Mel scale
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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 <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>
