Swiss metronome chronograph with stop function Circa 1880

Silver duplex chronograph 
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Exceptionally rare Swiss silver open faced keyless metronome chronograph with stop function and duplex escapement, circa 1880.
Polished bassine case, silver hinged cuvette, start and stop slide at 2 o’clock. White enamel dial with an outermost scale divided into 20 parts corresponding to half a second, an inner radial musical score and a gold chronograph hand. Frosted gilt movement, 12 jewels, duplex escapement, three-arm balance, blued steel at balance spring. The dial, movement, case and cuvette are stamped with the same serial number.
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Diameter: 51 mm
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Signed: Patek Philippe & Cie Genève
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The metronome is one of the rarest Patek Philippe mechanisms. It is also the most mysterious Patek Philippe creation known. No one knows what the score is and no one, including Patek Philippe, knows what the beat is for. Only four or five of these pieces are known. All are identical with a single digit serial number.