There are many non-linear frequency scales that approximate the sensitivity of the human ear. For example:
In practice, there is not much to chose from, unless you are interested in auditory model research.
The mel scale is common amongst engineers as it has a simple analytical form:
where f is the frequency in Hz and m is the resulting mel scaled frequency.
For example, this may look like: Filter specifications for a 19 - channel vocoder (Holmes 1980).
Figure 12: The Holmes filter bank
Another reason to use a non-linear frequency analysis is to get around the frequency/time resolution tradeoff. Using a narrow bandwidth at low frequencies enables harmonics to be resolved but gives poor onset information. Using a larger bandwidth at higher frequencies allows for high temporal resolution of bursts, etc.