Noise: Colors & Spectral Shape
White noise sounds bright because each octave contains twice as many Hz. The "color" of noise is the spectral slope, and it's just a filter applied to raw randomness.
What Is Noise?
Noise is a random signal with no discernible pitch. Every frequency is present simultaneously. There are no harmonics, no fundamental, no repeating pattern. Where an oscillator produces a waveform you can predict, noise is entirely unpredictable from sample to sample.
Color = Spectral Slope
All noise starts as white, flat power per Hz. The "color" is just a spectral shaping filter applied on top. Pink rolls off at −3 dB/octave so each octave carries equal power (sounds balanced). Brown rolls off at −6 dB/octave (deep rumble). The color filter is the first stage; your own filter is the second.
Two Filters in Series
The demo below chains two filters: the color filter shapes the raw noise into white, pink, or brown. Then your filter sculpts it further: lowpass to darken, bandpass to isolate a region, highpass to thin it out. Watch the spectrum change at each stage.
Try it: start with white noise and watch the flat spectrum. Switch to pink and see the slope appear. Then add a bandpass filter and sweep the cutoff to isolate different frequency bands.
References
- Wikipedia: Colors of Noise, spectral density definitions
- Wikipedia: Pink Noise, 1/f noise and its applications