Squaring a band value produces a soft onset-ish punch that pops on loud hits without requiring true onset detection

Because the bridge provides no discrete onset events, an exponential curve (a.fft[i]²) is the canonical approximation of a felt onset. Squaring keeps quiet bands near zero and amplifies loud transients non-linearly, so the curve pops visibly when the band spikes (e.g. on a kick) and stays quiet between hits. This is always an energy approximation — not a detected event — and will mis-fire on sustained loud bass and miss quiet kicks. It is the only currently supported proxy for the entire blocked class of onset/sidechain/beat-lock couplings. Always label it an approximation; never claim it detects or isolates the kick.

Examples

scale(()=>1+a.fft[0]*a.fft[0]*0.6) — scale stays near 1 between beats and punches up to ~1.6 on a strong kick, faking a sidechain-pump feel. Compare a.fft[0]*0.6 (linear) which stays elevated during sustained bass, losing the transient feel.

Assessment

Write two Hydra scale thunks — one linear, one exponential — on the bass band. Predict how each will respond during: (a) a sustained synth bass note with no kick, (b) a kick with instant decay. Explain which fake-onset behavior each produces.