JULY 01, 2022

THE WAY OF RESONANCE

A closer look at one of watchmaking’s most fascinating and elusive phenomena.

WORDS Cheryl Chia

The principle of resonance has been known and observed for a long time, though its scientific appreciation had moved on a slow trajectory. It underlies the very fabric of the universe from the smallest subatomic particle to the biggest galaxies but manifests itself most tangibly in the field of pure mechanics.

In horology, resonance forms the bedrock of every mechanical watch as it ensures that the balance wheel and hairspring oscillate at the same frequency. The same principle also underlies the importance of a higher beat rate in wristwatches as the balance tends to experience the most disturbance when the frequency of wrist motions approaches that of the balance wheel.

However, specifically when it comes to its application in the way of coupled oscillations — two pendulums or balances keeping pace with each other in a synchronized stable rate, resonance has stood on experimental footing for most of its history and still remains a rarity today. A term originally derived from the field of acoustics, resonance occurs when two close vibrating frequencies synchronize, mutually absorbing each other’s energy and eventually arriving at the same frequency. 

The one-of-a-kind Armin Strom Resonance Zeitgeist launched in celebration of five years of its patented resonance technology 

This phenomenon was first recognized by Galileo Galilei (1564–1642) in the early 17th century when he undertook the study of pendular oscillations, though in a non-harmonic excitation. He learned that a heavy pendulum can be moved from its rest position simply by blowing against it with a frequency that matches that of the pendulum. However, it was Dutch scientist Christiaan Huygens (1629–1695) who, apart from being the first to present a reliable pendulum clock, discovered the effect of coupled oscillations in the way we most commonly refer to today when we talk about resonance watches. 

While bedridden with a brief illness, Huygens observed that two identical pendulum clocks, which were suspended from a common wooden beam, started to display a sympathetic motion. Namely, the pendulums were oscillating in perfect synch with the same period and amplitude but in opposite directions. Upon his recovery, Huygens conducted a series of experiments to identify the cause of this behavior and concluded that it was due to the weak coupling of the two clocks. 

His findings would later inform the pioneering work of Antide Janvier (1751–1835), the royal clockmaker to Louis XVIII who applied the principle to three clocks, each with double pendulums driven by two distinct systems — a double pendulum long case clock No. 400, double pendulum wall regulator No. 453 and the coupling regulator No. 470. Abraham-Louis Breguet (1747–1823) also experimented the phenomenon in clocks — Breguet No. 3177 and No. 3671 — before becoming the first horologist to achieve the phenomenon in pocket watches — Breguet No. 2788, 2794 and 2667.

The Breguet Resonance Pocket Watch No. 2788 was acquired by the Prince Regent as a gift to his father, King George III, in 1818. (Image: Sotheby’s)

Formula for Resonance

Following Breguet’s milestone, resonance in watchmaking came to a halt for more than two centuries. Eventually, his experiments and findings, as uncovered by George Daniels in his book, The Art of Breguet, would prove pivotal in providing a mechanical introduction for its usage in contemporary watchmaking and furthermore, by way of discovering how minimal the effect air currents had on coupling, offered a jumping-off point for watchmakers to enhance the phenomenon. 

Breguet’s resonance pocket watches were described by Daniels as “examples of an experiment to demonstrate Breguet’s theory of dynamics as applied to oscillating bodies.” Although it was a known phenomenon in pendulum clocks, Breguet recognized its benefits in portable timekeepers. Daniels goes on to note, “With these watches, Breguet was concerned to eliminate small variations in rate due to errors of construction and adjustment of the watch. His experiments with clocks led him to conclude that the whole of the matter composing the frame was in continuous microscopic motion with the vibration of the pendulum. He realized that the same phenomena must occur in a balance wheel system where the motion would be transmitted to the plate of the watch by the couple of the balance and spring at the limit of arc of vibration. If two systems were employed in contra direction, then the movement of the plate would be equalized and cancelled. In the event of one system gaining or losing relative to the other the induced movement of the plate would act favorably to reduce the vibration.” 

The Breguet No. 2788 has two subsidiary dials for mean solar time; Breguet encircled each balance with a thin steel guard to minimize the effect of air disturbance but was surprised to find that resonance still occurred, concluding that air turbulence had little influence on coupling. (Image: Sotheby’s)

Breguet’s pocket watches were built such that the distance between the balance wheel could be adjusted to assess the extent to which air disturbance would influence the effect of resonance. He even installed a thin smooth steel guard around the balance wheels to isolate them in the No. 2788 and recorded his discoveries in his notes, “I was very surprised to find that it [air turbulence] influenced the mechanism far less than the effort accorded to each other by the impulsion of their mutual movements.”

Breguet went as far as to place the watch in a vacuum chamber. Within the same set of notes on his experiments, Breguet goes on to explain, “The first of these double watches [No. 2788] was three months in the hands of M. M. Bouvard and Arago without the seconds hands having parted by the smallest part of a second; it was put twice in a vacuum and maintained in ‘absolute void’ for 24 hours, as well as worn, laid flat, and hanging from a chain without ceasing to keep to the second.” 

With that, Breguet concluded that resonance depended primarily on the transmission of vibrations through a movement plate and had less to do with proximity or air friction. This crucial observation would narrow the focus for improvement to induce the phenomenon. 

Different Strokes

F.P. Journe Chronometre a Resonance Platinum (2000), Chronometre a Resonance in Platinum and Rose Gold 2020 (Image: The Hour Glass)

The first watchmaker who succeeded in incorporating the effect of resonance in a wristwatch was none other than François-Paul Journe. In 2000, he unveiled the Chronomètre à Résonance, which was inspired by Breguet’s No. 3177 clock which he had encountered during his time as a restorer. 

Achieving the effect of resonance in a moving object such as a wristwatch is a considerable feat, particularly when it relies purely on the transmission of energy through a shared mainplate, without any mechanical linkage. The rates of both balances have to be adjusted as close to each other as possible while being free sprung, as having an index regulator reduces the effect of the vibration exerted on the mainplate. While Breguet noted that each balance had to be regulated to within a deviation of 20 seconds per day from the other, Journe found that they needed to be adjusted to within five seconds per day in a wristwatch because the driving force is smaller. 

In the Chronomètre à Résonance, the crown at 12 o’clock winds both barrels simultaneously and each powers an independent gear train that drives a subsidiary time display on the dial. Notably, a rack attached to the balance cock enables the proximity of both balances to be adjusted.

The original Chronomètre à Résonance was produced from 2000 to 2019 before Journe introduced a new resonance movement, the caliber 1520, on the year of the watch’s 20th anniversary. In the new movement, the twin gear trains are driven by a single barrel, thanks to a differential which divides power to each train. Additionally, each gear train is now equipped with its own remontoir d’égalité that recharges every second to address the problem of unequal torque delivered to each balance as the mainspring unwinds. As a result, each balance achieves more constant amplitude and consequently a higher degree of rate stability. When in unison, these properties are heightened. 

The gear trains of the F.P. Journe Chronomètre à Résonance, powered by a single barrel; The Armin Strom Mirrored Force Resonance with the patented spring clutch coupling both hairsprings

While Journe’s resonance watch relies on the transmission of vibrational energy from the hairspring to the balance cock to the shared mainplate, several other watchmakers have devised new solutions at enhancing the phenomenon, most notably Armin Strom.  

The Armin Strom Mirrored Force Resonance of 2016 marked a major leap forward as it built and improved upon earlier efforts and experiments by strengthening the coupling structure between two oscillators. Since then, the brand has become one of the few watchmakers to create serially produced resonance watches. In fact, it has developed such an efficient and reliable method to achieve resonance to the extent that a large part of the brand is built on this single solution. Its secret lies in a patented clutch spring that links the outer terminal curves of both hairsprings to provide a more direct and robust connection, effectively inducing the phenomenon without having to rely on the transfer of vibrations to a shared mainplate. 

The exotic Haldimann H2 Flying Resonance equipped with a double-balance flying tourbillon, which by definition relies on a single gear train

The spring pins at the hairspring studs and surrounds the balance wheels, forming the shape of a butterfly and is secured to the balance bridges on both ends. As one hairspring winds and unwinds, it transmits a small amount of vibrational energy to the other directly, thereby influencing and amplifying the vibration of each other to achieve an averaged, more stable rate. This uniquely shaped steel spring also aids in shock resistance. In the event of a shock or disturbance, it only requires a few minutes for both balances to vibrate back in synch, making it one of the fastest, most efficient methods of achieving resonance in a wristwatch on the market. Its relative simplicity in construction, reproducibility, robustness, and reliability represent an altogether different level of achievement that remains unequaled by any of its ilk. 

The Vianney Halter Deep Space Tourbillon Resonance with a triple-axis tourbillon housing two balance wheels. The two balance assemblies are mounted opposite and co-axial to each other on the fixed fourth wheel in a pillar-type construction while both hairsprings are pinned to a common stud carrier

One of the most exotic developments in the field is the Haldimann H2 Flying Resonance launched in 2005. In contrast to the aforementioned resonance watches, in which there are two independent gear trains and oscillators, the H2 Flying Resonance is a tourbillon, which by design is driven by a single gear train. 

The tourbillon carriage houses two balances and escapements. Because an escapement controls the rate of unwinding of a mainspring, a single gear train theoretically cannot drive two escapements. As such, one escape wheel is equipped with a remontoir spring so as to prevent the transmission system from locking up, allowing some buffer and in a way, enables the escapements to decouple. Additionally, the hairsprings in the H2 Flying Resonance are physically linked by a straight spring, enabling the direct transmission of vibrations, which once again works to enhance the phenomenon. 

The tourbillon cage held by ruby jaws on a poising tool and a porotype fourth wheel with the shared stud holder attached to its hub

The second watchmaker to incorporate the effect of resonance in a tourbillon watch is Vianney Halter. The Deep Space Resonance Tourbillon is visually impressive as both balances are housed in a central triple-axis tourbillon. The innermost cage rotates on the first axis once a minute. This cage sits in a traversal structure that rotates around a horizontal axis in six minutes and the entire structure is in turn mounted on a cradle which completes one revolution on its vertical axis in 30 minutes. But crucially, beneath all the kinetic extravagance are novel solutions to enhance the effect of resonance. The two balance assemblies are mounted opposite and co-axial to each other on the fixed fourth wheel in a pillar-type construction, while both hairsprings share a common stud holder.

While these solutions may have been dwarfed in the Deep Space Resonance Tourbillon, they received their due spotlight in the time-only La Resonance unveiled this year. The movement has a particularly intriguing construction for a resonance watch as it was built without a baseplate. The gears are instead held in place by slim but sturdy titanium bridges and pillars. Conventionally, the transmission of vibrations is dependent on the lateral force exerted by the hairspring on the base plate, making the latter a crucial component for resonance to occur. But without it, other solutions had to be introduced to provide a physical connection. Hence, like the Deep Space Resonance Tourbillon, both balances are mounted on a common bridge while the hairspring studs are attached to a shared carrier, essentially establishing a direct physical connection, through which small vibrations can traverse quickly with minimal disturbances.    

The Vianney Halter La Resonance spotlights the solutions to enhancing resonance; the balances are mounted in a co-axial configuration with a shared bridge connecting them while the hairsprings share a common stud holder

The Big Picture

Despite its long history, watches incorporating the phenomenon of resonance remain few and far between, and for practical reasons. They are complex and costly to produce, effectively being two movements in one watch, thus requiring twice the number of wheels and pinions. Beyond that, you’re faced with the fact that the pairing forces between two oscillators in a moving object are small and weak. Matching them is a painstakingly complex task and coupling them is equally challenging.

As such, they are almost not worth the effort when comparing with conventional, micro but sufficiently reliable alternatives used in modern watchmaking to achieve a greater rate stability. At the same time, research and effort in this domain is a claim to fame when it yields results. It is remarkably fascinating to see the concept of forced oscillations taken further with clever enhancements by a diverse handful of independent watchmakers. Regardless of how the effort may seem to outweigh its practical effect, it still does not detract from the ingenious engineering involved in constructing movements conducive enough to host the phenomenon. Beyond that, harnessing and manipulating a phenomenon that occurs in nature to benefit timekeeping is something truly special and falls nothing short of wizardry.

Cheryl Chia

Cheryl Chia is a watch writer based in Singapore and is currently serving as Editor-at-Large of Revolution. Having spent the last seven years covering watches across various horological titles, she has cultivated a deep passion for independent watchmaking. Even though watches have elevated from lowly tools to luxury goods with an emotional dimension, she believes they can still be assessed objectively in terms of effort with respect to price.

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