The goal of this study is to test the hypothesis about the models of the so-called realistic artificial neural networks that are in dynamic states, demonstrating behavior close to the self-organized criticality mode and are capable of generating musical patterns. The patterns are sequences of sounds subjectively perceived by a person as musical, which on a more formal level should mean such an internal organization of sound sequences that would allow us to speak about the presence in them, in particular, of such musical characteristics as melody, harmony or meter. An important condition for the generation of musical patterns is the absence of intervention in the dynamics of the neural network from the outside, like the training with the teacher. We talk about the numerical sequences, which subsequently are the base for creating the sound series. Numerical sequences are determined solely by the internal dynamics of the model. The realism of the network means the comparability of the dynamic behavior of the model with the processes occurring in the ensembles of human cortex nerve cells. The model of a modified neural network by Kropotov-Pakhomov is used in our work. The algorithm for constructing musical patterns is described. Examples of both monophonic and polyphonic musical patterns, which are the result of interneuronic interaction in a neural network, are given, and free parameters of realistic artificial neural network models are studied and described. As a result, it was found that the complex dynamics of a realistic artificial neural network can be transformed and interpreted in terms of musical patterns. We defined the areas of the neural network parameters that do not allow us to transform the dynamics of the network into musical patterns, that are far from the phases corresponding to the modes of self-organized criticality. Thus, the studies conducted in the work indirectly confirmed the fact known in neurophysiology and cognitive science that the normal (non-pathological) human brain functions successfully on the “order-chaos” border, namely in a state of self-organized criticality. The materials of the article are of practical value primarily for cognitive scientists and neuroscientists, who use quantitative methods in their research. They are also relevant for musicians, as they reveal some quantitative connections between music and consciousness.