This octave can also be designated with three hash marks (i.e. C''') or in the 6th octave under Acoustical Society of America system (i.e. C6). The MIDI Octave Designation System has two versions, one where note 1 (8.176 Hz) is octave "0" making the Three-line octave the seventh octave (i.e. C7), and the other with note 1 (8.176 Hz) at octave "-2" making the Three-line octave the fifth octave (i.e. C5).
The indication 8va (shown below) can be used to represent the same pitches without as many ledger lines.
Play Three-line Octave Example (MIDI file format)