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Re: 1/f spectra

Dear Jan,

The following page appears to have some useful links pertaining to
your topic.


The classic paper you're probably thinking of is by Voss and Clarke
(1975), "1/f noise in music and speech", Nature, 258:317-318

You can also try a paper by David Brillinger (1998):

"An investigation of the Second-and Higher-order Spectra of Music"

The abstract for that paper is:

"For a variety of musical pieces the following questions are
addressed: Are the power spectra of 1/f form? Are the processes
Gaussian? Are the higher-order spectra of 1/f form? Are the processes
linear? Is long-range dependence present? Both score and acoustical
signal representations of music are discussed and considered.
Parametric forms are fit to sample spectra. Approximate distributions
of the quantities computed are basic to drawing inferences. In
summary, 1/f seems to be a reasonable approximation to the overall
spectra of a number of pieces selected to be representative of a broad
population. The checks for Gaussianity, really for bispectrum 0, in
each case reject that hypothesis. The checks for linearity, really for
bicoherence, reject that hypothesis in the case of the instantaneous
power of the
acoustical signal but not for the zero crossings of the signal or the
score representation."

I don't know where it was published though it can be found at



Craig Atencio
Department of Bioengineering UCSF/UCB
W.M. Keck Center for Integrative Neuroscience UCSF
513 Parnassus Ave.
HSE 834, Box 0732
San Francisco, CA, 94143-0732, USA
office: 415-476-1762 (UCSF)
cell: 510-708-6346

----- Original Message -----
From: "Jan Schnupp" <jan.schnupp@PHYSIOL.OX.AC.UK>
Sent: Friday, November 14, 2003 10:29 AM
Subject: 1/f spectra

> Dear List,
> I have heard it said on a number of occasions that 1/f spectra are
> commonly encountered among natural signals, and one might perhaps
> the auditory system to reflect this fact in its design
> (perhaps the fact that auditory filters get wider at higher CF and
> approximately logarithmically spaced is a simple relfection of the
> nature of many sounds?)
> However, I don't know ANY literature that discusses this 1/f
phenomenon. I
> seem to remember somebody mentioning at a conference that there is a
> "classic" Science paper that marks the "discovery of the 1/f
> If that is the case, I'd love to know the citation for it. Any other
> references for other (particularly recent!) work relating to 1/f and
> role in audition would of course also be very welcome. (Even better
> be pdf files of relevant papers, if anyone has any).
> Thank you very much in advance for your help,
> Jan Schnupp
> Dr. Jan Schnupp
> University Laboratory of Physiology
> Parks Road, Oxford OX1 3PT, UK
> Tel: +44-1865-272513  Fax: +44-1865-272469
> E-mail: jan.schnupp@physiol.ox.ac.uk