https://doi.org/10.48550/arXiv.2201.05452
This publication descibes how multiphonics can be modeled by the Impulse Pattern Formulation (IPF). In wind instruments, multiphonics refer to the presence of multiple pitches within the sound, and can be produced in several ways. For instance, they can appear at low blowing pressure when complex fingerings are used.
While modeling wind instruments played with blowing pressures at the threshold of tone onset, the IPF captures transitions between regular periodicity at nominal pitch, bifurcations, and noise. This corresponds to behavior found in wind instruments where multiphonics appear at the transition between noise and regular musical note regimes. Using the IPF, complex fingerings correspond to multiple reflection points at open finger holes with different reflection strengths. Multiphonics can be modeled if reflection points farther away show higher reflection strength and thus, disrupt periodic motion.
The IPF can also synthesize multiphonic sounds,
which carefully reproduce the dynamic behaviour of a recorded multiphonic.
By concatenating typical wind instrument waveforms at adjacent impulse time points, a more realistic reproduction can be obtained.