Mel scale

The mel scale, proposed by Stevens, Volkman and Newman in 1937 is a perceptual 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. In other words,

Many musicians and psychologists prefer a two-dimensional representation of pitch by tone color (or chroma) and tone-height , or a three-dimensional one such as the helical structure advocated by Roger Shepard , as more representative of other properties of musical hearing.

To convert f hertz into m mel use:

m = 1127.01048log_e(1 + f / 700).

And the inverse:

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

See also

• Bark scale