In this work, an Elman recurrent neural network is used for automatic musical structure composition based on the style of a music previously learned during the training phase. Furthermore, a small fragment of a chaotic melody is added to the input layer of the neural network as an inspiration source to attain a greater variability of melodies. The neural network is trained by using the BPTT (back propagation through time) algorithm. Some melody measures are also presented for characterizing the melodies provided by the neural network and for analyzing the effect obtained by the insertion of chaotic inspiration in relation to the original melody characteristics. Specifically, a similarity melodic measure is considered for contrasting the variability obtained between the learned melody and each one of the composite melodies by using different quantities of inspiration musical notes.