Re: frequency to mel formula

["McCreery, Ryan W" <McCreeryR@xxxxxxxxxxxx>]

Hi Jim,

I don't know if this is the first reference to the mel scale, but it's one that I have read before and seen cited:

Stevens, S.S. & Volkmann, J. (1940) The relation of pitch to frequency: A revised scale.  The American Journal of Psychology 53(3), 329-

I hope this helps.

Ryan McCreery

-----Original Message-----
From: AUDITORY - Research in Auditory Perception [mailto:AUDITORY@xxxxxxxxxxxxxxx] On Behalf Of James W. Beauchamp
Sent: Wednesday, July 15, 2009 1:11 PM
To: AUDITORY@xxxxxxxxxxxxxxx
Subject: frequency to mel formula

Dear List,

On the Wikipedia page 
  http://en.wikipedia.org/wiki/Mel_frequency_scale

a formula for computing frequency in terms of mels is given as:

mel = log(1 + fr/700)*1127 .

It is easily inverted to fr = 700*exp(mel/1127 - 1) .

My question is: Where do these formulas come from? I.e., I need
a journal reference for these formulas.

Thanks much,

Jim Beauchamp
Univ. of Illinois at Urbana-Champaign