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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. Specification in terms of octaves is therefore common in audio electronics.

Along with the decade, it is a unit used to describe frequency bands/frequency ratios.

Ratios and slopes※

A frequency ratio expressed in octaves is the base-2 logarithm (binary logarithm) of the ratio:

${\displaystyle {\text{number of octaves}}=\log _{2}\left({\frac {f_{2}}{f_{1}}}\right)}$

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). 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?

${\displaystyle {\text{number of octaves}}=\log _{2}\left({\frac {13}{4}}\right)=1.7}$

${\displaystyle {\text{Mag}}_{13{\text{ kHz}}}=52{\text{ dB}}+(1.7{\text{ oct}}\times -2{\text{ dB/oct}})=48.6{\text{ dB}}.\,}$

See also※

• Octave
• Octave band
• One-third octave

Notes※

References※