There is an increasing interest in the automatic digitization of medieval music documents. Despite efforts in this field, the detection of the different layers of information on these documents still poses difficulties. The use of Deep Neural Networks techniques has reported outstanding results in many areas related to computer vision. Consequently, in this paper, we study the so-called Convolutional Neural Networks (CNN) for performing the automatic document processing of music score images. This process is focused on layering the image into its constituent parts (namely, background, staff lines, music notes, and text) by training a classifier with examples of these parts. A comprehensive experimentation in terms of the configuration of the networks was carried out, which illustrates interesting results as regards to both the efficiency and effectiveness of these models. In addition, a cross-manuscript adaptation experiment was presented in which the networks are evaluated on a different manuscript from the one they were trained. The results suggest that the CNN is capable of adapting its knowledge, and so starting from a pre-trained CNN reduces (or eliminates) the need for new labeled data.