There are 6 messages totalling 358 lines in this issue.
Topics of the day:
1. frequency to mel formula (6)
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Date: Wed, 15 Jul 2009 13:11:27 -0500
From: "James W. Beauchamp" <jwbeauch@xxxxxxxxxxxxxxxxxxxxxx>
Subject: frequency to mel formula
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
------------------------------
Date: Wed, 15 Jul 2009 14:01:02 -0500
From: "McCreery, Ryan W" <McCreeryR@xxxxxxxxxxxx>
Subject: Re: frequency to mel formula
Hi Jim,
I don't know if this is the first reference to the mel scale, but it's I have read before and seen cited:
Stevens, S.S. & Volkmann, J. (1940) The relation of pitch to frequency: A r=
evised scale. The American Journal of Psychology 53(3), 329-
I hope this helps.
Ryan McCreery
-----Original Message-----
From: AUDITORY - Research in Auditory Perception [mailto:AUDITORY@xxxxxxxxx=
ILL.CA] On Behalf Of James W. Beauchamp
Sent: Wednesday, July 15, 2009 1:11 PM
To: AUDITORY@xxxxxxxxxxxxxxx
Subject: frequency to mel formula
Dear List,
On the Wikipedia page=20
http://en.wikipedia.org/wiki/Mel_frequency_scale
a formula for computing frequency in terms of mels is given as:
mel =3D log(1 + fr/700)*1127 .
It is easily inverted to fr =3D 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
------------------------------
Date: Wed, 15 Jul 2009 15:03:45 -0400
From: Dan Ellis <dpwe@xxxxxxxxxxxxxxx>
Subject: Re: frequency to mel formula
We discussed this last year. See
http://www.auditory.org/mhonarc/2008/msg00191.html
http://www.auditory.org/mhonarc/2008/msg00189.html
and the surrounding thread.
I think the actual origin is Fant in a paper in Swedish from 1949,
summarized in his 1973 book:
Fant, C G M "Analys av de svenska konsonantljuden" LM Ericsson
protokoll H/P 1064, 1949: 139pp.
referenced on p. 48 of
Fant, G "Speech Sounds and Features", MIT Press, 1973.
but Fant uses log(1+f/1000). The log(1+f/700) was attributed to
O'Shaughnessy, D. (1978) Speech communication: Human and machine.
Addison-Wesley, New York, page 150.
DAn.
On Wed, Jul 15, 2009 at 2:11 PM, James W.
Beauchamp<jwbeauch@xxxxxxxxxxxxxxxxxxxxxx> wrote:
Dear List,
On the Wikipedia page
=C2=A0http://en.wikipedia.org/wiki/Mel_frequency_scale
a formula for computing frequency in terms of mels is given as:
mel =3D log(1 + fr/700)*1127 .
It is easily inverted to fr =3D 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
------------------------------
Date: Wed, 15 Jul 2009 15:55:25 -0400
From: Dan Ellis <dpwe@xxxxxxxxxxxxxxx>
Subject: Re: frequency to mel formula
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.
On Wed, Jul 15, 2009 at 3:34 PM, James D. Miller<jamdmill@xxxxxxxxxxx> wrot=
e:
As Dan explained last time this was discussed, the correct reference to t=
he formula cited by Beauchamp is
LL Beranek, Acoustic Measurements, Wiley, New York, 1949), p.329.
as the source for mel(f) =3D 1127 ln(1 + f/700)
Jim Miller
-----Original Message-----
From: AUDITORY - Research in Auditory Perception [mailto:AUDITORY@xxxxxxx=
CGILL.CA] On Behalf Of Dan Ellis
Sent: Wednesday, July 15, 2009 3:04 PM
To: AUDITORY@xxxxxxxxxxxxxxx
Subject: Re: [AUDITORY] frequency to mel formula
We discussed this last year. =C2=A0See
http://www.auditory.org/mhonarc/2008/msg00191.html
http://www.auditory.org/mhonarc/2008/msg00189.html
and the surrounding thread.
I think the actual origin is Fant in a paper in Swedish from 1949,
summarized in his 1973 book:
Fant, C G M "Analys av de svenska konsonantljuden" LM Ericsson
protokoll H/P 1064, 1949: 139pp.
referenced on p. 48 of
Fant, G "Speech Sounds and Features", MIT Press, 1973.
but Fant uses log(1+f/1000). =C2=A0The log(1+f/700) was attributed to
O'Shaughnessy, D. (1978) Speech communication: Human and machine.
Addison-Wesley, New York, page 150.
=C2=A0DAn.
On Wed, Jul 15, 2009 at 2:11 PM, James W.
Beauchamp<jwbeauch@xxxxxxxxxxxxxxxxxxxxxx> wrote:
Dear List,
On the Wikipedia page
=C2=A0http://en.wikipedia.org/wiki/Mel_frequency_scale
a formula for computing frequency in terms of mels is given as:
mel =3D log(1 + fr/700)*1127 .
It is easily inverted to fr =3D 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
------------------------------
Date: Wed, 15 Jul 2009 17:29:47 -0400
From: Christine Rankovic <rankovic@xxxxxxxxxxxxxxxx>
Subject: Re: frequency to mel formula
I just checked Beranek's book: Acoustic Measurements. Beranek cites
Stevens and Volkman as the source of his plot on page 203 (Beranek provides
no equation) . The full reference provided by Beranek is: S.S. Stevens and
J. Volkman, "The relation of pitch to frequency: a revised scale," Amer.
J. Psychol., vol. 53, 329 (1940).
Christine Rankovic
----- Original Message -----
From: "Dan Ellis" <dpwe@xxxxxxxxxxxxxxx>
To: <AUDITORY@xxxxxxxxxxxxxxx>
Sent: Wednesday, July 15, 2009 3:55 PM
Subject: Re: frequency to mel formula
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.
On Wed, Jul 15, 2009 at 3:34 PM, James D. Miller<jamdmill@xxxxxxxxxxx>
wrote:
As Dan explained last time this was discussed, the correct reference to
the formula cited by Beauchamp is
LL Beranek, Acoustic Measurements, Wiley, New York, 1949), p.329.
as the source for mel(f) = 1127 ln(1 + f/700)
Jim Miller
-----Original Message-----
From: AUDITORY - Research in Auditory Perception
[mailto:AUDITORY@xxxxxxxxxxxxxxx] On Behalf Of Dan Ellis
Sent: Wednesday, July 15, 2009 3:04 PM
To: AUDITORY@xxxxxxxxxxxxxxx
Subject: Re: [AUDITORY] frequency to mel formula
We discussed this last year. See
http://www.auditory.org/mhonarc/2008/msg00191.html
http://www.auditory.org/mhonarc/2008/msg00189.html
and the surrounding thread.
I think the actual origin is Fant in a paper in Swedish from 1949,
summarized in his 1973 book:
Fant, C G M "Analys av de svenska konsonantljuden" LM Ericsson
protokoll H/P 1064, 1949: 139pp.
referenced on p. 48 of
Fant, G "Speech Sounds and Features", MIT Press, 1973.
but Fant uses log(1+f/1000). The log(1+f/700) was attributed to
O'Shaughnessy, D. (1978) Speech communication: Human and machine.
Addison-Wesley, New York, page 150.
DAn.
On Wed, Jul 15, 2009 at 2:11 PM, James W.
Beauchamp<jwbeauch@xxxxxxxxxxxxxxxxxxxxxx> 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
------------------------------
Date: Wed, 15 Jul 2009 20:54:45 -0500
From: "James W. Beauchamp" <jwbeauch@xxxxxxxxxxxxxxxxxxxxxx>
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.
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End of AUDITORY Digest - 14 Jul 2009 to 15 Jul 2009 (#2009-160)
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