In this paper, we present a machine-learning approach to pitch correction for voice in a karaoke setting, where the vocals and accompaniment are on separate tracks and time-aligned. The network takes as input the time-frequency representation of the two tracks and predicts the amount of pitch-shifting in cents required to make the voice sound in-tune with the accompaniment. It is trained on examples of semi-professional singing. The proposed approach differs from existing real-time pitch correction methods by replacing pitch tracking and mapping to a discrete set of notes---for example, the twelve classes of the equal-tempered scale---with learning a correction that is continuous both in frequency and in time directly from the harmonics of the vocal and accompaniment tracks. A Recurrent Neural Network (RNN) model provides a correction that takes context into account, preserving expressive pitch bending and vibrato. This method can be extended into unsupervised pitch correction of a vocal performance---popularly referred to as autotuning.