Background The golden ratio (ϕ ≈ 1. 618) has been proposed as an organizing principle for EEG frequency bands, potentially minimizing spurious cross-frequency synchronization. However, 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), which quantifies spectral frequency ratio proximity (note: “coupling” here refers to frequency ratio relationships, not phase-amplitude coupling), quantifying proximity to ϕ vs. harmonic 2:1 organization. Spectral centroids were computed from eyes-closed resting-state EEG across two independent datasets ( N = 320): PhysioNet EEGBCI ( N = 109) and LEMON Mind-Brain-Body ( N = 211). We performed comprehensive validation including: (1) null model simulation, (2) per-dataset replication, (3) robust statistics, (4) ϕ-specificity parameter sweep, (5) epsilon sensitivity analysis, and (6) frontal theta validation. Results Across 320 subjects, 80.0% showed ϕ-organization (PCI 0). PCI was strongly associated with theta-alpha convergence r = 0.54, p 10 −25 ; Spearman ρ = 0.82 (higher rank correlation reflects monotonic association with bounded transform). This effect: (1) exceeded null model expectation by 5 SD; (2) replicated across both datasets ( r = 0.50-0.63); (3) was robust to outliers; (4) showed ϕ-specificity in parameter sweep; (5) remained qualitatively consistent across epsilon values ( r = 0.41-0.78); and (6) critically, frontal theta analysis yielded even stronger effects ( r = 0.718, p ≈ 10 −35 ), providing evidence against volume conduction artifacts. Demographic controls in LEMON (partial correlation controlling for age) yielded r = 0.490, virtually identical to uncorrected r = 0.497, indicating age does not substantially confound the effect. However, pre-planned exploratory subgroup analyses revealed meaningful individual differences: the association was stronger in younger adults (age 40: r = 0.574, N = 142) than older adults ( r = 0.344, N = 69; note: reduced statistical power in older subgroup), and notably stronger in females ( r = 0.680, N = 77) than males ( r = 0.429, N = 134), consistent with known sex differences in alpha oscillation characteristics. High-ϕ subjects (PCI median) showed frequency profiles converging toward the 8 Hz boundary (θ = 6.24 Hz, α = 9.75 Hz) compared to low-ϕ subjects (θ = 5.85 Hz, α = 10.20 Hz), with no age confound (mean ages 37.7 vs. 35.7 years). Conclusions PCI demonstrates a robust association with theta-alpha convergence that exceeds structural expectations, replicates across datasets, and shows specificity to the golden ratio. The striking frontal theta validation ( r = 0.718) provides converging evidence against a simple spatial-mixing explanation and is consistent with neurophysiological organization.
Andrei Ursachi (2026) studied this question.