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There are many forms of noise with various frequency characteristics that are classified by "color".
The next most commonly used color is pink noise. Its frequency spectrum is not flat, but has equal power in octave bands. Pink noise is perceptually white. That is, the human auditory system perceives equal magnitude on all frequencies. The power density decreases by -3 dB per octave (density proportional to 1/f).
Brown noise is similar to pink noise, but with a decrease of -6 dB per octave power density (density proportional to 1/f2). It can be generated by an algorithm which simulates Brownian motion.
There are also many "less official" colors.
Red noise (common definition within the oceanographic field, contributed by P.J. "Josh" Rovero) (Anyone have the spectrum?) is oceanic ambient noise (ie, noise distant from the sources) is often described as "red" due to the selective absorption of higher frequencies."
Orange noise(Anyone foolish enough to want the spectrum?) is quasi-stationary noise with a finite power spectrum with a finite number of small bands of zero energy dispersed throughout a continuous spectrum. These bands of zero energy are centered about the frequencies of musical notes in whatever system of music is of interest. Since all in-tune musical notes are eliminated, the remaining spectrum could be said to consist of sour, citrus, or "orange" notes. Orange noise is most easily generated by a roomfull of primary school students equipped with plastic soprano recorders.
Green noise (defined by some folks producing relaxation tapes, Mystic Moods, I believe) is supposedly the background noise of the world. A really long term power spectrum averaged over several outdoor sites. Rather like pink noise with a hump added around 500Hz.
Blue noise's (FS-1037C) power density increases 3dB per octave with increasing frequency (density proportional to f) over a finite frequency range. This can be good noise for dithering.
Purple noise's power density increases 6dB per octave with increasing frequency (density proportional to f^2) over a finite frequency range. Differentiated white noise. AKA violet noise.
Grey noise is noise subjected to a psychoacoustic equal loudness curve (such as an inverted a-weight curve) over a given range of frequencies, so that it sounds like it is equally loud at all frequencies. This would be a better definiton of "white noise" than the "equal power at all frequencies" definition, since real "white light" has the power spectrum of a 5400K black body, not an equal power spectrum.
Brown noise's power density decreases 6dB per octave with increasing frequency (density proportional to 1/f^2) over a frequency range which does not include DC. Is not named for a power spectrum that suggests the color brown, rather, the name is a coruption of Brownian motion. If we were going to pick a color, red might be good since pink noise lies between this noise and white noise. Unfortuantly, red is already taken. AKA "random walk" or "drunkard's walk" noise.
Black noise, or silent noise, has three definitions:
1. Whatever comes out of an active noise control system and cancles an existing noise, leaving the world world noise free. (The comic book character "Iron Man" used to have a "black light beam" that could darken a room like this, and popular SCI-FI has an annoying tendancy to portray active noise control in this light.)
2. (seen in the sales literature for an ultrasonic vermin repeller) power density is constant for a finite frequency range above 20kHz. Ultrasonic white noise. This black noise is like the so-called "black light" with frequencies too high to be preceived as sound, but still capable of affecting you or your surroundings.
3. (Manfred Schroeder, "fractals, chaos, power laws") has an f ^ -beta spectrum, with beta > 2, and is characteristic of "natural and unnatural catastrophes like floods, droughts, bear markets, and various outrageous outages, such as those of electrical power." further, "Because of their black spectra, such disasters often come in clusters."
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