Physical Modeling Synthesis: How Plugins Simulate Real Instruments

What is physical modeling synthesis?

Physical modeling synthesis computes a sound from a mathematical description of a vibrating object: what it is made of, how big it is, and how it is struck, plucked or bowed. There is no recording underneath. The instrument calculates every note as you play it.

That is the key difference from sampling. A sampled guitar replays the same recording each time you hit a key, maybe with a few velocity layers. A modeled string keeps vibrating between notes, so a new note interacts with the one still ringing. Apple's Sculpture documentation describes exactly this: retriggering a note that is still vibrating changes the harmonic spectrum, which is why repeated notes on an acoustic guitar sound organic and sampled guitars often do not^[1].

It is also different from building a tone out of sine waves, which is the job of additive synthesis. Additive describes the result; physical modeling describes the cause and lets the physics produce the result. For a wider comparison of synthesis methods, see the synthesis types overview.

How does the exciter-resonator model work?

Almost every physical modeling instrument splits the sound into an exciter, which injects energy, and a resonator, which rings at its own frequencies. Change the exciter and you change the attack; change the resonator and you change what the instrument is.

Logic's Sculpture uses up to three objects to excite, disturb or damp its string^[1]. Ableton's Collision feeds a Mallet and a Noise oscillator into a pair of stereo resonators, and its manual notes that the resonator settings shape the character of the sound most^[2].

• Exciter The pluck, pick, bow, hammer, mallet, breath or noise burst. Its hardness and length decide how bright and sharp the attack is.
• Resonator The string, bar, plate, membrane or tube. Its size, material and damping decide pitch, decay time and whether the overtones are harmonic or metallic.
• Damper Anything that drains energy, such as a finger on a string or piano felt. It is how a model makes palm mutes and short staccato notes.
• Body or pickup The guitar body, marimba tube or electric pickup that colors and amplifies the vibration before it reaches your speakers.

What is the Karplus-Strong algorithm?

Karplus-Strong is a plucked-string algorithm that loops a short burst of noise through a delay line and a simple averaging filter, so the tone starts bright and gets darker as it decays. Kevin Karplus and Alex Strong published it in Computer Music Journal in 1983^[5].

Its efficiency is the headline. The paper reports that additive synthesis at Bell Labs needed as many as 30 sine oscillators to match the realism of the plucked-string algorithm, which itself costs about as much as one or two sine oscillators^[5].

1. Fill a buffer with noise
   Load a short delay line with random values. Julius O. Smith at CCRMA describes this white-noise initial condition as what makes the algorithm Karplus-Strong in the strict sense^[6].
2. Set pitch with buffer length
   The loop length sets the period of the note. At a 44.1 kHz sample rate, a 110 Hz note needs a loop of roughly 401 samples (44,100 divided by 110).
3. Filter on every pass
   Average neighboring samples as they recirculate. Higher harmonics die faster than low ones, which the authors credit for the natural, guitar-like decay^[5].
4. Map velocity to brightness
   Lowpass the noise burst before it enters the loop. The cutoff works as a dynamics control, because real strings sound brighter when played harder^[6].
5. Try the drum variant
   The original paper describes a blend factor that, at 1/2, makes the output drum-like instead of pitched^[5]. Intermediate values sit between string and drum.

Karplus-Strong in a normal synth

You can approximate it in most modern synths without any special engine. Use a noise oscillator with an amp envelope of about 1 ms attack and 5-15 ms decay, run it into a comb filter with keytracking at 100% and high feedback, then use a lowpass after the comb to set the brightness. Feedback controls sustain, the noise decay controls pick hardness, and the result is a playable pluck. The pluck design guide shows how to finish a sound like this for a mix.

What is modal synthesis?

Modal synthesis models an object as a set of resonant modes, each one a filter with its own frequency, damping and gain, all driven by an excitation such as a strike or pluck. CCRMA defines it as a source-filter model in which the object is represented as a superposition of individual modes^[7].

Modal models shine on bars, plates, bells and drums, where the overtones are inharmonic and each one decays at its own rate. Instead of simulating the whole object point by point, you only describe the frequencies that matter. That makes modal synthesis easier to tweak musically: move a few mode ratios and a glass bar turns into a metal plate.

Arturia added a Modal physical-modeling engine to Pigments, which sits alongside its wavetable, granular, sample, harmonic and virtual analog engines^[8]. Ableton's Collision gives you seven resonator types, including Beam, Marimba, String, Membrane, Plate, Pipe and Tube^[2].

Which plugins use physical modeling?

The physical modeling instruments most producers can reach are Collision, Tension and Corpus in Ableton Live, Sculpture in Logic Pro, Pianoteq for pianos and the Modal engine in Arturia Pigments. Check your DAW before buying anything, since two of the biggest DAWs already include one.

Third-party options keep appearing. For a look at a newer plugin in this category, read the Baby Audio Atoms breakdown.

Why is physical modeling so CPU-heavy?

Physical modeling is CPU-heavy because the instrument computes the vibration of every voice in real time, sample by sample, instead of reading audio from disk. Detailed models with many vibrating elements, oversampling and long decays multiply that cost across your polyphony.

Sculpture shows the tradeoff clearly. Its Basic render mode allows up to 100 string elements and carries a lower processing load, Extended allows up to 1,000, and High Definition adds 2x oversampling and is significantly more processor-intensive^[10]. The flip side is disk and RAM: Pianoteq generates notes in real time and installs at about 50 MB because it ships no sample library^[4].

Not every model is expensive. Karplus-Strong ran in real time on early 8-bit chips such as the Intel 8080A^[5]. The cost comes from detail: body resonance, multiple interacting objects and high resolution.

1. Lower the resolution
   Use the lowest quality or render mode that still sounds clean on the notes you actually play. Low bass notes usually tolerate less resolution than high leads.
2. Cap polyphony
   Limit voices to 4-8 for plucks and basses. Long decays with 16 voices stacking up are the most common reason a modeled part spikes the CPU meter.
3. Freeze or bounce early
   Once the part is written, freeze the track or print it to audio. Keep the MIDI so you can re-render if you change notes.
4. Raise the buffer while mixing
   Record at 128 samples or less, then move to 512 or 1,024 samples for mixing. The extra latency does not matter once nothing is being played live.

How do producers use physical modeling in beats?

Producers mostly use physical modeling for organic plucks, mallets and basses that respond to velocity in a way samples struggle to match, and for resonators that turn drums into tuned percussion. You do not need realism for it to be useful.

• Mallet melodies A soft mallet on a wooden bar with short decay gives lo-fi and trap melodies a kalimba or marimba feel. Lower the mallet stiffness for a rounder attack. The trap bells and plucks guide covers patterns that suit these tones.
• Plucked bass A picked string an octave down, with the damper set fairly high, gives a short bass that sits between a synth bass and a real electric. Layer a sine sub underneath if it needs more weight below 60 Hz.
• Resonant drums Put a resonator effect such as Corpus on a clap or rim and tune it to the key of the song. The hit gains a pitched ring that locks into the harmony.
• Impossible instruments Swap materials mid-note with modulation, or pair a bowed exciter with a plate resonator. Collision's manual encourages this kind of misuse, but warns that some parameter combinations cause sudden volume jumps^[2], so keep a limiter on the channel while experimenting.