Simulating Chromatic Harmony in Romantic Era Music using Diophantine Approximation

Abstract

The Romantic period of music is known for its intricate and emotionally expressive harmonic style. Nevertheless, recreating authentic melodies of the Romantic period in contemporary compositions poses a considerable challenge for composers and musicians. In this paper, we present a method for simulating chromatic harmony in Romantic Era music through the use of Diophantine Approximation. Inspired by the works of renowned composers of that period, such as Richard Wagner, Franz, Liszt, and Frederic Chopin, my transitional model was constructed to preserve the essence of the preceding melody as the harmonic progression unfolds. The model helps with the creation of harmonic progressions that contain the nuances of the preceding harmonic structure and musical style, providing composers with a novel way to explore a wide range of musical possibilities. Experimental validation involving human hearing shows that the model is successful in imitating authentic Romantic-era harmonic structures. This finding suggests that the model is a promising tool that could inspire contemporary composers to create almost authentic chromatic harmonic progressions.