Digital waveguide synthesis
Encyclopedia
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. For this reason, digital waveguides constitute a major part of most modern physical modeling synthesizers.
A lossless digital waveguide realizes the discrete form of d'Alembert's
solution of the one-dimensional wave equation
as the superposition
of a right-going wave and a left-going wave,
where
is the right-going wave and 
is the left-going wave. It can be seen from this representation that sampling the function 
at a given point 
and time 
merely involves summing two delayed copies of its traveling waves. These traveling waves will reflect at boundaries such as the suspension points of vibrating strings or the open or closed ends of tubes. Hence the waves travel along closed loops.
Digital waveguide models therefore comprise digital delay line
s to represent the geometry of the waveguide which are closed by recursion, digital filter
s to represent the frequency-dependent losses and mild dispersion in the medium, and often non-linear elements. Losses incurred throughout the medium are generally consolidated so that they can be calculated once at the termination of a delay line, rather than many times throughout.
Waveguides such as acoustic tubes are three-dimensional, but because their lengths are often much greater than their cross-sectional area, it is reasonable and computationally efficient to model them as one dimensional waveguides. Membranes, as used in drum
s, may be modeled using two-dimensional waveguide meshes, and reverberation in three dimensional spaces may be modeled using three-dimensional meshes. Vibraphone
bars, bells
, singing bowl
s and other sounding solids (also called idiophone
s) can be modeled by a related method called banded waveguides
where multiple band-limited digital waveguide elements are used to model the strongly dispersive
behavior of waves in solids.
The term "Digital Waveguide Synthesis" was coined by Julius O. Smith III who helped develop it and eventually filed the patent. It represents an extension of the Karplus-Strong algorithm. Stanford University
owns the patent rights for digital waveguide synthesis and signed an agreement in 1989 to develop the technology with Yamaha.
An extension to DWG synthesis of strings made by Smith is commuted synthesis, wherein the excitation to the digital waveguide contains both string excitation and the body response of the instrument. This is possible because the digital waveguide is linear
and makes it unnecessary to model the instrument body's resonances after synthesizing the string output, greatly reducing the number of computations required for a convincing resynthesis.
The prototype software implementation by Smith and colleagues was done in the Synthesis Toolkit
(STK).
Synthesizer
A synthesizer is an electronic instrument capable of producing sounds by generating electrical signals of different frequencies. These electrical signals are played through a loudspeaker or set of headphones...
of audio
Audio frequency
An audio frequency or audible frequency is characterized as a periodic vibration whose frequency is audible to the average human...
using a digital waveguide
Waveguide
A waveguide is a structure which guides waves, such as electromagnetic waves or sound waves. There are different types of waveguides for each type of wave...
. Digital waveguides are efficient computational models for physical media through which acoustic waves propagate. For this reason, digital waveguides constitute a major part of most modern physical modeling synthesizers.
A lossless digital waveguide realizes the discrete form of d'Alembert's
Jean le Rond d'Alembert
Jean-Baptiste le Rond d'Alembert was a French mathematician, mechanician, physicist, philosopher, and music theorist. He was also co-editor with Denis Diderot of the Encyclopédie...
solution of the one-dimensional wave equation
Wave equation
The wave equation is an important second-order linear partial differential equation for the description of waves – as they occur in physics – such as sound waves, light waves and water waves. It arises in fields like acoustics, electromagnetics, and fluid dynamics...
as the superposition
Superposition principle
In physics and systems theory, the superposition principle , also known as superposition property, states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually...
of a right-going wave and a left-going wave,
where
is the right-going wave and is the left-going wave. It can be seen from this representation that sampling the function at a given point and time merely involves summing two delayed copies of its traveling waves. These traveling waves will reflect at boundaries such as the suspension points of vibrating strings or the open or closed ends of tubes. Hence the waves travel along closed loops.Digital waveguide models therefore comprise digital delay line
Digital delay line
A digital delay line is a discrete element in digital filter theory, which allows a signal to be delayed by a number of samples. If the delay is an integer multiple of samples digital delay lines are often implemented as circular buffers...
s to represent the geometry of the waveguide which are closed by recursion, digital filter
Digital filter
In electronics, computer science and mathematics, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is...
s to represent the frequency-dependent losses and mild dispersion in the medium, and often non-linear elements. Losses incurred throughout the medium are generally consolidated so that they can be calculated once at the termination of a delay line, rather than many times throughout.
Waveguides such as acoustic tubes are three-dimensional, but because their lengths are often much greater than their cross-sectional area, it is reasonable and computationally efficient to model them as one dimensional waveguides. Membranes, as used in 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...
s, may be modeled using two-dimensional waveguide meshes, and reverberation in three dimensional spaces may be modeled using three-dimensional meshes. Vibraphone
Vibraphone
The vibraphone, sometimes called the vibraharp or simply the vibes, is a musical instrument in the struck idiophone subfamily of the percussion family....
bars, bells
Bell (instrument)
A bell is a simple sound-making device. The bell is a percussion instrument and an idiophone. Its form is usually a hollow, cup-shaped object, which resonates upon being struck...
, singing bowl
Singing bowl
Singing bowls are a type of bell, specifically classified as a standing bell. Rather than hanging inverted or attached to a handle, singing bowls sit with the bottom surface resting...
s and other sounding solids (also called idiophone
Idiophone
An idiophone is any musical instrument which creates sound primarily by way of the instrument's vibrating, without the use of strings or membranes. It is the first of the four main divisions in the original Hornbostel-Sachs scheme of musical instrument classification...
s) can be modeled by a related method called banded waveguides
Banded Waveguide Synthesis
Banded Waveguides Synthesis is a physical modeling synthesis method to simulate sounds of dispersive sounding objects, or objects with strongly inharmonic resonant frequencies efficiently. It can be used to model the sound of instruments based on elastic solids such as vibraphone and marimba bars,...
where multiple band-limited digital waveguide elements are used to model the strongly dispersive
Dispersive
*Dispersive partial differential equation*Dispersive phase from Biological dispersal*Dispersive medium*dispersive line*dispersive mass transfer*dispersive power*dispersive fading...
behavior of waves in solids.
The term "Digital Waveguide Synthesis" was coined by Julius O. Smith III who helped develop it and eventually filed the patent. It represents an extension of the Karplus-Strong algorithm. 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...
owns the patent rights for digital waveguide synthesis and signed an agreement in 1989 to develop the technology with Yamaha.
An extension to DWG synthesis of strings made by Smith is commuted synthesis, wherein the excitation to the digital waveguide contains both string excitation and the body response of the instrument. This is possible because the digital waveguide is linear
Linear
In mathematics, a linear map or function f is a function which satisfies the following two properties:* Additivity : f = f + f...
and makes it unnecessary to model the instrument body's resonances after synthesizing the string output, greatly reducing the number of computations required for a convincing resynthesis.
The prototype software implementation by Smith and colleagues was done in the Synthesis Toolkit
Synthesis Toolkit
The Synthesis Toolkit is an open source API for real time audio synthesis with an emphasis on classes to facilitate the development of physical modelling synthesizers. It is written in C++ and is written and maintained by Perry Cook at Princeton University and Gary Scavone at CCRMA...
(STK).
Licensees
- Yamaha
- VL1 (1994) — expensive keyboard (about $10,000 USD)
- VL1m, VL7 (1994) — tone module and less expensive keyboard, respectively
- VP1 (prototype) (1994)
- VL70m (1996) — less expensive tone module
- EX5 (1999) — workstation keyboard that included a VL module
- PLG-100VL, PLG-150VL (1999) — plug-in cards for various Yamaha keyboards, tone modules, and the SWG-1000 high-end PC sound card. The MU100R rack-mount tone module included two PLG slots, pre-filled with a PLG-100VL and a PLG-100VH (Vocal Harmonizer).
- YMF-724, 744, 754, and 764 sound chips for inexpensive DS-XG PC sound cards and motherboards (the VL part only worked on Windows 95, 98, 98SE, and ME, and then only when using .VxDVxDVxD is the device driver model used in Microsoft Windows/386, the 386 enhanced mode of Windows 3.x, Windows 9x, and to some extend also by the Novell DOS 7, OpenDOS 7.01, and DR-DOS 7.02 multitasker...
drivers, not .WDMWindows Driver ModelIn computing, the Windows Driver Model — also known at one point as the Win32 Driver Model — is a framework for device drivers that was introduced with Windows 98 and Windows 2000 to replace VxD, which was used on older versions of Windows such as Windows 95 and Windows 3.1, as well...
). No longer made, presumably due to conflict with AC-97 and AC-99 sound card standards (which specify wavetablesWavetable synthesisWavetable synthesis is used in certain digital music synthesizers to implement a restricted form of real-time additive synthesis. The technique was first developed by Wolfgang Palm of PPG in the late 1970s and published in 1979, and has since been used as the primary synthesis method in...
based on RolandRoland Corporationis a Japanese manufacturer of electronic musical instruments, electronic equipment and software. It was founded by Ikutaro Kakehashi in Osaka on April 18, 1972, with ¥33 million in capital. In 2005 Roland's headquarters relocated to Hamamatsu in Shizuoka Prefecture. Today it has factories in Japan,...
’s XG-competing GSRoland GSRoland GS, or just GS, sometimes expanded as General Standard or General Sound, is an extension of General MIDI specification. It requires that all GS-compatible equipment must meet a certain set of features and it documents interpretations of some MIDI commands and bytes sequences, thus defining...
sound system, which Sondius-XG [the means of integrating VL instruments and commands into an XG-compliant MIDI stream along with wavetable XG instruments and commands] cannot integrate with). The MIDI portion of such sound chips, when the VL was enabled, was functionally equivalent to an MU50 Level 1 XG tone module (minus certain digital effects) with greater polyphony (up to 64 simultaneous notes, compared to 32 for Level 1 XG) plus a VL70m (the VL adds an additional note of polyphony, or, rather, a VL solo note backed up by the up-to-64 notes of polyphony of the XG wavetable portion). The 724 only supported stereo out, while the others supported various four and more speaker setups. Yamaha’s own card using these was the WaveForce-128, but a number of licensees made very inexpensive YMF-724 sound cards that retailed for as low as $12 at the peak of the technology’s popularity. The MIDI synth portion (both XG and VL) of the YMF chips was actually just hardware assist to a mostly software synth that resided in the device driver (the XG wavetable samples, for instance, were in system RAM with the driver [and could be replaced or added to easily], not in ROM on the sound card). As such, the MIDI synth, especially with VL in active use, took considerably more CPU power than a truly hardware synth would use, but not as much as a pure software synth. Towards the end of their market period, YMF-724 cards could be had for as little as $12 USD brand new, making them by far the least expensive means of obtaining Sondius-XG CL digital waveguide technology. The DS-XG series also included the YMF-740, but it lacked the Sondius-XG VL waveguide synthesis module, yet was otherwise identical to the YMF-744. - S-YXG100plus-VL Soft Synthesizer for PCs with any sound card (again, the VL part only worked on Windows 95, 98, 98SE, and ME: it emulated a .VxD MIDI device driver). Likewise equivalent to an MU50 (minus certain digital effects) plus VL70m. The non-VL version, S-YXG50, would work on any Windows OS, but had no physical modeling, and was just the MU50 XG wavetable emulator. This was basically the synth portion of the YMF chips implemented entirely in software without the hardware assist provided by the YMF chips. Required a somewhat more powerful CPU than the YMF chips did. Could also be used in conjunction with a YMF-equipped sound card or motherboard to provide up to 128 notes of XG wavetable polyphony and up to two VL instruments simultaneously on sufficiently powerful CPUs.
- S-YXG100plus-PolyVL SoftSynth for then-powerful PCs (e. g. 333+MHz Pentium IIIPentium IIIThe Pentium III brand refers to Intel's 32-bit x86 desktop and mobile microprocessors based on the sixth-generation P6 microarchitecture introduced on February 26, 1999. The brand's initial processors were very similar to the earlier Pentium II-branded microprocessors...
), capable of up to eight VL notes at once (all other Yamaha VL implementations except the original VL1 and VL1m were limited to one, and the VL1/1m could do two), in addition to up to 64 notes of XG wavetable from the MU50-emulating portion of the soft synth. Never sold in the USA, but was sold in Japan. Presumably a much more powerful system could be done with today’s multi-GHz dual-core CPUs, but the technology appears to have been abandoned. Hypothetically could also be used with a YMF chipset system to combine their capabilities on sufficiently powerful CPUs.
- KorgKorgis a Japanese multinational corporation that manufactures electronic musical instruments, audio processors and guitar pedals, recording equipment, and electronic tuners...
- ProphecyKorg ProphecyThe Korg Prophecy is considered one of the earliest "virtual analog" synthesizers, although its synthesis capabilities went beyond many of its VA contemporaries....
(1995) - Z1, MOSS-TRI (1997)
- EXB-MOSS (2001)
- OASYS PCI (1999)
- 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...
(2005) with some modules, for instance the STR-1 plucked strings physical model - 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...
(2011) same as OASYS
- Prophecy
- TechnicsTechnicsTechnics may refer to:* Technics turntables, no longer in production.* Technics , a brand name of the Panasonic Corporation* An anglicization of the Ancient Greek term techne, used primarily in media theory...
- WSA1 (1995)
- CakewalkCakewalk (company)Cakewalk, Inc. is a company based in Boston, Massachusetts that develops and sells music production software. The company's best known product is their comprehensive music sequencer named SONAR, which is designed for professional use. SONAR incorporates multi-track recording and editing of both...
- Dimension Pro (2005) - software synthesizer for OS X and Windows XPWindows XPWindows XP is an operating system produced by Microsoft for use on personal computers, including home and business desktops, laptops and media centers. First released to computer manufacturers on August 24, 2001, it is the second most popular version of Windows, based on installed user base...
.
- Dimension Pro (2005) - software synthesizer for OS X and Windows XP
Further reading
- Yamaha VL1. Virtual Acoustic Synthesizer, Sound on SoundSound on SoundSound on Sound is an independently-owned monthly music technology magazine published by SOS Publications Group, based in Cambridge, UK. The magazine includes product tests of electronic musical performance and recording devices, and interviews with industry professionals...
, July 1994 - Brian Heywood (22 Nov 2005) Model behaviour. The technology your PC uses to make sound is usually based on replaying an audio sample. Brian Heywood looks at alternatives., PC Pro
External links
- Julius O. Smith III's ``A Basic Introduction to Digital Waveguide Synthesis"
- Waveguide Synthesis home page
- Virtual Acoustic Musical Instruments: Review and Update
- Modeling string sounds and wind instruments - Sound on SoundSound on SoundSound on Sound is an independently-owned monthly music technology magazine published by SOS Publications Group, based in Cambridge, UK. The magazine includes product tests of electronic musical performance and recording devices, and interviews with industry professionals...
magazine, September 1998 - Jordan RudessJordan RudessJordan Rudess is an American keyboardist best known as a member of the progressive metal band Dream Theater and the progressive rock supergroup Liquid Tension Experiment.-Biography:...
playing on Korg Oasys Youtube recording. Note the use of the joystick to control the vibrato effect of the plucked strings physical model. - Yamaha VL1 with breath controller vs. traditional synthesizer for wind instruments