octave
musical interval spanning eight staff positions, including the perfect octave (12 semitones), the diminished octave (11 semitones), and the augmented octave (13 semitones)
augmented octave
musical interval of 13 semitones spanning eight staff positions, enharmonically equivalent to a minor ninth
diminished octave
musical interval of 11 semitones spanning eight staff positions
perfect octave
musical interval of 12 half-tones with a frequency ratio of 2:1 (exactly)