Why Your Generated Tone Clicks, and How an Envelope Fixes It

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, and apply an envelope to smooth it. Everything is plain C++ with no libraries, and every number here is captured from a real run of the code. Where the click comes from A tone is a list of samples tracing a sine wave. A speaker turns those samples into sound by physically moving: the sample value sets the position of the speaker cone at each instant, where 0 is its resting position and larger values push it further forward or pull it back. Playing the tone moves the cone in and out 44,100 times a second to recreate the wave. When playback starts, the cone is at rest, at position 0. But the first sample of the tone is usually not 0. It is wherever the wave happens to be at that instant, and if that value is far from zero, the cone has to move from rest to that position in a single sample step, about 22 microseconds at this sample rate. That near instant movement is the click. A cone moving gradually pushes the air smoothly and produces a smooth sound. A cone forced to a distant position in one sample makes a sharp, abrupt movement of the air, which your ear hears as a click or pop. You can see it directly in the numbers. Here are the first six samples of a plain 440 Hz tone at half amplitude: n=0 raw=0 n=1 raw=1026 n=2 raw=2048 n=3 raw=3063 n=4 raw=4065 n=5 raw=5051 The wave leaves zero and climbs fast. Between the silence before playback and sample 1, the signal jumps by 1026 in one step. The same thing happens at the end: if the tone stops while the wave is partway through a cy