Helmholtz and combination tones. (Wiebe Horst )


Subject: Helmholtz and combination tones.
From:    Wiebe Horst  <j.w.horst@xxxxxxxx>
Date:    Fri, 5 Aug 2011 09:35:04 +0200
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

--Apple-Mail-1--784944404 Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes Content-Transfer-Encoding: 7bit For unresolved harmonics there is definitely an influence of phase in single fiber responses. See http://asadl.org/jasa/resource/1/jasman/v88/i6/p2656_s1, figs 10 and 12 Wiebe Horst To me that argues for a strong post-cochlear neural effect. I don't have a library access right now, annoyingly. On Thu, Aug 4, 2011 at 10:36 PM, Richard F. Lyon <DickLyon@xxxxxxxx> wrote: It has been done. You get a stronger pitch percept when the phases give strong envelope modulation, and less pitch percept otherwise, such as for random phases. I don't have a ref handy, but I saw a figure in something I was looking at just the other day. John Pierce's 1991 JASA paper is another example of the pitch depending on the phasing of high harmonics. http://asadl.org/jasa/resource/1/jasman/v90/i4/p1889_s1 Dick At 7:07 PM -0700 8/4/11, James Johnston wrote: > I don't know if it's been done, but it would be interesting to see > what happens when you set up the various harmonics for a missing- > fundamental probe in different phases, and see what happens when > they do and do not all cross zero at the same time. > On Thu, Aug 4, 2011 at 6:16 PM, William Hartmann > <hartmann@xxxxxxxx> wrote: > Dear List, > > A recent post from Randy Randhawa says, "Consider that even > Helmholtz had to appeal to non-linear processes (never really > described) in the auditory system to account for the missing > fundamental and combination tones." > > Because this comment raises questions about what Helmholtz did and > did not describe, I would draw attention to Appendix XII in "On the > Sensation of Tone." There Helmholtz begins with the simple harmonic > oscillator dynamical equation and adds a quadratic term to the > restoring force, clearly conceived as just the second term in an > expansion in the displacement. He solves this to first and second > order in small quantities and finds that the second order term leads > to combination tones, which could include a missing fundamental. > > An interesting feature of his solution is that summation tones are > much weaker than difference tones, which agrees with observation. > Specifically, for two frequencies f1 and f2, the summation tone > amplitude goes as 1/[(f2+f1)^2-fo^2] and the difference tone > amplitude goes as 1/[(f2-f1)^2-fo^2], where fo is the natural > frequency of the oscillator. > > Bill Hartmann > > PS Singularities in the amplitudes occur because there is no damping > in the dynamical equation and resonances are unbounded. > > > > -- > James D. (jj) Johnston > Independent Audio and Electroacoustics Consultant -- James D. (jj) Johnston Independent Audio and Electroacoustics Consultant --Apple-Mail-1--784944404 Content-Type: text/html; charset=US-ASCII Content-Transfer-Encoding: quoted-printable <html><body style=3D"word-wrap: break-word; -webkit-nbsp-mode: space; = -webkit-line-break: after-white-space; ">For unresolved harmonics there = is definitely an influence of phase in single fiber responses. = See&nbsp;<div><a = href=3D"http://asadl.org/jasa/resource/1/jasman/v88/i6/p2656_s1">http://as= adl.org/jasa/resource/1/jasman/v88/i6/p2656_s1</a>, figs 10 and = 12</div><div><br></div><div>Wiebe = Horst<br><div><br></div><div><br></div><div><br></div><div>To me that = argues for a strong post-cochlear neural effect.&nbsp; I don't have a = library access right now, annoyingly.<br><br><div class=3D"gmail_quote">On= Thu, Aug 4, 2011 at 10:36 PM, Richard F. Lyon&nbsp;<span = dir=3D"ltr">&lt;<a = href=3D"mailto:DickLyon@xxxxxxxx">DickLyon@xxxxxxxx</a>&gt;</span>&nbsp;wrot= e:<br><blockquote class=3D"gmail_quote" style=3D"margin-top: 0px; = margin-right: 0px; margin-bottom: 0px; margin-left: 0.8ex; padding-left: = 1ex; border-left-color: rgb(204, 204, 204); border-left-width: 1px; = border-left-style: solid; position: static; z-index: auto; = "><u></u><div><div>It has been done.&nbsp; You get a stronger pitch = percept when the phases give strong envelope modulation, and less pitch = percept otherwise, such as for random phases.&nbsp; I don't have a ref = handy, but I saw a figure in something I was looking at just the other = day.</div><div><br></div><div>John Pierce's 1991 JASA paper is another = example of the pitch depending on the phasing of high = harmonics.</div><div><a = href=3D"http://asadl.org/jasa/resource/1/jasman/v90/i4/p1889_s1" = target=3D"_blank">http://asadl.org/jasa/resource/1/jasman/v90/i4/p1889_s1<= /a></div><div><br></div><div>Dick</div><div><br></div><div><br></div><div>= At 7:07 PM -0700 8/4/11, James Johnston wrote:</div><blockquote = type=3D"cite">I don't know if it's been done, but it would be = interesting to see what happens when you set up the various harmonics = for a missing-fundamental probe in different phases, and see what = happens when they do and do not all cross zero at the same = time.<br></blockquote><blockquote type=3D"cite">On Thu, Aug 4, 2011 at = 6:16 PM, William Hartmann &lt;<a href=3D"mailto:hartmann@xxxxxxxx" = target=3D"_blank">hartmann@xxxxxxxx</a>&gt; wrote:<br><blockquote>Dear = List,<br><br>A recent post from Randy Randhawa says, "Consider that even = Helmholtz had to appeal to non-linear processes (never really described) = in the auditory system to account for the missing fundamental and = combination tones."<br><br>Because this comment raises questions about = what Helmholtz did and did not describe, I would draw attention to = Appendix XII in "On the Sensation of Tone." There Helmholtz begins with = the simple harmonic oscillator dynamical equation and adds a quadratic = term to the restoring force, clearly conceived as just the second term = in an expansion in the displacement. He solves this to first and second = order in small quantities and finds that the second order term leads to = combination tones, which could include a missing fundamental.<br><br>An = interesting feature of his solution is that summation tones are much = weaker than difference tones, which agrees with observation. = Specifically, for two frequencies f1 and f2, the summation tone = amplitude goes as 1/[(f2+f1)^2-fo^2] and the difference tone amplitude = goes as 1/[(f2-f1)^2-fo^2], where fo is the natural frequency of the = oscillator.<br><br>Bill Hartmann<br><br>PS Singularities in the = amplitudes occur because there is no damping in the dynamical equation = and resonances are unbounded.<br></blockquote></blockquote><blockquote = type=3D"cite"><br><br><br>--<br></blockquote><blockquote = type=3D"cite">James D. (jj) Johnston</blockquote><blockquote = type=3D"cite">Independent Audio and Electroacoustics = Consultant</blockquote><div><br></div></div></blockquote></div><br><br = clear=3D"all"><br>--&nbsp;<br><div>James D. (jj) = Johnston</div><div>Independent Audio and Electroacoustics = Consultant</div><div><br></div></div></div></body></html>= --Apple-Mail-1--784944404--


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