# 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 from one 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. The name mel comes from the word melody to indicate that the scale is based on pitch comparisons.

A popular formula to convert f hertz into m mel is:[1]

And the inverse:

An alternate formula, not depending on choice of log base, is noted in Fant (1968):

Data from which some of these formulas derive are tabulated in Beranek (1949). Other formulas are in Lindsay & Norman (1977).

## Contents

### Bibliography

• Beranek, Leo L. (1949). Acoustic measurements. New York: McGraw-Hill.
• Fant, Gunnar. (1968). Analysis and synthesis of speech processes. In B. Malmberg (Ed.), Manual of phonetics (pp. 173-177). Amsterdam: North-Holland.
• Lindsay, Peter H.; & Norman, Donald A. (1977). Human information processing: An introduction to psychology (2nd ed.). New York: Academic Press.
• Douglas O'Shaughnessy (1987). Speech communication: human and machine. Addison-Wesley. p. 150. ISBN 9780201165203.
• Stevens, Stanley Smith; Volkman; John; & Newman, Edwin. (1937). A scale for the measurement of the psychological magnitude of pitch. Journal of the Acoustical Society of America, 8 (3), 185–190.
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