Clocks and watches made as resonant systems have to date been highly distinctive and therefore expensive. Being thus very well made, the oscillators in such systems are closely matched, have a high Q, and have rigid mountings, meaning that they will remain synchronized with only the minutest amount of energy transfer between them, although they do require to be closely regulated (their frequencies have to closely match).
As such, their operating in a sustained state of synchronization can be inferred to be a good indicator of the mechanical rigor of their construction.
Micro-perturbations are sensitively felt that would otherwise be swamped in less perfect systems. To employ a literary analogy, only a princess is capable of feeling the pea hidden under 20 feather beds because she is highly refined and accustomed to perfection in every aspect of her sophisticated existence.
This “rigor factor,” may we call it the R-Factor, reflects:
- How loosely the balances are coupled (i.e., how rigid the mounting is).
- How closely their frequencies have to be matched before they will.
Artificial “connections” between the oscillators, like the ARF15’s clutch spring, mean they are likely to resonate more easily, even under conditions that are sub-optimal. But there is evidence to suggest that timekeeping stability under these conditions of enforced resonance is also likely to be lower.
For instance, Abraham-Louis Breguet performed experiments on pairs of clocks mounted to a common frame with the pendulums hung off a very heavy bracket. He noted that with the bracket at full mass, the pendulums would synchronize when they differed from each other by up to three seconds’ rate, but not at four. He then filed away part of the bracket, introducing some flexibility.
This time, they would synchronize at up to ten seconds, but not at 13 seconds. Finally, he hung the pendulums off a much lighter bracket and found they would synchronize at up to 21 seconds difference, but under these conditions the clocks “did not go too well.”
His words, quoted above, encapsulate my concern about synchronized oscillators that are made with such a high degree of enforced communication that they will synchronize over a large range of frequencies. It seems unlikely that such a wide ability to synchronize comes without any cost. Perhaps there is long-term instability due to lack of isochronism?
For oscillators with different frequencies to synchronize, their amplitude must periodically rise and fall, and the greater the rate difference between the oscillators, the bigger the changes in amplitude. Of course, some watches can be made almost completely isochronous, making them superior to pendulums in this regard.
In considering the “rigor” of a synchronized watch or clock, it’s worth considering the range of frequencies the system will tolerate before the device loses synchronization. It might be very small, maybe even just one. Here, think of the Journe watch or the Breguet clock, whose oscillators need to be tightly constrained to within a few seconds per day of each other or the timepiece will fail to operate.
Is this a good thing? Well, if what you’re after is high precision, then I would argue definitely yes. The Journe watch is a chronometer. However, there are trade-offs; such a watch is highly intolerant of effects that alter its tuned state (strong shocks and vibrations, pronounced temperature changes, diverging conditions between its two trains in the state of oil, and so on).
A watch like the ARF15, on the other hand, is less fussy – it can tolerate up to 250 seconds per day variance between its oscillators before they fall permanently out of step with each other. There is an electronic analog to this: if we design a radio receiver to have a wide bandwidth when tuned to a frequency, it will be prone to spurious additional signals at the output.