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






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 (
[spl,freq_base] = iso226(10);
hold on;
for phon = 0:10:90
[spl,freq] = iso226(phon);%equal loudness data
plot(freq_base,spl);%equal loudness curve
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
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