What is a critical band?

Definition

The human sensitivity to differentiate two tones at different frequencies is variable.

A same frequency difference of 20 Hz between two tones is easily distinguishable at low-frequency ...
(From 440 to 460 Hz : well-perceived difference)

... while it is not noticeable at higher frequency.
(From 6 000 to 6 020 Hz : unperceived difference)
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Some frequency bands can be defined such that two tones within the same band are not distinguished. In the literature 24 critical bands are defined describing the human ear frequency-sensitivity.

The increasing width of the bands can be noticed according to the frequency: the higher the played tones, the less we are able to differentiate their frequencies.

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Application

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When two tones are very close in frequency, the human ear detects a single tone with a low frequency-based loudness modulation.
That creates fluctuation strength.

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When the two tones are more spaced but still in the same critical band, the human ear perception is constant and could be described as a rapid unpleasant beating.
That creates roughness.

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When the two tones come from separate critical bands, the human ear is able to distinguish them.

In electric motors, PWM excitations due to magnetic forces are source of tones whose spacing depends on speed and PWM strategy, generating more or less tonality, fluctuation strengh and roughness.

Biological explanation

The ear is composed of three parts.

  • The outer and the middle ears allow localization of sound sources and efficient transmission of the sound.
  • The inner ear transforms the transferred stimulus into a neural signal.

The inner ear main part is a rolled up spiral called the cochlea which includes the basilar membrane, a resonant structure which varies in width and stiffness. Due to its changing characteristics along its length, a sound component at a given frequency excites a specific location on the basilar membrane. The basilar membrane is widest and softer at the apex of the cochlea allowing low-frequency detection. It is narrowest and stiffest at the base, allowing high-frequency sounds detection. That explains the human ear frequency-sensitivity to noise.

Figure 1 : Uncoiled cochlea with basilar membrane [1]

On the figure above, the cochlea is unrolled and the frequency sensitivity is mapped on the membrane. It can be noticed that the space dedicated to the high frequencies is lower. A same frequency interval covers a longer distance on the membrane at low frequencies than at higher ones. That’s why the ear is less sensitive to frequency-difference for higher pitch noise.

Source

[1] Kern A, Heid C, Steeb W-H, Stoop N, Stoop R (2008) Biophysical Parameters Modification Could Overcome Essential Hearing Gaps. PLoS Comput Biol 4(8): e1000161. https://doi.org/10.1371/journal.pcbi.1000161

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