Introduction to Sound Synthesis Pitch
Noise
Noise is a signal that never repeats. Its energy is spread across a wide range of frequencies rather than concentrated at a fundamental and its harmonics, and that is why it has no clear pitch.
A pitched tone has a spectrum made of separate lines, one for each harmonic. Noise has a continuous spectrum: every frequency in its range is present, at a level that changes from moment to moment at random. White and pink noise are named by analogy with light. White light contains every colour in roughly equal amounts, and white noise contains every frequency at the same average level. Pink noise has more energy at low frequencies, as pink light has more red. Brown noise is named after a person, the botanist described below. The tool below plays three kinds of noise through a filter and draws the spectrum as it plays, measured from the audio itself. The frequency axis is marked in octaves, the way pitch is heard.
Noise through a filter
White, pink or brown noise passes through a lowpass, bandpass or highpass filter. The spectrum is measured live. The presets set the filter, and two of them, Wind and Surf, also move the cutoff and the level slowly up and down.
Listen for White noise is a bright hiss, pink is more even, and brown is a low rumble. A bandpass filter with high resonance narrows the noise to a band with a vague pitch, and moving its cutoff slowly gives the sound of wind. A lowpass with the level rising and falling every twelve seconds or so sounds like surf.
White, pink and brown
White noise has the same power at every frequency, so its spectrum is flat when it is plotted against hertz. It still sounds bright, because each octave contains twice as many hertz as the one below it. The top octave of hearing, from 10 kHz to 20 kHz, spans 10,000 Hz, while the octave from 20 Hz to 40 Hz spans only 20, so most of white noise's power is in the treble. On the octave-scaled plot above, white noise rises towards the right.
Pink noise has the same power in every octave. Its level falls by 3 dB each time the frequency doubles, which compensates exactly for the doubling of the octave's width, and it sounds roughly even from bass to treble. That evenness is why pink noise is used to measure loudspeakers and rooms. Brown noise falls by 6 dB per octave and sounds like a low roar. It is the signal produced by adding up white noise over time, a random walk, and it is named after the botanist Robert Brown, who in 1827 described the random motion of particles suspended in water.
Filtering noise
Because noise contains every frequency, a filter can shape it into almost any broad spectrum. A lowpass filter removes the high frequencies that are heard as hiss and leaves a softer rushing sound. A highpass filter leaves only the high frequencies, which, kept short, are the basis of most synthesised hi-hats. A bandpass filter with high resonance keeps a narrow band around its cutoff. That band has a vague pitch, because most of its energy is near one frequency, and sweeping the cutoff slowly up and down gives a sound like wind. A snare drum on most analogue drum machines is a short burst of filtered noise mixed with a pitched tone, shaped by an envelope.
Noise is also a control source. A sample and hold takes the level of a noise signal at each clock pulse and holds it, which turns noise into a series of random steps for pitch, filter cutoff or another setting. Noise passed through a lowpass filter with a very low cutoff and used directly as a control signal gives a random drift rather than steps.
Common questions
What is the difference between white, pink and brown noise?
White noise has equal power at every frequency, which sounds bright and hissy. Pink noise has equal power in every octave, so its level falls by 3 dB each time the frequency doubles, and it sounds more even. Brown noise falls by 6 dB per octave and sounds deep, like a distant waterfall or the rumble inside an aeroplane.
Why does white noise sound so bright if every frequency is equally loud?
White noise sounds bright because each octave contains twice as many frequencies as the one below it. The octave from 10 kHz to 20 kHz spans 10,000 Hz and the octave from 20 Hz to 40 Hz spans 20 Hz, so with equal power per hertz the top octave carries far more of the total. The ear groups frequencies by octave, so it hears that as a tilt towards the treble.
Why is it called brown noise?
It is named after the botanist Robert Brown, who in 1827 described the random jiggling of tiny particles suspended in water, now called Brownian motion. The signal follows the same kind of random walk. It is sometimes called red noise as well.
What is noise used for in a synthesiser?
Noise is used as a sound source, filtered to make wind, surf, breath, snare drums, hi-hats and cymbals. It is also used as a control source: a sample and hold samples it to give random voltages or values. Mixed in small amounts with an oscillator, it adds breathiness to a tone.
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