Two notes that are one octave apart do not share the same frequency, as the frequency of a note one octave higher is double that of the original note. Therefore, option A is incorrect.
When considering "pitch", while the two notes will not have the exact same pitch (as one will be higher than the other), they are perceived as musically the same note in different registers. However, the word "pitch" typically refers to the specific frequency, thus option B is problematic.
On the other hand, "interval" refers to the distance between two pitches, and an octave is the specific interval we are discussing. Therefore, option C doesn't fit because we are asking about what characteristic the notes themselves share, not the relationship between them.
Finally, notes that are one octave apart do indeed share the same name. For instance, the note A in one octave and the note A in the next octave after it are both named “A.” Thus, option D is correct.
The best answer is:
O D. name.
