It is going to be the relative amplitudes of the overtones. Pure tone (like flute) is bright, many overtones present with the appropriate mix can sound dark (fr

It is going to be the relative amplitudes of the overtones. Pure tone (like flute) is bright, many overtones present with the appropriate mix can sound dark (french horn). Next, you are going to ask me for the coefficients, but I don’t know that. Break into the nearest church with a proper pipe organ and start pulling and pushing stops to see what happens. (Or ask your friend the organist to take you so that you don’t get arrested)