Throughout this thesis, we are interested in modeling music composition. To do so, we study the association of music theory concepts with the learning capabilities of recurrent neural networks. Especially, we explore numerical formalizations of music so that our models operate on data containing useful information to decide how to combine particular rhythms and notes in specified musical contexts. The first part introduces the Deep Artificial Composer, a generative model of monophonic melodies. We present a network architecture that considers the temporal and instantaneous relationships between the pitch and duration of notes. By combining Irish with klezmer melodies to train the Deep Artificial Composer, we study how it reacts to heterogeneous data. Furthermore, we show how to generate melodies containing Irish or Klezmer folk music’s characteristics from our probabilistic model of notes. The second part presents BachProp, a model for the composition of polyphonic music. We discover how scores of different styles can be generated from models using neural networks. In particular, we train BachProp with Bach’s chorales and the English folk music corpus Nottingham. Also, we verify that generated compositions share specific properties with the original corpus it processes. Especially, our musical novelty statistics show that BachProp generates musical sequences as innovative as those present in the original corpora. Finally, a large audience appreciated the Ada string quartet performances of BachProp’s compositions. Whereas BachProp operates on any music in the usual MIDI format, the BeethovANN algorithm, introduced in the last part, needs the information contained in scores in the MusicXML format. These digital scores allow us to formalize relevant musical characteristics in order to generate music with BeethovANN. Thus, to create new voices that can be played in accompaniment to Beethoven string quartets, we take into account not only the note sequences, but also the harmonic progression, interactions between voices, and the rhythm of each instrument. Eventually, professional musicians misclassified BeethovANN musical phrases for Beethoven’s original compositions.