Fourier series on math tells us that any complex periodic function can be decomposed into a myriad of sine and cosine functions orthogonal; in turn called synthesis. For example, the keyboard can imitate the sounds of different instruments piano, violin, French horn, etc., the principle is to record the sound of different instruments to break down into different frequency and amplitude of the sine, cosine harmonic, then electronically simulate these harmonics, then they are synthesized.
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