You do not need the mathematics. Each colour describes how a sound's energy is spread across frequencies, and every practical consequence of that reaches you as texture.
What the colours actually mean
White noise spreads energy evenly across every frequency — the crisp hiss of an untuned radio. Because human hearing is more sensitive at the top of its range, an even spread reads as bright, sharp, almost aggressive.
Pink noise tilts the energy downward, losing a fixed amount with every octave: quieter in the treble, softer at the edges. Steady rain, wind through trees, a waterfall heard from a distance. It is white noise with the edge sanded off.
Brown noise — properly Brownian, named for the random walk of a particle rather than for the colour — tilts down harder still, leaving a low rumble with almost no hiss in it at all. Distant surf, a jet cabin, thunder a county away.
Which is best for sleep?
There is no crowned winner in the research, and anyone selling you a scientifically proven deep-sleep frequency is selling something. What steady noise reliably does is mask: it raises the floor of a room so the spikes that actually wake you — a door, a truck, a phone buzzing on a table — no longer clear the threshold.
Any colour can do that job, so the choice is about which one you can tolerate at the volume the job needs. The pattern is consistent: people find white harsh at masking volume and find brown the easiest to live under for eight hours. Pink sits between the two, which is most of why rain is the best-loved sleep sound on earth.
How to pick yours
Give each colour a whole night, not a five-minute audition. The test is not whether it sounds nice while you are awake and paying attention to it; the test is whether you notice it at three in the morning when you are not.
If you catch your ear following the sound, go a shade darker. If you wake with the sound feeling like pressure, go a shade lighter, or a notch quieter. And if pure noise feels sterile, use its real-world relatives: rain is roughly pink with a story attached, and a box fan is brown-ish with a motor's heartbeat in it.
Whatever you choose, keep it quiet
Masking works at a modest level. The sound should sit under the level of a quiet conversation, not compete with what it is covering. Louder is not deeper sleep — it is eight hours of unnecessary level, every night, for your ears. Solve a persistent noise problem with the darkest colour that works quietly, never with the loudest volume of a bright one.
Where Hush comes in
Hush ships white, pink and brown with honest labels and no invented science, alongside their real-world versions — rain, a downpour, a far-off storm, fans, surf. Every one of them is synthesized as it plays rather than played back from a recording, so there is no seam to find and no eight-hour night that repeats itself.
That is also why it is one payment of $19.99 — no sound packs to buy: there is no catalogue being hosted and nothing being streamed, so there is no monthly cost on our side to pass on to you. Layer a brown floor under the rain, set the timer to fade, and let it run with the radio off.