In electronics, an octave is a doubling or halving of a frequency. The term is derived from the Western musical scale (an octave is a doubling in frequency) and is therefore common in audio electronics. (The prefix octa-, denoting eight, refers to the eight notes of a diatonic scale.) Along with the decade, it is a unit used to describe frequency bands or frequency ratios.
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 ±6dB 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
Example
1. The distance between the frequencies 20 Hz and 40 Hz is 1 octave.
2. An amplitude of 52 dB at 4 kHz decreases as frequency increases at −2 dB/octave. What is the amplitude at 13 kHz?