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We describe a prototype scalable viscometer aimed at facilitating rapid measurements of multiple samples. The device simultaneously measures the viscosity of four samples in an array of Couette cells. Each cell contains a rotor with an embedded permanent magnet that is driven by an oscillating magnetic field generated by a two-axis Helmholtz coil. The angular displacement of the rotors is recorded by a charge-coupled device camera. Image analysis determines the amplitude and phase of the rotors with respect to the coil's sinusoidal current. The viscosity of each sample influences the amplitude and phase of the rotor, which can be predicted with a viscously damped oscillator model. We present data for Newtonian fluids with viscosities from 50 to 2000 mPa s