How Physical Modeling Synthesis Works

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Physical modeling synthesis is a special type of software-based sound generation (learn more). It uses careful calculations and computer algorithms to mimic the sounds of traditional instruments.

It considers factors like how tight a string is or the shape of a drum’s surface in mathematical terms. These details help to create a realistic representation of a sound from real life.

Because of its precision, this technique can make very realistic and detailed sounds. It gives sound designers the tools to create audio landscapes that feel like the real thing.

In this guide, you’ll get a complete overview of how it works and how it’s done.

The Fundamentals of Sound

Understanding how sound is made in the natural world (as opposed to how it’s synthesized) is very important to understanding physical modeling. This is because it’s the base for how physical modeling calculations and techniques.

Sound is made when things like air or water vibrate. These things are like a ride for the sound waves. The vibrations come from energy that makes something shake back and forth. This could be guitar strings, a clarinet reed, or human voice boxes.

Turning this energy into sound we can hear is a complex process.

It involves the thing that’s vibrating, called the driver, and the things around it. Every driver is different and affects the sound’s quality and intensity.

For example, how the driver is excited – like plucking, bowing, or hitting – affects the energy conversion and how the sound wave moves.

In physical modeling synthesis, these sound-making processes are copied digitally.

The synthesis copies resonators, which are things or places that naturally make sound louder and shape it.

By acting like these resonators and copying the properties of the drivers, physical modeling synthesis can make sounds that are very close to the real sounds we hear in nature.

Physical Modelling Techniques

Looking into the details of physical modeling techniques shows a world where complex formulas bring acoustic instruments to life.

The success of these digital copies really depends on the accuracy of these formulas that carefully mimic the way sound is made.

The design of the resonator is very important because it affects how well the synthesizer can copy the body of an instrument, like the hollow part of a violin or the metal end of a trumpet.

Being accurate makes sure the sound produced is not only believable but also reacts properly to changes in input, like how hard a keyboard key is struck or how much breath is used in a wind controller.

This focus on the details in the formulas allows the synthesizer to respond in real time, giving musicians the fine-tuned expressiveness they would expect from their acoustic instruments.

Copying the real world involves more than just the sound itself. Beyond drivers and resonators, physical modeling calculations have to include the way instruments behave under different playing conditions.

The advanced models consider how small changes in environment or technique can affect the sound.

Parameters Diagram
Diagram from PerfectCircuit

Specific Methods of Physical Modeling

There are many different ways to do physical modeling. Here are the most common ones:

  1. Direct Physical Modelling: Involves the direct simulation of physical laws that govern the behavior of musical instruments. This often uses mathematical techniques like the Finite Difference Time Domain (FDTD) method.
  2. Modal Synthesis: This technique involves the analysis of a system’s modes of vibration and synthesizing sound by triggering and controlling these modes.
  3. Wavetable Synthesis: This method captures a series of waveforms or sound samples, which are then looped continuously.
  4. Karplus-Strong Algorithm: A special case of physical modelling synthesis that replicates the sound of plucked strings.
  5. Waveguide Synthesis: This is a popular technique that uses delay lines, filters, and frequency-dependent feedback to simulate the propagation of waves in a musical instrument.
  6. Mass Interaction Networks: This involves simulating the interaction of multiple elementary components or “masses”, each obeying simple physical laws.
  7. Finite Element Method: This technique is used to break down an object into smaller, simpler parts, and then solve the equations describing the physical behavior of each part.
  8. Sample-based Synthesis: This involves recording the sound produced by a physical model, which is then played back under real-time control.
  9. Convolution Synthesis: This involves using impulse responses from real-world objects to shape the sound of a synthesizer.
  10. Stochastic/Statistical Methods: These techniques use random processes and probability distributions to model the complex, unpredictable aspects of musical instrument sounds.

Advanced Modelling Methods

Advanced modelling methods in sound synthesis use smart algorithms to copy the detailed interactions of an instrument’s parts. This gives a very real sound quality.

These hardworking algorithms figure out the science of how strings vibrate, how air moves, and how other structures resonate with great accuracy.

The outcome is a diverse set of sounds with new textures that can’t be copied by traditional sampling or subtractive synthesis.

Hybrid synthesis methods are becoming more common. They mix the benefits of physical modelling with other types of synthesis to make dynamic interactions and unique sound qualities.

This means we can make instruments that can change over time or react to subtle differences in performance in ways that were once impossible.

Advanced physical modelling methods do more than just copy existing sounds; they let sound designers make completely new instruments.

These instruments react to the player’s input with changing harmonics and articulation, much like their real acoustic counterparts.

Synthesizer Interaction Dynamics

Synthesizers mimic the sound of real instruments by copying how an instrument’s parts work together.

For example, they can copy how a bow, pluck, or breath (the exciter/driver) gets a string, drumhead, or column of air (the resonator) to make sound.

Synthesizers also copy how sound bounces around inside an instrument. This is called resonance.

By doing this, they can make sounds that are very close to real life. This lets them copy the special sounds that only certain instruments can make.

Synthesizers also use feedback. This is when the sound that an instrument makes affects how it continues to make sound.

This can lead to interesting sound effects, like the buzzing of a wind instrument or the echo of a string instrument. This lets people playing computer-made instruments feel like they’re playing real ones.

Detailed Modelling Components

In sound synthesizers, the way exciters and resonators interact is very important.

To mimic the sound of real instruments, we use detailed models.

These models are key to making the sound feel real and alive. The goal is to make sure the sound produced by the player—like plucking, bowing, or blowing—creates a vibration that feels real.

These interactions are described using precise math formulas.

They show how the energy from the player is changed by the instrument to produce sound. They capture the small changes that can occur in a live performance.

These details are very important. If we oversimplify things, the sound produced might not feel authentic.

How Models, Formulas and Algorithms are Generated for Physical Modeling

  1. Define the Sound: The first step in creating a mathematical model for sound synthesis is to define the sound you want to mimic. This could be a musical instrument, a human voice, or any other sound.
  2. Analyze the Sound: Engineers would start by examining a sound’s frequency, amplitude, and phase. One key technique in acoustical engineering is the use of Fourier analysis, which decomposes a sound into its individual frequencies. Understanding the acoustical properties and behavior of the sound in different environments (such as in an open field versus within a closed room) is also crucial. This involves studying sound reflections, absorptions, diffractions, and refractions, which are all influenced by the geometry and materials of the surroundings.
  3. Develop a Mathematical Model: The next step is to develop a mathematical model that describes the physical properties of the sound you just analyzed. This model will often use differential equations to represent the behavior of the sound over time.
  4. Create Algorithms: Using the mathematical model, one then creates algorithms that simulate the behavior of the sound. These algorithms will typically be implemented in a computer programming language and will use methods such as digital signal processing to reproduce the sound.

The Evolution of Physical Modelling

Exploring how we make sounds with computers and technology is super interesting. It’s like going on a journey from the old days of big, clunky machines to the super-smart digital tools we have now.

This journey shows us how making music has changed, thanks to lots of cool tech developments.

Back in the day, the first synthesizers were big and not easy to carry around. They made sounds using oscillators and filters. But, they could only do so much because the technology wasn’t that advanced.

Then, as computers got better, so did the ability to make sounds that were closer to real life. This change was huge because it meant that sounds could be as detailed and rich as the real thing (almost…).

Now, we have physical modelling synthesizers. Some of the most lauded synths that have physical modelling capabilities include:

  1. Yamaha VL1: The Yamaha VL1, part of the VL Series, was one of the pioneering synthesizers in physical modeling synthesis when it was released in the early ’90s. It used Yamaha’s Virtual Acoustic technology to simulate the physical properties of acoustic instruments, making it groundbreaking at the time.
  2. Korg Wavestation: The Korg Wavestation is another influential synthesizer that, while not exclusively a physical modeling synth, incorporated advanced vector synthesis and wave sequencing that allowed for evolving sounds which, in some uses and implementations, mimicked physical modeling. It’s worth noting, however, that the Wavestation’s primary acclaim was not in physical modeling in the purest sense, but it paved the way for future exploration in synthesizers.
  3. Roland V-Synth: The Roland V-Synth, particularly in its later versions, incorporates several synthesis techniques, including physical modeling. It has been celebrated for its expressive capabilities and the ability to manipulate and model sounds in a very tactile and intuitive way, which includes aspects of physical modeling among its synthesis toolkit.
Yamaha VL1
Yamaha VL1 Physical Modeling Synthesizer

But this is just the beginning. As computers get even smarter and faster, we’ll see even more amazing ways to create music.

The Future of Modelling Synthesis

Looking ahead in sound design, the future is bright for physical modeling synthesis.

This method will soon make digital sounds as real and complex as never before. We’re going to see new tech make it easier to create sounds that blur the line between digital and real-life sounds.

As tech gets better, we’ll get a wider range of sounds and more detailed ways to control them.

The aim is also to make these tools simpler to learn while giving artists more creative power. They’ll be able to bring out the fine details that, until now, only acoustic instruments could.

As digital sounds become more like real ones, the future of physical modeling synthesis isn’t just about copying the real world. It’s about making new sounds and instruments that can only exist digitally, yet feel as real and vibrant as traditional ones.

What to Do Next

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