ORIGINAL RESEARCH article
Front. Hum. Neurosci.
Sec. Brain Imaging and Stimulation
Golden Ratio Organization in Human EEG is Associated with Theta-Alpha Frequency Convergence: A Multi-Dataset Validation Study
Provisionally accepted
- independent researcher, bucharest, Romania
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Background: The golden ratio (φ ≈ 1.618) has been proposed as an organizing principle for EEG frequency bands, potentially minimizing spurious cross-frequency synchronization. Whether individual differences in φ-organization have functional correlates remains unexplored. Objective: We investigated whether proximity of theta-alpha frequency ratios to φ is associated with theta-alpha frequency convergence near the 8 Hz boundary. Methods: We developed the Phi Coupling Index (PCI), quantifying spectral proximity to φ versus harmonic 2:1 organization. Spectral centroids were computed from eyes-closed resting-state EEG across two datasets (N=320): PhysioNet EEGBCI (N=109) and LEMON (N=211). Validation included null model simulation, per-dataset replication, φ-specificity parameter sweep, epsilon sensitivity analysis, and frontal theta validation. Results: Across 320 subjects, 80% showed φ-organization (PCI>0). PCI was strongly associated with theta-alpha convergence (r=0.54, p<10⁻²⁵). This effect: (1) exceeded null expectation by >5 SD (Monte Carlo z=8.6-12.9); (2) replicated across datasets (r=0.50-0.63); (3) showed φ-specificity; and (4) critically, frontal theta analysis yielded even stronger effects (r=0.718), providing evidence against volume conduction artifacts. Subgroup analyses revealed stronger associations in younger adults (r=0.574) than older adults (r=0.344), and in females (r=0.680) than males (r=0.429). Conclusions: PCI demonstrates a robust association with theta-alpha convergence that exceeds structural expectations and replicates across datasets. The frontal theta validation provides converging evidence against spatial-mixing explanations, consistent with neurophysiological organization.
Keywords: Cross-frequency coupling, EEG, golden ratio, individual differences, oscillations, spectral analysis, Theta-alpha
Received: 05 Jan 2026; Accepted: 11 Feb 2026.
Copyright: © 2026 Ursachi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Andrei Ursachi
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