Multiphonic modeling using impulse pattern formulation - Simon Linke and Rolf Bader and Robert Mores (The journal of the Acoustical Society of America, 2019)
Multiphonics, the presence of multiple pitches within the sound of wind-instruments can be produced in several ways. Either complex fingerings are used or the blowing pressure is very low or very high. Such multiphonics can be modeled by the Impulse Pattern Formulation (IPF) proposed previously [R. Bader, Nonlinearities and Synchronization in Musical Acoustics and Music Psychology (2013)]. This top-down method assumes musical instruments to work with impulses which are produced at a generator, travel through the instrument, are reflected at various positions, are exponentially damped, and finally trigger or at least interact with succeeding impulses produced by the generator. While modeling sounds produced at blowing-threshold, the IPF fully captures transitions between regular periodicity at nominal pitch, bifurcation scenarios, and noise, just like regular instruments do, when multiphonics appear in the transition regime. Using IPF, complex fingerings translate to multiple reflection points at open finger holes with different reflection strengths. Here, complex multiphonics can be modeled. The IPF can also synthesize multiphonic sounds when applying the typical impulse form of wind instruments.
Keywords: Musical acoustics; Musical instruments