The mel frequency scale is a perceptually motivated frequency scale based on the human auditory system's response to sound. It is named after the unit of measurement used, which is the mel (after the word _melody_). The mel scale was designed by playing simple tones (sinusoids) to human listeners that were required to divide a given frequency range into four perceptually equal intervals or to adjust the frequency of a stimulus tone to be half as high as that of a comparison tone. Mel-scale frequency analysis has been widely used in modern speech recognition systems. It can be approximated by: $ m(f) = 2595 \log_{10} \left( 1 + \frac{f}{700} \right) $ This gives the following graph:  Source: [Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Mel-Hz_plot.svg) One advantage of representing the [[power spectrum]] of a speech signal using the mel frequency scale is that it better aligns with human perception of sound. The use of the mel frequency scale can help improve the accuracy of speech recognition systems and other related tasks by better capturing the relevant features of speech signals.