The motor commands required to control voluntary movements under various environmental conditions may be formed by adaptively combining a fixed set of motor primitives. Since this motor output must contend with state-dependent physical dynamics during movement, these primitives are thought to depend on the position and velocity of motion. Using a recently developed “error-clamp” technique, we measured the fine temporal structure of changes in motor output during adaptation. Interestingly, these measurements reveal that motor primitives echo a key feature of the neural coding of limb motion—correlated tuning to position and velocity. We show that this correlated tuning explains why initial stages of motor learning are often rapid and stereotyped, whereas later stages are slower and stimulus specific. With our new understanding of these primitives, we design dynamic environments that are intrinsically the easiest or most difficult to learn, suggesting a theoretical basis for the rational design of improved procedures for motor training and rehabilitation.