Style transfer is a technique for combining two images based on the activations and feature statistics in a deep learning neural network architecture. This paper studies the analogous task in the audio domain and takes a critical look at the problems that arise when adapting the original vision-based framework to handle spectrogram representations. We conclude that CNN architectures with features based on 2D representations and convolutions are better suited for visual images than for time-frequency representations of audio. Despite the awkward fit, experiments show that the Gram matrix determined "style" for audio is more closely aligned with timbral signatures without temporal structure whereas network layer activity determining audio "content" seems to capture more of the pitch and rhythmic structures. We shed insight on several reasons for the domain differences with illustrative examples. We motivate the use of several types of one-dimensional CNNs that generate results that are better aligned with intuitive notions of audio texture than those based on existing architectures built for images. These ideas also prompt an exploration of audio texture synthesis with architectural variants for extensions to infinite textures, multi-textures, parametric control of receptive fields and the constant-Q transform as an alternative frequency scaling for the spectrogram.