Equal Loudness Curves (ISO226)

What is loudness?  No, it is not the setting of your volume knob.  In audio processing, loudness refers to a family of curves that generally describes how the the human ear perceives how "loud" a particular frequency is.  Experiments on this subject go back as far as 1937 when Harvey Fletcher and Wilden Munson released the first equal-loudness contours.  (http://en.wikipedia.org/wiki/Fletcher%E2%80%93Munson_curves)

Basically, in these experiments users listened to a 1kHz tone at a given amplitude (units of measure are in phons)  Then they listend to a different frequency and were allowed to adjust the volume until they felt that this new frequency was as loud as the previous 1kHz control singal.  One of the most obvious results from this study is that Bass needs ALOT of gain to sound as loud as the 1kHz - 3kHz range.  As human, our ears are very sensitive in the 1kHz to 3kHz range and some people have theorized that we have evolved to tune our ears into human speech.

Years passed and many other scientists tried to nail down the curve with other similar experiments.  And of course their data differed from the Fletcher-Munson results.  But in 2003, and ISO committee sought to fit a curve that would fit all the equal-loudness studies in the previous 60+ years of research.  The code below is the Matlab code which generates the equal-loudness curves described in the resulting standard: ISO 226.

What can you do with this code?  Well, if you know the accoustic sound pressure level (SPL) of a 1kHz tone at any given volume knob setting, it is possible to use this data to make all frequencies sound like they are at the same level.  Of course, you would need to Equalize(EQ) the audio content, but these family of curves would tell you HOW to EQ your signal.

function [spl, freq] = iso226(phon);
%
% Generates an Equal Loudness Contour as described in ISO 226
%
% Usage:  [SPL FREQ] = ISO226(PHON);
% 
%         PHON is the phon value in dB SPL that you want the equal
%           loudness curve to represent. (1phon = 1dB @ 1kHz)
%         SPL is the Sound Pressure Level amplitude returned for
%           each of the 29 frequencies evaluated by ISO226.
%         FREQ is the returned vector of frequencies that ISO226
%           evaluates to generate the contour.
%
% Desc:   This function will return the equal loudness contour for
%         your desired phon level.  The frequencies evaulated in this
%         function only span from 20Hz - 12.5kHz, and only 29 selective
%         frequencies are covered.  This is the limitation of the ISO
%         standard.
%
%         In addition the valid phon range should be 0 - 90 dB SPL.
%         Values outside this range do not have experimental values
%         and their contours should be treated as inaccurate.
%
%         If more samples are required you should be able to easily
%         interpolate these values using spline().
%
% Author: sparafucile17 03/01/05

%                /---------------------------------------\
%%%%%%%%%%%%%%%%%          TABLES FROM ISO226             %%%%%%%%%%%%%%%%%
%                \---------------------------------------/
f = [20 25 31.5 40 50 63 80 100 125 160 200 250 315 400 500 630 800 ...
     1000 1250 1600 2000 2500 3150 4000 5000 6300 8000 10000 12500];

af = [0.532 0.506 0.480 0.455 0.432 0.409 0.387 0.367 0.349 0.330 0.315 ...
      0.301 0.288 0.276 0.267 0.259 0.253 0.250 0.246 0.244 0.243 0.243 ...
      0.243 0.242 0.242 0.245 0.254 0.271 0.301];

Lu = [-31.6 -27.2 -23.0 -19.1 -15.9 -13.0 -10.3 -8.1 -6.2 -4.5 -3.1 ...
       -2.0  -1.1  -0.4   0.0   0.3   0.5   0.0 -2.7 -4.1 -1.0  1.7 ...
        2.5   1.2  -2.1  -7.1 -11.2 -10.7  -3.1];

Tf = [ 78.5  68.7  59.5  51.1  44.0  37.5  31.5  26.5  22.1  17.9  14.4 ...
       11.4   8.6   6.2   4.4   3.0   2.2   2.4   3.5   1.7  -1.3  -4.2 ...
       -6.0  -5.4  -1.5   6.0  12.6  13.9  12.3];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%    

%Error Trapping
if((phon < 0) | (phon > 90))
    disp('Phon value out of bounds!')
    spl = 0;
    freq = 0;
else
    %Setup user-defined values for equation
    Ln = phon;

    %Deriving sound pressure level from loudness level (iso226 sect 4.1)
    Af=4.47E-3 * (10.^(0.025*Ln) - 1.15) + (0.4*10.^(((Tf+Lu)/10)-9 )).^af;
    Lp=((10./af).*log10(Af)) - Lu + 94;

    %Return user data
    spl = Lp;  
    freq = f;
end