In recent years, the quality and public interest in music generation systems have grown, encouraging research into various ways to control these systems. We propose a novel method for controlling surprisal in music generation using sequence models. To achieve this goal, we define a metric called Instantaneous Information Content (IIC). The IIC serves as a proxy function for the perceived musical surprisal (as estimated from a probabilistic model) and can be calculated at any point within a music piece. This enables the comparison of surprisal across different musical content even if the musical events occur in irregular time intervals. We use beam search to generate musical material whose IIC curve closely approximates a given target IIC. We experimentally show that the IIC correlates with harmonic and rhythmic complexity and note density. The correlation decreases with the length of the musical context used for estimating the IIC. Finally, we conduct a qualitative user study to test if human listeners can identify the IIC curves that have been used as targets when generating the respective musical material. We provide code for creating IIC interpolations and IIC visualizations on https://github.com/muthissar/iic.