Mapping your hearing

Every page on this site that throws sound away, the MP3 encoder above all, leans on a model of hearing: how quiet a sound can be before you miss it, and how a loud sound hides a quieter one nearby. Those models are averages, measured on many young listeners decades ago. This page measures yours, with the same methods hearing researchers use, and then runs an encoder with your ears in it.

It leans on:

Sampling and reconstruction, for decibels and full scale.
Inside an MP3 encoder, whose psychoacoustic model is built from the textbook versions of the curves measured here.
The Fourier transform, for what “a band of noise” means.

This isn’t a medical hearing test. A browser can’t know how loud your headphones are, and a clinic’s audiometer is calibrated in a quiet booth. If you’re worried about your hearing, see an audiologist. What this page can do well is compare: your left ear against your right, you this year against you next year, and how one sound hides another, which doesn’t depend on the calibration at all.

0 · Setting up

Use headphones (any will do; good ones are better), somewhere quiet. Play the reference tone and set your computer’s volume so it’s clearly audible but comfortable, about as loud as a quiet conversation. Then don’t touch the volume again: every level on this page is measured against that setting. Nothing here plays louder than 10 dB above the reference tone.

Check that left is in your left ear and right in your right. The reference tone is 1 kHz at −20 dBFS (20 dB below a full-scale sine). Your results are kept in this browser only; copy them to keep them elsewhere.

Levels here are in dBFS: decibels below a full-scale sine, the loudest the computer can play. To compare with curves measured in dB SPL (decibels of sound pressure), the page assumes the reference tone plays at about 60 dB SPL, so dB SPL ≈ dBFS + 80. That’s a guess about your volume setting, and the comparisons with textbook curves are only as good as it is.

1 · How quiet can you hear?

A tone, getting quieter in steps. At some point it’s gone. Where that happens is your threshold for that tone: the quietest level you can hear.

A 1 kHz tone, 5 dB quieter each second, from the reference level down. Press I can’t hear it any more when it’s gone. It’s a rough answer: you were expecting the next step, and you may have been guessing at the end.

Two things make a measurement like that unreliable. You know when to expect the tone, so you’re tempted to hear it a step longer than you do. And where you draw the line between “faint” and “gone” is up to you. Hearing researchers have two ways round this, and the page uses both.

Tracking. Georg von Békésy’s 1947 audiometer let the listener drive: hold a button while you hear the tone, and it gets quieter; let go when you can’t, and it gets louder. The level zigzags across your threshold, and the threshold is the middle of the zigzag. It’s quick, and the line you draw (between hearing and not) matters less, because you cross it from both sides.

Forced choice. Play three sounds, one different, and ask which. Now there’s no line to draw: you either pick the right one or you don’t (a third of the time by luck). A staircase sets the difficulty: two right answers in a row make it harder, one wrong makes it easier. Harry Levitt showed in 1971 that this settles where you’re right 70.7% of the time, since two right in a row then happens half the time ( $0.707^2 = 0.5$ ). Section 7 uses it.

2 · Your audiogram

An audiogram is your threshold at each frequency, from deep bass to the top of hearing. Clinics measure it from 250 Hz to 8 kHz; here it goes from 125 Hz to 16 kHz.

Hold here (or hold Space) while you can hear the beeps

Start, then hold Space (or press and hold the pad) while you can hear the beeping: it fades. When it’s gone, let go: it comes back, and when you hear it again, hold again. At each frequency you’ll press three times and let go three times, then it moves to the next frequency, starting 10 dB above the threshold it just found; a frequency you can’t hear even at the loudest is skipped after 15 seconds. About a minute or two an ear.

Take your time: wait until you’re sure the beeping is there before you press, and sure it’s gone before you let go. The level moves at 5 dB a second, so the zigzag overshoots your threshold, by a few decibels each way. That’s expected: your threshold is taken as the middle of each swing, so a late press (above it) and a late release (below it) cancel, as long as you’re about as quick either way. A slow, steady zigzag gives a better answer than chasing the line with quick taps.

Your headphones are part of the measurement. Few are flat enough to measure with: most consumer headphones have peaks and dips of 10 dB or more, especially between 5 and 10 kHz, where the shape of your ear and the fit of the earcup also matter. A dip in the headphones looks exactly like a hearing loss at that frequency, and a peak like better hearing. If both ears show the same notch, suspect the headphones; measuring again on a different pair tells you which it is.

The dashed line is the textbook threshold (Terhardt’s formula, which the MP3 page’s model uses) at this page’s assumed volume: lowest near 3.3 kHz, where the ear canal resonates, and rising steeply at both ends. Earlier runs stay on the plot, dotted. How high can you hear? plays a tone gliding up from 8 kHz at the reference level: press It’s gone when it disappears.

Things to look for:

The shape, not the height. Your whole curve sits higher or lower than the textbook one depending on your volume setting. What matters is its shape, and where it bends.
The top end. Hearing above about 8 kHz fades with age for nearly everyone (presbycusis), and the highest frequency you can hear falls by several kilohertz over a lifetime. Your headphones’ own top end is in this measurement too: try another pair if you can.
A dip around 4 kHz in one or both ears is the classic sign of noise damage: loud machinery, gunfire, or years of loud music. The ear is most sensitive there, and that’s where it’s hurt first.
Left against right. Your headphones’ response cancels out in this comparison, so a difference between your ears is about your ears.

3 · Loud and quiet aren’t the same at every pitch

Equal levels don’t sound equally loud. A bass note has to be much more intense than a 1 kHz tone to sound as loud, and the difference is biggest when everything is quiet. In 1933 Harvey Fletcher and Wilden Munson measured this as equal-loudness contours: the levels at which tones of different frequencies sound equally loud, today standardised as ISO 226. Their unit is the phon: a sound at 40 phon is as loud as a 1 kHz tone at 40 dB SPL.

Match each tone to the 1 kHz reference: Listen plays the reference, then the test tone, over and over; move its level until they sound equally loud, then press They sound the same (it moves on to the next frequency). Do it at both loudnesses. The dashed lines are ISO 226 at 30 and 50 phon (this page’s assumed volume): at 100 Hz, a tone must be 24.4 dB above a 1 kHz tone to sound as loud at 40 phon, but only 12.5 dB above at 80 phon. Your headphones’ frequency response is mixed into your matches, especially in the bass.

That squashing of the bass curve at higher levels is why music played quietly sounds thin, and why old amplifiers had a loudness button that lifts the bass (and a little treble) at low volume. It’s also why the loudness meters on the dynamics page weight frequencies before adding them up.

4 · One sound hiding another

A loud sound makes quieter sounds near it inaudible: it masks them. This is the effect a perceptual audio coder exploits: any noise it adds is fine if a louder sound nearby hides it. Here, a band of noise around 1 kHz masks a tone, and you find how loud the tone must be to be heard, at frequencies above and below the noise.

Hold here (or hold Space) while you can hear the beeps

A band of noise from 900 to 1,100 Hz plays all the time (shaded); track the beeping tone as before, at each frequency. The dashed lines are the textbook prediction: Schroeder’s spreading function (from the MP3 page’s model), 5 dB below the noise. Its shape is the same at both levels; real ears’ isn’t. Masking spreads further up than down, and further up the louder the masker is: compare your two curves.

Masking spreads upwards more than downwards. The cochlea sorts sound by frequency along its length, high frequencies near its entrance and low ones at the far end. A sound’s vibration travels in from the entrance, peaks at its own place, then dies quickly. So a low sound shakes everything on its way to its place, which is where the higher frequencies are detected; a high sound barely reaches the places of lower ones. The louder the sound, the further the shaking spreads: this upward spread of masking is why a loud bass line can hide a quiet melody.

5 · The ear’s filters: critical bands

The cochlea acts like a bank of overlapping band-pass filters. A tone is masked only by the noise that gets through the same filter as it. Harvey Fletcher’s 1940 experiment shows this: a tone in a band of noise, and the noise made wider and wider, at the same level per hertz. At first, wider noise means more noise in the tone’s filter, and the tone gets harder to hear. Once the noise is wider than the filter, the extra noise falls outside it, and the threshold stops rising.

Hold here (or hold Space) while you can hear the beeps

A 1 kHz tone in noise centred on 1 kHz, from 25 to 1,600 Hz wide, all at the same level per hertz (a 100 Hz band is at −40 dBFS). The orange line is the best fit of “rising 3 dB per doubling, then flat”, and where it bends is your critical band at 1 kHz. The textbook value is Brian Glasberg and Brian Moore’s equivalent rectangular bandwidth: 133 Hz at 1 kHz.

It’s a hard measurement, and the bend is soft (the ear’s filters aren’t rectangular), so don’t be surprised if yours lands somewhere between half and double the textbook figure, or further. Thresholds often keep creeping up past the bend, because a wide band of noise also masks upwards from its low end (section 4), and that pushes the fitted bend higher. If yours never levels off at all, the figure says so. The filters widen with frequency, roughly in proportion above 500 Hz, which is why the MP3 page groups its frequencies on the Bark scale, one Bark per critical band.

6 · Masking in time

A loud sound also hides quieter sounds just after it (forward masking, for up to about 200 ms), and even just before it (backward masking, a few milliseconds): a loud sound reaches the brain quickly enough to overtake a quiet one that started a moment earlier.

Hold here (or hold Space) while you can hear the beeps

A 10 ms click at 2 kHz, before and after 200 ms of noise at −30 dBFS (shaded), and on its own. Track it as before. The click ends 40, 10 and 0 ms before the noise starts, then starts 5, 10, 20, 40, 80 and 200 ms after it ends, and last of all plays alone: the readouts are how much louder it had to be than alone.

This is why the MP3 encoder switches to short blocks for drum hits: a long block would spread its noise across the moment before the hit, where backward masking covers only a few milliseconds, and you’d hear a pre-echo.

7 · How fine is your hearing?

Two more measurements, both by forced choice: three sounds, one different.

Three sounds play; one is different. Answer with the buttons or the keys 1, 2 and 3.

Pitch: three tones near 1 kHz (the base pitch varies a little from trial to trial, so only the difference helps), one higher by the amount shown. Gaps: three bursts of noise, one with a silent gap in the middle. Each starts easy (a semitone, 100 cents; a 20 ms gap) and the staircase homes in. Green dots: right; orange: wrong. The result is the difference you pick out 70.7% of the time.

Trained listeners hear a pitch change of a few cents at 1 kHz (a cent is a hundredth of a semitone), much finer than the ear’s filters are wide: the ear also follows the timing of the waveform itself. Gap detection, for young listeners, is a few milliseconds, and it often gets worse with age even when the audiogram looks normal: one reason older listeners find fast speech harder to follow.

8 · An encoder tuned to your ears

Now use the measurements. The masking model below does what the MP3 encoder’s psychoacoustic model does: for each short stretch of sound, it works out the level of noise that would go unheard, from the threshold in quiet and the masking spread from every band. But instead of adding noise up to that level, it removes everything quieter than it: the parts of the sound these ears couldn’t hear anyway.

Ears: the textbook model (Terhardt’s threshold at this page’s assumed volume, Schroeder’s spreading 6 dB down), or your audiogram from section 2, with your masking curve from section 4 if you’ve measured one. Listen to what’s kept against the original: if the model fits your ears, you can’t tell them apart. What’s taken away is played 20 dB louder, or you wouldn’t hear it at all. With ears that hear less at the top, more of the top is taken away.

It works because the levels are real: your thresholds were measured at the same volume setting the music plays at. Turn the volume up, and the model would be wrong: things it took away would become audible. Real encoders can’t know your volume either, so they assume the music will be played loud, and keep more than they’d need to.

Summary

Your threshold is the quietest sound you can hear. Tracking (Békésy) and forced choice with a staircase (Levitt) keep guessing out of the measurement.
An audiogram maps the threshold across frequency: most sensitive around 3–4 kHz, falling away at the top with age, and often dipping at 4 kHz after noise damage.
Equal-loudness contours show bass needs more level to sound as loud, most of all when it’s quiet.
Masking hides quiet sounds near loud ones, spreading further up in frequency than down, more for louder maskers; and in time, for up to about 200 ms after a sound and a few milliseconds before.
The ear works like a bank of filters, the critical bands, about 133 Hz wide at 1 kHz.
Perceptual coders throw away what masking and the threshold hide; with your own curves, the model is tuned to you.

Mapping your hearing

0 · Setting up

1 · How quiet can you hear?

2 · Your audiogram

3 · Loud and quiet aren’t the same at every pitch

4 · One sound hiding another

5 · The ear’s filters: critical bands

6 · Masking in time

7 · How fine is your hearing?

8 · An encoder tuned to your ears

Summary

Further reading