The Probert Encyclopaedia of Music

OCTAVE

An octave is the eighth tone in the scale; the interval between one and eight of the scale, or any interval of equal length; an interval of five tones and two semitones. The term octave is also applied to the whole diatonic scale itself. The ratio of a musical tone to its octave above is 1: 2 as regards the number of vibrations producing the tones.
Research Octave