The term is derived from the Western musical scale where an octave is a doubling in frequency.
[note 1] Specification in terms of octaves is therefore common in audio electronics.
[1][2] A frequency ratio expressed in octaves is the base-2 logarithm (binary logarithm) of the ratio: An amplifier or filter may be stated to have a frequency response of ±6 dB per octave over a particular frequency range, which signifies that the power gain changes by ±6 decibels (a factor of 4 in power), when the frequency changes by a factor of 2.
This slope, or more precisely 10 log10(4) ≈ 6 decibels per octave, corresponds to an amplitude gain proportional to frequency, which is equivalent to ±20 dB per decade (factor of 10 amplitude gain change for a factor of 10 frequency change).
An amplitude of 52 dB at 4 kHz decreases as frequency increases at −2 dB/oct.