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$EVWUDFWA bandwidth-independent, linear and scalable method for carrier-envelope phase drift measurement demonstrated. Our experiments reveal that carrier-envelope phase drift of a picosecond pulse train can be directly obtained from the spectrally resolved interference pattern of a length-stabilized multiple-beam interferometer. The retrieved phase from the pattern correlates well with the strongly CEP-sensitive coupling signal between the frequency combs of the picosecond oscillator and an ultra-high finesse Fabry-Perot interferometer. Our results can lead to the generation of a robust CEP-stabilized seed pulse train for high resolution comb spectroscopy as well as to compact Compton X-ray and gamma-ray sources.