If you have generated a pure tone in code and played it back, you may have noticed a small click at the start, the end, or both. The tone itself is clean, but the edges are not. That click is not a bug in your sine wave. It is a real and well understood artifact, and the fix is a technique you will reuse in every sound you ever synthesize: an envelope. This piece builds directly on generating a basic tone from scratch . We take a tone that clicks, look at the actual sample values to see why,...