Origin of the Mel frequency scale equation? (Rachel van Besouw )

Subject: Origin of the Mel frequency scale equation?
From:    Rachel van Besouw  <rvb@xxxxxxxx>
Date:    Tue, 11 Mar 2008 09:45:32 +0000

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@xxxxxxxx Tel +44 (0)23 8059 1818

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