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The Allure of Physical Modeling

Roger Linn

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This underappreciated synthesis technique may be the key to greater musical expression.

Ever since I first laid my hands on a Moog modular synth at around age 13, I’ve been fascinated with its subtractive synthesis model: oscillator to lowpass filter to VCA, using envelope generators and LFOs as modulators. It seemed that I could make any musical sound I could imagine. 

Except I couldn’t. However, I could quickly get a reasonably close approximation of many of the sounds I could imagine. Even with improvements such as more complex oscillators, sampled waveforms, different filter types, and multiple voice partials, I found it difficult to create new sounds that contained the type of complex harmonic richness that I found in acoustic instruments. To me, most sounds ended up sounding somewhat buzzy. Yes, replacing oscillators with sampled waveforms helped achieve the harmonic richness I sought, but only in specific pitch ranges or dynamic levels. And these sounds weren’t very malleable in ways that I found musical useful. 

Expressive MPE Controllers Demand More from Synthesis

Today, with the introduction of expressive MPE controllers such as the Haken Continuum, Roli Seaboard, or my LinnStrument, it is more important than ever to create new sounds that are not only harmonically rich and complex, but also respond naturally to the performed changes in pitch, loudness, and timbre that these new controllers enable. 

Wouldn’t it be great to have the complex sonic richness of acoustic instruments or samples, but with the malleability of synthesis, especially when played by expressive MPE controllers? 

Enter Physical Modeling

Instruments using a new synthesis technology called physical modeling first appeared in the 1990s. This technique creates sound by using software to mathematically simulate a physical object’s acoustic vibrations. Physical modeling synthesis resulted in new sounds that have the character and harmonic complexity of acoustic samples but the malleability of more traditional synthesis techniques.

Yamaha’s VP1 was one of the first commercially available physical modeling synthesizers.

To synthesize a cello, for example, a physical modeling synth generates a software representation of a string, with adjustments for material, tension, damping, and more, in order to fine-tune the string’s tone, response, and decay time. But a string will make no sound by itself, so the synth also models a variety of stimulation sources, like a pick or a bow or wind or a dulcimer-like hammer. Finally, a string without an instrument body doesn’t sound very good, so the synth also generates a simulation of the resonances of an instrument body. 

I’m excited by the ability to synthesize entirely new instrument sounds that have the sonic richness and harmonic complexity of a physical instrument, yet respond in a natural way to the gestural control of the new expressive MPE controllers. 

Here’s a brief video showing two of my favorite physical modeling synths, played from my LinnStrument. The two synths are SWAM Cello, by Audio Modeling, and Sculpture, by Apple. 

It’s hard to believe that SWAM Cello isn’t a sampled instrument, because it sounds like a perfect cello. Unlike samples, though, it responds naturally to wide pitch slides, pressure control, and Y-axis timbre movements such as those performed on LinnStrument. SWAM is an acronym for Synchronous Waves Audio Modeling. Other SWAM instruments include solo strings (violin, viola, and double bass) and solo woodwinds (clarinets, flutes, saxophones, and double reeds).

Sculpture was added to Apple Logic Pro way back in 2004, but its rich sounds, innovative GUI, and acoustic body resonances make it one of my favorites for creating new sounds. It allows you to specify not only the materials that make up an instrument and their properties, but also how and even where the instrument is played.

If you’re a math whiz and wish to learn more about the innards of physical modeling, here’s a web site on the topic by Professor Julius Smith of Stanford’s CCRMA computer music school. Julius is pretty much the god of physical modeling synthesis, having created many of the underlying algorithms in use. Warning: it’s pretty heady stuff and certainly over my head.

Why Isn’t Physical Modeling More Popular?

With its many advantages, it’s interesting to note that physical modeling synths haven’t attained widespread acceptance. They certainly haven’t knocked subtractive synthesis off its perch. I think there are two reasons for this.

First, when played from a MIDI keyboard’s on/off switches, physical models often don’t sound all that different from samples. But when performed by new expressive MPE controllers like LinnStrument, the limitations of samples become far more apparent, and the expressive malleability of synthesis becomes far more important.

Second, the user interface controls used in physical modeling synthesizers usually aren’t as simple to understand and use as in subtractive synthesis. They tend to be less intuitive and predictable, or simplicity comes as the expense of a limited sonic palette. 

Regarding the first problem, expressive MPE controllers are quickly growing in popularity. Given the advantages of physical modeling for these new controllers, I suspect we’ll start to see increasing popularity of this type of synthesis. 

Regarding the second problem, I’d like to see…

A New Type of Physical Modeling Synthesizer

The current offerings in physically modeling synths have some wonderful ideas and sounds, but I’d like to see improvements in the user interface. That would allow musicians to better unlock the potential of this powerful technology.

I’m not a synth designer, but I do have a few thoughts on this topic.

Given the difficulty of designing a complex timbre like a violin from scratch, a better method might be to morph between existing preset timbres. This idea was proposed years ago by the late David Wessell, founder of University of California, Berkeley’s Center for New Music and Audio Technologies (CNMAT). For example, a screen would present a rectangle onto which you could drag a number of timbre icons— violin, Fender Telecaster guitar, and a filtered pulse-wave synthesizer, for example. By moving an “ear” icon between the timbre icons, you’d create a new timbre that is somewhere between the three, and the heavy lifting would be done internally by morphing between the many parameters of each of the source timbres.

For timbral modifiers, instead of engineering-focused controls like pulse width or wave symmetry or modulation ratio, I’d prefer music-focused controls such as brightness, thin/full, soft/hard, consonant/dissonant, simple/complex, body character, or solo/ensemble. It would certainly not be easy for synth makers to connect such ideal musical controls to the underlying technology in an effective way, but isn’t that the designer’s job? Or must we all become engineers in order to play music?

Under expressive touch control in three dimensions, envelope generators and LFOs aren’t very useful. Why? Because MPE instruments let you perform the envelope with your finger pressure, and you perform periodic movements like vibrato (by wiggling your finger left and right) or tremolo (by pulsing your finger pressure). However, envelope shapes like sharp attack and long decay can be difficult to perform with finger pressure. Instead of an envelope generator, how about an envelope modifier? Its decay control could slow down a performed pressure release, permitting long-decay sounds that are cumbersome to perform by slowly releasing pressure. And its attack knob could slow down or even accelerate a performed pressure attack. (Note also that a physical model of a string naturally decays as a string does, so extended envelope decay isn’t always needed.) 

Take a Test Drive

Quite a few good physical modeling synths are currently available, and each presents uniquely beautiful sounds that reflect the designer’s individual take on the technology. Here are a couple of helpful links: 

Wikipedia’s page on physical modeling, with lists of some products 

KVR Audio’s listing of physical modeling plug-in instruments

I encourage you to try out some of these synths, especially if you play an expressive MPE controller. I suspect you’ll discover a new universe of sounds that will inspire you to new and exciting musical directions.

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