Re: two cycles

["Alain de Cheveigne'" <Alain.de.Cheveigne@xxxxxx>]

An illuminating contribution to understanding 
this paradox (paradox because accurate frequency 
measurement of a short stimulus seems to 
contradict the time-frequency tradeoff rules of 
Heisenberg/Gabor) is that of J.O. Nordmark (1968, 
1970), who credits Kneser (1948) for pointing out 
that we use the same word 'frequency' for two 
distinct concepts (see quotation below).

Sorry for the plug, but I'd also recommend my 
chapter on 'Pitch perception models' in the 
recent book on pitch by Plack, Oxenham, Fay and 
Popper.  It addresses many such issues related to 
pitch perception and periodicity analysis.

A final word of caution: the fact that subjects 
agree to report two-period sinusoidal stimuli as 
'pitch-like' does not imply that they are 
actually measuring the period.  The fact that 
they can perform accurate frequency 
discrimination on such stimuli also does not 
imply that the discrimination is based on pitch 
as determined by measurement of the fundamental 
period.  They could be using other cues (such as 
timbre) that co-vary with frequency.  To narrow 
the interpretation down to pitch (or abstraction 
of fundamental frequency from other possibly 
covarying cues) might require comparing pitch 
between complex stimuli that differ in timbre 
across intervals.  I'm not sure if this has been 
done.

Alain

---
@article{
   Author = {Nordmark, J.O.},
   Title = {Mechanisms of frequency discrimination},
   Journal = {J. Acoust. Soc. Am.},
   Volume = {44},
   Pages = {1533-1540},
   Note = {"...Kneser (1948) was the first to 
point out that there are two separate
meanings of frequency in common use, each measuring and defining
different physical quantities.  The first of these,
phase frequency, he defines as the reciprocal of the time interval between
two events of equal phase. The accuracy with which this can be determined
is, in principle, independent of the duration of the waveform under
investigation and therefore not subject to the uncertainty relation
between time and frequency. The second, group frequency, is the concept
used in the Fourier analysis of periodic waves.  For a time function of
limited duration, an analysis will yield a series of sine and cosine waves
grouped around the phase frequency.  No exact value can be given the group
frequency, which is thus subject to the uncertainty relation."},
 Year = {1968} }

@incollection{
   Author = {Nordmark, J.O.},
   Title = {Time and frequency analysis},
   BookTitle = {Foundations of modern auditory theory},
   Editor = {Tobias, J.V.},
   Publisher = {Academic Press},
   Address = {New York},
   Pages = {55-83},
 Year = {1970} }

@article{
   Author = {Kneser},
   Title = {Bemerkungen über Definition und Messung der Frequenz},
   Journal = {Archiv der Elektrishen Übertragung},
   Volume = {2},
   Pages = {167-169},
 Year = {1948} }

@incollection{
   Author = {de Cheveigné, A.},
   Title = {Pitch perception models},
   BookTitle = {Pitch - Neural coding and perception},
   Editor = {Plack, C.J. and Oxenham, A. and Fay, R.R. and Popper, A.N.},
   Publisher = {Springer},
   Address = {New York},
   Pages = {169-233},
 Year = {2005} }


> Hi list,
>
> In many of the papers published by Georg von 
> Békésy he makes the statement that the 
> fundamental frequency was determined by the 
> auditory system "even when the stimulus was only 
> two cycles" in length. In at least one of his 
> publications {The Missing Fundamental and 
> Periodicity Detection in Hearing  JASA 1972 512) 
> 631-637) he attributes this to his own 
> experiments and to a paper by Savart.[Annalen 
> der Physik und Chemie 1840 53 ( ) 555-561 in 
> german]. It is quite true that Savart found that 
> the fundamental was determined in two cycles but 
> it was published in an earlier paper by Savart 
> (Ueber die Empfindlichkeit des Gehörorgans Felix 
> Savart Annalen der Physik und Chemie 1830 20( ) 
> 290-304 in german)and no mention of the two 
> cycles is mentioned in the citation by 
> Békésy. Actually from a historical point of view 
> the original paper by Felix Savart was published 
> in French in: Annales de chimie et de Physique 
> 1830 44 ( )  337-352 in French.
>
> Can anyone point me to literature which shows 
> how the auditory system performs the "two cycle" 
> feat, or to papers which show how such a "two 
> cycle" feat might be acomplished mathematically 
> or to any papers of a more recent origin which 
> discusses this ability.
>
> Thanks,
>
> Fred
> --
> Fred Herzfeld, MIT '54
> 78 Glynn Marsh Drive #59
> Brunswick, Ga.31525
> USA