Multiphonic modeling using Impulse Pattern Formulation (IPF)

TL;DR

This paper introduces the Impulse Pattern Formulation (IPF), a novel top-down modeling approach for wind instrument multiphonics, capturing complex behaviors like bifurcations, noise, and the effects of fingerings through impulse reflections and damping.

Contribution

The paper presents the IPF as a new method for modeling and synthesizing multiphonic sounds in wind instruments, explaining complex dynamics via impulse reflections and damping.

Findings

IPF captures transitions between noise and regular tones.

Multiphonics modeled by reflection points with varying strengths.

IPF can synthesize multiphonic sounds effectively.

Abstract

Multiphonics, the presence of multiple pitches within the sound, can be produced in several ways. In wind instruments, they can appear at low blowing pressure when complex fingerings are used. Such multiphonics can be modeled by the Impulse Pattern Formulation (IPF). This top-down method regards musical instruments as systems working with impulses originating from a generating entity, travel through the instrument, are reflected at various positions, and are exponentially damped. Eventually, impulses return to the generating entity and retrigger or interact with subsequent impulses. Due to this straightforward approach, the IPF can explain fundamental principles of complex dynamic systems. 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 by concatenating typical wind instrument waveforms at adjacent impulse time points.