Schumann Resonance (7.83 Hz) and Graph Theory in Music Composition - Hery Budiawan; Clifton Callender; Eli Irawati; Ari Nugraha Wijayanto; Iwan Sugihartono (Institut Seni Indonesia Yogyakarta, 2026)
Previous studies have examined overtone and rhythmic systems, but rarely integrated natural low-frequency phenomena into a unified compositional framework. This study uses the Schumann resonance frequency (7.83 Hz) as its proportional foundation Employing a practice-led computational composition approach, harmonic frequencies were generated through overtone expansion using the formula producing a harmonic series spanning infrasonic and lowaudible frequency regions. To enable musical implementation, harmonic frequencies were transformed into audible musical material through logarithmic MIDI pitch mapping and a fixed octave-normalization procedure (+3 octaves) with a range of 62.64 Hz – 501.12 Hz, thereby preserving the proportional relationships of the original harmonic series. series. Simultaneously, inverse frequency–time mapping generated proportional rhythmic durations, allowing pitch and temporal structures to emerge from a shared mathematical framework. The resulting harmonic and temporal relationships were subsequently modelled as a graph-theoretical network in which nodes represent harmonic frequency components and their associated proportional rhythmic values, while edges represent overtone-derived and proportional relationships among these elements. Rather than serving solely as a visualization tool, the graph model functions as an analytical framework for examining structural connectivity, relational density, and degree centrality within the compositional system. Network analysis revealed that the fundamental Schumann resonance node (7.83 Hz) exhibited the highest degree centrality, indicating its role as the principal structural reference, while the high relational density among harmonic and temporal nodes confirmed the preservation of proportional coherence throughout the compositional network. These findings demonstrate that a single low-frequency source can generate integrated pitch, rhythm, and network structures while maintaining structural consistency across multiple compositional dimensions. This study establishes a formal, computational framework for structural music synthesis. While focusing on compositional design and structural analysis, it provides a foundational model for future empirical research in frequency-based audio perception.