combination tones and the ear

“Relating frequency to pitch as perceived by the musician, two notes will “sound” similar if they are spaced apart in frequency by a factor of two, or octave. This means that the frequency interval between 100 and 200 hertz sounds the same as that between 1,000 and 2,000 hertz or between 5,000 and 10,000 hertz. In other words, the tuning of musical scales and musical intervals is associated with frequency ratios rather than absolute frequency differences in hertz.”

Ohm’s law of hearing is a statement of the fact that the perception of the tone of a sound is a function of the amplitudes of the harmonics and not of the phase relationships between them. This is consistent with the place theory of hearing, which correlates the observed pitch with the position along the basilar membrane of the inner ear that is stimulated by the corresponding frequency.


The ear is responsive to the periodicity of a wave, so that it will hear the frequency of a complex wave as that of the fundamental whether or not the fundamental is actually present as a component in the wave, although the wave will have a different timbre than it would were the fundamental actually present. This effect, known as the missing fundamental, subjective fundamental, or periodicity pitch, is used by the ear to create the fundamental in sound radiating from a small loudspeaker that is not capable of providing low frequencies.

If the intensity of a sound is sufficiently great, the wave shape will be distorted by the ear mechanism, owing to its nonlinearity. The spectral analysis of the sound will then include frequencies that are not present in the sound wave, causing a distorted perception of the sound. If two or more sounds of great intensity are presented to the ear, this effect will introduce what are called combination tones. Two pure tones of frequency f1 and f2will create a series of new pure tones: the sum tones,

and the difference tones,

(Here n and m are any two integers.) Sum tones are difficult to hear because they are masked by the higher-intensity tones creating them, but difference tones are often observed in musical performance. For example, if the two tones are adjacent members of the harmonic series, the fundamental of that series will be produced as a difference tone, enhancing the ability of the ear to identify the fundamental pitch.

the ear

combination tones and the ear

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