Re: On pitch and periodicity (was "correction to post") (ita katz )


Subject: Re: On pitch and periodicity (was "correction to post")
From:    ita katz  <itakatz@xxxxxxxx>
Date:    Tue, 2 Aug 2011 22:15:11 +0300
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

--20cf3005da2623eaf304a98a919e Content-Type: text/plain; charset=ISO-8859-1 Richard, I almost totally agree with you. My intention wasn't to imply that the auditory system has some arithmetic-related capabilities --- I was just mentioning the simple arithmetic principles. In other words (and relating to a different phenomenon), although the trajectory of a tennis ball flying through air can be modeled by some complex partial differential equations, I would not state that a person catching a flying tennis ball have some part of its brain actually integrating these equations. The only question I wanted to ask, is why there are many references to the missing fundamental as being an auditory illusion, while the periodicity is not an illusion at all. I agree that saying that the auditory system percepts periodicity is oversimplifying and not 100% correct. Thanks for your comments. On Tue, Aug 2, 2011 at 8:49 PM, Richard F. Lyon <DickLyon@xxxxxxxx> wrote: > At 5:55 PM +0300 8/2/11, ita katz wrote: > >> The periodicity is determined by the least-common-multiple of the >> periodicities of the present harmonics, so if (for example) a sound is >> composed of sines of frequencies 200Hz, 300Hz, and 400Hz, the periods are >> 5msec, 3 1/3msec, and 2.5msec, so the least-common-multiple is 10msec (2 >> periods of 5msec, 3 periods of 3.33msec, and 4 periods of 2.5msec), which is >> of course the periodicity of the sum of the sines, or in other words 100Hz. >> (actually it is the same as the greatest-common-divisor of the frequencies). >> > > Ita, that explanation is sort of OK, but as written implies that the > auditory system has the ability to do number-theory operations on periods > (or frequencies), and depends on there being harmonics present and > separately measureable. > > It would be much more robust to say that "The pitch is determined based on > an approximately common periodicity of outputs of the cochlea," which I > believe is consistent with your intent. > > Why is this better? First, it doesn't say the periodicity is determined; > what is determined is the pitch (even that is a bit of stretch, but let's go > with it). Second, it doesn't depend on whether the signal is periodic, that > is, whether harmonics exist. Third, it doesn't depend on being able to > isolate and separately characterize components, harmonic or otherwise. > Fourth, it doesn't need "multiples" (or divisors), but relies on the > property of periodicity that a signal with a given period is also periodic > at multiples of that period, so it only needs to look for "common" > periodicities--which doesn't require any arithmetic, just simple neural > circuits. Fifth, it admits approximation, so that things like "the strike > note of a chime" and noise-based pitch can be accommodated. Sixth, it > recognizes that the cochlea has a role in pitch perception. It's still not > complete or perfect, but I think presents a better picture of how it > actually works, in a form that can be realistically modeled. > > Is this "tortured use of existing signal processing techniques" as Randy > puts it? I don't think so. Is it "a unique way to do frequency analysis > and to meet the dictum in biology that 'form follows function'"? Sure, why > not? But why call it "frequency analysis"? How about "a unique way to do > sound analysis" (if by "unique" we mean common to many animals)? > > I do have some sympathy for Randy's concern that we are far from a complete > understanding, and that hearing aids are not as good as they would be if we > understood better, but yes, he sounds way too harsh in overblowing it so. > I'm wondering what's behind that, and whether it's just confusion about all > the confusing literature on pitch perception, which I agree is a complicated > mess -- or is the problem, indicated by Randy's previous posts, just that he > doesn't understand basic linear systems and signal processing, and that's > why it all seems "tortured"? > > Dick > --20cf3005da2623eaf304a98a919e Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable <div dir=3D"ltr">Richard,<br><br>I almost totally agree with you. My intent= ion wasn&#39;t to imply that the auditory system has some arithmetic-relate= d capabilities --- I was just mentioning the simple arithmetic principles. = <br> <br>In other words (and relating to a different phenomenon), although the t= rajectory of a tennis ball flying through air can be modeled by some comple= x partial differential equations, I would not state that a person catching = a flying tennis ball have some part of its brain actually integrating these= equations.<br> <br>The only question I wanted to ask, is why there are many references to = the missing fundamental as being an auditory illusion, while the periodicit= y is not an illusion at all. I agree that saying that the auditory system p= ercepts periodicity is oversimplifying and not 100% correct.<br> <br>Thanks for your comments.<br><br><br><div class=3D"gmail_quote">On Tue,= Aug 2, 2011 at 8:49 PM, Richard F. Lyon <span dir=3D"ltr">&lt;<a href=3D"m= ailto:DickLyon@xxxxxxxx">DickLyon@xxxxxxxx</a>&gt;</span> wrote:<br><blockquo= te class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc so= lid;padding-left:1ex;"> At 5:55 PM +0300 8/2/11, ita katz wrote:<br> <blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1p= x #ccc solid;padding-left:1ex"> The periodicity is determined by the least-common-multiple of the periodici= ties of the present harmonics, so if (for example) a sound is composed of s= ines of frequencies 200Hz, 300Hz, and 400Hz, the periods are 5msec, 3 1/3ms= ec, and 2.5msec, so the least-common-multiple is 10msec (2 periods of 5msec= , 3 periods of 3.33msec, and 4 periods of 2.5msec), which is of course the = periodicity of the sum of the sines, or in other words 100Hz. (actually it = is the same as the greatest-common-divisor of the frequencies).<br> </blockquote> <br> Ita, that explanation is sort of OK, but as written implies that the audito= ry system has the ability to do number-theory operations on periods (or fre= quencies), and depends on there being harmonics present and separately meas= ureable.<br> <br> It would be much more robust to say that &quot;The pitch is determined base= d on an approximately common periodicity of outputs of the cochlea,&quot; w= hich I believe is consistent with your intent.<br> <br> Why is this better? =A0First, it doesn&#39;t say the periodicity is determi= ned; what is determined is the pitch (even that is a bit of stretch, but le= t&#39;s go with it). =A0Second, it doesn&#39;t depend on whether the signal= is periodic, that is, whether harmonics exist. =A0Third, it doesn&#39;t de= pend on being able to isolate and separately characterize components, harmo= nic or otherwise. =A0Fourth, it doesn&#39;t need &quot;multiples&quot; (or = divisors), but relies on the property of periodicity that a signal with a g= iven period is also periodic at multiples of that period, so it only needs = to look for &quot;common&quot; periodicities--which doesn&#39;t require any= arithmetic, just simple neural circuits. =A0Fifth, it admits approximation= , so that things like &quot;the strike note of a chime&quot; and noise-base= d pitch can be accommodated. =A0Sixth, it recognizes that the cochlea has a= role in pitch perception. =A0It&#39;s still not complete or perfect, but I= think presents a better picture of how it actually works, in a form that c= an be realistically modeled.<br> <br> Is this &quot;tortured use of existing signal processing techniques&quot; a= s Randy puts it? =A0I don&#39;t think so. =A0Is it &quot;a unique way to do= frequency analysis and to meet the dictum in biology that &#39;form follow= s function&#39;&quot;? =A0Sure, why not? =A0But why call it &quot;frequency= analysis&quot;? =A0How about &quot;a unique way to do sound analysis&quot;= (if by &quot;unique&quot; we mean common to many animals)?<br> <br> I do have some sympathy for Randy&#39;s concern that we are far from a comp= lete understanding, and that hearing aids are not as good as they would be = if we understood better, but yes, he sounds way too harsh in overblowing it= so. =A0I&#39;m wondering what&#39;s behind that, and whether it&#39;s just= confusion about all the confusing literature on pitch perception, which I = agree is a complicated mess -- or is the problem, indicated by Randy&#39;s = previous posts, just that he doesn&#39;t understand basic linear systems an= d signal processing, and that&#39;s why it all seems &quot;tortured&quot;?<= br> <br> Dick<br> </blockquote></div><br></div> --20cf3005da2623eaf304a98a919e--


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