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. Below about 500 Hz the mel and
hertz scales coincide; above that, 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
chroma[?] or tone colour and tone-height.
To convert <math>f</math> hertz into <math>m</math> mel use:
- <math>m = 1127.01048 \log(1+f/700).</math>
And the converse:
- <math>f = 700(e^{m/1127.01048} - 1).</math>