% This notebook tests pure versus equal tempered harmonics. Of
% course, creating a sine wave is not real life.
>load sound
% Create the time values for 4 seconds of sound.
>t=soundsec(4);
% Let 440 Hz be our basic frequency.
>f=440;
% New listen to a 220 Hz sound.
>s=sin(f*t/2);
>savewave("test.wav",s); playwave("test.wav");
% This is a pure quint.
>s=sin(f*t)+sin(f*3/2*t);
>savewave("test.wav",s); playwave("test.wav");
% Now we add the lower octave and vary the quint in pitch. First
% the pure quint.
>s=sin(f*t)+sin(f*3/2*t)+sin(f*t/2);
>savewave("test.wav",s); playwave("test.wav");
% Now the equal tempered quint. The difference is small.
>s=sin(f*t)+sin(f*2^(7/12)*t)+sin(f*t/2);
>savewave("test.wav",s); playwave("test.wav");
% Now a quint wich is too much off.
>s=sin(f*t)+sin(f*1.49*t)+sin(f*t/2);
>savewave("test.wav",s); playwave("test.wav");
% Here are the corresponing numbers
>3/2, 2^(7/12), 1.49
          1.5 
      1.49831 
         1.49 
% Repeat the same with the major terz.
>s=sin(f*t)+sin(f*5/4*t)+sin(f*t/4);
>savewave("test.wav",s); playwave("test.wav");
>s=sin(f*t)+sin(f*2^(4/12)*t)+sin(f*t/4);
>savewave("test.wav",s); playwave("test.wav");
>s=sin(f*t)+sin(f*1.27*t)+sin(f*t/4);
>savewave("test.wav",s); playwave("test.wav");
>5/4, 2^(4/12), 1.24
         1.25 
      1.25992 
         1.24 
>