Rhythm — the inhibitory clock sets the band

The population rhythm's band is set by the inhibitory time-constant: faster inhibition gives a higher band, so one excitatory–inhibitory circuit spans δ→θ→γ, and theta gates gamma (~17× at the preferred phase). Added excitatory drive shifts the dominant rhythm up (the autism direction); neurodegenerative burden slows it toward δ (the Alzheimer direction).

The band of the population rhythm is set by the inhibitory time-constant τ_inh: faster inhibition → higher band, so one E/I circuit spans δ→θ→γ. Theta and gamma separate, and theta gates gamma (≈17× more gamma at the preferred theta phase). Two disease directions move the dominant rhythm: added excitatory drive shifts it up toward gamma (the autism direction), while neurodegenerative burden slows it down toward δ and weakens it (the Alzheimer direction). The band is wiring and context, robust to the individual cell.

τ_inh sets the band

What fixes the frequency of the population rhythm is not the excitatory cell but the inhibitory one: the time-constant τ_inh of inhibition sets how fast the circuit can re-cock. Faster inhibition gives a higher band, slower inhibition a lower one. So the band is a property of the wiring and context, not of any single cell's identity — a robustness that matters for the disease reads below.

Theta gates gamma

The slow rhythm and the fast rhythm are not independent. Theta and gamma separate cleanly, and theta gates gamma: gamma power is concentrated at one preferred phase of the theta cycle, on the order of 17× higher there than at the opposite phase. This cross-frequency coupling — a slow carrier organising fast packets — is the structure the working-memory code in §4 exploits.

What is pinned here is not the absolute frequencies but their ratio. The number of gamma cycles nested in one theta cycle — the dimensionless ratio γ/θ — comes out near seven, in the 7±2 range Miller measured for working-memory capacity, and this is the one part of the picture with a direct causal test: rhythm-locked tACS that changes the ratio changes capacity. The absolute theta and gamma frequencies in hertz are not derived here — they depend on the absolute inhibitory time-constant, which is an external calibration — so they stay open [O]. Only the dimensionless γ/θ ≈ 7±2 is claimed as validated; the hertz values are not.

One circuit, δ→θ→γ

Because τ_inh sets the band, a single E/I network spans the whole range: slow it down and the dominant rhythm is δ, speed it up and it is γ, with θ between. Anchored to a measured excitatory channel (the SCN2A read), the same circuit walks δ → θ → γ as τ_inh shortens. There is no need for separate machines per band; there is one machine with a knob.

Direction match

Two clinical directions follow, and they match the data in sign. Add excitatory drive — raise E:I — and the dominant rhythm shifts up toward gamma; this is the autism direction. Add neurodegenerative burden and the rhythm slows toward δ and loses amplitude; this is the Alzheimer direction (and connects to the bistable collapse of §6's trauma/loss reads). These are directional, real-data-matched claims; the absolute Hz and any clinical calibration remain open (§9).