the marvelous depths of strikingly real and strikingly unreal sounds.

Plonk comes with Object (aka “resonator”) modes for strings, beams, marimbas, drums, membranes, and plates. You also get 128 save slots and the ability to create sounds either by your own design or by randomizing parameters. Pair this with a well-considered mallet model for the exciter, flexible noise sourcing, and two-voice polyphony for a veritable physical modeling factory (as expertly demonstrated by Andrew Huang in this fun demo).

To my mind, Plonk is almost a physical modeling sampler thanks to how quickly it can create a singular sound and then create another entirely singular sound by the next strike. While the nine buttons and digital screen may make the Plonk seem involved and menu dive-y, Intellijel are absolute pros in UX and operating the module is as breezy as the demos make it seem. If you’re curious about physical modeling, the Plonk slots in pretty handily to any system.

WMD Crucible

Often thought of simply as a drum set component, cymbals are a fascinating world unto themselves complete with distinctive types, timbres, and sounds. Ranging from the teensiest splash to a glassy ride to a full-throated crash all the way to a booming gong, the high-frequency metallic bloom and skitter are showcased with the highest marks in the WMD Crucible.

Clocking in at only 8HP, the Crucible packs an impressive amount of sound options and editable parameters in its relatively tiny space. WMD translated this format into other percussion-focused modules like snares, claps, and kicks, but only the Crucible is physical modeling in the true sense (my personal favorite is the Fracture). Three modes (cymbal, cracked cymbal, curved metal plate) and six controls chosen for their salience to actual cymbals give you CV’able sway over Size, Decay, Pitch, and Excite. Additional CV jacks grant options like a Choke to rein in decays at will and Edge/Mid jacks for which part of the “cymbal” will be hit (plugging in both triggers a third option: the Bell!).

Other entries in this article will provide a more robust palette of physically-modeled instruments/objects, but for those who specifically want to investigate physical modeling in the context of cymbals and metal, you’d be hard-pressed to do better than the Crucible.

Qu-Bit Electronix Surface Physical Modeling Voice

Sleek, elegant, and intuitive, the Qu-Bit Electronix Surface reflects the company’s design and engineering ethos with a unique take on physical modeling. Similar in design to Rings, the Surface boasts four distinct models (plucked string, mallet, tuned drum, snare/tuned noise) and up to eight voices of polyphony, but it’s the voice selection that distinguishes the Surface.

Users have the option to stack similar voices, say different kicks/bowed strings/etc, but this module gets really fun and weird when you stack voices from different modeled instruments on top of each other.

So: if you ever wanted to find out what a string turning into a bass drum turning into a tuned crackle and back into a string, the Surface is an ideal avenue.

2hp Pluck/Bell Physical Modeling Voices

We’re finishing out with a return to the first physical modeling technique discussed in this article: Karplus-Strong string synthesis, and you won’t find a more concise and faithful representation of it than the 2hp Pluck and Bell modules.

True to the company name, each module measures only 2hp and contains a full plucked string or struck bell physically-modeled voice. Both have an Input and CV-controllable v/Oct jack: the Pluck features two controls for Damp and Decay while the Bell sports Mallet and Bar inputs.

Tightly focused, well-conceived, and fantastic in tone, the Pluck and Bell are the most affordable options for taking the step (and you should take it) into the world of eurorack physical modeling synthesis.

Looking Forward

The world of physical modeling synthesis is still largely underexplored in the context of hardware instruments. That said, Eurorack was one of physical modeling's first in-depth hardware proving grounds—and today, some of its earliest Eurorack implementations have spun out into many other products via Émilie Gillet's open-source code for modules like Rings, Elements, and more.

Outside of Eurorack, new devices are beginning to emerge: the Erica Synths Steampipe, Korg Volca Drum, and Expressive E Osmose (among other Eaganmatrix-imbued devices) have begun to plot a course toward broader embrace of physical modeling. One thing is certain: the future is truly exciting.