Its very hard to hear this with sine waves. Sine waves work to visualize the concepts but real instrument notes almost always are better modeled as a large num

Its very hard to hear this with sine waves. Sine waves work to visualize the concepts but real instrument notes almost always are better modeled as a large number of sine waves with a mathematical relationship that sound simultaneously and in varying amplitudes that combine to create the timbre of the note. Then when those notes sound together we get combinations of all those sine waves together to create a very complex wave that sounds a certain way to our ear based on the interactions between all of these waves at once. So to visualize it or reason about it, my comment here makes sense: https://news.ycombinator.com/item?id=30363653 https://news.ycombinator.com/item?id=30363653 But to hear it you would be much better off with triangle or sawtooth waves or samples of actual musical instruments.