Re: Origin of the Mel frequency scale equation?

["James D. Miller" <jamdmill@xxxxxxxxxxx>]

Gunnar Fant long ago suggested the Technical Mel(TM) scale and it is in
his 1974 Book "Speech Sounds and Features (MIT Press 1974).

   He gave us TM = [1000/log(2)]*log[1+f/1000],

     Where the log is to the base 10 and f is in Hz.

    This fits the Mel Scale of Stevens and Volkman (1940) except at 
the very high frequencies. See the figure in Fant's book.

    I have  developed a quadratic that fits the 1940 scale very 
accurately and modification of the Fant equation that also fits the 
1940 scale over its entire range.

     I have no idea of where the Mel = C*log (1 + f/700) came from in 
the the speech-engineering literature. With the appropriate choice of 
C, I expect it doesn't differ too much from Fant's TM over the ranges 
of interest to speech engineers.

    Jim Miller
    jamdmill@xxxxxxxxxxx

Quoting Christine Rankovic <rankovic@xxxxxxxxxxxxxxxx>:

> It might be:
>
> Stevens, S., and J. Volkmann (1940).  The relation of pitch to
> frequency:  A revised scale.  Am. J. Psychol. 53:329-353.
>
> Sincerely,
>
> Christine Rankovic, PhD
> rankovic@xxxxxxxxxxxxxxxx
>
>
> ----- Original Message ----- From: "Arturo Camacho" <acamacho@xxxxxxxxxxxx>
> To: <AUDITORY@xxxxxxxxxxxxxxx>
> Sent: Monday, March 10, 2008 1:09 AM
> Subject: Origin of the Mel frequency scale equation?
>
>
> > Dear members of the list,
> >
> > I am looking for the reference of first use of the equation
> >
> > m = C log(1+f/700)
> >
> > known as mel frequency scale transformation. In Wikipedia says that the
> > scale was originated by Stevens, Volkman and Newman in 1937 (J. Acoust.
> > Soc. Am 8(3) 185--190), but the paper only has tabulated data and no
> > equation. The paper by S.B. Davis & P. Mermelstein (1980), "Comparison of
> > parametric representations for monosyllabic word recognition in
> > continuously spoken sentences", IEEE Trans. on ASSP 28, 357-366 is usually
> > cited in the speech recognition community as origin of MFCCs, but the
> > equation is absent there as well.
> >
> > Thanks,
> >
> > Arturo
> >
> > --
> > __________________________________________________
> >
> > Arturo Camacho, PhD
> > Alumni
> > Computer and Information Science and Engineering
> > University of Florida
> >
> > E-mail: acamacho@xxxxxxxxxxxx
> > Web page: www.cise.ufl.edu/~acamacho
> > __________________________________________________



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