Origin of the Mel frequency scale equation?

[Rachel van Besouw <rvb@xxxxxxxxxxxxxxxx>]

Hi all,

I have Fant (1973, p.47-48) as being the first to fit a function to the
data of Stevens & Volkmann (1940):

M = [1000/log(2)]*log[1+f/1000]

(as given by Jim Miller)

then Pederson (1965) proposed the following relation between mel and Hz
scales:

f = 0.146750532*10^(-12)*M^(5) - 0.795481794*10^(-9)*M^(4)
      +0.152864002*10^(-5)*M^(3) - 0.687099785 * 10^(-3)*M^(2)
               +0.805045046*M+2.14597315

and  then O'Shaughnessy (1978, p.150) proposed:

M = 2595*log(1 + f/700)

Fant, G. (1973) Speech sounds and features. MIT Press, Massachusetts.
O'Shaughnessy, D. (1978) Speech communication: Human and machine.
Addison-Wesley, New York.
Pederson, P. (1965) The mel scale. Journal of Music Theory, 9(2),
295-308. 
Stevens, S.S. & Volkmann, J. (1940) The relation of pitch to frequency:
a revised scale. American Journal of Psychology, 53(3), 329-353.

\Rachel

_______________________________
Rachel van Besouw | Research Fellow
ISVR | University of Southampton
Highfield | Southampton
SO17 1BJ | UK
rvb@xxxxxxxxxxxxxxxx
Tel +44 (0)23 8059 1818