Artificial Evolution has shown great potential in the musical domain. One task in which Evolutionary techniques have shown special promise is in the automatic creation or composition of music. However, a major challenge faced when constructing evolutionary music composition systems is finding a suitable fitness function.Several approaches to fitness have been tried. The most common is interactive evaluation. However, major efficiency challenges with such an approach have inspired the search for <i>automatic</i> alternatives.In this thesis, a music composition system is presented for the evolution of novel melodies. Motivated by the repetitive nature of music, a <i>quantitative</i> approach to automatic fitness is pursued. Two techniques are explored that both operate on frequency distributions of musical events. The first builds on <i>Zipf's Law</i>, which captures the scaling properties of music. Statistical <i>similarity</i> governs the second fitness function and incorporates additional domain knowledge learned from existing music pieces.Promising results show that pleasant melodies can emerge through the application of these techniques. The melodies are found to exhibit several favourable musical properties, including rhythm, melodic locality and motifs.