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Re: Robust method of fundamental frequency estimation.

The only comment I have is that pitch is indeed a stochastic property
(described neatly by Goldstein) and thus a pitch algorihtm should not
predict "THE PITCH" but the "PDF of the PITCH". In 1988 I wrote a
stochastic subharmonic pitch extraction algorithm that uses the idea of
generating gaussian subharmonic function from which the PITCH PDF can be
predicted, the idea was patented by Philips, a description of the idea
can be found in chapter 5 of my PhD. (see

John Beerends
TNO Information and Communication Technology 
The Netherlands

-----Original Message-----
From: AUDITORY - Research in Auditory Perception
[mailto:AUDITORY@xxxxxxxxxxxxxxx] On Behalf Of Fred Herzfeld
Sent: Thursday, February 01, 2007 01:38
To: AUDITORY@xxxxxxxxxxxxxxx
Subject: Re: Robust method of fundamental frequency estimation.

Hello Roisin,

I am sure that you do not really want to calculate the "fundamental" 
frequency of your note. The fundamental frequency is a well defined
mathematical concept while on the other hand "pitch" is what we hear and
is defined by the receiver (the ear in your case). It is also
unfortunate that many well known researchers use the word "inharmonic" 
erroneously. As part of a larger work on "hearing" I have written a
small section entitled "The Fundamental Frequency of a Vibration" which
I am sending as an attachment. I think you and others on this list will
find it most interesting. One problem that I do not mention in the above
section is that the pitch of a note actually changes with amplitude. It
is something that you should consider. A section on "pitch" is not yet

If anyone on the list would  like to comment on tne attachment I am
ready to defend it.


Roisin Loughran wrote:
> Dear list,
> I was wondering if any of you know the most robust way to calculate 
> the fundamental frequency of a note across the range of a variety of 
> instruments?
> I'm currently working on a matlab program and have tried using the 
> auto-correlation method and the cepstrum method but have found that 
> these both have difficulty in calculating f0 of timbre-rich tones such

> as those from a piano - particularly in the lower pitch ranges. Does 
> anyone know of a method that is more reliable in these regions or is 
> it necessary that I investigate such complex tones by a different
>  From examining a number of the FFTs from these signals it is tempting

> to just pick the first strongest partial - the complex overtones just 
> seem to confuse the more complicated algorithms, but I realise that 
> this is hardly a reliable approach.
> Any suggestion would be greatly appreciated, Thanks in advance,
> Roisin Loughran
> ----------------------------------------------------------------------
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Fred Herzfeld, MIT '54
78 Glynn Marsh Drive #59
Brunswick, Ga.31525

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