What does transposition up or down one octave involve in music?

Transposition up or down one octave in music refers to shifting the pitch of a melody so that it sounds either one octave higher or one octave lower than the original. This process does not involve altering the key of the melody; rather, it maintains the same set of notes, just at a different pitch level. By transposing an octave, the melodic contour and relationships between the notes remain intact, but their actual pitches are elevated or lowered by twelve semitones.

In this context, the focus is on how the music is being moved up or down in pitch rather than changing the key signature, which introduces a new tonal center or scale. Thus, option B accurately captures the essence of what it means to transpose the melody by one octave, making it the correct choice.