A new method to determine the spin tune is described and tested. In an idealplanar magnetic ring, the spin tune - defined as the number of spin precessionsper turn - is given by $\nu_s = \gamma G$ (gamma is the Lorentz factor, $G$ themagnetic anomaly). For 970 MeV/c deuterons coherently precessing with afrequency of ~120 kHz in the Cooler Synchrotron COSY, the spin tune is deducedfrom the up-down asymmetry of deuteron carbon scattering. In a time interval of2.6 s, the spin tune was determined with a precision of the order $10^{-8}$,and to $1 \cdot 10^{-10}$ for a continuous 100 s accelerator cycle. Thisrenders the presented method a new precision tool for accelerator physics:controlling the spin motion of particles to high precision is mandatory, inparticular, for the measurement of electric dipole moments of charged particlesin a storage ring.
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