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Electrical Impedance Myography (EIM) is a non-invasive, painless clinical technique for the diagnosis and monitoring of a variety of neuromuscular diseases including amyotrophic lateral sclerosis and focal nerve injuries. It involves the application of a low-intensity alternating current to a muscle group and the measurement of the consequent surface voltage patterns. This paper presents a system for the rapid and accurate acquisition of data employing an interrogating signal composed of multiple tones with frequencies between 10 kHz and 4 MHz. The use of this composite signal makes possible measurement of impedance at multiple frequencies simultaneously. In addition, this system takes impedance measurements at multiple orientations with respect to the muscle fibers by means of an electronically reconfigurable electrode array and utilizes the linearity of muscle tissue to reduce the required measurement time. Testing of the EIM system on beef has established the capability of this system to rapidly detect the anisotropic conductive properties of muscle tissue at multiple frequencies.