Masking and masked threshold

A loud tone or noise makes quieter tones nearby inaudible – in the spectrum and shortly before and after. Drag maskers and test tone and read the masked threshold.

Explanation Tasks

What is happening?

When one sound swallows another

In a café the voice of the person opposite you is lost as soon as the coffee grinder starts – although it is as loud as before. A loud sound (the masker) can make a quieter one (the test tone) inaudible, even though the quieter one alone would be clearly above the threshold in quiet. This is called masking. The threshold the test tone must exceed in the presence of the masker is the masked threshold.

In the diagram “Simultaneous masking in the spectrum” the threshold in quiet is dashed and the masked threshold is drawn as a thick dark line; whatever lies below is shaded grey. The test tone is a circle – filled when it is audible, hollow when it is masked. Its distance from the threshold is shown next to it and under “Test tone margin”.

Common misconception: masking is a cancellation. The quiet tone is fully present in the signal, a spectrum analyser shows it – only hearing does not perceive it. Try it: with “Tone 1 kHz, 60 dB” the test tone at 1.5 kHz and 30 dB is audible. Drag it to the left: below about 1.27 kHz the circle turns hollow. Listen: turn the sound on and switch “Listen” between “simultaneous” (masker continuous, test tone pulsing) and “test tone only”.

Critical bands and Bark

Why does a tone also mask neighbouring frequencies? In the inner ear each frequency excites not one point on the basilar membrane but a whole section. If a quiet tone lies within the excited region of a louder one, its excitation is lost in it.

The width of these sections is described by the critical bands: below 500 Hz about 100 Hz wide, growing above that – about 160 Hz at 1 kHz, about 690 Hz at 4 kHz, about 1.7 kHz at 8 kHz. Lined up without gaps they give the critical-band rate in Bark: the range of hearing spans about 24 Bark, 1 kHz lies at 8.5 Bark. The readouts “Critical-band rate” and “Critical bandwidth” apply to the frequency of the test tone.

Try it: switch the “Frequency axis” to “Bark (critical bands)” – the low end is stretched, the highs are compressed. Set masker 1 (60 dB) first to 250 Hz, then to 4 kHz: in Hz the masked range of a 30 dB test tone becomes about five times wider (about 270 Hz → 1400 Hz), in Bark it stays similar (2.6 and 1.9 Bark).

Peak and slopes of the masked threshold

The masked threshold of a masker has a peak at its frequency and two slopes. The peak lies below the masker level; the distance is shown by “Masking index (peak − masker level)”. It is −6.025 − 0.275 · z dB for a sine tone and −2.025 − 0.175 · z dB for noise, with z as the critical-band rate of the masker in Bark.

Worked example: a 1 kHz sine tone at 60 dB SPL lies at z ≈ 8.5 Bark. Its masking index is −6.025 − 0.275 · 8.5 ≈ −8.4 dB, so the peak lies at about 51.6 dB. Upwards the threshold falls by 17 dB/Bark in the first Bark, then only by 17 − 0.15 · 60 = 8 dB/Bark. Downwards it falls by 0.4 · 60 + 6 = 30 dB/Bark in the first Bark, then by 17 dB/Bark. At 1.5 kHz, 2.7 Bark above, this gives 51.6 − 17 − 1.7 · 8 ≈ 21 dB: a 30 dB test tone is audible there almost 9 dB above the threshold. At 800 Hz – 200 Hz below instead of 500 Hz above – the threshold is nevertheless lower at about 16 dB.

Loud maskers reach upwards

Masking is asymmetric: with the 1 kHz tone at 60 dB, a 30 dB test tone is masked only from about 890 Hz to 1.27 kHz – 0.7 Bark below, but 1.6 Bark above. Low tones therefore mask high ones better than the other way round. With increasing level this gets stronger, because the upper slope becomes flatter (17 − 0.15 · L dB/Bark with the masker level L in dB, i.e. 5 dB/Bark at 80 dB) and the lower one steeper. A loud masker masks disproportionately much above its frequency (upward spread of masking).

Try it: put the test tone at 2 kHz and 30 dB and raise the level of masker 1 (1 kHz) from 60 via 70 to 80 dB. The masked threshold at 2 kHz rises from about 7 via 21 to 37 dB: 20 dB more masker level raise it here by about 30 dB. At 80 dB the masking of a 30 dB tone reaches up to about 2.5 kHz, almost 6 Bark above, but downwards only to about 820 Hz.

Common misconception: “Only what lies at the same frequency is masked.” Loud low signals in particular – bass, kick, hum, footfall noise – cover a large part of the spectrum above them, while a loud high tone hardly affects the bass. That is why a high-pass filter on tracks without useful bass content often makes a mix clearer.

Noise and several maskers

Noise masks more than a sine tone of the same level: at 1 kHz the masking index is about −8.4 dB for the tone but only about −3.5 dB for noise – about 5 dB more masking. One explanation: next to a sine tone a test tone gives itself away by beats; in irregular noise such cues are missing. Set the “Type” of masker 1 to “Noise”: it is drawn as a band one critical band wide and played that way too. A test tone at 1.5 kHz and 24 dB then flips from “audible” (+2.8 dB) to “masked” (−2 dB).

“Use a second masker” adds masker 2. The thresholds of both maskers then appear individually as thin dashed lines in their colour; the thick line is the combined masked threshold. Individual thresholds and the threshold in quiet are added as powers: two equally strong contributions raise the threshold by 10 · log₁₀(2) ≈ 3 dB, a much weaker one changes hardly anything.

Try it: “Bass noise + tone 3 kHz” combines a 250 Hz noise at 70 dB with a 3 kHz tone at 60 dB. The test tone at 600 Hz and 35 dB lies more than 3 Bark above the noise and is still just masked (threshold about 36.6 dB).

Masking in time

Masking also acts before and after the masker. After a loud sound ends, hearing stays less sensitive for about 100 to 200 ms (post-masking). Even shortly before the onset a quiet tone is masked (pre-masking, only about 10 to 20 ms) – probably because loud signals are processed faster than quiet ones.

The diagram “Temporal masking at the test tone frequency” shows a masker from 0 to 200 ms and the threshold for a short test tone: during the masker the masked threshold from the spectrum, before and after it a decay down to the dashed threshold in quiet. Set the time with “Time (masker 0–200 ms)” or drag the test tone in the diagram.

Worked example with “Post-masking” (1 kHz noise at 80 dB, test tone 1 kHz at 40 dB): during the noise the threshold is about 76.5 dB, 5 ms after the end about 57 dB, 20 ms after it 38.5 dB – the test tone becomes audible about 19 ms after the end. Before the onset it is masked only in the last 2 ms. Try it: start “Run the test tone through time” and watch when the circle fills. Listen: in “temporal” mode a 200 ms masker is followed by a 20 ms test tone at the set time, repeated every 1.2 s.

In the studio and in the codec

In mixing, masking explains why instruments in the same frequency range cover each other. Pushing up the vocal fader helps only so much, because then the vocal masks more itself. Often more effective: cut the masker by a few dB with the EQ where the quiet part lies, for example the guitar in the vocal's presence range around 2 to 4 kHz. The masked threshold drops there, and the vocal becomes audible without getting louder. Bass and kick drum are split into frequency ranges, or the bass ducks briefly via sidechain on every kick – which uses temporal masking.

Lossy codecs such as MP3 and AAC compute the masked threshold for each short section and quantise so coarsely that the quantisation noise stays below it. With sharp transients the noise spreads over a whole transform block, including before the attack – since pre-masking covers only a few milliseconds, audible pre-echoes appear.

Limits of the model

Spectral masking follows psychoacoustic model 1 of MPEG-1 (ISO/IEC 11172-3) with Bark scale, masking index for tone and noise and a level-dependent spreading function. MPEG-1 evaluates it only from −3 to +8 Bark; here the slopes are continued beyond that. Several maskers and the threshold in quiet (Terhardt's approximation) are added as powers.

Temporal masking is a schematic model after Zwicker and Fastl for a 200 ms masker: pre-masking over 20 ms, post-masking over 200 ms, each decaying roughly linearly over the logarithm of time. Effects such as beats for test tones close to the masker frequency and the large variation between people are not included.

When listening, the level ratios are always right, the absolute dB SPL values only after calibration in the settings menu (gear). Whether you hear the test tone also depends on headphones and hearing.

Tasks

Practice questions

Questions from studio, stage and mastering – to think about, discuss and check with the module.

1. In the mix, bass and kick drum disappear into each other and the guitar masks the vocal. What helps, and why does a narrow EQ cut often do more than a louder fader?

Show answer

Masking happens within critical bands. If the vocal gets louder it does rise above the masked threshold, but then masks more itself. Cutting the guitar by a few dB in the vocal's presence range (about 2–4 kHz) instead lowers the masked threshold there, and the vocal becomes audible without getting louder. For bass and kick the ranges are split (kick punch around 60 Hz, bass fundamental above, or vice versa) or the bass ducks briefly via sidechain – which uses temporal masking. Since low signals mask upwards, a high-pass filter on all tracks without bass content pays off.
2. Why does a 128 kbit/s MP3 usually sound fine, but applause, harpsichord or castanets often sound “washy” or have pre-echoes?

Show answer

The encoder places the quantisation noise below the computed masked threshold. With dense, noise-like signals such as applause there are many components that must be estimated precisely; if the bit rate is not enough, the noise becomes audible (washy, “metallic”). Pre-echoes appear with sharp transients: the noise spreads over a whole transform block, including before the attack. Pre-masking only covers a few milliseconds. Encoders therefore switch to short blocks at transients. For production and editing, lossless formats are used, because repeated encoding and later EQ can make the hidden noise audible again.
3. Why is the noise of a microphone preamp or a tape machine heard mainly in quiet passages and at the end of a piece?

Show answer

During loud music the noise lies below the music's masked threshold in most critical bands and is masked. In quiet passages the masked threshold drops, and at the end only the threshold in quiet remains after the 100–200 ms of post-masking – now the noise is freely audible, especially around 2–5 kHz where the ear is most sensitive. Noise reduction systems (Dolby, dbx) and noise gates exploit this: they reduce the noise only when no signal masks it. Dithering likewise pushes the noise into ranges where hearing is insensitive (noise shaping).

Tasks

Predict first, then try it out, then open the solution. “Load starting point” sets the matching initial values.

1. Asymmetric masking

A 1 kHz sine tone at 60 dB masks. Move the 30 dB test tone along the frequency axis: between which frequencies is it masked? How far does the range extend downwards and upwards in Bark?

Load starting point

Show solution

The test tone is masked between about 890 Hz and 1.27 kHz, i.e. roughly 0.7 Bark below and 1.6 Bark above the masker. Upwards the masking reaches more than twice as far. At 1.5 kHz the masked threshold is about 21 dB, the test tone is audible almost 9 dB above it; at 800 Hz (the same distance in Hz downwards) it is only about 16 dB.
2. Louder masks more upwards

The test tone is at 2 kHz and 30 dB. Raise the masker level from 60 to 70 and 80 dB. How does the masked threshold at 2 kHz change?

Load starting point

Show solution

At 60 dB the masked threshold at 2 kHz is about 7 dB, at 70 dB about 21 dB and at 80 dB about 37 dB – the test tone becomes masked. 20 dB more masker level raise the threshold here by about 30 dB, because the upper slope gets flatter with level. At 80 dB the masking of a 30 dB tone reaches up to about 2.5 kHz, almost 6 Bark above; downwards only to about 820 Hz.
3. Tone or noise

The test tone is at 1.5 kHz and 24 dB. Compare a sine tone and a narrow-band noise as masker (both 1 kHz, 60 dB). Also watch the masking index.

Load starting point

Show solution

With the sine tone the masked threshold is about 21 dB, the test tone is just audible (+2.8 dB). With noise it rises to about 26 dB and the test tone is masked (−2 dB). The masking index is about −8.4 dB for the tone and only about −3.5 dB for the noise: noise masks about 5 dB more. Codecs therefore distinguish tonal and noise-like components.
4. Hertz or Bark

A masker at 250 Hz and 60 dB. Find the range in which a 30 dB test tone is masked. Then set the masker to 4 kHz and repeat. Switch the axis between Hz and Bark.

Load starting point

Show solution

At 250 Hz the test tone is masked from about 170 to 440 Hz (around 270 Hz wide), at 4 kHz from about 3.6 to 5 kHz (around 1400 Hz wide) – five times as wide in hertz. In Bark it is 2.6 and 1.9 Bark, i.e. similar: hearing works in critical bands. The critical bandwidth is about 100 Hz at 250 Hz and about 690 Hz at 4 kHz.
5. Pre- and post-masking

A 1 kHz noise at 80 dB lasts from 0 to 200 ms. A short 40 dB test tone at 1 kHz follows 5 ms after the end. Let the test tone run through time: from when is it audible after the end, and how long before the onset is it already masked?

Load starting point

Show solution

During the noise the threshold is about 76.5 dB. 5 ms after the end it is still about 57 dB and the test tone is masked; only about 19 ms after the end does it become audible. For a 20 dB tone post-masking lasts about 70 ms. Before the onset the 40 dB tone is masked only in the last 2 ms: pre-masking is about ten times shorter than post-masking.

Settings

Sound

Level calibration (dB SPL)

MIDI keyboard

Masking and masked threshold