White vs Pink vs Brown Noise

White, pink and brown noise are all steady, random sound with no tune and no rhythm. They differ in one way only: how their energy is shared between low and high frequencies. The color is a name for that shape. ScreenTail makes all three in your browser: White Noise, Pink Noise and Brown Noise.

One idea: power per octave

Hearing works in octaves. Going up an octave doubles the frequency, from 100 Hz to 200 Hz, or from 1,000 Hz to 2,000 Hz, and each octave sounds like an equal step to the ear. But each octave up contains twice as many hertz as the one below it. That single fact explains all three colors.

The figures are power, in decibels. White noise is defined as having “equal power per hertz” and pink noise “equal power per octave”, in the words of the ATIS Telecom Glossary, the American National Standard glossary that replaced the U.S. government’s Federal Standard 1037C; brown noise’s power falls with the square of the frequency.

White noise

White noise is, in ATIS’s words, “noise having a frequency spectrum that is continuous and uniform over a specified frequency band”, with “equal power per hertz”. The name is an analogy with light: Georgia State University’s HyperPhysics explains that it is called white “by analogy to white light, which is a mixture of all visible wavelengths.”

Flat per hertz is not flat to the ear. HyperPhysics works it through: since each octave has twice as many hertz as the one below, “the power in white noise will increase by a factor of two for each octave band”, which is “a 3 decibel increase”. The result is a sound with a lot of treble. HyperPhysics compares it to “steam escaping from an overheated steam boiler”; Rational Acoustics says it “sounds trebly and even harsh when played at high levels.”

Pink noise

Pink noise is filtered so that every octave carries the same power. ATIS defines it, in acoustics, as “noise in which there is equal power per octave.” Measured per hertz, that means its power falls: HyperPhysics describes it as decreasing “by a factor of two or 3 decibels per octave”, which adds up to a drop of 30 dB across the ten octaves of hearing.

"Since pink noise has relatively more bass than white noise, it sounds more like the roar of a waterfall than like the higher hissing sound of white noise." — HyperPhysics, Georgia State University

That equal-per-octave balance is why audio engineers use it. Rational Acoustics, which makes acoustic measurement software, says “pink noise is used to measure the frequency response of a room or a system”, and HyperPhysics that it “is often the choice for testing and equalizing rooms and auditoriums”: on an analyzer that shows octave bands, pink noise draws a straight horizontal line.

Brown noise

Brown noise tilts further still. MathWorks, whose signal-processing software generates all three, describes it as behaving like “the integral of a white noise process”, with power that “decreases 6 dB per octave”. In other words, it is the sound of a random walk: each sample is the last one plus a small random step.

The name has nothing to do with the color brown. It comes from Brownian motion, named after the botanist Robert Brown, who, as EBSCO’s reference entry puts it, “discovered the erratic movement of pollen in water.” It is also called red noise, because red light sits at the low-frequency end of the spectrum, just as this noise is weighted toward low frequencies.

To the ear it is a low rumble with little hiss. Rational Acoustics notes that it “has a significant amount of low frequency energy and exhibits an overall lower level.”

How ScreenTail makes them

None of the three is a recording. Each is generated in your browser as you listen, so there is no file to download and no loop point you can hear.

1. 1

   White is a stream of random values, equally likely anywhere in their range.

2. 2

   Pink is that stream passed through a widely published filter that removes about 3 dB per octave.

3. 3

   Brown adds up the random values as a random walk, with a small leak so it never drifts off the scale, which removes about 6 dB per octave.

The slopes are not taken on trust. ScreenTail’s own tests measure the power in each octave band of the generated sound and compare it with those figures, so a wrong setting could not pass quietly.

Which one to use

For masking sound around you, the choice is mostly about what you find comfortable, and it is worth trying all three:

• White has the most treble of the three, so it is the brightest and the most hissy.
• Pink is the middle ground: the same spread of sound with the hiss turned down.
• Brown is the deepest, and the one to try against low, rumbling sounds such as traffic or machinery.

What the research does not do is back any of them as a sleep aid. A 2021 systematic review in Sleep Medicine Reviews found that “the quality of evidence for continuous noise improving sleep was very low, which contradicts its widespread use”, and called for more research “before promoting continuous noise as a sleep aid, especially since it may also negatively affect sleep and hearing.” Whatever you choose, keep the volume moderate.

If you are setting up a room or checking speakers rather than masking noise, the Speaker / Channel Test plays short tones on each channel so you can check that left and right are the right way round.

Questions

How this guide was made

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Vivek Kumar runs ScreenTail from New Delhi. He has worked with computers for about 25 years and studied Computer Science. He is not a display engineer or a color scientist, and each guide says where its facts come from so you can check them.