Filter pole count determines the steepness of frequency rolloff: each pole adds 6dB per octave of attenuation

A filter’s ‘slope’ — how steeply it attenuates frequencies beyond the cutoff — is determined by its pole count. Each pole contributes 6dB of attenuation per octave, so a 2-pole filter attenuates at 12dB/octave and a 4-pole (Moog-style) filter at 24dB/octave. By the cookbook’s convention the ‘first octave’ above a 4kHz cutoff is 8kHz, so a 24dB/oct filter attenuates 8kHz material 24dB more than 4kHz material. Steeper slopes give a more dramatic, ‘surgical’ character; shallower slopes sound gentle and natural. Note a subtlety: SuperCollider’s LPF is actually a 2-pole (12dB/oct) Butterworth filter, so the cookbook’s Figure 26 uses it to illustrate the slope idea rather than as a literal 4-pole. TwoPole is the plain 2-pole; RLPF/Resonz add a resonant peak.

Examples

// SC's LPF: 2-pole, 12dB/oct Butterworth
LPF.ar(in: WhiteNoise.ar(0.4), freq: 4000)
// TwoPole: also 12dB/oct, no resonance
TwoPole.ar(in: WhiteNoise.ar(0.4), freq: 4000)

Assessment

A 4-pole (24dB/oct) LPF has a 2kHz cutoff. By how many dB is a frequency at 8kHz (two octaves above cutoff) attenuated relative to the cutoff? Show the calculation.