It is called convolution, it is pretty nasty stuff if you are not familiar with the mathematics involved. Though what is posted above is a graphical way of doing it but not practical. This site may assist in understanding how it works better http://www.jhu.edu/signals/convolve/

That is why we deal with these things as frequency components. Have you heard of the frequency spectrum?

EDIT: for that applet, y(t) is the resultant wave we 'hear', also the resultant of the convolution. Alternatively you can use the applet here http://www.jhu.edu/signals/listen-new/listen-newindex.htm under harmonic contribution, simply click at the magnitude spectrum to add a frequency together and hear what it sounds like, you'll get the idea.

This post has been edited by befitozi: Sep 20 2010, 07:59 PM

That's what the applets are for =D

Converting 2pi to degrees is 360 degrees, thus forming a complete circle or in this case,a complete period.

The frequencies are not added up,it is the complete sinusoid is added up. The expression where you see terms of cos are added up is as simple as it gets bar simplifying it into a summation term. Though it must be of harmonic signals only, as so Fourier series is defined as such.

Integration would bring this into the realm of Fourier Transform which converts signals from the time domain to the frequency domain. In terms of musical notes, it is not necessary since the notes are already defined in frequency.

I could go to great lengths on this directly related to music notes when i progress into my 3rd and 4th year of my engineering course. Looking at this field particularly. Developing a device where an input music file (mp3) would output a music score sounds interesting Though it is severely limited hahaha, for undergraduates at least