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*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Re: Robinson/Dadson curve equations?*From*: Jont Allen <jba@xxxxxxxxxxxxxxxx>*Date*: Tue, 19 Dec 2000 14:52:22 -0500*Comments*: To: Bruce Walker <walkerb@RUF.RICE.EDU>*Organization*: HA1530000*References*: <Pine.GSO.4.21.0012191135020.22772-100000@kennel.ruf.rice.edu>*Reply-to*: jba@xxxxxxxxxxxxxxxx*Sender*: AUDITORY Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>

Bruce Walker wrote: > Happiest of holidays! > > Could anyone possibly provide a source for *equations* that accurately > represent the equal-loudness contours from Robinson & Dadson (1956), or > subsequent similar works? If you are willing to use the Fletcher Munson 1933 equi-loudness contours, then the formulas and coef's are given in: @article{Allen97b ,author={Allen, J. B. and Neely, S. T.} ,title={Modeling the relation between the intensity {JND} and loudness for pure tones and wide--band noise} ,journal=JASA ,year=1997 ,month=dec ,volume=102 ,number=6 ,pages={3628--3646} ,note_={} } See Appendix B on page 3644. I have been told by several researcher that these 1933 curves are proving to be more accurate that Robinson and Dadson. These statements were based on new data, and a detailed set of comparisons. I aslo have matlab code to generate these coef's (i.e., the 1997 table BI) from the raw data, and the isoloudness curves. If there were interest I could post it on an ftp site. Jont > > Basically, I need to be able to plug a frequency into an equation (on the > fly), and have it spit out the "corrected" loudness that I need to use in > order to match a given reference tone. (I want a whole series of tones to > be equated for loudness.) > > If the actual equations are not available, then perhaps a set of data that > I can stick into Maple to derive the equations would be fine, too. > > Note that R&D _do_ provide quadratic equations that cover parts of the > curve ranges. However, I'd estimate that a 6-degree polynomial would give > a better approximation to the the curves over the entire data ranges. Six > or eight degree polys were obviously not calculable by hand, which is why > R&D used quadratics. > > Thanks in advance, > --Bruce > > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ > Bruce Walker, Ph.D. (PC86-88) Rice University Psychology Dept. > email: walkerb@rice.edu 6100 Main St., Houston, TX, 77005 > ph: (713) 522-2969 (home) (713) 348-3772 (office) > http://www.owlnet.rice.edu/~walkerb (713) 348-5221 (fax) > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -- Jont B. Allen AT&T Labs-Research, Shannon Laboratory, E161 180 Park Ave., Florham Park NJ, 07932-0971 973/360-8545voice, x7111fax, http://www.research.att.com/~jba

**References**:**Robinson/Dadson curve equations?***From:*Bruce Walker

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