In
electronics
Electronics is a scientific and engineering discipline that studies and applies the principles of physics to design, create, and operate devices that manipulate electrons and other Electric charge, electrically charged particles. It is a subfield ...
, an octave (symbol: oct) is a
logarithmic unit
A logarithmic scale (or log scale) is a method used to display numerical data that spans a broad range of values, especially when there are significant differences among the magnitudes of the numbers involved.
Unlike a linear scale where each u ...
for
ratio
In mathematics, a ratio () shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
s between
frequencies
Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
, 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
In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referr ...
is a doubling in frequency. Specification in terms of octaves is therefore common in
audio electronics
Audio most commonly refers to sound, as it is transmitted in signal form. It may also refer to:
Sound
*Audio signal, an electrical representation of sound
* Audio frequency, a frequency in the audio spectrum
*Digital audio, representation of soun ...
.
Along with the
decade
A decade (from , , ) is a period of 10 years. Decades may describe any 10-year period, such as those of a person's life, or refer to specific groupings of calendar years.
Usage
Any period of ten years is a "decade". For example, the statement ...
, it is a
unit used to describe
frequency band
Spectral bands are regions of a given spectrum, having a specific range of wavelengths or frequencies. Most often, it refers to electromagnetic bands, regions of the electromagnetic spectrum.
More generally, spectral bands may also be means in ...
s or
frequency ratios.
[Perdikaris, G. (1991). ''Computer Controlled Systems: Theory and Applications'', p. 117. .]
Ratios and slopes
A frequency ratio expressed in octaves is the base-2
logarithm
In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of to base is , because is to the rd power: . More generally, if , the ...
(
binary logarithm
In mathematics, the binary logarithm () is the exponentiation, power to which the number must be exponentiation, raised to obtain the value . That is, for any real number ,
:x=\log_2 n \quad\Longleftrightarrow\quad 2^x=n.
For example, th ...
) 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
The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a ...
(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 decibels per octave, corresponds to an amplitude gain proportional to frequency, which is equivalent to ±20 dB per
decade
A decade (from , , ) is a period of 10 years. Decades may describe any 10-year period, such as those of a person's life, or refer to specific groupings of calendar years.
Usage
Any period of ten years is a "decade". For example, the statement ...
(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
*
Octave
In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referr ...
*
Octave band
*
One-third octave
Notes
References
{{Reflist
Acoustics
Audio electronics