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Do you have a guitar or other stringed instrument handy? I can tell you how to produce beating: Play a perfect fifth (open B string, second fret high E string, for example), and listen as you turn the tuner slightly up and down. When the fifth is in tune, it will sound uniform. When the interval diverges from a fifth you will begin to hear a pulse, a sort of wobble...slow at first (when very close to the right pitch) and faster as they get further apart (and then, eventually, if you go far enough in any direction the beating will get slow and stop again as you approach another perfect interval). To visualize it, you can maybe think of sine waves at certain frequency ratios of each other (a fifth is a 3:2 ratio, fourth is 4:3, octave is 2:1; these are the "perfect" intervals that don't audibly beat when played together, and are not considered at all "dissonant"). The phase cancellation between this is regular enough and frequent enough and not complete so we don't perceive it as beating, but as a specific singular sound of its own. Most people aren't hearing two independent notes when hearing these intervals, though people with some training or with perfect/absolute pitch can recognize it for the combination of notes that it is. But, as they drift out of tune, the phase cancellation happens in a shifting pattern up and down, so you end up with very clearly audible changes; this is called "beating" (at least, that's what I've always called it, and I believe it is the proper term in physics, audio research, and music...pretty much anywhere we talk about the phase of waves, I think?). Here's a page with some diagrams of the basic idea of what is happening and what you're hearing, as well as audio samples of what it sounds like (it's more complex with the complexity of a guitar's timbre, but the principle is the same): http://www.animations.physics.unsw.edu.au/jw/beats.htm |