A method for musical audio synthesis using autoencoding neural networks is proposed. The autoencoder is trained to compress and reconstruct magnitude short-time Fourier transform frames. The autoencoder produces a spectrogram by activating its smallest hidden layer, and a phase response is calculated using real-time phase gradient heap integration. Taking an inverse short-time Fourier transform produces the audio signal. Our algorithm is light-weight when compared to current state-of-the-art audio-producing machine learning algorithms. We outline our design process, produce metrics, and detail an open-source Python implementation of our model.