Source
Donoghue, Schaworonkow and Voytek (2021), LIT-1999, pp. 24–27 of the PsyArXiv preprint; read in NOTE-1529.
What was actually shown
A simulated non-sinusoidal 10 Hz alpha rhythm, band-passed at 15–25 Hz, shows a beta envelope that dips at a particular alpha phase, “indicating phase-amplitude coupling, which is driven by the waveform shape of the alpha rhythm”, where a pure beta sinusoid shows none (Fig. 5D–E caption, p. 27). The text: such values “reflect a relationship between frequencies in the spectral domain”, and the fallacy is to read them as “coupling between independent rhythms, when in fact no such interaction between multiple rhythms need exist” (p. 25). The proposed diagnostic is the extent of the coupled band: narrow ranges at exact multiples suggest shape (p. 26).
Check. In a 60 s simulation (scipy Butterworth filters, Hilbert transform, 18-bin Tort modulation index), exp(3 cos φ) at 10 Hz plus noise gave MI = 0.021 for 8–12 Hz phase with 25–60 Hz amplitude, against 0.0001 for cos φ; 15–25 Hz and 80–250 Hz amplitude bands gave ≤ 0.00006 for both. The effect needs a band that holds several harmonics, which is why it is confined to them. The paper’s single-band 15–25 Hz case was not reproduced with a strictly periodic wave.
What this does not say
- That any reported PAC is spurious. The paper re-analyses no empirical result.
- That broadband coupling far above the harmonics, such as 2–5 Hz phase with 80–250 Hz amplitude (THEORY-1317), is a shape artefact. By the paper’s own diagnostic it is the less suspect kind; it remains uncontrolled.
- That PAC is never one rhythm gating another. Genuine nesting is possible; the point is that the measure alone does not show it.