Musicians often employ subjective terminology to describe musical phenomena, characterizing certain chords as stable, final, and resolved, while describing others as unstable, tense, and unresolved. From a scientific perspective, it is more rigorous to associate such descriptions with the physical and mathematical properties inherent in a chord's harmonic structure. This book presents a comprehensive formal framework grounded in the forced harmonic oscillator model to characterize the harmonic complexity of just intonation chords. In this approach, the relationships between parameters are expressed through elementary arithmetic—an approach that echoes the spirit of Pythagoras. While alternative techniques, such as those from signal processing, could be employed, elementary arithmetic proves to be a sufficiently powerful, accessible, and elegant tool that merits renewed attention. The diverse topics explored in this book, along with its rich historical context, make it well-suited for undergraduate students in Mathematics, Physics, or Engineering. The work aligns with the growing interest in mathematical and computational applications to music theory and practice. Additionally, the problems and concepts addressed are highly relevant to university-level Music studies, particularly for students seeking to deepen their mathematical and scientific understanding of musical structures. Key Features:Well-illustrated with accessible geometrical representations that enhance understanding and clarify complex conceptsProvides a unique analytical tool grounded in fundamental arithmetic to evaluate and compare harmonic consonance and dissonance in chords by expressing them in their simplest formOffers a comprehensive study of chord harmonicity and periodicity that ranges from foundational principles—enriched with historical context—to advanced topics suitable for research-level exploration, allowing readers to engage with the material at a depth appropriate to their interests and expertise
