The generalized command response (GCR) model represents intonation as a superposition of muscle responses to spike command signals. We have previously shown that the spikes can be predicted by a two-stage system, consisting of a recurrent neural network and a post-processing procedure, but the responses themselves were fixed dictionary atoms. We propose an end-to-end neural architecture that replaces the dictionary atoms with trainable second-order recurrent elements analogous to recursive filters. We demonstrate gradient stability under modest conditions, and show that the system can be trained by imposing temporal sparsity constraints. Subjective listening tests demonstrate that the system can synthesize intonation with high naturalness, comparable to state-of-the-art acoustic models, and retains the physiological plausibility of the GCR model.