The phase of frequencies is very important to the final signal produced. A simple example would be two sinusoidal waves, at an interval of a perfect 5th. (Frequency ratio 1:1.5) Depending on the phase of the underlying sinusoids, the produced signal looks noticeably different.
I understand that instruments are much more complicated than sinusoid generators as they produce an overtone series along with the fundemental frequency. The propogation of sound waves along with interactions from different types of instruments further complicates the issue. As is pointed out in another question, the phase of the signal produced is constantly changing due to all of the above factors.
However, when two instruments play a chord, it always "sounds" the same, as long as the underlying notes being played are kept constant. So what is this "average" chord that we are hearing and how do we calculate it?
