Antheil’s Ballet Mécanique, in its original conception for sixteen synchronized player pianos, required that all sixteen instruments advance their paper rolls at exactly the same rate throughout the performance. This sounds simple. It is not. Two independently running mechanical systems — even two systems using identical mechanisms — will drift over time due to tiny differences in spring tension, friction, wear, and resistance. A clock mechanism that runs two seconds per hour faster than another will be thirty-two seconds ahead after sixteen hours; in a musical performance, even a fraction-of-a-second drift between two pianos produces an audible discrepancy.
Antheil’s solution was rigorous calibration of the spring clock motors that drove each roll. The motors were set to run at exactly the same constant speed, verified against a single standard, and relied upon to maintain that speed throughout the performance without communication between instruments. This was not perfect synchronization — it was synchronization maintained by independent accuracy, each mechanism faithful to the same standard without reference to the others.
This is exactly the principle that the frequency-hopping patent uses. The transmitter on the surface ship and the receiver in the torpedo each carry identical paper strips. Each strip is driven by a spring clock motor calibrated to advance at the same constant speed. Both mechanisms start simultaneously, triggered by the torpedo’s launch. From that moment, both systems hop through the same frequency sequence at the same rate, without any communication between them that could be intercepted.
The elegance of the solution is that the adversary cannot predict or block the frequency sequence without knowing the specific pattern of the paper strip. The synchronization is maintained not by continuous communication but by advance agreement — both sides know the strip, both sides run the same strip, and the system’s security derives from the secrecy of the strip’s design rather than from any signal that passes between them.