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*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Re: two cycles*From*: "Alain de Cheveigne'" <Alain.de.Cheveigne@xxxxxx>*Date*: Sat, 4 Nov 2006 10:40:15 +0100*Delivery-date*: Sat Nov 4 04:56:46 2006*In-reply-to*: <454BB628.8040200@alum.mit.edu>*List-help*: <mailto:LISTSERV@LISTS.MCGILL.CA?body=INFO AUDITORY>*List-owner*: <mailto:AUDITORY-request@LISTS.MCGILL.CA>*List-subscribe*: <mailto:AUDITORY-subscribe-request@LISTS.MCGILL.CA>*List-unsubscribe*: <mailto:AUDITORY-unsubscribe-request@LISTS.MCGILL.CA>*References*: <454BB628.8040200@alum.mit.edu>*Reply-to*: "Alain de Cheveigne'" <Alain.de.Cheveigne@xxxxxx>*Sender*: AUDITORY Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>

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

**Follow-Ups**:**Re: two cycles***From:*Mike Ravicz

**References**:**two cycles***From:*Fred Herzfeld

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