Mel scale - Definition and Overview

The mel scale, proposed by Stevens, Volkman and Newman in 1937 is a scale of pitches judged by listeners to be equal in distance one from another. The reference point between this scale and normal frequency measurement is defined by equating a 1000 Hz tone, 40 dB above the listener's threshold, with a pitch of 1000 mels. Above about 500 Hz, larger and larger intervals are judged by listeners to produce equal pitch increments. As a result, four octaves on the hertz scale above 500 Hz are judged to comprise about two octaves on the mel scale. Many musicians and psychologists prefer a two-dimensional representation of pitch by tone color (or chroma) and tone-height, such as the helical structure advocated by Roger Shepard.

To convert <math>f<math> hertz into <math>m<math> mel use:

<math>m = 1127.01048 \log_e(1+f/700).<math>

And the inverse:

<math>f = 700(e^{m/1127.01048} - 1).<math>

See also

Bark scale