The design of the Roger Dubuis Excalibur Quatuor is the most interesting thing about it. This statement is not as disparaging as it sounds. In fact, it’s quite the opposite. What I’m saying is — despite the intriguing premise of a watch equipped with four sprung balances of identical frequency linked by differentials to form what is theoretically the most chronometrically stable timepiece in existence, despite the patented power-reserve display whose method of indicating level of wind requires yet another differential, despite the fact that the Quatuor reads an average of 32 vibrations per second, making it in effect a 16Hz (115,200vph) watch, despite all this! — there is still something even more fascinating about the timepiece. And it’s staring you right in the face.

Horology 101: Resonance and watches

Whenever the word “resonance” is brought up with relation to timepieces, it is invariably dismissed as a showy feature of no actual chronometric benefit, the purview of independent watchmakers with a predilection for overwrought illustrations of obscure horological esoterica. Clearly, this is not (totally) true.

What is mechanical resonance? It is the tendency for a mechanical system to exhibit its greatest oscillatory amplitude when excited at a rate that matches its natural frequency. This is why balance assemblies require regulation, so that they attain a certain natural frequency (say, 3Hz) when impulsed.

The four oscillators of the Roger Dubuis Excalibur Quatuor are coupled via differentials (one for each of the two oscillators seen on the upper half of the dial, another for the lower two and a third differential for the resultant two averages) to give a heretofore-never-realised stability of rate in timekeeping.

The four oscillators of the Roger Dubuis Excalibur Quatuor are coupled via differentials (one for each of the two oscillators seen on the upper half of the dial, another for the lower two and a third differential for the resultant two averages) to give a heretofore-never-realised stability of rate in timekeeping.

When the frequency of the given impulse matches the natural frequency of the balance — thanks to the escapement’s dual purpose of locking the energy transmission and conveying energy to the balance — the balance achieves its most stable and efficient period of oscillation. In other words, resonance is at work right in the heart of every single mechanical watch ever made.

Oscillating systems with the same natural frequency can also be pulled into period with each other, a phenomenon that most of us associate with the word “resonance” in watches, although this is not strictly a cognate definition. In a watch, this can happen when one or more oscillators are linked, their individual vibrations exciting each other into a synchronous phase.

With two or more oscillators vibrating in phase, each oscillator becomes both exciter and resonator — it provides energy to and absorbs energy from its mates. With their optimized conversion of energy from potential to kinetic forms, the oscillators become locked in an energy feedback loop. In effect, they are all in resonance with each other. All other factors accounted for, the half-life of energy loss is extended and the coupled oscillators will exhibit far greater amplitude for a much longer time than a single oscillator.

In theory, harmonic coupling of the balances provides for much greater stability of rate. If there is a disturbance to one or more of the oscillators, for instance, when the watch is subject to shock, the sympathetic relationship between the balances draws them back into phase. This rate correction occurs much faster than in the case of a single oscillator settling back into rhythm after experiencing a shock. Thanks to the resonance effect, a balance in paired harmonic oscillation spends far less time keeping the wrong time than its single counterpart. Of course, this is contingent on the balances being perfectly regulated and perfectly matched in the first place, otherwise the resonance between them can in fact exacerbate errors. From a practical point of view, this probably explains why no one has actually bothered to put a resonance timepiece into mass production.

Movement: Caliber RD0101 manual-winding movement; hours and minutes; 40-hour power reserve and indication | Case: 48mm in pink gold

Movement: Caliber RD0101 manual-winding movement; hours and minutes; 40-hour power reserve and indication | Case: 48mm in pink gold

Why Roger Dubuis bothered with the Excalibur Quatuor

Ladies and gentlemen of the jury, exhibit number one is the Roger Dubuis Excalibur Quatuor with four sprung balances; and the reason why its design is so amazing is that despite having four oscillators crammed together in a movement of 16.75 lignes (37.8mm) in diameter, the watch shows no sign of harmonic mechanical resonance. Let me state that again: no sign of harmonic mechanical resonance.

We’ve established that all it takes for two or more oscillators to fall into resonance with each other is for them to be near each other, such that even the mild air turbulence that results from their vibration is sufficient to pull them into phase. As such, the four balance assemblies of the Excalibur Quatuor are positioned as far away from each other as possible, with a 90° angle offset between them at the edge of the movement. To further restrict the flow of air between the four balances, the movement itself — the arrangement and shape of its plates and bridges, and the layout of its components — is designed to maximally physically isolate each balance from the others.

The entire movement is also engineered so as to have a natural frequency as far removed as possible from the balance frequency. To vastly simplify and extrapolate from what is an eye-wateringly complicated chapter of structural engineering, kinetic energy is most efficiently transferred between systems when the natural frequency of the exciter is a multiple or factor of the natural frequency of the resonator. To inhibit energy from being transferred between the oscillators through the plates, the movement had to be designed to actively dampen this transfer, which involves working through a bunch of (really tedious) mathematical functions related to mass and material inertia.

Horology 201: Rebat

In watchmaking parlance, rebat, or knocking, is what happens when a balance wheel, given too much energy, extends too far on the half-swing and hits the outer surfaces of the pallet fork with the roller jewel. Given that the balance is what gives a watch its timekeeping properties, any such interference with its oscillation is unequivocally a bad thing, which is why the ideal amplitude for a balance is usually between 275° and 315°. With four oscillators in a closed system of harmonic excitation, each egging the others on to larger and larger amplitudes, knocking would have been a severe problem.

In any case, what the Excalibur Quatuor aims to achieve is not to have all its balances singing together in unison. Mathematically speaking, four oscillators vibrating in harmonic resonance do not yield statistically discrete results that can be used to calculate a meaningful average. And so, if you observe the Quatuor in action, you’ll notice that each balance is beating out of phase with the others. It is also possible, says Gregory Bruttin, associate director of movement development, that although the oscillators are all fed from the same two barrels, they can still achieve different amplitudes, through variation in position (or any of the other little errors that a timepiece can pick up on the way from conception to execution). Although the Quatuor doesn’t have a small seconds indication to assist in chronometric testing, Manufacture Roger Dubuis utilizes a method similar to Timelab’s certification of chronometers, which is to capture computerized images of the watch every 24 hours for detailed analysis and comparison. In this way, even minute variations in timing can be detected. And here is the proof of the pudding: the Quatuor’s initial test results show a negligible timing variation per day — effectively zero seconds of error. Out of cacophony, a consensus.

One might say that the Roger Dubuis Excalibur Quatuor is an example of deliberately making things complex for complexity’s sake — but then that would be missing the whole point of mechanical watchmaking. And what is every scientific and artistic endeavor in the history of the human race, if not an attempt to bring beauty and order out of chaos?