I’m trying to think of a word that I’m not sure even exists. It describes the phenomenon of two occurrences—two blinking lights, two beeping sounds, etc.—that each happen at regular but different intervals. Because of the difference between these intervals, the two occurrences will seem to happen in unison, then gradually fall out of sync before again returning to a synchronous instance. For example, blinking light ‘A’ flashes every 9 seconds and light ‘B’ flashes every 10 seconds. At a certain point in time (in this case, every 90 seconds), both lights will flash simultaneously; but at the next flash, light ‘A’ will flash one second sooner than ‘B’. For 45 seconds, the amount of time between light ‘A’ and light ‘B’ will increase with each flash, until the flashes are substantially opposed—light ‘A’ will flash, 5 seconds later light ‘B’ will flash, and 4 seconds after that light ‘A’ will flash again. The flashes will then occur with successively diminishing amounts of time between them until they once again flash in unison.

You’ll see examples of this with those battery-powered yellow construction lights, lights on antennae or the spires of two different buildings (and sometimes the same building), two faucets dripping, the back-up-beeping noises of construction equipment, two people dribbling basketballs, etc. Any two things that happen regularly but at different periods will come in and out of sync.

It seems that there must be a word for something as common as this, but I’ve Googled all sorts of variations on this description without any satisfaction. The closest I can get is “phase synchronization”, which I’m not happy with. There is a rather interesting conversation on the subject at ask.metafilter.

I’d like to point out that I’m throwing terms around here that I don’t understand and probably aren’t correctly used, but it’s the best I can do with zero physics training.

Update 28 April 2009: Well, by total coincidence, here we are exactly two years later and still no closer to a word to describe this phenomenon. I’ve put together a little example with JavaScript that uses two flashing boxes to illustrate this behavior. I’ve timed it so the thing starts syncronized, goes out of sync, and then returns to sync every 11 seconds, which I think demonstrates it pretty well.

Click the start button to begin the boxes flashing at slightly different intervals.

The left box changes to grey for .5 seconds, changes to white for .5 seconds, and then changes back to grey.

The right box changes to grey for .5 seconds, changes to white for .6 seconds, and then changes back to grey.

This extra .1 second of white on the right box makes the two boxes flash grey at different intervals.

Notice how they get increasingly out of sync until the flashing is perfectly opposed – when one is flashing grey, the other is flashing white. Then they gradually return to sync – flashing grey simultaneously one time before going out of sync again. The whole cycle repeats every 11 seconds.

Update 24 August 2009: I might be getting closer to actually finding the word(s). A friend suggested “recurring instances”, which sounds good, but doesn’t really communicate the going in and out of sync thing, in that the instances could recur simultaneously each time. The crux here is that the two repeating events are asynchronous.

Incidentally, xkcd has a comic on the subject, titled Turn Signals. It is referred to in the comic as beat frequency, which is a term typically used to describe audible phenomenon. I found a few informative pages describing Beat Frequencies in Sound and Beat Frequency of Sound Waves that also have some audio examples, which closely match what I’m trying identify.

But beat frequency still isn’t exactly it, to my mind. It’s just the audible-only equivalent of it.

Update 17 May 2011: Harmonic oscillation, which is usually visualized by a spring with a mass attached bouncing up and down, seems to be a close relative to what I’m looking for. A simple harmonic oscillator showing the simple harmonic motion of three undamped mass-spring systems is very similar to my flashing lights phenomenon. Each spring system has a period, which is the time it takes to start at one position, cycle through the motion, and return to the starting position. Systems with different periods will occasionally all be at their starting positions at the same time.

Update 1 July 2011: I think the word is polyrhythm. Polyrhythm is usually described in terms of music, but it certainly seems to apply here.

airlock

Yes, everyone knows what an airlock is, but I still really like the word.

catenary

Another favorite obscure word for a rather familiar phenomenon is “catenary“.

In mathematics, the catenary is the shape of a hanging flexible chain or cable when supported at its ends and acted upon by a uniform gravitational force (its own weight). The chain is steepest near the points of suspension because this part of the chain has the most weight pulling down on it. Toward the bottom, the slope of the chain decreases because the chain is supporting less weight.

The catenary is the ideal form for an arch which supports only itself. If made of individual elements whose contacting surfaces are perpendicular to the curve of the arch, no significant shear forces will be present at the joints, and the thrust into the ground will be directly along the line of the arch. The Gateway Arch in Saint Louis, Missouri, United States follows the form of an inverted catenary.
Wikipedia

Catenary curves are not to be confused with the arc formed by the cable of a suspension bridge; that is a parabolic curve.