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

Tina, and others,


Here are some of my notes on the topic of the cochlear map, Fletcher, Greenwoods function, and its various estimates based on pitch, critical bands and speech articulation.

I found six Fletcher articles in my notes, that discuss the cochlear map.


Steinberg, who worked for Fletcher, was the very first to work out the map function. However Wegel and Lane 1924 probably were pretty aware of it, but I dont know if they had a formula for it.


Besides these, Galt spent many years trying to get his ideas published, about how the cochlear map and the articulation index were related. However, I saw the reviews, and they were pretty harsh. He went to his grave knowing this relationship, as discussed in Fletcher and Galt's paper, but he never really got the credit for his important discovery.
Very sad.


Manfred Schroeder has also worked out a formula or two for the cochlear map, and you would find that in JASA.


As best I know, none of these people seem to be aware of each other, and nobody seems to reference the other.


Regarding my papers, that reference and discuss some or all of this, as I mentioned, are:

@incollection{Allen88,
author = {Allen, J. B.},
editor = {Jahn, A. F. and Santos-Sacchi, J.},
title = {Cochlear signal processing},
booktitle = {Physiology of the ear},
pages = {243-270},
publisher = {Raven Press},
year = {1988}

Filename: raven.pdf/djvu
@incollection{Allen01b
,author={Allen, J. B.}
,title={Nonlinear Cochlear Signal Processing}
,booktitle={ Physiology of the Ear, Second Edition }
,publisher={Singular Thomson Learning}
,year=2001
,editor={ Jahn, A.F. and Santos-Sacchi, J.}
,chapter={19}
,pages={393--442}
,address={ 401 West A Street, Suite 325 San Diego, CA 92101 }

Filename: hb13-003-final-22.08.2007.pdf/djvu
@incollection{Allen08a
,author={Allen, J. B.}

,title={Nonlinear Cochlear Signal Processing and Masking in speech perception} ,booktitle={ Springer Handbook on speech processing and speech communication }
,publisher={Springer}
,year=2008
,editor={Benesty, Jacob and Sondhi, Mohan}
,chapter={3}
,pages={1-36}

@article{Allen96f
,author={Allen, J. B.}
,title={Harvey {F}letcher's role in the creation of communication
acoustics}
,journal=JASA
,year=1996
,nonomonth=apr
,volume={99}
,number={4}
,pages={1825--1839}
,note_={Reprint of material from preface of {F}letcher's 53 book, with some
important additions on the critical band.} }

At least some of these are at:
http://auditorymodels.org/jba/PAPERS/AllenOverviews/
http://auditorymodels.org/jba/PAPERS/Allen/

Fletcher references:

Any time it refers to the "Monograph" it is talking about a very large set of books (20 feet of them) that only exists inside of Bell labs that contain all the publications from bell labs, from 1929 to about 1960, when they stopped the collection. That series is a gold-mine. I almost got a set they were tossing out, but at the last minute, as I was walking out the door with them, they changed their minds. They got wind of what I planed to do with them (scan them). There are only a few sets of these books.

@article{Fletcher30a,
author={Fletcher, Harvey},
title={A space-time pattern theory of hearing},
journal=JASA,
year={1930},
nomonth=apr,
volume=1,
number=1,
pages={311--343},
note_={
This theory of the cochlea predates Ranke, but not Wegel and Lane (1924).
The paper was written after \cite{Fletcher29a} and clearly
shows the progression of Fletcher's thinking in 1930.
He concludes the ear drum impedance must
be stiffness dominated at lower frequencies ($<$1000 Hz) (p. 314).
He then estimates the variation of cochlear map
from physical properties, such as the width of the BM.
He rejects the von B\'ek\'esy eddy theory.
Using the cochlear map and pure tone masking
data, he plots excitation space'' patterns as a function of level.
Discusses a spread of excitation'' model of loudness.  }}
note_={ Points out that Wegel and Lane data are on Fletcher's left
ear (Page 325).

The non-linear character of the middle ear with subjective
harmonics is discussed.  These space patterns for the entire length
of the membrane, however, can be obtained form the masking data.''
Did he clearly have the concept of the critical band in mind in 1930?
Read this paper to find out.

"There is no doubt that loudness is closely associated with the
total discharges reaching the brain." Page 336
Page 339 determines the level a 1kHz tone so that its loudness equals
that of 6 tones of equal SPL (-20 dB re ?).

Several minor errors: he confuses the fundamental and the
first harmonic (page 315), after carefully defining it (page 313).
Is the word phrases'' a typo, that should have been phases''
on p.\ 311, item (4) of second set of items? B--499
}

@article{Fletcher37a,
author={Fletcher, Harvey and Munson, W.A.},
journal=JASA,
year={1937},
volume={9},
pages={1--10},
note_={
First paper to explore the critical band in detail.
This paper was used in Chapter 4 of Stevens and Davis, 1938.
They showed that the cochlear map function and the critical
bandwidths are closely related functions, and argued that they
could be derived from each other (see \cite{Fletcher38a}).
This paper was the first to normalize the cochlea in terms of the
percent of its full length.
Presented at the Acoustical Society meeting, May 1937.

@article{Fletcher38a,
author={Fletcher, Harvey},
title={Loudness, Masking and Their Relation to the Hearing
Process and the Problem of Noise Measurement},
journal=JASA,
year={1938},
nomonth=apr,
volume={9},
pages={275--293},
note_={
This is the first time that the cochlear map is derived from
critical band masking data. It is compared to that derived from
pitch experiments, and found to be similar. Thus a relation
between the frequency JND and masking is demonstrated.
The formula for $\kappa$ the critical bandwidth in dB is
described here in Eq. 15. A plot is given in Fig. 6.
He calculates the signal to noise ratio at the masked threshold and
finds it to be 0.5 dB, except at low levels where it is 3 to 4 dB
(p.\ 284).  The relation between the loudness and the masked threshold
for any sound is described.
These data are refinements on \cite{Fletcher37a}.  B--1067} }

@article{Fletcher40a,
author={Fletcher, Harvey},
title={Auditory Patterns},
journal={Reviews of Modern Physics},
year={1940},
nomonth=may,
volume={12},
number=1,
pages={47--65},
note_={This is a review/tutorial article. Fletcher states that the
development of the instrumentation required to study the ear
led to the development of radio and sound pictures.
This paper has been heavily referred to because it describes some
direct critical band measurements.
Many have referenced this paper as the first to introduce the
critical band, which is incorrect.
It has a basic review of the calculation of $C$ and the cochlear map.
Bell Labs monograph B--1205} }

@article{Fletcher51a,
author={Fletcher, Harvey},
title={On the dynamics of the cochlea},
journal=JASA,
year={1951},
nomonth=nov,
volume={23},
pages={637--645},
note_={Theory of cochlea, including scalae viscosity. Matches von
B\'ek\'esy data.} }

Steinberg reference:

@article{Steinberg37a
,author={Steinberg, J.C.}
,title={ Positions of stimulation in the cochlea by pure tones  }
,journal=JASA
,year=1937
,nomonth={}
,volume=8
,number={}
,pages={176--180}
,note={Cochlear map estimate; Monograph B-973} }

Thats all I have for now.

jont

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

=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:

=3DPR13&ots=3D4lcYLbTP9E&sig=3DmgminuGa_-Sv9_AqTLf4e3NXv4k

Margaret

<LISTSERV@xxxxxxxxxxxxxxx> wrote:

AUDITORY Digest - 15 Jul 2009 to 16 Jul 2009 (#2009-161)

frequency to mel formula (3)
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>

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


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:


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.

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.
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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
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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>

<meta content="text/html;charset=ISO-8859-1" http-equiv="Content-Type">
  <title></title>
<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>
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<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>
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--------------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,

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

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

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--

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End of AUDITORY Digest - 16 Jul 2009 to 17 Jul 2009 (#2009-162)
***************************************************************