This octave can also be designated with one hash mark (i.e. C') or in the 4th octave under Acoustical Society of America system (i.e. C4). The MIDI Octave Designation System has two versions, one where note 1 (8.176 Hz) is octave "0" making the One-line octave the fifth octave (i.e. C5), and the other with note 1 (8.176 Hz) at octave "-2" making the One-line octave the third octave (i.e. C3).
The indication 8vb (shown below) can be used to represent the same pitches. Typically, this indication (8vb) would not be used with the treble clef staff, and since most of the notes in this octave are on the staff, using this designation would not make reading the notes any easier for the performer.
Play One-line Octave Example (MIDI file format)