Subject: Re: [AUDITORY] Number of critical bands in human hearing? From: Christopher Shera <christopher.shera@xxxxxxxx> Date: Thu, 14 Sep 2023 05:43:07 -0700--0000000000006bc28006055105d6 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable If one does the calculation Dick suggests, then the number of ERBs between 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-Shera= -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>= 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 soun= d > levels than at high sound levels. 24 sounds plausible for moderate sound > 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= .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 cite= s >> 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 some >> 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/privatlivspol= itik/> >> >> >> >> >> > --=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 --0000000000006bc28006055105d6 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">If = one does the calculation Dick suggests, then the number of ERBs between fre= quencies fa and fb is</div><div class=3D"gmail_default" style=3D"font-size:= small">=C2=A0 =C2=A0 N(fa,fb) =3D \int_{fa}^{fb} (1/ERB(f)) df</div><div cl= ass=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"font-size:small"><b= r></div><div class=3D"gmail_default" style=3D"font-size:small">Using either= of the approximate formulae for Qerb(f) at low sound levels given <a href= =3D"https://apg.mechanicsofhearing.org/downloads/papers/Leschke-Orellana-Sh= era-Oxenham-HearRes-2022.pdf">here</a> (Leschke J, Rodriguez-Orellana G, Sh= era CA, Oxenham AJ. Auditory filter shapes derived from simultaneous and fo= rward masking at low frequencies: Implications for human cochlear tuning. H= ear Res 2022; 420:108500) yields N approx 60 over the range 20 Hz to 20 kHz= .</div><div class=3D"gmail_default" style=3D"font-size:small"><br></div><di= v class=3D"gmail_default" style=3D"font-size:small">Chris</div></div><br><d= iv 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">dicklyon@xxxxxxxx</a>> wrote:<br></div><blockquote class=3D"gma= il_quote" style=3D"margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,2= 04,204);padding-left:1ex"><div dir=3D"ltr"><div class=3D"gmail_default" sty= le=3D"font-size:small">I think critical bands are not discrete countable th= ings.</div><div class=3D"gmail_default" style=3D"font-size:small">But if yo= u want to divide up the range of 20 Hz to 20 kHz into CB-size bands, then t= here should be an answer, though it will be more at low sound levels than a= t high sound levels.=C2=A0 24 sounds plausible for moderate sound level.=C2= =A0 If you count ERBs at low level, you'll get more than that, maybe ab= out 40.<br></div><div class=3D"gmail_default" style=3D"font-size:small">Dic= k</div><div class=3D"gmail_default" style=3D"font-size:small"><br></div></d= iv><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"ma= ilto:dmorris@xxxxxxxx" target=3D"_blank">dmorris@xxxxxxxx</a>> wrote:<= br></div><blockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8e= x;border-left:1px solid 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_-13= 38531396353553701m_-5301221719702691337Billede_x0020_1" alt=3D"Title: SD_Lo= go">=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> --0000000000006bc28006055105d6--