We present a new approach for audio bandwidth extension for music signals using convolutional neural networks (CNNs). Inspired by the concept of inpainting from the field of image processing, we seek to reconstruct the high-frequency region (i.e., above a cutoff frequency) of a time-frequency representation given the observation of a band-limited version. We then invert this reconstructed time-frequency representation using the phase information from the band-limited input to provide an enhanced musical output. We contrast the performance of two musically adapted CNN architectures which are trained separately using the STFT and the invertible CQT. Through our evaluation, we demonstrate that the CQT, with its logarithmic frequency spacing, provides better reconstruction performance as measured by the signal to distortion ratio.