Physical modelling synthesis
Encyclopedia
In sound synthesis, physical modelling synthesis refers to methods in which the waveform
of the sound
to be generated is computed by using a mathematical model
, being a set of equation
s and algorithm
s to simulate a physical source of sound, usually a musical instrument
. Such a model consists of (possibly simplified) laws of physics that govern the sound production, and will typically have several parameters, some of which are constants that describe the physical materials and dimensions of the instrument, while others are time-dependent functions that describe the player's interaction with it, such as plucking a string, or covering toneholes.
For example, to model the sound of a drum
, there would be a formula for how striking the drumhead injects energy into a two dimensional membrane. Thereafter the properties of the membrane (mass density, stiffness, etc.), its coupling with the resonance of the cylindrical body of the drum, and the conditions at its boundaries (a rigid termination to the drum's body) would describe its movement over time and thus its generation of sound.
Similar stages to be modelled can be found in instruments such as a violin
, though the energy excitation in this case is provided by the slip-stick behavior of the bow against the string, the width of the bow, the resonance and damping behavior of the strings, the transfer of string vibrations through the bridge, and finally, the resonance of the soundboard in response to those vibrations.
Although physical modelling was not a new concept in acoustics
and synthesis, having been implemented using finite difference approximations of the wave equation by Hiller and Ruiz in 1971, it was not until the development of the Karplus-Strong algorithm
, the subsequent refinement and generalization of the algorithm into the extremely efficient digital waveguide synthesis
by Julius O. Smith III and others, and the increase in DSP
power in the late 1980s that commercial implementations became feasible.
Yamaha signed a contract with Stanford University
in 1989 to jointly develop digital waveguide synthesis, and as such most patents related to the technology are owned by Stanford or Yamaha.
The first commercially available physical modelling synthesizer made using waveguide synthesis was the Yamaha VL1 in 1994.
While the efficiency of digital waveguide synthesis made physical modelling feasible on common DSP hardware and native processors, the convincing emulation of physical instruments often requires the introduction of non-linear elements, scattering junctions, etc. In these cases, digital waveguides are often combined with FDTD, finite element or wave digital filter methods, increasing the computational demands of the model.
Examples of physical modelling synthesis:
While not purely a hardware synth, the DS-XG sound cards based on the Yamaha YMF-7#4 family of audio chipsets (including 724, 744, 754, and 764), including the Yamaha WaveForce 192 (SW192XG) as well as many from other manufacturers and even some PC motherboards with such an audio chipset, included hardware-assisted software VL physical modelling (like a VL70m or PLG-VL, and compatible with same) along with the Yamaha XG, wave audio, and 3D gaming sound capabilities of the chipset. Unfortunately, only the VxD (Virtual Device Drivers) drivers for pre-NT kernel versions of Windows (3.x, 9#, and ME) support the physical modelling feature. Neither the .WDM (Windows Device Model) drivers for Windows 98, 98SE, nor ME, nor any driver for any NT-kernel version of Windows (NT, 2000, XP, Vista, Windows 2003 Server, Windows 7, Windows 2008 Server, nor likely any future OSes) support this, nor can they for technical reasons. Those OSes do support the other features of the card, though.
In their prime, the DS-XG sound cards were easily the most affordable way of obtaining genuine VL technology for anyone who already had a Windows 3.x, 9#, or ME PC. Such cards could be had brand new for as low as $12 USD (YMF-724 versions). But since they were not fully compatible with the AC-97 and later AC-98 standards, these chipsets faded from the market and have not been manufactured by Yamaha in nearly a decade.
Technics WSA1 and it's rackmounted counterpart WSA1R was Technics' first and only try at high-end synthesizers. It featured 64 voices of polyphony with a combination of sample playback (for inititial transitents) and DSP acoustic modelling. Technics WSA1 was launched in 1995, but the musical community did not have enough confidence in Technics to buy a $5000 hardware synth. Only about 600 keyboards and 300 rack models were ever made, and most were sold at highly discounted prices.
Waveform
Waveform means the shape and form of a signal such as a wave moving in a physical medium or an abstract representation.In many cases the medium in which the wave is being propagated does not permit a direct visual image of the form. In these cases, the term 'waveform' refers to the shape of a graph...
of the sound
Sound
Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...
to be generated is computed by using a mathematical model
Mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...
, being a set of equation
Equation
An equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions on either side of an equals sign , for examplex + 3 = 5\,asserts that x+3 is equal to 5...
s and algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
s to simulate a physical source of sound, usually a musical instrument
Musical instrument
A musical instrument is a device created or adapted for the purpose of making musical sounds. In principle, any object that produces sound can serve as a musical instrument—it is through purpose that the object becomes a musical instrument. The history of musical instruments dates back to the...
. Such a model consists of (possibly simplified) laws of physics that govern the sound production, and will typically have several parameters, some of which are constants that describe the physical materials and dimensions of the instrument, while others are time-dependent functions that describe the player's interaction with it, such as plucking a string, or covering toneholes.
For example, to model the sound of a drum
Drum
The drum is a member of the percussion group of musical instruments, which is technically classified as the membranophones. Drums consist of at least one membrane, called a drumhead or drum skin, that is stretched over a shell and struck, either directly with the player's hands, or with a...
, there would be a formula for how striking the drumhead injects energy into a two dimensional membrane. Thereafter the properties of the membrane (mass density, stiffness, etc.), its coupling with the resonance of the cylindrical body of the drum, and the conditions at its boundaries (a rigid termination to the drum's body) would describe its movement over time and thus its generation of sound.
Similar stages to be modelled can be found in instruments such as a violin
Violin
The violin is a string instrument, usually with four strings tuned in perfect fifths. It is the smallest, highest-pitched member of the violin family of string instruments, which includes the viola and cello....
, though the energy excitation in this case is provided by the slip-stick behavior of the bow against the string, the width of the bow, the resonance and damping behavior of the strings, the transfer of string vibrations through the bridge, and finally, the resonance of the soundboard in response to those vibrations.
Although physical modelling was not a new concept in acoustics
Acoustics
Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics...
and synthesis, having been implemented using finite difference approximations of the wave equation by Hiller and Ruiz in 1971, it was not until the development of the Karplus-Strong algorithm
Karplus-Strong string synthesis
Karplus-Strong string synthesis is a method of physical modelling synthesis that loops a short waveform through a filtered delay line to simulate the sound of a hammered or plucked string or some types of percussion....
, the subsequent refinement and generalization of the algorithm into the extremely efficient digital waveguide synthesis
Digital waveguide synthesis
Digital waveguide synthesis is the synthesis of audio using a digital waveguide. Digital waveguides are efficient computational models for physical media through which acoustic waves propagate...
by Julius O. Smith III and others, and the increase in DSP
Digital signal processor
A digital signal processor is a specialized microprocessor with an architecture optimized for the fast operational needs of digital signal processing.-Typical characteristics:...
power in the late 1980s that commercial implementations became feasible.
Yamaha signed a contract with Stanford University
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
in 1989 to jointly develop digital waveguide synthesis, and as such most patents related to the technology are owned by Stanford or Yamaha.
The first commercially available physical modelling synthesizer made using waveguide synthesis was the Yamaha VL1 in 1994.
While the efficiency of digital waveguide synthesis made physical modelling feasible on common DSP hardware and native processors, the convincing emulation of physical instruments often requires the introduction of non-linear elements, scattering junctions, etc. In these cases, digital waveguides are often combined with FDTD, finite element or wave digital filter methods, increasing the computational demands of the model.
Examples of physical modelling synthesis:
- Karplus-Strong string synthesisKarplus-Strong string synthesisKarplus-Strong string synthesis is a method of physical modelling synthesis that loops a short waveform through a filtered delay line to simulate the sound of a hammered or plucked string or some types of percussion....
- Digital waveguide synthesisDigital waveguide synthesisDigital waveguide synthesis is the synthesis of audio using a digital waveguide. Digital waveguides are efficient computational models for physical media through which acoustic waves propagate...
- Formant synthesis
Virtual instruments
- Tension, Electric, Collision and Corpus included with Ableton Live Suite.
- Ultrabeat, EVP88, EVB3, and EVD6 included with Logic ProLogic ProLogic Pro is a hybrid 32 / 64 bit digital audio workstation and MIDI sequencer software application for the Mac OS X platform. Originally created by German software developer Emagic, Logic Pro became an Apple product when Apple bought Emagic in 2002...
- Native Instrument Reaktor
- Cycling`74 Max/MSP
- Modartt PianoteqPianoteqPianoteq is a software, MIDI-controlled, stand alone or VSTi musical instrument, which uses virtual modeling techniques to emulate the piano, and also harpsichord, electric piano and vibraphone...
- Pianos - AAS String Studio - Guitars, basses, harps, clavinets, bowed instruments, percussion
- ArturiaArturiaArturia is a software company located in Grenoble, France and founded in 1999 by Frédéric Brun and Gilles Pommereuil, both INPG-qualified engineers. The company's focus is on the development of electronic music software and tools - primarily emulation of vintage analog synthesizers...
BRASS - Trumpet, trombone and saxophone - Sculpture (part of Logic StudioLogic StudioLogic Studio is a music production suite by Apple Inc. The first version of Logic Studio was unveiled on September 12, 2007.It claims to be the largest collection of modeled instruments, sampler instruments, effect plug-ins, and audio loops ever put in a single box.The package contains Logic Pro,...
) - Strings - Keolab Spicy Guitar - acoustic guitars
- Kong Drum Designer (Part of Reason (software)) - Drums
- Yamaha S-YXG100 plus VL and S-YXG1000 plus PolyVL (the latter released in Japan only). These were basically software-only equivalents to the hardware (and hardware-assisted software) MIDI synth capabilities of the DS-XG cards / YMF chipsets mentioned in the next section. The PolyVL had eight voice polyphony for the physical modelling, whereas the VL and all of the hardware Yamaha VL synths only had one voice, or two for the original VL-1. Like the DS-XG .VxD drivers required for VL support of the DX-XG chipsets, these would work only on pre-NT kernel versions of Windows (9# and ME), and not on NT, 2000, XP, etc. Yamaha quietly discontinued these years ago.
Hardware synthesizers
- Korg OASYSKorg OASYSThe Korg OASYS was a workstation synthesizer released in early 2005, 1 year after the successful Korg Triton Extreme. Unlike the Triton series, the OASYS was implemented on a custom Linux operating system and was designed to be arbitrarily expandable via software updates, with its functionality...
and Korg KronosKorg KronosThe Kronos is a music workstation manufactured by Korg that combines nine different synthesizer sound engines with a sequencer, digital recorder, effects, a color touchscreen display and a keyboard...
- STR-1 Plucked string - Korg OASYS PCI
- Korg ProphecyKorg ProphecyThe Korg Prophecy is considered one of the earliest "virtual analog" synthesizers, although its synthesis capabilities went beyond many of its VA contemporaries....
- Korg Z1
- Korg KARMAKorg KARMAThe Korg KARMA music workstation was released in 2001 as a specialised member of the Korg Triton family.Unlike most other Korg workstation names, the KARMA name is rendered in capitals as an acronym for the Kay Algorithmic Realtime Music Architecture...
(with MOSS chip installed) - Yamaha VL1, VP1 and VL7
- Yamaha VL70m, PLG-100VL and 150VL (VL70m in the form of a plug-in card that can be installed into any of several Yamaha keyboards, tone modules, and the SW1000XG high-end PC midi sound card), EX5
- Technics WSA1 / WSA1R
- Clavia Nord Modular G2
- Alesis FusionAlesis FusionAlesis Fusion is a music production workstation produced by Alesis introduced in early 2005. The workstation is available in two models. The Fusion 6HD is a sixty-one note semi-weighted keyboard workstation. The Fusion 8HD is an eighty-eight note weighted keyboard workstation. The two models...
- Pianoid
- Physis Unico
- Hartmann NeuronHartmann NeuronThe Hartmann Neuron was an electronic musical instrument designed and built by industry designer Axel Hartmann of the German company Hartmann Music in the years 2001-2005. The Neuron synthesizer used an Artificial Neural Network to create a digital computer model from sampled sounds, implementing a...
and Neuron VS
While not purely a hardware synth, the DS-XG sound cards based on the Yamaha YMF-7#4 family of audio chipsets (including 724, 744, 754, and 764), including the Yamaha WaveForce 192 (SW192XG) as well as many from other manufacturers and even some PC motherboards with such an audio chipset, included hardware-assisted software VL physical modelling (like a VL70m or PLG-VL, and compatible with same) along with the Yamaha XG, wave audio, and 3D gaming sound capabilities of the chipset. Unfortunately, only the VxD (Virtual Device Drivers) drivers for pre-NT kernel versions of Windows (3.x, 9#, and ME) support the physical modelling feature. Neither the .WDM (Windows Device Model) drivers for Windows 98, 98SE, nor ME, nor any driver for any NT-kernel version of Windows (NT, 2000, XP, Vista, Windows 2003 Server, Windows 7, Windows 2008 Server, nor likely any future OSes) support this, nor can they for technical reasons. Those OSes do support the other features of the card, though.
In their prime, the DS-XG sound cards were easily the most affordable way of obtaining genuine VL technology for anyone who already had a Windows 3.x, 9#, or ME PC. Such cards could be had brand new for as low as $12 USD (YMF-724 versions). But since they were not fully compatible with the AC-97 and later AC-98 standards, these chipsets faded from the market and have not been manufactured by Yamaha in nearly a decade.
Technics WSA1 and it's rackmounted counterpart WSA1R was Technics' first and only try at high-end synthesizers. It featured 64 voices of polyphony with a combination of sample playback (for inititial transitents) and DSP acoustic modelling. Technics WSA1 was launched in 1995, but the musical community did not have enough confidence in Technics to buy a $5000 hardware synth. Only about 600 keyboards and 300 rack models were ever made, and most were sold at highly discounted prices.
External links
- Julius. O Smith III's A Basic Introduction to Digital Waveguide Synthesis
- Music synthesis approaches sound quality of real instruments — Stanford University's 1994 news release
- Audities Foundation Yamaha VL-1
- SoundSynthesis project
- Virtual Violin using finite elements by Christian Geiger und Michael Schreiner (including sound samples)
- ACROE Physical modelling Sound Library
- Physical Modeling on the Nord Modular G2
- NUSofting - Innovative physical modelling VST/AU instruments for computer musicians
- Pianoid - Pianoid, a piano emulating synthesizer
- Acoustic Alchemy - 1995 Review of Technics WSA1 hardware synthesizer.