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# Re: Robinson/Dadson curve equations?

```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
```