Physical modelling synthesis

Physical modelling synthesis refers to sound synthesis methods in which the waveform of the sound to be generated is computed using a mathematical model, a set of equations and algorithms to simulate a physical source of sound, usually a musical instrument. Modelling attempts to replicate laws of physics that govern 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 describing the player's interaction with the instrument, such as plucking a string, or covering toneholes. For example, to model the sound of a drum, there would be a mathematical model of how striking the drumhead injects energy into a two-dimensional membrane. Incorporating this, a larger model would simulate 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), describing 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. In addition, the same concept has been applied to simulate voice and speech sounds. In this case, the synthesizer includes mathematical models of the vocal fold oscillation and associated laryngeal airflow, and the consequent acoustic wave propagation along the vocal tract. Further, it may also contain an articulatory model to control the vocal tract shape in terms of the position of the lips, tongue and other organs.