Frequency ABX Test — Pitch Drill

A blind frequency discrimination test measures the auditory system’s ability to detect subtle pitch variations between two sequential sine tones. By presenting randomized tone pairs without visual cues, the test determines a listener’s difference limen for frequency, establishing the threshold in Hertz where pitch changes become consistently recognizable. This drill fixes the reference at 1 kHz and shrinks the gap from an obvious 50 Hz down to a single cycle per second.

How to use it

1. Pick a rung. The ladder runs 50, 20, 10, 5, 2, and 1 Hz above a 1 kHz reference. Signal A is 1000 Hz; Signal B is 1000 Hz plus your selected delta.
2. Hear both references openly until the direction of the shift is familiar, then move to the blind section.
3. Answer which one X was. The assignment is re-randomized every trial; the panel updates trials, correct count, streak, running p-value, and confidence.
4. Descend the ladder methodically. Play each rung to a verdict before going finer; a chance result at 2 Hz after a significant 5 Hz result is a real boundary, not a failure.
5. Re-test across days, not hours. Thresholds drift with fatigue and practice, and a single session is a data point, not a diagnosis.

Pitch resolution: what “fine” actually means

Pitch perception operates through two complementary mechanisms. Place coding reads which region of the cochlea’s basilar membrane resonates: high frequencies peak near the base, low frequencies near the apex. Temporal phase-locking lets auditory nerve fibers fire in synchrony with the waveform’s cycles, useful up to roughly 4–5 kHz. Around 1 kHz both channels are working well, which is why the reference sits there.

The scale that matters is the auditory filter width. At 1 kHz the equivalent rectangular bandwidth (ERB) is about 133 Hz, so even a “large” 50 Hz shift moves excitation across only about 38% of one critical band, and a 5 Hz shift nudges it by under 4%. Measured human performance is nevertheless sharp: JND studies compiled in the psychoacoustics literature put the pure-tone frequency limen near 3 Hz below 500 Hz and around 0.6% of the reference above 1 kHz (roughly 10 cents), while the best-conditioned listeners in classical experiments by Ritsma (1965) and Nordmark (1968) fell below 1 Hz difference at around 1 kHz with long, level-controlled tones. The ear can resolve on the order of 1,400 distinct pitch steps across its range in total.

Converting the rungs into musical units uses the standard cents formula: interval = 1200 × log2(f2 / f1), where 100 cents is one equal-tempered semitone.

Delta at 1 kHz	Cents	% of one ERB (133 Hz)	Musically
1 Hz	1.7	0.8%	Below most untrained listeners
2 Hz	3.5	1.5%	The typical DLF floor
5 Hz	8.6	3.8%	Trained ear territory
10 Hz	17.2	7.5%	Comfortable for many
20 Hz	34.3	15.1%	Clearly sharp/flat
50 Hz	84.5	37.7%	Nearly a semitone

One practical corollary: because the Weber fraction for pitch is roughly proportional, ±Δ in hertz means less as the reference climbs. The same 10 Hz gap at 8 kHz is only 2.2 cents, far below threshold, which is why drills like this hold the reference fixed and vary the step. And if you want to cheat the sequential limen honestly, play the two tones together on the Tone Generator: interference produces beats at exactly the difference frequency, so two tones 2 Hz apart audibly wobble twice per second even when sequential comparison calls them identical.

Turning forced choice into a threshold measurement

The statistical skeleton is the standard ABX contract used across this site’s Blind ABX hub: known references A and B, a hidden X drawn at random from the pair on every trial, forced choice with no abstain option, and a verdict issued by cumulative upper-tail binomial probability against a 50% guessing baseline at p ≤ 0.05. The design kills the two failure modes of casual pitch self-assessment: response bias (saying “different” only when certain shifts the threshold without changing the ear, which is why guessing is allowed and still priced correctly by the p-value) and reference drift (comparing today’s 2 Hz rung against yesterday’s memory of a different tone).

What makes this drill a threshold instrument rather than a quiz is the staircase: each finer rung is about half the step width of its neighbor, and your boundary between significant and chance verdicts localizes your difference limen in hertz. Report it properly: your DLF is the finest rung at which a fresh session still reaches significance, ideally confirmed by repeating that rung three separate days. Expect slow improvement at the fine rungs with practice; frequency discrimination is one of the more trainable auditory attributes, which is exactly why an ABX record beats an impression.

Accuracy, limits and troubleshooting

• Level and timing must be stable. A louder tone reads as different for reasons unrelated to pitch; the engine normalizes both, so do not reintroduce the cue with the volume knob mid-session.
• Hearing asymmetry matters. If one ear is muffled (congestion, recent noise exposure), high-frequency thresholds shift and fine rungs become luck-tests; re-run when symmetric, and screen with the Hearing Test.
• Cheap Bluetooth links band-limit and wobble. Codec resampling adds micro-delay jitter that can smear tone onsets; run the drill over wired output if 5 Hz feels impossibly hard at moderate volume.
• Below about 2 Hz you are near the physical floor of sequential short-tone discrimination on any day; a chance verdict there is normal physiology, not an ear problem.

Related tools

• Blind Pitch (Cents) Drill — the musical-interval sibling, 25 down to 2 cents at 440 Hz.
• Tone Generator — set up beat-based comparisons with two simultaneous sines.
• Frequency Check — map your audible range before judging discrimination.
• Blind ABX hub — level, timing, polarity, dynamics, and bit-depth thresholds in one series.