Program B · 1 section
Whether the peaks above alpha are oscillations of their own or the shape of alpha itself, and what couples to what.
Supported associationAlpha carries a phase-locked companion at twice its frequency, strongest under LSD: the 21–22 Hz “beta” peak reads as a harmonic of alpha's waveform rather than a separate oscillation.
11 — Alpha harmonics Retrospective · exploratory
Analysis basis 56-recording cohort (19 vs 37) · dataset release 2026.10.10 · last recomputed in analysis release 4.26 · current
Under LSD the spectrum grows a peak at exactly twice the alpha frequency. The evidence that separates a harmonic from an unrelated beta oscillation is phase, not power. Strong phase coupling supports a harmonic interpretation rather than an unrelated beta oscillator, although a distinct oscillator entrained 2:1 is not uniquely excluded.
A peak at 2α could be a separate beta oscillator that happens to sit there, or it could be the second harmonic of a non-sinusoidal alpha. The two are indistinguishable by power. Phase discriminates between them: a harmonic is phase-locked to its fundamental, cycle for cycle, and an unrelated oscillation is not. Locking does not identify the mechanism uniquely — a distinct oscillator entrained 2:1 to alpha would also lock — but it rules out independence.
Two statistics test it. Bicoherence at (α, α → 2α) measures quadratic phase coupling between the fundamental, itself, and the double frequency; it is near zero for independent oscillations and approaches one for a rigid waveform, which is one important mechanism that produces it. The 1:2 phase-locking value between the alpha phase and the doubled 2α phase, tested against circular-shift surrogates, asks the same question from the time domain.
Psychedelic vs non-psychedelic median, 19 vs 37 cohort recordings, permutation p = 0.0006 (20,000 permutations of the median difference).
Median surrogate z-score, 19 vs 37. Under psychedelics the 2α component is rigidly locked to alpha (18 of 19 recordings above z = 10); without them it usually is not (5 of 37).
A median of 0.05 psychedelic against 0.12 non-psychedelic. The harmonic is not extra beta power; the alpha peak simply dwarfs it.
Highest of the four classes (six sessions), ahead of ayahuasca (0.40, four sessions), DMT (0.37, seven) and psilocybin (0.22, two).
A perfectly sinusoidal oscillation has no harmonics. Harmonics appear when the waveform is shaped — sharper troughs than peaks, steeper rises than falls, the arch-like alpha that the older EEG literature called "mu-like". Cole and Voytek (2017)10 argue that this shape is not decoration: it reflects how synchronously the underlying population fires within each cycle. A sharper trough means a more tightly synchronized excitatory volley. Bicoherence measures quadratic phase coupling; a non-sinusoidal waveform is one important mechanism that produces it, and the most direct reading here. On that reading the observation is that in psychedelic-labeled sessions — LSD most of all — each alpha cycle is a more synchronous, more nonlinear event, even as alpha power is lower overall. Whether the psychedelic is the cause cannot be separated here from eye state, posture and setting.
That combination is unusual and is not what "cortical desynchronization" would predict. It fits the wave picture better: alpha is smaller but more organized in both space and waveform. Whether 5-HT2A-driven excitability of layer-5 pyramidal cells accounts for the steeper cycle is a hypothesis this archive can motivate but not test.
First, the harmonic tracks strong eyes-closed alpha, and psychedelic sessions have strong eyes-closed alpha. The four non-psychedelic rest recordings — Resting baseline 003 (part 2) at 0.67 (on 1.6 clean posterior minutes), Resting baseline 002 at 0.51, Resting baseline 001 at 0.30 and Resting baseline 003 (part 1) at 0.26 — sit inside the psychedelic range of 0.16–0.67, and the strongest workday recordings now do too: Workday recording 023 at 0.55 and Workday recording 017 at 0.47. The 41-recording cohort's statement that the top of the distribution was specific to the psychedelics is withdrawn: two of the five most harmonic recordings in the archive are non-psychedelic (a resting baseline and a workday recording), and four non-psychedelic recordings reach the LSD median of 0.46. What remains specific is the pairing of a high bicoherence with rigid locking: 18 of the 19 psychedelic recordings have a 1:2 phase-locking z above 10, against 5 of the 37 non-psychedelic recordings, and the most harmonic workday recordings lock weakly (Workday recording 023, z = 6; Workday recording 017, z = 7).
Second, a consequence for the literature. With alpha at 10.5–11 Hz under LSD (six sessions), its harmonic lands at 21–22 Hz — squarely in beta. A band-power analysis that does not check phase would report an LSD "beta increase" and be describing the alpha waveform. Some published psychedelic beta findings may be exactly this.
The October additions. The three psychedelic sessions recorded after this claim was published behave as it predicts. Ayahuasca experiments 018 and 019 have posterior bicoherences of 0.39 and 0.42 with 1:2 locking at z = 51 and z = 31, and Psilocybin experiment 017, analyzed as one recording that includes its first 30 minutes before ingestion, has 0.28 at z = 51; all three sit above the non-psychedelic median of 0.20 and inside the psychedelic range, with 2α ÷ α power ratios of 0.03–0.04. The eleven new ordinary recordings are the other half of the picture: Workday recordings 020–028 span 0.17–0.55, Daily-life recordings 004 and 005 sit at 0.08 and 0.15, and Workday recording 009 stays at 0.08 when its 3-minute fragment is replaced by the full 95 minutes. Workday recording 023 (0.55, from 9.9 clean posterior minutes) is the most harmonic workday recording in the archive and the third most harmonic recording overall, yet its locking z of 6 is a sixth of the psychedelic median. The new rows' phase-locking z and surrogate p come from 200 random circular-shift surrogates, as the archive's did, so they reproduce only to within a few percent; the bicoherence, phase-locking value and power ratios are deterministic.
About 45 minutes after the dose, LSD experiment 016 grew a second peak near 5.3 Hz, largest at O1 and sitting at half of the session's 10.75 Hz alpha. The section above asks whether 2α is alpha's harmonic. This asks the mirror question: is the 5 Hz line alpha's subharmonic, the first step of a period doubling? The answer has two parts, and the more interesting one is not in the EEG.
From about minute 65 the headset's motion sensors pick up a small rhythmic head movement near 5.4 Hz, and that movement is phase-locked 2:1 to alpha at 13 of the 14 electrodes (z up to 21 against time-shifted surrogates; 0 of 14 in the first hour). Motion explains none of the alpha band itself, so this is neither alpha leaking into the motion sensor nor movement leaking into alpha: something moving at half of alpha's frequency is keeping time with alpha. Most of the 5 Hz line in the EEG is the electrical shadow of that movement — at O1 the peak falls from 0.61 to 0.13 above background once motion is regressed out — and a weak 2:1 locking to alpha survives the regression at six channels, mainly frontal. One session.
Each EEG channel was regressed on the headset's seven motion signals — three accelerometer axes and four orientation components — band-limited to 1.5–14 Hz and offered at 33 time lags spanning half a second either way, so the filter can absorb whatever delay and resonance lie between a moving head and a shifting electrode. The coefficients were always learned on one set of 20-second blocks and applied to the other, which stops the filter from removing signal it merely happens to correlate with. Before it, the coherence between O1 and the accelerometer in the 5 Hz band was 0.009 in the first hour, 0.20 at minutes 65–70 and 0.33 at minutes 78–93, against a chance level near 0.01; in the alpha band it never left chance.
The map above also shows a fainter line near 2.6 Hz on the same plateau, strongest at O2 and P8 and bound 2:1 to the 5 Hz line far more tightly (PLV 0.14–0.19) than the 5 Hz line is bound to alpha (0.05). A tightly bound 2.6–5.2 Hz pair only loosely tied to alpha is what a mechanical rhythm with its own half-rate component looks like, and the regression agrees: that locking is gone at every channel afterwards. The later movement episode carries the same comb — 2.6, 5.4, 8 and 10.9 Hz — on every channel.
| Channel | θ above 1/f | α above 1/f | 2:1 PLV | z | Locked? | θθ→α bicoh. | αα→2α bicoh. | Audit votes | Reference |
|---|---|---|---|---|---|---|---|---|---|
| AF3 | 0.17 | 1.45 | 0.036 | 2.9 | yes | 0.164 | 0.53 | 2 | sensitive · artifact-linked |
| F7 | 0.21 | 1.53 | 0.074 | 6.5 | yes | 0.147 | 0.52 | 2 | robust · artifact-linked |
| F3 | 0.22 | 1.66 | 0.028 | 2.8 | yes | 0.047 | 0.51 | 2 | robust · artifact-linked |
| FC5 | 0.17 | 1.46 | 0.023 | 1.9 | marginal | 0.079 | 0.50 | 3 | robust |
| T7 | 0.27 | 0.83 | 0.014 | 0.3 | no | 0.054 | 0.19 | 1 | robust |
| P7 | 0.04 | 1.72 | 0.041 | 4.7 | yes | 0.057 | 0.58 | 0 | robust |
| O1 | 0.40 | 1.76 | 0.049 | 4.3 | yes | 0.049 | 0.57 | 1 | robust |
| O2 | -0.02 | 1.69 | 0.020 | 0.8 | no | 0.079 | 0.48 | 2 | robust |
| P8 | -0.06 | 1.59 | 0.031 | 2.5 | marginal | 0.073 | 0.37 | 1 | robust |
| T8 | -0.14 | 0.82 | 0.024 | 1.9 | marginal | 0.067 | 0.23 | 1 | robust |
| FC6 | -0.06 | 1.09 | 0.037 | 3.3 | yes | 0.134 | 0.44 | 2 | robust |
| F4 | 0.02 | 1.21 | 0.032 | 2.5 | marginal | 0.115 | 0.38 | 1 | sensitive · artifact-linked |
| F8 | -0.04 | 1.05 | 0.042 | 3.1 | marginal | 0.059 | 0.48 | 3 | robust |
| AF4 | 0.08 | 1.25 | 0.035 | 2.7 | yes | 0.139 | 0.48 | 3 | robust · artifact-linked |
Clean plateau, minutes 65–93, 4 s chunks above 300 µV dropped; 16 s epochs, 300 phase-rotation surrogates per channel; bicoherence from 4 s Hann segments. "Audit votes" and "Reference" are from the whole-session mechanism audit (phase locking, bicoherence and cycle-shape criteria with 500 surrogates and FDR; robustness to common-average reference and a stricter mask). The audit's own summary was a mixture: harmonic expression in a frontocentral–O2 subset alongside a largely separate posterior alpha generator; the plateau-only re-test moves O1 and P7 into the locked set.
The dynamics. One oscillator settling into step with another at a whole-number ratio is entrainment, and 1:2 is the simplest ratio after 1:1: a slower oscillator with a natural frequency near half the driver's falls into a rhythm of one cycle for every two of the driver's. Here the driver is alpha and the slower oscillator is in the body. Tremor is not purely mechanical — it has central generators as well as the resonances of the limb or head it moves59 — so a head tremor near 5 Hz that locks to a 10.8 Hz cortical oscillation is a coupling between two oscillators that are both, in part, neural. The session shows the loop being pushed in a consistent order: alpha got faster (+1 Hz, §18), larger, sharper in its cycle (the 2α harmonic above), and then the body fell into step at half its rate. Cross-frequency n:m phase locking is a normal feature of cortex3233; what is unusual here is a 1:2 lock between a cortical oscillation and a movement, appearing with the plateau.
The reading this replaces. Period doubling of the corticothalamic loop itself — a Floquet multiplier reaching −1, successive alpha cycles alternating, a line at half the frequency34 — is a real route in mean-field models when gain is turned up35, and slow cortical dynamics do move toward the edge of chaos under LSD36. It remains a possible account of the small frontal component that survives the regression. But the posterior line no longer requires it, and the simpler account — a movement, entrained — explains more of the data with fewer assumptions.
Why it is still interesting, and how to test it. If the movement is entrained to alpha, its frequency must follow alpha's as alpha drifts, staying at half; if it is an independent tremor that happens to sit near 5.4 Hz, it will not. Alpha rose by about 1 Hz per hour in this session, so the existing recording can already be asked. For the neural remainder, the photic rig is the right instrument: period doubling is not exotic in the visual system — under fast bright flicker the retina answers only every other flash37, and flicker drives subharmonic responses in visual cortex38 — so drive at f0/2 with the head supported and look for a response at f0.
Subjective correlates — a prediction, not an observation. No ratings were logged for this session. A head oscillating five times a second in step with visual alpha modulates everything that depends on head position at that rate — vestibular input always, and with the eyes open the retinal image — in phase with alpha. That is a candidate for the throbbing or breathing quality of the visual field that LSD reports describe, and diffuse flicker in the 5–25 Hz range is itself enough to generate geometric phosphenes39. The test is cheap: on the next plateau, note whether a fine tremor is felt, log the pulsation rate of the visuals, and compare both with the motion sensor.
The non-psychedelic resting baseline recorded two days after the LSD-labeled session (Resting baseline 003, part 2) has a posterior bicoherence of 0.67 with the flicker intervals masked, the highest non-psychedelic value in the archive and above the LSD-labeled median of 0.46; the desk session with flicker (Workday recording 015) sits at 0.29, inside the psychedelic range; the eyes-open desk session without flicker (Workday recording 014) at 0.06. The values of 0.47 and 0.37 given here in the September release came from an earlier computation that predates the masking of the stimulation intervals and cannot be reproduced from the current tables; the whole-recording posterior medians above are the ones every other number in this section uses. With the flicker masked, square-wave flicker, which is harmonic-rich by construction, no longer explains the resting baseline's value; strong eyes-closed alpha does, on 1.6 clean minutes. The claim therefore stays where the September release moved it, from “tracks LSD” toward “tracks a steep, organized alpha cycle, however produced”. In the LSD-labeled session beta fell across the hour while alpha rose, so the harmonic again did not appear as extra beta power. §18.
A single-subject EEG archive: 56 recordings, 100.1 hours, 19 acute sessions, four psychedelic classes, 34 photic resonance sweeps, thirteen light-noise runs, one brain, February to October 2026. All 56 recordings form the analysis cohort.