Octave (auxiliary unit)
Physical unit | |
---|---|
Unit name | octave |
Unit symbol | |
Physical quantity (s) | Frequency interval |
Formula symbol | |
dimension | |
In SI units | |
Named after | Greek ὄκτω , óktō = "eight" |
See also: Cent , Millioctave , Neper , Savart |
The octave ( symbol O) is an auxiliary unit that is used in music , acoustics and high frequency engineering. It acts as a reference word that refers to the interval with the frequency ratio 2: 1 in the dual or binary logarithmic representation of frequency intervals .
The name comes from the music where this frequency interval is called an octave ( lat. Octo = eight) because it describes the distance between the eighth tone of a diatonic scale and its root .
The frequency ratio belongs to a frequency interval of octaves
- (with )
After converting the logarithm from two to ten, this becomes:
A sub-unit of the octave is the cent :
use
The unit of measurement octave is used in high-frequency engineering when a bandwidth depends on the frequency and the precise cut-off frequencies are either variable or irrelevant. For example, a specific assembly with a bandwidth of 1 octave can be used in the frequency ranges
- 1 to 2 GHz or
- 6.2 to 12.4 GHz.
The specification of frequency ranges in octaves is particularly widespread in antenna technology, especially for horn radiators .
Remarks
- ↑ so referred to in Meyers Lexikon Technik und exact Naturwissenschaften , Bibliographisches Institut AG, Mannheim 1970, p. 1852.
- ↑ binary logarithm (lb for short), base 2 logarithm, also known as logarithm of two or dyadic logarithm (sometimes also with the abbreviation ld for logarithm dualis ).
- ↑ The addition (or omission) of the factors or is possible because purely mathematically they are nothing more than renaming the number 1 based on the formal definition: