Banded waveguide synthesis

Banded waveguides synthesis is a <a href="/facts/Physical_modeling_synthesis/vkEbmbKm">physical modeling synthesis</a> method to simulate sounds of <a href="/facts/Acoustic_dispersion/u8BX64RJ">dispersive</a> sounding objects, or objects with strongly <a href="/facts/Inharmonic/xDSTCe95">inharmonic</a> <a href="/facts/Resonant/q7VLALUz">resonant</a> <a href="/facts/Frequencies/QUSbPaW8">frequencies</a> efficiently. It can be used to model the sound of <a href="/facts/Musical_instrument/UMSjL1Ks">musical instruments</a> based on elastic solids such as <a href="/facts/Vibraphone/sXguIYEL">vibraphone</a> and <a href="/facts/Marimba/tfIfmArp">marimba</a> bars, <a href="/facts/Singing_bowls/E9PTqDTP">singing bowls</a> and <a href="/facts/Bell_(instrument)/oU1E1JHg">bells</a>. It can also be used for other instruments with inharmonic partials, such as membranes or plates. For example, simulations of <a href="/facts/Tabla/xlNP7Cpf">tabla</a> drums and <a href="/facts/Cymbal/URddskPF">cymbals</a> 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 <a href="/facts/Georg_Essl/Nh5zlw2r">Georg Essl</a> and <a href="/facts/Perry_Cook/SHN3r4t3">Perry Cook</a> to synthesize the sound of <a href="/facts/Bow_(music)/YeljX6SM">bowed</a> <a href="/facts/Vibraphone/sXguIYEL">vibraphone</a> bars.
In the case of the standard one-dimensional <a href="/facts/Wave_equation/J2ksD2Az">wave equation</a> 
 
 
 
 
 y
 
 t
 t
 
 
 =
 
 c
 
 2
 
 
 
 y
 
 x
 x
 
 
 
 
 {\displaystyle y_{tt}=c^{2}y_{xx}}
 
 disturbances of all frequencies travel with the same constant speed 
 
 
 
 c
 
 
 {\displaystyle c}
 
. In dispersive media, the traveling speed of disturbances depends on their frequency, and we get 
 
 
 
 c
 (
 ω
 )
 
 
 {\displaystyle c(\omega )}
 
, where 
 
 
 
 ω
 
 
 {\displaystyle \omega }
 
 is the frequency of the disturbance. Many physical systems are dispersive, for example, the elastic beams described by the <a href="/facts/Euler%25E2%2580%2593Bernoulli_beam_theory/3DyQV9do">Euler–Bernoulli beam equation</a> 
 
 
 
 
 y
 
 t
 t
 
 
 =
 k
 
 y
 
 x
 x
 x
 x
 
 
 
 
 {\displaystyle y_{tt}=ky_{xxxx}}
 
, where 
 
 
 
 k
 
 
 {\displaystyle k}
 
 is a material constant.
Banded waveguides model dispersive behavior by splitting the propagation of disturbances into <a href="/facts/Frequency_band/94Rq1PkQ">frequency bands</a>. Each frequency band is modeled using a <a href="/facts/Band-limited/LrYmxzlA">band-limited</a> version of the standard <a href="/facts/Digital_waveguide_synthesis/yYsV8FdX">digital waveguide</a> method. Each frequency band is tuned to the <a href="/facts/Resonant/q7VLALUz">resonant</a> <a href="/facts/Frequencies/QUSbPaW8">frequencies</a> of the sounding object to be modeled to avoid any <a href="/facts/Discretization/JvjSzwyk">discretization</a> error at the dominant and audible frequencies.
Banded waveguide synthesis is implemented in most available sound-synthesis libraries and programs such as:

<ul><li><a href="/facts/Synthesis_Toolkit/l6sxjxMG">STK</a></li>
<li><a href="/facts/ChucK/CuSNkLhf">ChucK</a></li>
<li><a href="/facts/Pure_Data/t5kpU4q0">pd</a> and <a href="/facts/Max%2fMSP/3RaJECeF">Max/MSP</a> via PerCoLate</li>
<li>RTCMix</li>
<li><a href="/facts/SuperCollider/nTQ1aTQo">SuperCollider</a></li>
<li><a href="/facts/CSound/SWFhJBnw">CSound</a></li>
<li><a href="/facts/Common_Lisp_Music/JcWDkcsL">Common Lisp Music</a></li></ul>

Banded waveguide synthesis open-in-new

Banded waveguide synthesis