Hearing’s own nonlinearity produces audible difference tones even in distortion-free equipment

Evidence

A transmission system containing a nonlinearity produces harmonics when transmitting a pure tone. Such distortion products are often neither annoying nor audible, because they match almost totally with the fundamental. Musical tones are complex tones and consist of several harmonics. In this case, the nonlinearity changes the amplitude of these harmonics somewhat. This change is also rarely detected. Further, masking, which is stronger above the frequency of the tone, leads to the fact that strong fundamentals mask the higher harmonics produced by the nonlinear transmission system. Difference tones, produced by the nonlinearity when two tones (the primaries) are presented, are easier to detect. The difference tones are produced at frequencies below those of the primaries. The masking effect at medium and high levels is much smaller, and the difference tones are more easily detected. The frequencies of the difference tones may appear unharmonically related to the primaries and may therefore be annoying, if audible. Even when using highquality electroacoustic equipment that does not produce audible nonlinear distortion products, we still hear difference tones that are produced by the nonlinearity of our hearing system. — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 1520

Categorization

• XREF: Connects to the loudness/specific-loudness models and the theme of the inner ear’s nonlinear mechanics, and to why combination tones arise physiologically (cochlear nonlinearity).
• DEFINE: Clarifies what difference tones are and why masking lets fundamentals but not difference tones go undetected.