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Re: frequency to mel formula
I've had a look in JASA 1937 and can confirm that the paper
"A Scale for the Measurement of the Psychological Magnitude Pitch"
by S.S. Stevens, J. Volkmann, E.B. Newman, J. Acoust. Soc. Am., vol. 8
(1937), pp. 185-190
introduces "mel" as a unit for perceived pitch. The first occurence of
"mel" is accompanied by the foot note:
"The name 'mel' was chosen as a name for the subjective pitch unit. It
was taken from the root of the word melody."
There's no formula, but experimental data for perceived half-pitch
frequencies and a plot of mel vs. Hz. It deviates from the formula
later adopted. Merely judging from the title of the 1940 AJP paper
("The relation of pitch to frequency: A revised scale"), the latter
seems to be a better reference for the mel scale than the 1937 paper.
On ven. 17 juil.09, at 07:24, Margaret Mortz wrote:
You might go back to Steven's original work which I found in
"The relation of pitch to frequency: A revised scale"
SS Stevens, J Volkmann - The American Journal of Psychology, 1940 -
The 1940 article has 196 citations, and I believe there has been
tuning of the mapping over the years.
[The citations are at
There's another reference at
SS Stevens, J Volkmann, EB Newman - J. Acoust. Soc. Am, 1937
There's a later reference in Steven's book via google.books
By Stanley Smith Stevens, Geraldine Stevens
On jeu. 16 juil.09, at 16:27, Ferguson, Sarah Hargus wrote:
Following Jim's tips, I found the mel formula appears on p. 128 in the
2nd edition of O'Shaughnessy. It's dubbed formula 4.2, and reads m =
2595log(1+f/700). The full reference for the book is
O'Shaughnessy, D. (2000). Speech communications: Human and machine
ed.). New York: IEEE Press.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Sarah Hargus Ferguson, Ph.D., CCC-A
Department of Speech-Language-Hearing: Sciences and Disorders
University of Kansas
1000 Sunnyside Ave., Room 3001
Lawrence, KS 66045
Speech Acoustics and Perception Lab: (785)864-0610
From: AUDITORY - Research in Auditory Perception
[mailto:AUDITORY@xxxxxxxxxxxxxxx] On Behalf Of James W. Beauchamp
Sent: Wednesday, July 15, 2009 8:55 PM
Subject: Re: frequency to mel formula
It would be good if someone could double check the O'Shaugnessy
reference, as given by Dan earlier today:
O'Shaughnessy, D. (1978) Speech communication: Human and machine.
Addison-Wesley, New York, page 150.
I think the title is actually Speech Communications: Human and
In the archived message
Dan gives the date of the book as 1987, so I'm not sure which is
At any rate, it is possible to buy a second edition of the book, which
copyrighted 2000. However, when perusing the Contents and the Index it
looks like the page has changed. Pages for 'mel scale' in the Index
128, 191, and 214. I hope the formula made it.
From: Dan Ellis <dpwe@xxxxxxxxxxxxxxx>
Date: Wed, 15 Jul 2009 15:55:25 -0400
Subject: Re: [AUDITORY] frequency to mel formula
Comments: To: "James D. Miller" <jamdmill@xxxxxxxxxxx>
I'm not sure if this is worth discussing on the full list, but...
After the discussion last year I actually got a hold of the Beranek
1949 book from our library's cold storage, and the reference is
In the book, Beranek gives empirical values for the Mel scale, but no
equation. Clearly, this reference got mangled somewhere along the
way: there may be a different early Beranek reference, but it isn't
I think Fant is the more appropriate reference (for log(1+f/1000))
O'Shaugnessy for log(1+f/700).