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Cepheid stars play a considerable role as extragalactic distances indicators,thanks to the simple empirical relation between their pulsation period andtheir luminosity. They overlap with that of secondary distance indicators, suchas Type Ia supernovae, whose distance scale is tied to Cepheid luminosities.However, the Period-Luminosity (P-L) relation still lacks a calibration tobetter than 5%. Using an original combination of interferometric astrometrywith optical and ultraviolet spectroscopy, we measured the geometrical distanced = 720.35+/-7.84 pc of the 3.33 d period Cepheid V1334 Cyg with anunprecedented accuracy of +/-1 %, providing the most accurate distance for aCepheid. Placing this star in the P-L diagram provides an independent test ofexisting period-luminosity relations. We show that the secondary star has asignificant impact on the integrated magnitude, particularly at visiblewavelengths. Binarity in future high precision calibrations of the P-Lrelations is not negligible, at least in the short-period regime. Subtractingthe companion flux leaves V1334 Cyg in marginal agreement with existingphotometric-based P-L relations, indicating either an overall calibration biasor a significant intrinsic dispersion at a few percent level. Our work alsoenabled us to determine the dynamical masses of both components, M1 = 4.288 +/-0.133 Msun (Cepheid) and M2 = 4.040 +/- 0.048 Msun (companion), providing themost accurate masses for a Galactic binary Cepheid system.

A geometrical 1% distance to the short-period binary Cepheid V1334 Cygni