Redefinition of EEG Frequency Bands: A Fractal Model Inspired by Blagg’s Titius-Bode Law

Abstract

The canonical frequency bands used to categorize human electroencephalographic (EEG) activity-delta, theta, alpha, beta, and gamma-have historically been defined using pragmatic and variably applied thresholds rather than a unifying mathematical principle. In this theoretical study, we propose a geometric framework for redefining EEG frequency bands based on logarithmic scaling, drawing on the exponential formulation introduced in Mary Blagg's refinement of the Titius-Bode law. Using the mean adult alpha rhythm as a reference frequency and applying a constant scaling ratio (R = 1.7275), we derive a mathematically ordered hierarchy of EEG band centers and boundaries within a continuous log-spaced spectrum. Unlike descriptive models of spectral 1/f scaling, the present framework provides an explicit generative rule for discrete band centers and transition frequencies. The resulting segmentation produces band definitions numerically consistent with commonly reported EEG frequency ranges while offering a fully proportional, non-overlapping structure. The model further introduces principled subdivisions within the alpha and gamma ranges and redefines the beta-gamma transition using geometric rather than conventional criteria. As a descriptive quantitative observation, the model-derived theta-alpha transition (similar to 7.98 Hz) lies in numerical proximity to the Earth's fundamental Schumann resonance (similar to 7.83 Hz); this correspondence arises from the predefined geometric rule and does not imply causal interaction. Overall, the proposed framework reframes EEG band organization as a mathematically explicit, scale-invariant system and provides a hypothesis-generating basis for future empirical evaluation of oscillatory structure.