A bandpass filter's Q is its center frequency divided by its bandwidth — high Q means a narrow, resonant peak

Q (quality factor) measures how sharply focused a bandpass filter is: Q = center frequency / (−3 dB bandwidth). A low Q gives a broad, gentle boost; a high Q gives a narrow spike centered on the resonant frequency. At high Q the filter ‘rings’ — excited near its center frequency it goes into oscillation and continues sounding for some time after the input stops, the basis of resonant, whistling filter sweeps. Because Q ties center frequency to bandwidth, at a fixed center frequency adjusting Q is the same as adjusting bandwidth. High-Q resonant filters excited by a pulse train can simulate tuned percussion (tablas, woodblocks, claves, marimba). A practical caution: the gain at a high-Q resonant peak can be large enough to overload and distort the signal, so many filters include gain compensation.

Examples

A bandpass with center 2000 Hz and −3 dB points at 1800 and 2200 Hz has Q = 2000/400 = 5. In Strudel a resonant sweep: s("sawtooth").lpf(sine.range(200,2000)).lpq(15) (high resonance rings the cutoff).

Assessment

A bandpass filter has a center frequency of 1000 Hz and a bandwidth of 100 Hz. Calculate its Q. Then describe what happens to the sound as you raise Q toward its maximum while holding the center frequency fixed.