Combination tone

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Combination tone' refers to a psychoacoustic phenomenon where the ear perceives additional frequencies that are not present in the original sound stimulus. These tones are the result of nonlinear interactions within the auditory system, leading to the generation of new frequencies that are mathematically related to the original frequencies. Combination tones can be categorized into two main types: difference tones and sum tones. The most commonly experienced type is the difference tone, where the frequency of the perceived tone is the difference between the frequencies of two simultaneously played tones. Sum tones, though less commonly perceived, involve the frequency of the perceived tone being the sum of the two original frequencies.

Types of Combination Tones

Combination tones are primarily of two types:

• Difference Tones: The most frequently observed type, where the frequency (\(f_{d}\)) of the combination tone is the difference between the frequencies of the two initiating tones (\(f_{1}\) and \(f_{2}\), where \(f_{1} > f_{2}\)). The formula for a difference tone is \(f_{d} = f_{1} - f_{2}\).
• Sum Tones: These are less commonly perceived and occur when the frequency (\(f_{s}\)) of the combination tone is the sum of the frequencies of the two initiating tones. The formula for a sum tone is \(f_{s} = f_{1} + f_{2}\).

Mechanism

The generation of combination tones is attributed to the nonlinear characteristics of the inner ear's cochlea. When two tones are played simultaneously, the nonlinear response of the cochlear mechanics can produce additional frequencies not present in the original stimulus. This phenomenon is a result of the ear's natural distortion of the incoming sound due to its complex biological and physical properties.

Historical Background

The phenomenon of combination tones was first documented by the German physicist and musician Georg Simon Ohm in the 19th century, and further investigated by the Italian scientist Giuseppe Tartini, who discovered them independently and after whom the difference tones are sometimes called "Tartini tones". Their discovery has played a significant role in the fields of acoustics, music theory, and psychoacoustics, providing insight into the nonlinear processing of sound by the human auditory system.

Applications and Significance

Combination tones have implications in various fields such as music, acoustics, and audio engineering. In music, understanding combination tones can help in the composition and performance of pieces to achieve desired harmonic effects. In acoustics and audio engineering, knowledge of combination tones is essential for designing spaces and equipment that minimize unwanted distortions.

See Also

• Psychoacoustics
• Harmonic
• Frequency
• Sound
• Auditory system

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