PxPixel
Master Class: Physical Modeling - EMusician

Master Class: Physical Modeling

A powerful form of synthesis that is easier to program than you think
Author:
Publish date:
Image placeholder title

Like FM, physical modeling (PM) is often perceived to be a complicated and arcane approach to synthesis. Fortunately, it’s more approachable if you understand a bit about its history and familiarize yourself with the creative tools you may already be using.

Applied Acoustic Systems (AAS) Chromaphone 2 is particularly intuitive to use once you understand the underlying concepts of physical modeling. It provides two resonators, which can be applied in parallel or in series, that can mimic an array of materials—string, beam, marimba, membrane, metal plate, and open and closed tubes.

Image placeholder title

For this article, I will demystify the elements of PM synthesis, first, by looking at its origins and, then, comparing the different features in two commonly used synths—Apple Structure and Ableton Collision.

A STRIKING HISTORY

Fig. 1. Kevin Karplus and Alexander Strong’s algorithm serves as the basis for early physical modeling. Graphic designed by PoroCYon (Creative Commons attribution).

Image placeholder title

The core principles of physical modeling are based on the Karplus-Strong algorithm, which was developed in 1983 by Alexander Strong and Kevin Karplus. Together, the duo developed a practical implementation of the algorithm and named it “Digitar,” because of the resulting sound’s string-like characteristics. The basic components of the Karplus-Strong approach are a very short noise burst (often called the “exciter”) followed by a very short delay with high feedback, augmented by a filter in the feedback loop that shapes the tone of the output (see Figure 1).

Fig. 2. By setting the delay time to 1 millisecond, with a high feedback amount, a 1kHz plucked string tone can be emulated.

Image placeholder title

You can quickly re-create a simple Karplus-Strong algorithm with two tools found in every modern DAW: a single drum hit (short snares and hi-hats work well) followed by a delay effect. While triggering the drum in a simple sequence, set the delay feedback amount between 95% and 99% (100% may generate an endless feedback loop), turn the wet/dry mix to 100% wet, and set the delay time to 1 millisecond (see Figure 2). This will result in a pitch of 1 kHz and a tone that sounds a bit like an upper octave clavinet.

Why 1 kHz? Here’s a little math on the topic: There are 1,000 milliseconds in a second, and setting up a 1 ms delay with high feedback will cause the signal to repeat 1,000 times per second. If you set the delay time to 2 ms, the signal would repeat 500 times per second (500 Hz); 4 ms would result in 250 Hz, and so on. So ultimately, the drum-hit-plus-delay approach is a great way to understand the Karplus-Strong principle and its relationship to pitch.

Very short delays are also the basis for comb filtering, which explains its resemblance to flanging, an effect that is also created using a short delay time with high feedback. In the case of a flanger, the delay time is modulated using an LFO for its signature sweep. In a comb filter, the filter frequency knob replaces the minutia of delay time, while delay feedback is handled by the resonance parameter. Even so, the end result is largely identical.

Fig. 3. Comb filtering, shown here in Xfer Serum, is another tool for understanding the foundations of physical modeling.

Image placeholder title

If you have a synth that offers a comb filter option—such as Propellerhead Thor or Xfer Serum—you can explore its relationship to physical modeling using white noise as your source input, followed by the comb filter (see Figure 3). Here, continuously sweeping the filter frequency will result in the familiar flange effect. To go a bit further, try setting the keyboard tracking to 100% and use it to control the frequency. In this way, the “flanged” pitch will track the keyboard musically. Interestingly, if you invert the phase of the comb filter—often designated by the minus (-) symbol—the filter’s tone will sound hollower, as if you are blowing through a tube. (The sound you get from switching the phase of a comb filter is reminiscent of the harmonic differences between sawtooth and square waves.)

Having experimented with both delays and comb filters, you now have an understanding of the essential principles that serve as the basis for physical modeling, which expands on the above techniques by adding mathematical waveguides to the resonant delays, further shaping the tonality of modeled instruments.

A GUIDE TO MODELING COMPONENTS

Most modern physical modeling synths simplify the design process greatly by breaking the system into two distinct components—the exciter and the resonator—and including a set of parameters for handling the behavior of each. Additionally, some PM synths add a “body” component to the chain, after the resonator, for improving the realism of the acoustic behavior. Here is a quick overview.

Exciter. Sometimes referred to as the “object,” “excitor” or even “excitatory,” the exciter is the initial pulse of energy that stimulates the resonator. In Karplus-Strong, the exciter is a short noise burst, but in PM synths, the exciter module can be much more complex, with properties that range from striking mallets to “picked” behavior to bowed or blown effects for re-creating violins and woodwinds, respectively. Many instruments allow for multiple simultaneous exciter types that can be blended to create a composite result for stimulating the resonator.

Resonator. This is where the mathematical waveguides come in. The resonator imitates the behavior of actual acoustic materials, ranging from advanced Karplus-Strong string models to pipes, plates, tubes, marimbas, and membranes (drums). Some instruments, such as Apple Logic and Main-Stage’s Sculpture, allow for continuous variation between these resonator materials, resulting in hybrid tones that are both organic and otherworldly.

Common properties across resonator types include parameters that govern how long the material resonates after being excited (decay), the level of detail (resolution, which directly effects CPU utilization), and material tension, which is often associated with a quick pitch shift at the attack of a note, much like an overblown brass instrument or hard-plucked string. One of the primary benefits of physical modeling is the ability to implement unusual combinations of exciters and resonators, like hitting tubes and pipes with mallets, or using bowed string exciters on glass or metallic materials.

Body. This component serves to reproduce the acoustic behavior of a resonant cavity, like the hollow body of an acoustic guitar or the soundboard of a grand piano. Practically speaking, it’s useful to think of the body elements as tiny reverb spaces with heavy EQ, which is ultimately how they behave, sonically.

Image placeholder title

SCULPTURE AND COLLISION

While there are quite a few physical modeling soft-synths available (AAS Chromaphone 2 stands out as one of the best), both Apple Logic and Ableton Live Suite include their own versions of this technology. For Logic, the synth is called Sculpture. In Live Suite, Ableton bundles three physically modeled synths—Electric (for electric piano models), Tension (for stringed instruments), and Collision, which is most similar to Logic’s Sculpture and AAS Chromaphone 2 in its operation. Focusing on the tools described in the previous section, let’s take a closer look at both.

APPLE SCULPTURE

Sculpture’s exotic interface elements make it slightly difficult to navigate, compared to many other modeling synths, but the principles are largely the same once you dig a little deeper. It adds waveshaping, filtering, stereo delay, and extensive modulation options, as well, though we’ll stick to the modeling-specific tools here.

Fig. 4. Apple Sculpture offers three discrete exciters, called “Objects”. A pickup simulator is shown in the middle.

Image placeholder title

In Sculpture, exciters are called Objects and there are three available simultaneously, each with a slightly different set of exciter options for stimulating its waveguide/resonator. The first two Objects include common selections like strike, pick, bow, and blow, along with a few others. The third provides unusual exciters that interact with the first two, often resulting in no sound at all when it’s the only active exciter. The second Object combines all exciter types (see Figure 4). This is important to note as you explore the synth.

To get the best feel for Sculpture’s overall sound, start your experiments with Object 1 and select a familiar option such as Strike or Pick. Then, after evaluating each exciter, select one of the exotic types from Object 2. (It is important to note that clicking the Object’s associated number toggles it on/off).

For the second Object, experiment with the Disturb and Bouncing types. Disturb adds a bit of rattling to the flavor, while Bouncing adds a “trampoline” effect to Object 1’s selection. Other types affect the damping characteristics of the exciter. Note that Object 3 offers only these modifiers. Every Object also provides dedicated controls that adjust its velocity sensitivity, adds slight randomization to every note event, or fine-tunes its timbral behavior. There’s a lot going on, so sticking with Object 1 for a while is the best strategy for mastering these tools.

In the middle of the three Objects is a set of “pickups” that allow you to move the exciters in relationship to each other, further affecting their behavior. Until you master the objects themselves, it’s best to stick with the pickups’ initialized defaults.

Fig. 5. Sculpture’s material editor lets you freely mix between four resonator types and tailor the behavior of their properties.

Image placeholder title

The Material section controls the tonal character of the resonator and is much easier to manipulate (see Figure 5). The X/Y axis has quadrants for nylon, steel, wood, and glass models, which can be freely blended. Surrounding this selector are parameters for media loss (decay), resolution (detail), and tension mod (pitch articulation). Sticking with the X/Y axis and above parameters, you can get a wide range of useful textures. Near the bottom are more advanced controls for adjusting the keyscaling and release behavior of the material.

Fig. 6. The Body module simulates acoustic properties of various instrument cavities.

Image placeholder title

In the lower right area of the interface is a Body section that’s toggled on/off by clicking on its label; blue means it’s active (see Figure 6). Here you can further modify the acoustic properties of the material by placing it in a resonant cavity, with options ranging from acoustic guitar models to various violin bodies. Each mode colors the sound in a distinct manner, a bit like EQ or filtering, with additional formant-shaping parameters for further customization.

ABLETON COLLISION

Compared to Sculpture’s myriad options and curious interface, understanding Collision is a breeze. Though its features are more succinct, Collision excels in a few areas that keep its functionality competitive with other modeling synths (which is not surprising since it was designed by AAS).

Fig. 7. Ableton Collision offers a more familiar approach to synthesizing different exciter types.

Image placeholder title

Despite having one syllable too many, Collision’s Excitator offers a more intuitive approach to customization, with two simultaneous tools for stimulating the resonator section (see Figure 7). The first is called Mallet, though its controls for noise, stiffness, and color are capable of nuanced pick-like behavior and heavier impacts.

The other Excitator should be instantly familiar to most synthesists, as it’s a filtered noise generator with a dedicated envelope. Here, the envelope allows for sustained stimulation of the resonator, required for blown and bowed effects, while the filter governs the frequency content of that excitement. For example, if you want a soft, blown flute, you’d shape the envelope accordingly, then use a lowpass filter on the noise. Need more air? Open the cutoff.

As for modeling the dynamics and scaling of acoustic instruments, every relevant parameter includes velocity and keyboard tracking, represented by simple V and K panels under the associated tools.

Because the two Excitators can be combined, you can blend a sharp mallet strike with a noise envelope with long decay/release, creating a reverb-like texture that would be difficult to replicate by other means.

Fig. 8. Collision’s dual resonators can be configured in parallel or series, for complex and/or layered results.

Image placeholder title

Collision’s dual Resonators can be configured in parallel or series, extending its timbral palette while keeping everything intuitive (see Figure 8). Both Resonators are identical and include straightforward tuning controls, adding to their approachability.

Figure 9: Here are Collision’s seven material options, represented visually.

Image placeholder title

Each Resonator includes a pull-down menu for selecting one of seven waveguide materials (see Figure 9): Beam (xylophone), marimba, string, membrane (great for congas and timpani), plate (bells and gongs), pipe (with variable opening), and tube (a cylinder open at both ends). Once selected, these materials can be quickly modified using an X/Y pad mapped to decay and material—or radius, in the case of the tube and pipe. Decay is self-explanatory, while the material parameter tilts the frequency spectrum low or high.

The other Resonator tools are easy to master, as well. In addition to Brightness, there’s a control for Inharmonics, which adjusts upper and lower dissonance by stretching or compressing the harmonics. The cryptic Listening and Hit parameters control the pickup/microphone position and exciter axis respectively. Finally, in the upper right corner of the resonator is a Quality pull-down menu, which determines the detail (and CPU utilization) of a given material.

As for Resonator configuration, in Parallel, the resonators are excited by the same source, which is useful for layered tones. In Series, the second resonator is fed by the first, which can sometimes lead to unruly results. When working in Series mode, it’s often wisest to give the first Resonator a fast decay, followed by tinkering with its Brightness, Listening and Hit parameters to make the sound behave more predictably. What’s more, the Series mode partially offsets the absence of an acoustic body simulator at the end of the chain.