Drawing an analogy with automatic image completion systems, we propose Music SketchNet, a neural network framework that allows users to specify partial musical ideas guiding automatic music generation. We focus on generating the missing measures in incomplete monophonic musical pieces, conditioned on surrounding context, and optionally guided by user-specified pitch and rhythm snippets. First, we introduce SketchVAE, a novel variational autoencoder that explicitly factorizes rhythm and pitch contour to form the basis of our proposed model. Then we introduce two discriminative architectures, SkResearch goal: What is the impact of conditioning on sparse user sketches versus dense context windows on the robustness and completion accuracy of generative music models evaluated on polyphonic datasets?Autonomous synthesis report generated by SOVEREIGN Research Kernel. Tribunal consensus score: 8.4/10.