The part about the harmonic oscillation frequency in the flame flicker is most interesting:"The frequency of these oscillations seems to be around 5 Hz, drifting up, and seems to be a fundamental parameter of the flame since it appears to be relatively constant in all observations."It appears that some (optical) flame detectors work by obtaining the frequency of this flicker: [1]"This flame scanner also monitors the rate of combustion by analysing the flicker frequency, or the fingerprint, of the flame... Since the flame is always burning back to the fuel source, the flame is always in motion. This motion allows the intensity of the flame to vary across a flame flicker frequency spectrum."From that link, it appears that the "flicker frequency" would be related to the exact fuel source and possible fuel/air mixture ratio, as the "flame is always burning back to the fuel source".Some other information about flame frequency-flicker: [2]"Under normal gravity conditions, the flames have a well defined oscillation frequency which is inversely proportional to the square root of the burner diameter, D, and to a good approximation can be written as f » 1.5/D½, with D given in meters."So, it would indeed seem that the flicker frequency is related to the particulars of the candle, its wick, etc.Very interesting article!

 This reminds me of the quote "How much can the ripples tell us about the object that fell in the water?"
 Or even the famous question "Can you hear the shape of a drum?", to which we have a constructive proof (under some mathematical idealizations) that the answer is " No".
 That's been simplified enough to distort the question. Real listeners are not limited to simple observation of frequencies they can move there ears around to get a more 3d picture.
 *their
 That's why I keep telling people there's no such thing as a perfect lie. People have no idea just how much information leak there is in every action they make; the only question is whether someone is dedicated enough to find the right side channel. And doing that is only getting cheaper thanks to progress of technology.

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