Explanation and definition
For example, if one note has a frequency of 440 Hz, the note one octave above is at 880 Hz, and the note one octave below is at 220 Hz. The ratio of frequencies of two notes an octave apart is therefore 2:1. Further octaves of a note occur at times the frequency of that note (where n is an integer), such as 2, 4, 8, 16, etc. and the reciprocal of that series. For example, 55 Hz and 440 Hz are one and two octaves away from 110 Hz because they are 1⁄2 (or
) times the frequency, respectively.
The number of octaves between two frequencies is given by the formula:
The octave is defined by ANSI as the unit of frequency level when the base of the logarithm is two.