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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@xxxxxxx>
>Date: Mon, 10 Aug 2009 22:04:06 -0700
>To: AUDITORY@xxxxxxxxxxxxxxx
>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