Subject: Re: frequency to mel formula From: =?ISO-8859-1?Q?FARNER_Snorre_Balli=E8re?= <farner@xxxxxxxx> Date: Fri, 17 Jul 2009 14:22:33 +0200 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>Dear list, 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. Best regards, -Snorre Farner On ven. 17 juil.09, at 07:24, Margaret Mortz wrote: > You might go back to Steven's original work which I found in > scholar.google.com > > "The relation of pitch to frequency: A revised scale" > SS Stevens, J Volkmann - The American Journal of Psychology, 1940 - > jstor.org > > The 1940 article has 196 citations, and I believe there has been > tuning of the mapping over the years. > [The citations are at > http://scholar.google.com/scholar?cites=13168086733343486057&hl=en&num=100 > ] > > 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 > > Psychophysics > By Stanley Smith Stevens, Geraldine Stevens > > http://tinyurl.com/kkvpsd > or: > http://books.google.com/books?hl=en&lr=&id=r5JOHlXX8bgC&oi=fnd&pg=PR13&ots=4lcYLbTP9E&sig=mgminuGa_-Sv9_AqTLf4e3NXv4k > > Margaret > 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 > (2nd > ed.). New York: IEEE Press. > > ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ > Sarah Hargus Ferguson, Ph.D., CCC-A > Assistant Professor > Department of Speech-Language-Hearing: Sciences and Disorders > University of Kansas > Dole Center > 1000 Sunnyside Ave., Room 3001 > Lawrence, KS 66045 > office: (785)864-1116 > Speech Acoustics and Perception Lab: (785)864-0610 > http://www.ku.edu/~splh/Faculty/FergusonBio.html > > -----Original Message----- > From: AUDITORY - Research in Auditory Perception > [mailto:AUDITORY@xxxxxxxx On Behalf Of James W. Beauchamp > Sent: Wednesday, July 15, 2009 8:55 PM > To: AUDITORY@xxxxxxxx > 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 > Machine. > In the archived message > http://www.auditory.org/mhonarc/2008/msg00189.html > Dan gives the date of the book as 1987, so I'm not sure which is > correct. > At any rate, it is possible to buy a second edition of the book, which > is > copyrighted 2000. However, when perusing the Contents and the Index it > looks like the page has changed. Pages for 'mel scale' in the Index > are > 128, 191, and 214. I hope the formula made it. > > Jim > > Original message: >> From: Dan Ellis <dpwe@xxxxxxxx> >> Date: Wed, 15 Jul 2009 15:55:25 -0400 >> To: AUDITORY@xxxxxxxx >> Subject: Re: [AUDITORY] frequency to mel formula >> Comments: To: "James D. Miller" <jamdmill@xxxxxxxx> >> >> 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 >> wrong. >> 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 >> this one. >> >> I think Fant is the more appropriate reference (for log(1+f/1000)) >> and >> O'Shaugnessy for log(1+f/700). >> >> DAn. >