Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013

59

√

1.4983

√

1.5874

√

1.6818

√

1.7818

√

1.8877

√

2

Table 4.7 Powers of

√

Column 5 is an estimate for n rounded to the nearest integer, which is the approximate

number of semitone steps from the beginning to the end of the band.

Column 6 is derived based on the n computed for column 5. If n is the number of

semitones in a critical band and there are 12 semitones in an octave, then is the size of the

critical band in octaves. Column 6 is .

4.3.3 A MATLAB Program for Equal Loudness Contours

You may be interested in seeing how Figure 4.11 was created with a MATLAB program. The

MATLAB program below is included with permission from its creator, Jeff Tacket. The

program relies on data available is ISO 226. The data is given in a comment in the program.

ISO is The International Organization for Standardization (www.iso.org).

figure;

[spl,freq_base] = iso226(10);

semilogx(freq_base,spl)

hold on;

for phon = 0:10:90

[spl,freq] = iso226(phon);%equal loudness data

plot(1000,phon,'.r');

text(1000,phon+3,num2str(phon));

plot(freq_base,spl);%equal loudness curve

end

axis([0 13000 0 140]);

grid on % draw grid

xlabel('Frequency (Hz)');

ylabel('Sound Pressure in Decibels');

hold off;

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