Banded Waveguide Synthesis
Encyclopedia
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, singing bowls and bells
. It can also be used for other instruments with inharmonic partials, such as membranes or plates. For example simulations of tabla drums
and cymbal
s have been implemented using this method. Because banded waveguides retain the dynamics of the system, complex non-linear excitations can be implemented. The method was originally invented in 1999 by Georg Essl and Perry Cook to synthesize the sound of bowed
vibraphone
bars .
In the case of the standard one-dimensional wave equation
disturbances of all frequencies travel with the same constant speed 
. In dispersive
media the traveling speed of disturbances depends on their frequency and we get
where 
is the frequency of the disturbance. Many physical systems are dispersive, for example the elastic beams described by the Euler-Bernoulli beam equation
where 
is a material constant.
Banded waveguides model dispersive
behavior by splitting the propagation of disturbances into frequency bands. Each frequency band is modeled using a band-limited version of the standard digital waveguide
method. Each frequency band is tuned to the resonant frequencies of the sounding object to be modeled to avoid any discretization
error at the dominant and audible frequencies .
Banded waveguide synthesis is implemented in most available sound synthesis libraries and programs such as:
Dispersive
*Dispersive partial differential equation*Dispersive phase from Biological dispersal*Dispersive medium*dispersive line*dispersive mass transfer*dispersive power*dispersive fading...
sounding objects, or objects with strongly inharmonic resonant frequencies efficiently. It can be used to model the sound of instruments
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...
based on elastic solids such as 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....
and marimba
Marimba
The marimba is a musical instrument in the percussion family. It consists of a set of wooden keys or bars with resonators. The bars are struck with mallets to produce musical tones. The keys are arranged as those of a piano, with the accidentals raised vertically and overlapping the natural keys ...
bars, singing bowls and 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...
. It can also be used for other instruments with inharmonic partials, such as membranes or plates. For example simulations of tabla drums
Tabla
The tabla is a popular Indian percussion instrument used in Hindustani classical music and in popular and devotional music of the Indian subcontinent. The instrument consists of a pair of hand drums of contrasting sizes and timbres...
and cymbal
Cymbal
Cymbals are a common percussion instrument. Cymbals consist of thin, normally round plates of various alloys; see cymbal making for a discussion of their manufacture. The greater majority of cymbals are of indefinite pitch, although small disc-shaped cymbals based on ancient designs sound a...
s have been implemented using this method. Because banded waveguides retain the dynamics of the system, complex non-linear excitations can be implemented. The method was originally invented in 1999 by Georg Essl and Perry Cook to synthesize the sound of bowed
Bow (music)
In music, a bow is moved across some part of a musical instrument, causing vibration which the instrument emits as sound. The vast majority of bows are used with string instruments, although some bows are used with musical saws and other bowed idiophones....
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 .
In the case of the standard 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...
disturbances of all frequencies travel with the same constant speed . In dispersiveDispersive
*Dispersive partial differential equation*Dispersive phase from Biological dispersal*Dispersive medium*dispersive line*dispersive mass transfer*dispersive power*dispersive fading...
media the traveling speed of disturbances depends on their frequency and we get
where is the frequency of the disturbance. Many physical systems are dispersive, for example the elastic beams described by the Euler-Bernoulli beam equationEuler-Bernoulli beam equation
Euler–Bernoulli beam theory is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case for small deflections of a beam which is subjected to lateral loads only...
where is a material constant.Banded waveguides model dispersive
Dispersive
*Dispersive partial differential equation*Dispersive phase from Biological dispersal*Dispersive medium*dispersive line*dispersive mass transfer*dispersive power*dispersive fading...
behavior by splitting the propagation of disturbances into frequency bands. Each frequency band is modeled using a band-limited version of the standard digital waveguide
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...
method. Each frequency band is tuned to the resonant frequencies of the sounding object to be modeled to avoid any discretization
Discretization
In mathematics, discretization concerns the process of transferring continuous models and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers...
error at the dominant and audible frequencies .
Banded waveguide synthesis is implemented in most available sound synthesis libraries and programs such as:
- STKSynthesis ToolkitThe 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...
- ChucKChucKChucK is a concurrent, strongly timed audio programming language for real-time synthesis, composition, and performance, which runs on Mac OS X, Linux, Microsoft Windows, and iPhone/iPad. It is designed to favor readability and flexibility for the programmer over other considerations such...
- pdPure DataPure Data is a visual programming language developed by Miller Puckette in the 1990s for creating interactive computer music and multimedia works. While Puckette is the main author of the program, Pd is an open source project with a large developer base working on new extensions to it. It is...
and Max/MSP via PerCoLate - RTCMixReal-time CmixReal-Time Cmix is one of the MUSIC-N family of computer music programming languages. RTcmix is descended from the MIX program developed by Paul Lansky at Princeton University in 1978 to perform algorithmic composition using digital audio soundfiles on a VMS mainframe computer. After synthesis...
- SuperCollider
- CSoundCsoundCsound is a computer programming language for dealing with sound, also known as a sound compiler or an audio programming language, or more precisely, a C-based audio DSL. It is called Csound because it is written in C, as opposed to some of its predecessors...
- Common Lisp MusicCommon Lisp MusicCLM is a music synthesis and signal processing package in the Music V family created by Bill Schottstaedt. It runs in a number of various Lisp implementations or as a part of the Snd audio editor . There is also a realtime implementation, Snd-rt which is developed by Kjetil S...