In electronics, an **octave** (symbol: *oct*) is a logarithmic unit for ratios between frequencies, with one octave corresponding to a doubling of frequency. For example, the frequency one octave above 40 Hz is 80 Hz. 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.

Along with the decade, it is a unit used to describe frequency bands or frequency ratios.^{[1]}^{[2]}

## Ratios and slopes

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 log_{10}(4) ≈ 6.0206 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). This would be a first-order filter.

## Example

The distance between the frequencies 20 Hz and 40 Hz is 1 octave. An amplitude of 52 dB at 4 kHz decreases as frequency increases at −2 dB/oct. What is the amplitude at 13 kHz?

## See also

## Notes

**^**The prefix octa-, denoting eight, refers to the eight notes of a diatonic scale; the association of the word with doubling is solely a matter of customary usage.

## References

**^**Levine, William S. (2010).*The Control Handbook: Control System Fundamentals*, p. 9–29. ISBN 9781420073621/ISBN 9781420073669.**^**Perdikaris, G. (1991).*Computer Controlled Systems: Theory and Applications*, p. 117. ISBN 9780792314226.