Subject: Re: AUDITORY Digest - 10 Aug 2009 to 11 Aug 2009 (#2009-180) From: Jont Allen <jontalle@xxxxxxxx> Date: Wed, 12 Aug 2009 09:50:39 -0500 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>Dick, While your into this, it seems that it would be nice to also put the Fletcher and the Steinberg data on top of this. I review the cochlear map story in my review of Fletcher, and I believe (hope) you will find all the references (mostly JASA) in this article. Fletcher claimed that the cochlear map was determined by the width of the BM, and I tried to verify that, and it is a reasonable hypothesis. Galt also found that the articulation index "importance function" is also prop to the critical bands, and if you integrate critical bands, then you get the cochlear map. In fact, that was the very first way it was done, I believe. I didn't see Don Greenwood's posting, you refer to. Was that a private one, or did I just miss it? I hope you publish a summary of all this, it would be good to pull together all the different cochlear maps into one grand scheme, with the proper references, and all. Jont REF: ,author={Allen, J. B.} ,title={Harvey {F}letcher's role in the creation of communication acoustics} ,journal=JASA ,year=1996 ,nonomonth=apr ,volume={99} ,number={4} ,pages={1825--1839} You can get it from my website if you like: http://auditorymodels.org/jba/PAPERS/Allen/Allen96.pdf AUDITORY automatic digest system wrote: > There are 2 messages totalling 144 lines in this issue. > > Topics of the day: > > 1. Frequency to Mel Formula (2) > > ---------------------------------------------------------------------- > > Date: Mon, 10 Aug 2009 22:04:06 -0700 > From: "Richard F. Lyon" <DickLyon@xxxxxxxx> > Subject: Re: Frequency to Mel Formula > > With respect to Umesh ("Fitting the Mel Scale", 1999), I hadn't > actually got hold of his paper until just now; sure enough, he > compared all the same fits, but started with a different table, from > Stevens and Volkman. > > Here are the Stevens and Volkman numbers: > f_stevens = [40; 161; 200; 404; 693; 867; 1000; 2022; 3000; 3393; > 4109; 5526; 6500; 7743; 12000] > mel_beranek = [43; 257; 300; 514; 771; 928; 1000; 1542; 2000; 2142; > 2314; 2600; 2771; 2914; 3229; > > Here are the Fant numbers that I used: > % Baranek's tabulated data that Fant said fit log(1 + f/1000): > f_baranek = [20; 160; 394; 670; 1000; 1420; 1900; 2450; 3120; 4000; > 5100; 6600; 9000; 14000]; > mel_beranek = (0:250:3250)'; > > I've added the Stevens table points on the svg plot at > http://dicklyon.com/tech/Hearing/Mel-like_scales.svg > The Umesh curve is closer to they data they fitted, naturally. > > Looks like the Fant numbers are indeed from Beranek: > http://books.google.com/books?id=yCsLAAAAMAAJ&q=mel+inauthor:beranek&dq=mel+inauthor:beranek&lr=&as_drrb_is=b&as_minm_is=0&as_miny_is=&as_maxm_is=0&as_maxy_is=1950&as_brr=0&ei=FbGASsuGFZuOkQTylZStCg > and > http://books.google.com/books?id=WKM8AAAAIAAJ&q=3450+inauthor:beranek&dq=3450+inauthor:beranek&lr=&as_brr=0&ei=SLGASraCI6KKkASh0OivCg > > Jim Beauchamp kindly asked the right questions that helped me clarify this. > > Dick > > >> Don, >> >> Thanks again for your great explanations of this complicated stuff. >> >> All that notwithstanding, I'm still poking around at why we have >> these two different mel scales, with breaks at 700 and 1000. So I >> got hold of Fant's book, which has Baranek's data table in it, and >> plotted up some comparisons. >> >> See http://dicklyon.com/tech/Hearing/Mel-like_scales.svg >> >> The "Mel 1000" curve comes pretty close to the Baranek table data up >> through about 4 kHz, then diverges far from it above that. The "Mel >> 700" curve misses pretty badly around 2-6 kHz, but fits better on >> average if you count the highest frequencies. >> >> The "Umesh" curve, f / (0.741 + 0.00024*f), doesn't fit particularly >> well, but has a good shape, so I did a "fit" and got f / (0.759 + >> 0.000252*f). >> >> I also did a mel-type fit, and found a broad optimum for the corner >> around 711.5 Hz (under the constraint that 1000 Hz maps to 1000, >> which I should probably have tried relaxing, but didn't). >> >> Anyway, here's my theory: Fant fitted to the frequency range he >> cared about, which probably only went to 4 kHz or so. And then >> someone else probably did a fit to the same Baranek table over the >> whole range, and got the 700 number (the plot shows that the 711.5 >> point are pretty much right on the 700 curve). And that's why we >> see Baranek referenced so much, maybe? >> >> I also looked at goodness of fit (sum squared error in mel space) >> including all the frequencies in the Fant/Baranek table. It turns >> out that the Umesh type fit has only 1/8 as much error as the >> mel-like fit, due to the Bark-like curvature at the high-frequency >> end. >> >> So for people who like Baranek's table (assuming Fant has a true >> copy of it), the Umesh type function should be a win. But I don't >> think that function extends well to the larger log-like range that >> we find in the ERB and Greenwood type curves, which are the ones >> that make more sense in auditory-based applications. >> >> That's my theory and I'm sticking to it. >> >> Dick > > ------------------------------ > > Date: Tue, 11 Aug 2009 11:41:07 -0500 > From: "James W. Beauchamp" <jwbeauch@xxxxxxxx> > Subject: Re: Frequency to Mel Formula > > Unfortunately, the "Stevens and Volkman numbers" had to be inferred > by Umesh et al (ICASSP '99) from the graph published in S & V's 1940 > AJP paper. Umesh et al say: > > "As we did not have access to the numerical data we read the points > from the graph of Stevens and Volkman. this of course produces some > errors but we believe it is accurate enought for our considerations" > > Still, the Beranek and Umesh versions of the Stevens and Volkman data > seem to fall pretty close to the same curve on Dick's plots. > > Jim > > Original message: >> From: "Richard F. Lyon" <DickLyon@xxxxxxxx> >> Date: Mon, 10 Aug 2009 22:04:06 -0700 >> To: AUDITORY@xxxxxxxx >> Subject: Re: [AUDITORY] Frequency to Mel Formula >> >> With respect to Umesh ("Fitting the Mel Scale", 1999), I hadn't >> actually got hold of his paper until just now; sure enough, he >> compared all the same fits, but started with a different table, from >> Stevens and Volkman. >> >> Here are the Stevens and Volkman numbers: >> f_stevens = [40; 161; 200; 404; 693; 867; 1000; 2022; 3000; 3393; >> 4109; 5526; 6500; 7743; 12000] >> mel_beranek = [43; 257; 300; 514; 771; 928; 1000; 1542; 2000; 2142; >> 2314; 2600; 2771; 2914; 3229; >> >> Here are the Fant numbers that I used: >> % Baranek's tabulated data that Fant said fit log(1 + f/1000): >> f_baranek = [20; 160; 394; 670; 1000; 1420; 1900; 2450; 3120; 4000; >> 5100; 6600; 9000; 14000]; >> mel_beranek = (0:250:3250)'; >> >> I've added the Stevens table points on the svg plot at >> http://dicklyon.com/tech/Hearing/Mel-like_scales.svg >> The Umesh curve is closer to they data they fitted, naturally. >> >> Looks like the Fant numbers are indeed from Beranek: >> http://books.google.com/books?id=yCsLAAAAMAAJ&q=mel+inauthor:beranek&dq=mel+inau >> thor:beranek&lr=&as_drrb_is=b&as_minm_is=0&as_miny_is=&as_maxm_is=0&as_maxy_is=1 >> 950&as_brr=0&ei=FbGASsuGFZuOkQTylZStCg >> and >> http://books.google.com/books?id=WKM8AAAAIAAJ&q=3450+inauthor:beranek&dq=3450+in >> author:beranek&lr=&as_brr=0&ei=SLGASraCI6KKkASh0OivCg >> >> Jim Beauchamp kindly asked the right questions that helped me clarify this. >> >> Dick > > ------------------------------ > > End of AUDITORY Digest - 10 Aug 2009 to 11 Aug 2009 (#2009-180) > *************************************************************** >
