Sound frequency is not coded by a single number anywhere in the auditory system — it is coded by which place along an ordered array of frequency-tuned neurons fires most strongly. Starting on the cochlea's basilar membrane and preserved all the way up through the cochlear nucleus, inferior colliculus and primary auditory cortex, units are arranged so that neighbouring units prefer neighbouring frequencies. This tonotopic map is idealised here as log-uniformly spaced characteristic frequencies (CF) across a population, each with a Gaussian tuning curve in log-frequency:
CF(x) = f_min · (f_max / f_min)^(x / L) [log-uniform place axis]
R(x) = R_max · exp( -0.5 · (Δoct / σ_eff)² ) Δoct = log2(f_stim / CF(x))
σ_eff = σ0 · (1 + k · max(0, (L_dB − 40) / 60)) [level-dependent broadening]
- Tone 1 / Tone 2 frequency — one or two simultaneous pure tones; each unit's response is combined as a saturating union of the two Gaussian tuning curves, so two tones far apart raise two separate activity peaks while close tones merge into one.
- Sound level — raises the response gain but also widens σ_eff: real cochlear and cortical tuning curves broaden at higher intensities because more of the traveling wave / more neighbouring channels cross threshold — this is why loud sounds are harder to pitch-discriminate than soft ones.
- Tuning sharpness (Q) — the baseline bandwidth σ0 of each unit; a sharper map (small σ0) resolves close frequencies into distinct peaks, a broad one blurs them together — this is the same trade-off that limits how many independent pitch channels a cochlear implant's electrode spacing can deliver.
- Decoded frequency — a population-vector estimate, the activity-weighted centroid of log2(CF) across the whole array, converted back to Hz; it is compared against the true stimulus frequency as a decode error in cents (100 cents = 1 semitone).
This is a simplified population-tuning model, not a literal wave simulation of the cochlear partition — it illustrates the general principle (used from the auditory nerve through auditory cortex) that pitch is read out from where the population activity peaks, not from any single neuron's firing rate alone.