Re: AUDITORY Digest - 16 Jul 2009 to 17 Jul 2009 (#2009-162)

[Donald D Greenwood <ddg@xxxxxxxxxxxxx>]

All involved:

This appears to be a long thread that I found among 669 emails  
awaiting me after a three week absence - and it is too late in the  
evening to try to scan completely or comment more than briefly.

The above was what i wrote two days ago at about midnight.   Now  
today, with the thread still not dead, and complete comments too long  
to undertake at one go, maybe some piecemeal comments can be made.

Simply as regards the Mel scale and the "history" Dick and others  
speak of:

1) There were two Mel scales.  The first in 1937 was steeper than the  
second in 1940.  The two scales were obtained by different methods and  
the second was intended by Stevens to replace the 1937 scale. That  
replacement was warranted.  It was the second scale that was later  
approximated closely by a function, Fant's as I have understood.  The  
second is the Mel scale that has been used ever since.

2)  The second Mel scale was based on equisections of each of three  
overlapping frequency ranges - but - as it appears later - without  
controls as to whether the subjects were basing their judgments  
primarily on listening to tones in ascending order, descending order,  
or both.

3)  Stevens later apparently thought about this lack of experimental  
control in the context of his later ideas (1956) about differences  
between different kinds of scales, such as pitch and loudness.  He was  
thinking in 1956 that "hysteresis" should not occur in pitch judgments  
(contrary to results of Titchener and all others - of which he may not  
have been aware).   He wanted to compare results obtained in an  
ascending listening order with those obtained in a descending order.   
This led to an experiment in 1956 (using the original equipment),  
which two students conducted for him, I being one.  He was  
disappointed and reported that hysteresis did occur in pitch- 
difference equisections (confirming Titchener and all others).   
Subjects set equisections higher when listening to tones in ascending  
order than when listening in descending order.  He very briefly  
reported this result in this paper:  Stevens, S.S. (1957) On the  
psychophysical law, Psychol. Rev., 64, 153-181.

4)  Later in 1960 or 61, I compared the ascending order and descending  
order data obtained 1956 to the 1940 Mel scale (which I had not done  
in 56 - being a busy first year student - and which I do not know  
whether or not Stevens did).  The concave ascending order data matched  
the 1940 Mel scale; the convex descending order data did not.  These  
outcomes - plotted on and compared to my cochlear map of 1961 - were  
later published (when a spare moment occurred) in the following papers:

Greenwood, D.D. (1997)  The Mel Scale's disqualifying bias and a  
consistency of pitch-difference equisections in 1956 with equal  
cochlear distances and equal frequency ratios, Hearing Res.  103,  
199-224.

A shorter paper (same data - shorter discussion) was presented (and  
published) in the Proceedings of the 97 Fechner Society meeting in  
Poznan under the title: "THE MEL SCALE'S BIAS AND EQUAL PITCH- 
DIFFERENCES:  IMPLICATIONS OF AN ALMOST LOGARITHMIC COCHLEA AND  
POSSIBLY SUBJECT-DEPENDENT CRITERIA".

5)  I would ask, why use the Mel scale now, since it appears to be  
biased?  If anyone wants a Mel scale they should do it over,  
controlling carefully for order bias and using plenty of subjects -  
more than in the past - and using both musicians and non-musicians to  
search for any differences in performance that may be governed by  
musician/non-musician differences or subject differences generally.   
Consult the reference lists of the two papers above for data and  
observations, from Stumpf onwards, as to why they should do so.

As regards some of the various cochlear maps:

1)  Steinberg's (1937) function was based on the data of Shower and  
Biddulph (1931 or 33) on the frequency difference threshold (JND).   
These differed systematically as a function of stimulus level.   
Steinberg hypothesized, as the basis for the construction of the map,  
that all frequency JNDs corresponded to equal distances along the  
cochlea - an expected assumption at that time but not a sure thing.   
Further assumptions were required to accommodate the differences in  
data as a function of level.

2a)  Steinberg's function and a non-identical function of Davis and  
Stevens (1935, I think) based largely on the same Shower and Biddulph  
frequency DL data (but clearly not in the same way), were later used  
by Feldtkeller and Zwicker [Feldtkeller, R. and  Zwicker, E.(1953)   
Die Grosse der Elementarstufen der Tonhohenempfindung und der  
Lautstarkeempfindung.  Acustica 3, 97-100.] to obtain two derivative  
functions.  An "average" derivative lying between them was then  
graphically determined.

2b)  That Mittelwert derivative (in the df/dx version) - and flattened  
horizontally below 300 Hz (later 500 Hz) later provided the SHAPE  
(i.e. form) of what became the Zwicker critical band curve.  You first  
see the Mittelwert df/dx curve (without yet the flattening) in the  
following paper:  Gassler, G. (1954) Uber die Horschwelle fur  
Schallereignisse mit verschieden breitem FrequenzsItpektrum.  Acustica  
4, 408-414.  By 1955 it was flattened ("generously rounded for  
engineering purposes" as Zwicker said, for example, at Keele 1977)  
below 300 Hz.

2c)  The Feldtkeller and Zwicker average derivative (with the added  
flattening below 300/500 Hz) obtained from the compromise between  
Steinberg's version of a cochlear map and Davis's and Stevens' version  
provided the SHAPE of the Zwicker critical band function seen from  
then on.

3)  That shape was NOT determined by the original critical band data  
themselves, summarized in Fig. 10 of Zwicker, Flottorp, and Stevens  
(1957), and the individual curves in Fig. 10 were NOT fit by the  
critical band curve which appeared in Fig. 11 of that paper.  In  
short, the curve in Fig. 11 is NOT the grand mean of the curves in  
Fig. 10, and only its ordinate position is based on them.

Larger figures (Figs. 10 to 15) showing how Zwicker's and Gassler's  
original critical band data are actually fit by the Zwicker critical  
band curve of Feldtkeller and Zwicker, Gassler, and Zwicker, Flottorp,  
and Stevens, as well as how they are fit by my critical band function  
of 1961 can be seen in:

Greenwood, D.D. (1991)  Critical bandwidth and consonance in relation  
to cochlear frequency-position coordinates, Hear. Res. 54, 164-208.

Questions:  Why, since the Zwicker (+ Feldtkeller and Gassler)  
critical band CURVE of 1955, 1957, and onwards) was NOT based on the  
shape of the actual critical band DATA they had obtained (but instead  
on the interpretive operations (in 3 different papers) based on much  
earlier frequency DL data - not necessarily equivalent) is it still  
being used - AS IF it had been based on the early (rather good)  
critical band data of Zwicker and Gassler in 1952 and 54?  Hasn't  
enough time passed that the critical band data themselves (and not the  
proxy curve that doesn't fit them) be given priority?

These are not unreasonable questions, since the BARK scale (a putative  
frequency-position scale) is simply, in effect, the integral of the  
derivative (as modified by flattening) obtained by Feldtkeller and  
Zwicker, based on frequency-position curves that were inferred from  
frequency DL data.  The Bark scale thus actually bypasses the Zwicker/ 
Gassler CB data that would have provided a differently shaped scale -  
and one actually based on their critical band data.

The total sequence:

a) Shower and Biddulph data on frequency DL hypothesized, in effect,  
to be derivatives of a cochlear map (i.e. to correspond to equal  
distances)
b) integrated in effect by Steinberg (with assumptions to cope with  
intensity variations)
c) same data in effect integrated by Davis and Stevens (with some  
quinea pig influence via in vitro physiological data)
d) the resulting two putative frequency-position functions (Steinberg  
and Davis-Stevens) then plotted and graphically differentiated by  
Feldtkeller and Zwicker
e) Mittelwert derivative drawn as a compromise derivative.
f) df/dx Mittelwert is proportional to Zwicker/Gassler critical band  
data in mid-frequency region (500 to 3000) but not elsewhere.
g) a non-mathematical function proportional to average df/dx  
derivative, that fits their CB data in mid frequencies, is flattened  
below 300 Hz and becomes the "critical band curve".
h) the flattened df/dx derivative is later integrated to obtain the  
Bark scale (after Barkhausen - Stevens suggestion was to name unit  
after Fletcher).
i) nobody appears to have thought that a curve called a critical band  
curve would be better based on actual estimates of critical bandwidth  
(ready, willing, and able to serve) - rather than on a back-and-forth  
sequence of integrations, differentiations, averaging, flattening, and  
a final integration that possesses more concavity than would have been  
obtained using an integration of the Zwicker/Gassler critical band data.
j) in other words, establishing a linkage between a) past data  
(frequency DLs) plus earlier efforts to infer a frequeny-position  
function and b) their own newer data (CBs) was evidently considered  
more important to Feldtkeller and Zwicker than fully relying on their  
own later CB data.  Obviously they felt a broader conceptual/ 
historical integration was desirable, which was/is defensible.  A CB  
function based on the CB data could have been obtained as well, of  
course, but wasn't (although average curves per experiment were  
offerred - see my Fig. 12 (1991).
k) it seems that very few in the non-German speaking (or reading)  
world were even aware of what occurred.  [Zwicker did comment good- 
humoredly, about 3 times at meetings that I attended, that more of us  
English speaking attendees should be able to read German.]

We can't change historical developments, but it should not be  
completely impossible to change perspectives on what occurred and what  
should follow.  The Bark scale as a cochlear map is not directly based  
on the data it has been thought to have been based on.  It is not in  
good agreement with the physiological data that we have.  But, of  
course, we are stuck with the fact that the physiological data we have  
(we're talking about humans) are from cadavers.  I think we can be  
glad that the data are not from us, the living, but it is inconvenient  
not to have in vivo data.
Nevertheless, it is some consolation that we have in vivo data from  
less fortunate species.  The introduction to, and some comments  
within, my 1990 paper offers some hope for the working hypothesis that  
the 1961/1990 function for humans may be close to correct,  
notwithstanding the lack of in vivo data.

In any case, I don't think the various cochlear maps are  
equipotential, although I agree with Jont that all are probably close  
enough that they all support the conclusions he would like to draw as  
regards their explanatory value for the data he references.   But  
unlike Jont, I have no objection to current usage in referring to the  
above cochlear map; it has a nice sound to me - maybe our preferences  
are attributable to differences in musical training.

This seems a good place to end - at least for now.  Although perhaps  
this thread has been extinguished.   Apologies for any egregious  
errors (or others).

 On 18 Jul, 2009, at 8:39 AM, Christine Rankovic wrote:

> Jont:
>
> Did they provide an equation?  If so, what was it?
>
> Tina
>
> ----- Original Message ----- From: "Jont Allen" <jontalle@xxxxxxxx>
> To: <AUDITORY@xxxxxxxxxxxxxxx>
> Sent: Saturday, July 18, 2009 1:34 AM
> Subject: Re: AUDITORY Digest - 16 Jul 2009 to 17 Jul 2009 (#2009-162)
>
>
> > Dear All,
> >
> > For the record, the mel scale and the cochlear map (Greenwoods  
> > function), namely the location of peak resp vs location along the  
> > BM, are the same thing (within experimental error). This function  
> > was first derived by Steinberg back in 1930, and again several  
> > times in Fletcher's work, by several means. I have discussed this  
> > relation many times in various review papers, and would be happy to  
> > provide refs and even pdfs for those of you interested. In any  
> > case, there is no mystery here.
> >
> > The cochlear map (as its called) shows up in the articulation  
> > index, distortion products, speech perception, pitch perception,  
> > masking experiments, excitation patterns, etc, etc. Any time the  
> > cochlea is relevant to some experimental result, this function  
> > appears. IMO it should be called the Fletcher map rather than  
> > Greenwoods function (I do appreciate that Don Greenwood fully  
> > appreciated it, and promoted the concept, and did a great job of  
> > explaining it to the world, but then Fletcher and Steinberg clearly  
> > were the first to describe it, as best I know). Right Don? Much  
> > credit is due you, and so delivered.
> >
> > Jont
> >
> > AUDITORY automatic digest system wrote:
> > > There are 6 messages totalling 551 lines in this issue.
> > >
> > > Topics of the day:
> > >
> > >  1. AUDITORY Digest - 15 Jul 2009 to 16 Jul 2009 (#2009-161)
> > >  2. frequency to mel formula (4)
> > >  3. Survey: music cognition courses
> > >
> > > ----------------------------------------------------------------------
> > >
> > > Date:    Thu, 16 Jul 2009 22:24:19 -0700
> > > From:    Margaret Mortz <migsmortz@xxxxxxxxxxxx>
> > > Subject: Re: AUDITORY Digest - 15 Jul 2009 to 16 Jul 2009  
> > > (#2009-161)
> > >
> > > 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.o=
> > > rg
> > >
> > > =A0 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=3D13168086733343486057&hl=3Den&num=
> > > =3D100]
> > >
> > > 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
> > > =A0By Stanley Smith Stevens, Geraldine Stevens
> > >
> > > http://tinyurl.com/kkvpsd
> > > or:
> > > http://books.google.com/books?hl=3Den&lr=3D&id=3Dr5JOHlXX8bgC&oi=3Dfnd&pg=
> > > =3DPR13&ots=3D4lcYLbTP9E&sig=3DmgminuGa_-Sv9_AqTLf4e3NXv4k
> > >
> > > Margaret
> > >
> > > <LISTSERV@xxxxxxxxxxxxxxx> wrote:
> > > > AUDITORY Digest - 15 Jul 2009 to 16 Jul 2009 (#2009-161)
> > > >
> > > > Table of contents:
> > > >
> > > > frequency to mel formula (3)
> > > > Academic position in audiology
> > > > AUDITORY Digest - 14 Jul 2009 to 15 Jul 2009 (#2009-160)
> > > >
> > > > frequency to mel formula
> > > >
> > > > Re: frequency to mel formula (07/16)
> > > > From: Jon Boley <jdb@xxxxxxxxxx>
> > > > Re: frequency to mel formula (07/16)
> > > > From: "Ferguson, Sarah Hargus" <safergus@xxxxxx>
> > > > Re: frequency to mel formula (07/15)
> > > > From: "Richard F. Lyon" <DickLyon@xxxxxxx>
> > > >
> > > > Academic position in audiology
> > > >
> > > > Academic position in audiology (07/16)
> > > > From: Sylvie H=E9bert <sylvie.hebert@xxxxxxxxxxxx>
> > > >
> > > > AUDITORY Digest - 14 Jul 2009 to 15 Jul 2009 (#2009-160)
> > > >
> > > > Re: AUDITORY Digest - 14 Jul 2009 to 15 Jul 2009 (#2009-160)  
> > > > (07/16)
> > > > From: Douglas Creelman <creelman@xxxxxxxxxxxxxxxxx>
> > > >
> > > > ________________________________
> > > > Browse the AUDITORY online archives.
> > >
> > > ------------------------------
> > >
> > > Date:    Fri, 17 Jul 2009 14:22:33 +0200
> > > From:    =?ISO-8859-1?Q?FARNER_Snorre_Balli=E8re?= <farner@xxxxxxxx>
> > > Subject: Re: frequency to mel formula
> > >
> > > 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@xxxxxxxxxxxxxxx] On Behalf Of James W. Beauchamp
> > > > Sent: Wednesday, July 15, 2009 8:55 PM
> > > > To: AUDITORY@xxxxxxxxxxxxxxx
> > > > 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@xxxxxxxxxxxxxxx>
> > > > > Date: Wed, 15 Jul 2009 15:55:25 -0400
> > > > > To: AUDITORY@xxxxxxxxxxxxxxx
> > > > > 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   
> > > > > 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.
> > >
> > > ------------------------------
> > >
> > > Date:    Fri, 17 Jul 2009 14:56:23 +0200
> > > From:    Guillaume Lemaitre <Guillaume.Lemaitre@xxxxxxxx>
> > > Subject: Re: frequency to mel formula
> > >
> > > This is a multi-part message in MIME format.
> > > --------------020304060601060400050204
> > > Content-Type: text/plain; charset=ISO-8859-1; format=flowed
> > > Content-Transfer-Encoding: quoted-printable
> > > X-MIME-Autoconverted: from 8bit to quoted-printable by  
> > > torrent.cc.mcgill.ca id n6HCuRvY004064
> > >
> > > Dear list
> > > Another lead: Malcom Slaney implemented mfcc calculations in the  
> > > Matlab=20
> > > Auditory Toolbox using a method that is different from the  
> > > formulae=20
> > > previously cited on the list. Once I compared his method to the  
> > > formula=20
> > > 2595*log10(1+hz/700) and found little difference. Malcom may  
> > > remember=20
> > > where he devised the method from (I would bet from Rabiner's book?).
> > >
> > > By the way, I found the  log10(1+hz/700) formula in the following=20
> > > conference paper:
> > > @InProceedings{mol01,
> > > author =3D "Sirko Molau and Michael Pitz and Ralf Schl=FCter and  
> > > Hermann=
> > > Ney",
> > >  title =3D "Computing Mel-Frequency Cepstral Coefficients on the  
> > > Power=20
> > > Spectrum",
> > >  booktitle =3D {International Conference on Acoustic, Speech  and  
> > > Signal=
> > > =20
> > > Processing},
> > >  year =3D      {2001},
> > >  address =3D      {Salt Lake City, UT},
> > >  month =3D      {June},
> > > }
> > > I don't currently have the paper at hand, but if someone could  
> > > check,=20
> > > they may cite their source.
> > > Hope that it helps.
> > > Best regards
> > > Guillaume
> > >
> > >
> > > --=20
> > >
> > > -------------------------------------------------------------------------=
> > > ---
> > >
> > > Guillaume Lemaitre, PhD
> > >
> > > /
> > > /
> > >
> > > Equipe Perception et Design Sonores /
> > >
> > > Sound Perception and Design Team
> > >
> > >
> > > STMS-IRCAM-CNRS     UMR 9912
> > >
> > > 1, place Igor Stravinsky F-75004 Paris - FRANCE
> > >
> > > tel  : (+33 1) 44.78.48.38
> > >
> > > fax : (+33 1) 44.78.15.40
> > >
> > > e-mail  : lemaitre@xxxxxxxx
> > >
> > > --------------------------------------=20
> > > --------------------------------------
> > >
> > >
> > > --------------020304060601060400050204
> > > Content-Type: text/html; charset=ISO-8859-1
> > > Content-Transfer-Encoding: 7bit
> > >
> > > <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
> > > <html>
> > > <head>
> > >  <meta content="text/html;charset=ISO-8859-1" http-equiv="Content- 
> > > Type">
> > >  <title></title>
> > > </head>
> > > <body bgcolor="#ffffff" text="#000000">
> > > Dear list<br>
> > > Another lead: Malcom Slaney implemented mfcc calculations in the  
> > > Matlab
> > > Auditory Toolbox using a method that is different from the formulae
> > > previously cited on the list. Once I compared his method to the  
> > > formula
> > > 2595*log10(1+hz/700) and found little difference. Malcom may  
> > > remember
> > > where he devised the method from (I would bet from Rabiner's  
> > > book?). <br>
> > > <br>
> > > By the way, I found the&nbsp; log10(1+hz/700) formula in the  
> > > following
> > > conference paper:<br>
> > > @InProceedings{mol01,<br>
> > > &nbsp;author = "Sirko Molau and Michael Pitz and Ralf  
> > > Schl&uuml;ter and Hermann
> > > Ney",<br>
> > > &nbsp; title = "Computing Mel-Frequency Cepstral Coefficients on  
> > > the Power
> > > Spectrum",<br>
> > > &nbsp; booktitle = {International Conference on Acoustic,  
> > > Speech&nbsp; and Signal
> > > Processing},<br>
> > > &nbsp; year = &nbsp;&nbsp;&nbsp; &nbsp;{2001},<br>
> > > &nbsp; address = &nbsp;&nbsp;&nbsp; &nbsp;{Salt Lake City, UT},<br>
> > > &nbsp; month = &nbsp;&nbsp;&nbsp; &nbsp;{June},<br>
> > > }<br>
> > > I don't currently have the paper at hand, but if someone could  
> > > check,
> > > they may cite their source.<br>
> > > Hope that it helps.<br>
> > > Best regards<br>
> > > Guillaume<br>
> > > <br>
> > > <br>
> > > <div class="moz-signature">-- <br>
> > > <meta http-equiv="Content-Type" content="text/html; ">
> > > <meta http-equiv="Content-Style-Type" content="text/css">
> > > <title></title>
> > > <meta name="Generator" content="Cocoa HTML Writer">
> > > <meta name="CocoaVersion" content="824.42">
> > > <style type="text/css">
> > >    p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica}
> > >  </style>
> > > <p  
> > > class 
> > > = 
> > > "p1 
> > > "> 
> > > ----------------------------------------------------------------------------< 
> > > br>
> > > </p>
> > > Guillaume Lemaitre, PhD<br>
> > > <p class="p1"><i><br>
> > > </i></p>
> > > <p class="p1">Equipe Perception et Design Sonores /</p>
> > > <p class="p1">Sound Perception and Design Team<br>
> > > </p>
> > > <p class="p1"><br>
> > > </p>
> > > <p class="p1">STMS-IRCAM-CNRS&nbsp;&nbsp;&nbsp;&nbsp; UMR 9912<br>
> > > </p>
> > > <p class="p1">1, place Igor Stravinsky F-75004 Paris - FRANCE</p>
> > > <p class="p1">tel<span class="Apple-converted-space">&nbsp; </span>:
> > > (+33 1) 44.78.48.38</p>
> > > <p class="p1">fax : (+33 1) 44.78.15.40</p>
> > > <p class="p1">e-mail<span class="Apple-converted-space">&nbsp; </ 
> > > span>:
> > > <a class="moz-txt-link-abbreviated"  
> > > href="mailto:lemaitre@xxxxxxxx";>lemaitre@xxxxxxxx</a></p>
> > > <p class="p1">--------------------------------------<span
> > > class="Apple-converted-space"> </ 
> > > span>--------------------------------------</p>
> > > </div>
> > > </body>
> > > </html>
> > >
> > > --------------020304060601060400050204--
> > >
> > > ------------------------------
> > >
> > > Date:    Fri, 17 Jul 2009 01:04:21 -0600
> > > From:    Julius Smith <jos@xxxxxxxxxxxxxxxxxx>
> > > Subject: Re: frequency to mel formula
> > >
> > > Hi Jim,
> > >
> > > Do you have a feel for why the mel scale is used instead of, say,  
> > > Bark or ERB scales?
> > >
> > > Just curious,
> > > Julius
> > >
> > > At 11:11 AM 7/15/2009, James W. Beauchamp wrote:
> > > > Dear List,
> > > >
> > > > On the Wikipedia page
> > > >  http://en.wikipedia.org/wiki/Mel_frequency_scale
> > > >
> > > > a formula for computing frequency in terms of mels is given as:
> > > >
> > > > mel = log(1 + fr/700)*1127 .
> > > >
> > > > It is easily inverted to fr = 700*exp(mel/1127 - 1) .
> > > >
> > > > My question is: Where do these formulas come from? I.e., I need
> > > > a journal reference for these formulas.
> > > >
> > > > Thanks much,
> > > >
> > > > Jim Beauchamp
> > > > Univ. of Illinois at Urbana-Champaign
> > >
> > > "Anybody who knows all about nothing knows everything" -- Leonard  
> > > Susskind
> > >
> > > ------------------------------
> > >
> > > Date:    Fri, 17 Jul 2009 10:00:26 -0400
> > > From:    Fred Herzfeld <herzfeld@xxxxxxxxxxxx>
> > > Subject: frequency to mel formula
> > >
> > > Guillaume and list,
> > >
> > > Malcom's formula and the others are actually the same. He used  
> > > [log base 10]  instead of
> > > [log base 2].
> > >
> > > Fred
> > > =============================================
> > > Fred Herzfeld, MIT '54
> > > 78 Glynn Marsh Drive #59
> > > Brunswick, Ga.31525
> > > USA
> > >
> > > ------------------------------
> > >
> > > Date:    Fri, 17 Jul 2009 14:07:44 -0800
> > > From:    Aniruddh Patel <apatel@xxxxxxx>
> > > Subject: Survey: music cognition courses
> > >
> > > --=====================_272854234==.ALT
> > > Content-Type: text/plain; charset="us-ascii"; format=flowed
> > >
> > > Dear List,
> > >
> > > I'm trying to collect some information on music perception/ 
> > > cognition courses
> > > being offered today.
> > >
> > > If you are involved in teaching such a course, I'd like to invite
> > > you to provide the information below **by July 27**.  I will be  
> > > collating the info
> > > and presenting it at the upcoming Society for Music Perception and  
> > > Cognition
> > > (SMPC) meeting, Aug 3-7, in Indianapolis, Indiana:
> > >
> > > http://music.iupui.edu/smpc2009/
> > >
> > > If you don't teach a course on this topic, but know a colleague  
> > > who does,
> > > please feel free to forward this message to him/her, even if he/she
> > > is in a different department.
> > >
> > > Thanks,
> > >
> > > Ani Patel
> > > President, SMPC
> > >
> > > -------------------------------------------------------------------------------------------------
> > > Summer 2009 Music cognition course survey
> > >
> > > Name of university
> > >
> > > Location of university (City, State/Region, Country)
> > >
> > > Name of course
> > >
> > > Department/Program in which it is offered
> > >
> > > Level (undergraduate, graduate)
> > >
> > > Names and home departments of professor(s)
> > >
> > > How old is the course (what year was it created)?
> > >
> > > How often is it offered (e.g., yearly, every other year)?
> > >
> > > What is the typical enrollment?
> > >
> > > Has enrollment grown, shrunk, or remained the same in the past few
> > > years?
> > >
> > > In the latest class, did you use any books?  If so, which ones?
> > >
> > > Course website (if it exists)
> > >
> > > If you can, please provide a one-sentence description of course  
> > > aims.
> > >
> > >
> > >
> > > Aniruddh D. Patel, Ph.D.
> > > Esther J. Burnham Senior Fellow
> > > The Neurosciences Institute
> > > 10640 John Jay Hopkins Drive
> > > San Diego, CA 92121
> > >
> > > 858-626-2085 tel
> > > 858-626-2099 fax
> > > apatel@xxxxxxx
> > > http://www.nsi.edu/users/patel
> > >
> > > --=====================_272854234==.ALT
> > > Content-Type: text/html; charset="us-ascii"
> > >
> > > <html>
> > > <body>
> > > Dear List,<br><br>
> > > I'm trying to collect some information on music perception/cognition
> > > courses<br>
> > > being offered today.<br><br>
> > > If you are involved in teaching such a course, I'd like to  
> > > invite<br>
> > > you to provide the information below **by July 27**.&nbsp; I will be
> > > collating the info<br>
> > > and presenting it at the upcoming Society for Music Perception and
> > > Cognition<br>
> > > (SMPC) meeting, Aug 3-7, in Indianapolis, Indiana:<br><br>
> > > <a href="http://music.iupui.edu/smpc2009/"; eudora="autourl">http://music.iupui.edu/smpc2009/ 
> > > </a><br><br>
> > > If you don't teach a course on this topic, but know a colleague who
> > > does,<br>
> > > please feel free to forward this message to him/her, even if he/ 
> > > she<br>
> > > is in a different department.<br><br>
> > > Thanks,<br><br>
> > > Ani Patel<br>
> > > President, SMPC<br><br>
> > > -------------------------------------------------------------------------------------------------< 
> > > br>
> > > Summer 2009 Music cognition course survey<br><br>
> > > <pre>Name of university
> > >
> > > Location of university (City, State/Region, Country)
> > >
> > > Name of course
> > >
> > > Department/Program in which it is offered
> > >
> > > Level (undergraduate, graduate)
> > >
> > > Names and home departments of professor(s)
> > >
> > > How old is the course (what year was it created)?
> > >
> > > How often is it offered (e.g., yearly, every other year)?
> > >
> > > What is the typical enrollment?
> > >
> > > Has enrollment grown, shrunk, or remained the same in the past  
> > > few&nbsp; years?
> > >
> > > In the latest class, did you use any books?&nbsp; If so, which ones?
> > >
> > > Course website (if it exists)
> > >
> > > If you can, please provide a one-sentence description of course  
> > > aims.
> > >
> > >
> > > </pre><x-sigsep><p></x-sigsep>
> > > Aniruddh D. Patel, Ph.D.<br>
> > > Esther J. Burnham Senior Fellow<br>
> > > The Neurosciences Institute<br>
> > > 10640 John Jay Hopkins Drive<br>
> > > San Diego, CA 92121<br><br>
> > > 858-626-2085 tel<br>
> > > 858-626-2099 fax<br>
> > > apatel@xxxxxxx<br>
> > > <a href="http://www.nsi.edu/users/patel"; eudora="autourl">http://www.nsi.edu/users/patel 
> > > <br>
> > > </a></body>
> > > </html>
> > >
> > > --=====================_272854234==.ALT--
> > >
> > > ------------------------------
> > >
> > > End of AUDITORY Digest - 16 Jul 2009 to 17 Jul 2009 (#2009-162)
> > > ***************************************************************