Nonmonotic behaviour of (2f1 - f2) explained by a saturation-feedback model

Area of Science:

• Auditory perception
• Psychoacoustics
• Nonlinear acoustics

Background:

• The generation of combination tones, particularly cubic difference tones (2f1 - f2), is a complex auditory phenomenon.
• Understanding the underlying mechanisms is crucial for explaining auditory perception and developing accurate hearing models.
• Previous models have struggled to fully capture the intricate relationship between primary tone levels and difference tone perception.

Purpose of the Study:

• To approximate and apply a saturation-feedback model to predict the level of the (2f1 - f2) difference tone.
• To investigate the dependence of the difference tone on the level (L1) of the lower primary tone.
• To elucidate the contribution of nonlinear saturation characteristics to difference tone generation.

Main Methods:

• Utilized a simplified saturation-feedback model for calculations.
• Calculated the (2f1 - f2) difference tone's dependence on the lower primary tone level (L1).
• Compared model-derived data with experimentally measured data.

Main Results:

• The model demonstrated astonishingly good agreement with measured data.
• Indicated that the cubic difference tone is a vector sum of multiple partials.
• Identified a nonlinear saturation characteristic with a knee point at 40 dB SPL as the source of these partials.

Conclusions:

• The saturation-feedback model provides a robust framework for understanding cubic difference tone generation.
• The nonlinear saturation characteristic is a key factor in producing the partials that constitute the difference tone.
• The findings support the vector sum hypothesis for cubic difference tones, linked to basilar membrane excitation patterns.