Temporal Theory of Pitch

Nerves fire in step with each wave cycle; the brain reads the spike timing (period = 1/f) as pitch, dominant below ~1 kHz where place theory struggles.

What it is

Pitch worked out by how fast a sound's wave repeats over time, read from the timing of nerve firings.

Key facts

• Pitch = perceived highness/lowness; for periodic sound it tracks the repetition rate of the waveform in Hz (cycles per second).
• Human hearing range: roughly 20 Hz to 20,000 Hz; the top end falls with age (often ~15-16 kHz by middle age).
• Temporal theory: auditory nerve fibres PHASE-LOCK, firing at a consistent point on each wave cycle, so spike timing encodes the period.
• Phase-locking is reliable below ~1,000-1,500 Hz, degrades up to ~4,000-5,000 Hz, and is essentially gone above ~5 kHz.
• A single nerve fibre maxes out at ~200-500 spikes/sec (refractory period ~1 ms), too slow to fire once per cycle at high pitch.
• Volley principle (Wever, 1949): groups of fibres take turns firing on different cycles; combined volleys reconstruct rates of a few kHz.
• Period T (seconds) = 1 / frequency (Hz). 100 Hz -> 10 ms between spikes; 1,000 Hz -> 1 ms.
• Missing fundamental: brain hears the low pitch from harmonic spacing even with no fundamental, e.g. 200+300+400 Hz heard as 100 Hz.
• Place theory (Helmholtz/Bekesy) maps frequency to a spot on the basilar membrane: high freqs at the base, low freqs at the apex.
• Duplex theory: TEMPORAL coding dominates below ~1-2 kHz, PLACE coding above ~4-5 kHz; doubling frequency = up one octave (A4 440 -> A5 880 Hz).

How it works

1. A periodic sound enters the ear and vibrates the basilar membrane.
2. Hair cells convert that vibration into electrical spikes in auditory nerve fibres.
3. Each fibre phase-locks, firing at the same phase of every wave cycle (or every few cycles).
4. The gap between spikes equals the wave's period (1 / frequency).
5. Many fibres fire in volleys, taking turns so the combined timing represents fast rates.
6. The brain measures that inter-spike timing pattern and reads it out as the pitch.

Real examples

• A 100 Hz bass note: nerves fire every 10 ms, an easy job for temporal coding to lock onto.
• Telephone/cheap speaker with no real bass still lets you hear a low voice pitch via the missing-fundamental effect.
• A male voice fundamental ~100-120 Hz sits squarely in the phase-locking zone, so pitch is rock solid.
• A 5 kHz cymbal shimmer is too fast to phase-lock, so the ear leans on place coding instead.
• Tuning a bass guitar by ear works because low-frequency pitch perception (temporal) is extremely precise.

How it helps in live sound

• Low end (sub/kick 30-120 Hz) is judged by timing, so tight phase alignment between subs and tops matters more than raw level for clean pitch.
• Use delay/alignment (measure with Smaart or a phase trace) so a 60 Hz kick and the top box arrive in phase, or the bass note smears.
• Beware comb filtering: two arrivals a few ms apart muddy low-frequency pitch; check arrival times, not just EQ.
• Muddy bass guitar is often a fundamental masked by room buildup; cut 200-400 Hz rather than boosting the (often missing) fundamental.
• Small PA with no sub still conveys bass-line pitch via missing fundamental, so don't over-boost lows hunting for the note.
• Content above ~5 kHz is placed by tone colour, not pitch timing, so brightness/air EQ won't fix a wrong-sounding bass note.