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Greenwood cochlear frequency-place calculator

Enter a frequency, a position along the cochlea and the length of the cochlea to get the place of that frequency from the apex and from the base, the frequency at your position, and the length of the cochlea devoted to an octave.

Updated on
Your inputs
Hz

Value out of range

%

Value out of range

mm

Value out of range

Results

Place of the frequency, from the apex

40.0 %

Distance from the apex
14.0 mm
Distance from the base
21.0 mm
Characteristic frequency at the position entered
1,710 Hz
Length of one octave above the frequency
4.54 mm
About 3 to 5 mm per octave over most of the audible range, as a human value

The Greenwood cochlear map calculator gives the place on the cochlea where a frequency is detected, in percent and in millimeters from the apex and the base, the frequency at a given position, and the length of an octave on the cochlea.

How the calculation works

  • Enter a frequency.
  • Enter a position from the apex and the cochlear length.
  • Read the place and the characteristic frequency.

Example

For 1000 Hz, x = log₁₀(1000 / 165.4 + 0.88) / 2.1 = 40.0 % of the length from the apex. For a cochlea of 35 mm that is 14.0 mm from the apex and 21.0 mm from the base. At 50 % of the length, f = 165.4 × (10^(2.1 × 0.5) − 0.88) = 1,710 Hz. The octave from 1000 to 2000 Hz covers about 4.54 mm.

Why it matters

The calculator helps students of auditory physiology and audiology, researchers in cochlear implants and hearing protection, and curious readers who want to know where each pitch is heard in the inner ear.

Good to know

The function was fitted by Donald Greenwood in 1990 to experimental data on the critical bands and the place of hearing, and it works well for humans from about 20 Hz to 20 kHz. The cochlea is about 35 millimeters long in an adult, with a range of 28 to 42 millimeters among people, and a cochlear implant electrode of about 20 to 28 millimeters reaches only part of the length, so the implant electrodes are placed at positions that correspond to frequencies higher than those assigned in the processor, a mismatch that the brain slowly adapts to. About 1.3 millimeters of the basilar membrane is devoted to each critical band at all frequencies, which is the reason for the roughly logarithmic map. The octave length is longest in the middle of the range, at around 5 millimeters, and shorter at the extremes. The values are averages, and real maps vary with the individual anatomy, so they cannot replace measurements by imaging in a clinical case.

The critical band calculator links frequency to the width of auditory filters, the DPOAE calculator treats the cochlea, the sound localization calculator treats the cues of the two ears and the loudness calculator converts phons and sones.

Frequently asked questions

What is the Greenwood function?

It is an equation that links a position on the basilar membrane to the frequency that excites it best: f = A (10^(a x) − k), with A = 165.4 Hz, a = 2.1 and k = 0.88 for humans, and x the fraction of the length counted from the apex.

Why is the base high-pitched?

The basilar membrane is narrow and stiff at the base, near the oval window, and wide and floppy at the apex. So high frequencies excite the base, low frequencies the apex, in an arrangement called tonotopy.

Where is it used?

It is used to assign frequencies to the electrodes of a cochlear implant, to model hearing loss, to study noise damage that starts at about 4 kHz, and in research on dead regions of the cochlea.

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Results are estimates provided for information purposes. They do not replace professional advice.

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