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'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"><<a href=3D"m= ailto:DickLyon@xxxxxxxx">DickLyon@xxxxxxxx</a>></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 "The pitch is determined base= d on an approximately common periodicity of outputs of the cochlea," w= hich I believe is consistent with your intent.<br> <br> Why is this better? =A0First, it doesn't say the periodicity is determi= ned; what is determined is the pitch (even that is a bit of stretch, but le= t's go with it). =A0Second, it doesn't depend on whether the signal= is periodic, that is, whether harmonics exist. =A0Third, it doesn't de= pend on being able to isolate and separately characterize components, harmo= nic or otherwise. =A0Fourth, it doesn't need "multiples" (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 "common" periodicities--which doesn't require any= arithmetic, just simple neural circuits. =A0Fifth, it admits approximation= , so that things like "the strike note of a chime" and noise-base= d pitch can be accommodated. =A0Sixth, it recognizes that the cochlea has a= role in pitch perception. =A0It'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 "tortured use of existing signal processing techniques" a= s Randy puts it? =A0I don't think so. =A0Is it "a unique way to do= frequency analysis and to meet the dictum in biology that 'form follow= s function'"? =A0Sure, why not? =A0But why call it "frequency= analysis"? =A0How about "a unique way to do sound analysis"= (if by "unique" we mean common to many animals)?<br> <br> I do have some sympathy for Randy'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'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 an= d signal processing, and that's why it all seems "tortured"?<= br> <br> Dick<br> </blockquote></div><br></div> --20cf3005da2623eaf304a98a919e--