Subject: Re: [AUDITORY] Number of critical bands in human hearing? From: Christopher Shera <christopher.shera@xxxxxxxx> Date: Thu, 14 Sep 2023 06:21:21 -0700--00000000000024a2c10605518ee9 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable Oops! I messed that calculation up by mistakenly calculating N(200,20000) rather than N(20,20000). Whereas the former is in the low 60s, the number of ERBs spanning 20 Hz to 20 kHz is closer to 70. Sorry for the confusion. Chris On Thu, Sep 14, 2023 at 5:43=E2=80=AFAM Christopher Shera < christopher.shera@xxxxxxxx> wrote: > If one does the calculation Dick suggests, then the number of ERBs betwee= n > frequencies fa and fb is > N(fa,fb) =3D \int_{fa}^{fb} (1/ERB(f)) df > where ERB(f) is the ERB at frequency f. > > Using either of the approximate formulae for Qerb(f) at low sound levels > given here > <https://apg.mechanicsofhearing.org/downloads/papers/Leschke-Orellana-She= ra-Oxenham-HearRes-2022.pdf> > (Leschke J, Rodriguez-Orellana G, Shera CA, Oxenham AJ. Auditory filter > shapes derived from simultaneous and forward masking at low frequencies: > Implications for human cochlear tuning. Hear Res 2022; 420:108500) yields= N > approx 60 over the range 20 Hz to 20 kHz. > > Chris > > On Wed, Sep 13, 2023 at 10:49=E2=80=AFPM Richard F. Lyon <dicklyon@xxxxxxxx= g> wrote: > >> I think critical bands are not discrete countable things. >> But if you want to divide up the range of 20 Hz to 20 kHz into CB-size >> bands, then there should be an answer, though it will be more at low sou= nd >> levels than at high sound levels. 24 sounds plausible for moderate soun= d >> level. If you count ERBs at low level, you'll get more than that, maybe >> about 40. >> Dick >> >> >> On Wed, Sep 13, 2023 at 9:14=E2=80=AFPM David Jackson Morris <dmorris@xxxxxxxx= m.ku.dk> >> wrote: >> >>> Dear all, >>> >>> >>> >>> In teaching an undergrad course on hearing science the students have >>> asked, how many critical bands are there in normal healthy hearing? The >>> text that we use says that there are 24. If I ask ChatGPT it also cit= es >>> Fletcher and Munson=E2=80=99s estimation of 24, but what would it know.= . . >>> >>> >>> >>> Am I right in suspecting that this may have been revised upwards at som= e >>> stage (?). Is the collective wisdom of the list able to help with this= or >>> point to an authoritative source? >>> >>> >>> >>> Cheers >>> >>> David >>> >>> >>> >>> >>> >>> *David Jackson Morris, PhD, LTCL* >>> >>> Associate Professor/Lektor >>> >>> >>> >>> *University of Copenhagen/K=C3=B8benhavns Universitet* >>> >>> Speech Pathology and Audiology/Audiologop=C3=A6di >>> >>> Department of Nordic Studies and Linguistics/Institut for Nordiske >>> Studier og Sprogvidenskab >>> >>> Emil Holms Kanal 2 >>> >>> 2300 Copenhagen S/K=C3=B8benhavn S >>> >>> >>> >>> Department Homepage >>> <https://nors.ku.dk/english/staff/?pure=3Den/persons/398661> >>> >>> >>> >>> >>> >>> [image: Title: SD_Logo] - >>> >>> >>> >>> S=C3=A5dan beskytter vi persondata >>> <https://informationssikkerhed.ku.dk/persondatabeskyttelse/privatlivspo= litik/> >>> >>> >>> >>> >>> >> > > -- > Christopher Shera > Auditory Physics Group <http://apg.mechanicsofhearing.org> > Caruso Department of Otolaryngology > Keck School of Medicine > University of Southern California > > "... to simplify means to eliminate the unnecessary so that > the necessary may speak." -- Hans Hofmann > --=20 Christopher Shera Auditory Physics Group <http://apg.mechanicsofhearing.org> Caruso Department of Otolaryngology Keck School of Medicine University of Southern California "... to simplify means to eliminate the unnecessary so that the necessary may speak." -- Hans Hofmann --00000000000024a2c10605518ee9 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable <div dir=3D"ltr"><div class=3D"gmail_default" style=3D"font-size:small">Oop= s! I messed that calculation up by mistakenly calculating N(200,20000) rath= er than N(20,20000).=C2=A0</div><div class=3D"gmail_default" style=3D"font-= size:small">Whereas the former is in the low 60s, the number of ERBs spanni= ng 20 Hz to 20 kHz is closer to 70.</div><div class=3D"gmail_default" style= =3D"font-size:small">Sorry for the confusion.</div><div class=3D"gmail_defa= ult" style=3D"font-size:small"><br></div><div class=3D"gmail_default" style= =3D"font-size:small">Chris</div></div><br><div class=3D"gmail_quote"><div d= ir=3D"ltr" class=3D"gmail_attr">On Thu, Sep 14, 2023 at 5:43=E2=80=AFAM Chr= istopher Shera <<a href=3D"mailto:christopher.shera@xxxxxxxx">christoph= er.shera@xxxxxxxx</a>> wrote:<br></div><blockquote class=3D"gmail_quote= " style=3D"margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);= padding-left:1ex"><div dir=3D"ltr"><div class=3D"gmail_default" style=3D"fo= nt-size:small">If one does the calculation Dick suggests, then the number o= f ERBs between frequencies fa and fb is</div><div class=3D"gmail_default" s= tyle=3D"font-size:small">=C2=A0 =C2=A0 N(fa,fb) =3D \int_{fa}^{fb} (1/ERB(f= )) df</div><div class=3D"gmail_default" style=3D"font-size:small">where ERB= (f) is the ERB at frequency f.</div><div class=3D"gmail_default" style=3D"f= ont-size:small"><br></div><div class=3D"gmail_default" style=3D"font-size:s= mall">Using either of the approximate formulae for Qerb(f) at low sound lev= els given <a href=3D"https://apg.mechanicsofhearing.org/downloads/papers/Le= schke-Orellana-Shera-Oxenham-HearRes-2022.pdf" target=3D"_blank">here</a> (= Leschke J, Rodriguez-Orellana G, Shera CA, Oxenham AJ. Auditory filter shap= es derived from simultaneous and forward masking at low frequencies: Implic= ations for human cochlear tuning. Hear Res 2022; 420:108500) yields N appro= x 60 over the range 20 Hz to 20 kHz.</div><div class=3D"gmail_default" styl= e=3D"font-size:small"><br></div><div class=3D"gmail_default" style=3D"font-= size:small">Chris</div></div><br><div class=3D"gmail_quote"><div dir=3D"ltr= " class=3D"gmail_attr">On Wed, Sep 13, 2023 at 10:49=E2=80=AFPM Richard F. = Lyon <<a href=3D"mailto:dicklyon@xxxxxxxx" target=3D"_blank">dicklyon@xxxxxxxx= .org</a>> wrote:<br></div><blockquote class=3D"gmail_quote" style=3D"mar= gin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1= ex"><div dir=3D"ltr"><div class=3D"gmail_default" style=3D"font-size:small"= >I think critical bands are not discrete countable things.</div><div class= =3D"gmail_default" style=3D"font-size:small">But if you want to divide up t= he range of 20 Hz to 20 kHz into CB-size bands, then there should be an ans= wer, though it will be more at low sound levels than at high sound levels.= =C2=A0 24 sounds plausible for moderate sound level.=C2=A0 If you count ERB= s at low level, you'll get more than that, maybe about 40.<br></div><di= v class=3D"gmail_default" style=3D"font-size:small">Dick</div><div class=3D= "gmail_default" style=3D"font-size:small"><br></div></div><br><div class=3D= "gmail_quote"><div dir=3D"ltr" class=3D"gmail_attr">On Wed, Sep 13, 2023 at= 9:14=E2=80=AFPM David Jackson Morris <<a href=3D"mailto:dmorris@xxxxxxxx= dk" target=3D"_blank">dmorris@xxxxxxxx</a>> wrote:<br></div><blockquote= class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-left:1px so= lid rgb(204,204,204);padding-left:1ex"><div> <div lang=3D"DA"> <div> <p class=3D"MsoNormal"><span lang=3D"EN-US">Dear all,<u></u><u></u></span><= /p> <p class=3D"MsoNormal"><span lang=3D"EN-US"><u></u>=C2=A0<u></u></span></p> <p class=3D"MsoNormal"><span lang=3D"EN-US">In teaching an undergrad course= on hearing science the students have asked, how many critical bands are th= ere in normal healthy hearing? The text that we use says that there are 24.= =C2=A0 =C2=A0If I ask ChatGPT it also cites Fletcher and Munson=E2=80=99s estimation of 24, but what would it know. . . =C2=A0<= u></u><u></u></span></p> <p class=3D"MsoNormal"><span lang=3D"EN-US"><u></u>=C2=A0<u></u></span></p> <p class=3D"MsoNormal"><span lang=3D"EN-US">Am I right in suspecting that t= his may have been revised upwards at some stage (?).=C2=A0 Is the collectiv= e wisdom of the list able to help with this or point to an authoritative so= urce?=C2=A0 <u></u><u></u></span></p> <p class=3D"MsoNormal"><span lang=3D"EN-US"><u></u>=C2=A0<u></u></span></p> <p class=3D"MsoNormal"><span lang=3D"EN-US">Cheers<u></u><u></u></span></p> <p class=3D"MsoNormal"><span lang=3D"EN-US">David<u></u><u></u></span></p> <p class=3D"MsoNormal"><span lang=3D"EN-US"><u></u>=C2=A0<u></u></span></p> <p class=3D"MsoNormal"><span lang=3D"EN-US"><u></u>=C2=A0<u></u></span></p> <div> <div> <p class=3D"MsoNormal" style=3D"line-height:8pt"><b><span lang=3D"EN-US" st= yle=3D"font-size:7.5pt;font-family:Verdana,sans-serif;color:gray">David Jac= kson Morris, PhD, LTCL</span></b><span lang=3D"EN-US" style=3D"font-size:12= pt;font-family:"Times New Roman",serif;color:black"><u></u><u></u= ></span></p> <p class=3D"MsoNormal" style=3D"line-height:8pt"><span lang=3D"EN-US" style= =3D"font-size:7.5pt;font-family:Verdana,sans-serif;color:gray">Associate Pr= ofessor/Lektor</span><span lang=3D"EN-US" style=3D"font-size:12pt;font-fami= ly:"Times New Roman",serif;color:black"><u></u><u></u></span></p> <p class=3D"MsoNormal" style=3D"line-height:8pt"><span lang=3D"EN-US" style= =3D"font-size:7.5pt;font-family:Verdana,sans-serif;color:gray">=C2=A0</span= ><span lang=3D"EN-US" style=3D"font-size:12pt;font-family:"Times New R= oman",serif;color:black"><u></u><u></u></span></p> <p class=3D"MsoNormal" style=3D"line-height:8pt"><b><span lang=3D"EN-US" st= yle=3D"font-size:7.5pt;font-family:Verdana,sans-serif;color:gray">Universit= y of Copenhagen/K=C3=B8benhavns Universitet</span></b><span lang=3D"EN-US" = style=3D"font-size:12pt;font-family:"Times New Roman",serif;color= :black"><u></u><u></u></span></p> <p class=3D"MsoNormal" style=3D"line-height:8pt"><span lang=3D"EN-US" style= =3D"font-size:7.5pt;font-family:Verdana,sans-serif;color:gray">Speech Patho= logy and Audiology/Audiologop=C3=A6di<u></u><u></u></span></p> <p class=3D"MsoNormal" style=3D"line-height:8pt"><span style=3D"font-size:7= .5pt;font-family:Verdana,sans-serif;color:gray">Department of Nordic Studie= s and Linguistics/Institut for Nordiske Studier og Sprogvidenskab<u></u><u>= </u></span></p> <p class=3D"MsoNormal" style=3D"line-height:8pt"><span lang=3D"SV" style=3D= "font-size:7.5pt;font-family:Verdana,sans-serif;color:gray">Emil Holms Kana= l 2</span><span style=3D"font-size:12pt;font-family:"Times New Roman&q= uot;,serif;color:black"><u></u><u></u></span></p> <p class=3D"MsoNormal" style=3D"line-height:8pt"><span style=3D"font-size:7= .5pt;font-family:Verdana,sans-serif;color:gray">2300 Copenhagen S/K=C3=B8be= nhavn S<u></u><u></u></span></p> <p class=3D"MsoNormal" style=3D"line-height:8pt"><span style=3D"font-size:7= .5pt;font-family:Verdana,sans-serif;color:gray"><u></u>=C2=A0<u></u></span>= </p> <p class=3D"MsoNormal" style=3D"line-height:8pt"><span style=3D"font-size:7= .5pt;font-family:Verdana,sans-serif;color:gray"><a href=3D"https://nors.ku.= dk/english/staff/?pure=3Den/persons/398661" target=3D"_blank"><span style= =3D"color:rgb(5,99,193)">Department Homepage</span></a></span><span style=3D"font-size:12pt;font-family:"= Times New Roman",serif;color:black"><u></u><u></u></span></p> <p class=3D"MsoNormal" style=3D"line-height:8pt"><span style=3D"font-size:7= .5pt;font-family:Verdana,sans-serif;color:gray">=C2=A0</span><span style=3D= "font-size:12pt;font-family:"Times New Roman",serif;color:black">= <u></u><u></u></span></p> <p class=3D"MsoNormal" style=3D"line-height:8pt"><span style=3D"font-size:7= .5pt;font-family:Verdana,sans-serif;color:gray">=C2=A0</span><span style=3D= "font-size:12pt;font-family:"Times New Roman",serif;color:black">= <u></u><u></u></span></p> <p class=3D"MsoNormal" style=3D"line-height:12pt"><span style=3D"font-size:= 7.5pt;font-family:Verdana,sans-serif;color:gray"><img border=3D"0" width=3D= "252" height=3D"87" style=3D"width: 2.625in; height: 0.9062in;" id=3D"m_-33= 69799585182331333m_-1338531396353553701m_-5301221719702691337Billede_x0020_= 1" alt=3D"Title: SD_Logo">=C2=A0 -</span><span style=3D"font-size:12pt;font-family:"Times New Roman&qu= ot;,serif;color:black"><u></u><u></u></span></p> <p class=3D"MsoNormal" style=3D"line-height:8pt"><span style=3D"font-size:7= .5pt;font-family:Verdana,sans-serif;color:gray">=C2=A0</span><span style=3D= "font-size:12pt;font-family:"Times New Roman",serif;color:black">= <u></u><u></u></span></p> <p class=3D"MsoNormal"><span style=3D"font-size:12pt;font-family:"Time= s New Roman",serif;color:black"><a href=3D"https://informationssikkerh= ed.ku.dk/persondatabeskyttelse/privatlivspolitik/" target=3D"_blank"><span = style=3D"font-size:7.5pt;font-family:Verdana,sans-serif;color:gray;text-dec= oration:none">S=C3=A5dan beskytter vi persondata</span></a><u></u><u></u></span></p> </div> </div> <p class=3D"MsoNormal"><u></u>=C2=A0<u></u></p> <p class=3D"MsoNormal"><u></u>=C2=A0<u></u></p> </div> </div> </div></blockquote></div> </blockquote></div><br clear=3D"all"><div><br></div><span class=3D"gmail_si= gnature_prefix">-- </span><br><div dir=3D"ltr" class=3D"gmail_signature"><d= iv dir=3D"ltr"><div><div dir=3D"ltr"><div><div dir=3D"ltr"><div><span style= =3D"font-family:arial,helvetica,sans-serif"><span></span><span><font color= =3D"#888888">Christopher Shera=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 = =C2=A0 =C2=A0 =C2=A0 =C2=A0 </font></span><br></span></div><div><span style= =3D"font-family:arial,helvetica,sans-serif"><span></span><span><font color= =3D"#888888"> <a href=3D"http://apg.mechanicsofhearing.org" target=3D"_blan= k">Auditory Physics Group</a><br></font></span></span></div><div><span styl= e=3D"font-family:arial,helvetica,sans-serif"><span><font color=3D"#888888">= Caruso Department of Otolaryngology<br></font></span></span></div><div><spa= n style=3D"font-family:arial,helvetica,sans-serif"><span><font color=3D"#88= 8888">Keck School of Medicine<br></font></span></span></div><div><span styl= e=3D"font-family:arial,helvetica,sans-serif"><span><font color=3D"#888888">= University of Southern California<br></font></span></span></div><div><span = style=3D"font-family:arial,helvetica,sans-serif"><span><font color=3D"#8888= 88"><br>"... to simplify means to eliminate the unnecessary so that</f= ont></span></span><span style=3D"font-family:arial,helvetica,sans-serif"><s= pan><font color=3D"#888888"><br>the necessary may speak." =C2=A0-- Han= s Hofmann</font></span></span></div></div></div></div></div></div></div> </blockquote></div><br clear=3D"all"><div><br></div><span class=3D"gmail_si= gnature_prefix">-- </span><br><div dir=3D"ltr" class=3D"gmail_signature"><d= iv dir=3D"ltr"><div><div dir=3D"ltr"><div><div dir=3D"ltr"><div><span style= =3D"font-family:arial,helvetica,sans-serif"><span></span><span><font color= =3D"#888888">Christopher Shera=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 = =C2=A0 =C2=A0 =C2=A0 =C2=A0 </font></span><br></span></div><div><span style= =3D"font-family:arial,helvetica,sans-serif"><span></span><span><font color= =3D"#888888"> <a href=3D"http://apg.mechanicsofhearing.org" target=3D"_blan= k">Auditory Physics Group</a><br></font></span></span></div><div><span styl= e=3D"font-family:arial,helvetica,sans-serif"><span><font color=3D"#888888">= Caruso Department of Otolaryngology<br></font></span></span></div><div><spa= n style=3D"font-family:arial,helvetica,sans-serif"><span><font color=3D"#88= 8888">Keck School of Medicine<br></font></span></span></div><div><span styl= e=3D"font-family:arial,helvetica,sans-serif"><span><font color=3D"#888888">= University of Southern California<br></font></span></span></div><div><span = style=3D"font-family:arial,helvetica,sans-serif"><span><font color=3D"#8888= 88"><br>"... to simplify means to eliminate the unnecessary so that</f= ont></span></span><span style=3D"font-family:arial,helvetica,sans-serif"><s= pan><font color=3D"#888888"><br>the necessary may speak." =C2=A0-- Han= s Hofmann</font></span></span></div></div></div></div></div></div></div> --00000000000024a2c10605518ee9--