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© Copyright 2003, Jim Loy
Above we have two nearly identical sine waves (blue and green) and their sum (red). The sum shows what are called beats, which you can easily hear. There is almost no sound between the beats, as the waves cancel each other out. With real musical instruments, however, there are other sounds being heard, and so the sound does not come so close to disappearing. The faster the beats, the more out of tune the sine waves are, the slower the beats, the more in tune they are. A piano tuner listens for these beats, but sometimes will use electronic tools which do the listening. The above diagram is meant to be the same note, and the tuning is easy. Octaves are also easy. Other notes, fifths for example, are more difficult, as the beats are not easily heard or timed. And so, a tuner either uses a separate sound (like a tuning fork or an electronic tone) to tune each note, or uses an electronic device which tells him/her if the note is in tune.
Also see Harmony and Sine Waves. I drew these graphs using Geometer's Sketchpad.