Infrequently Asked Questions: Why are musical notes an octave apart considered to be the same note?
Q. Why are musical notes an octave apart considered to be the same note? -Charlotte V., Seattle, WA
Notes an octave apart are the same note because of the mechanics of vibration. Consider a piano string that is hit by a hammer and vibrates 1000 vibrations per second. So in 1/1000th of a second, it does this: Starts at center, then is hit by hammer. Snaps upwards. Hits the upper limit of its vibration, when the tension pulls it back towards the center. Crosses the center but keeps moving because of the momentum. Hits the downward limit of its vibration. Snaps back towards the center. Crosses the center on its way upward again, completing one cycle.
The precise timing of this motion is:
0 Seconds - position center - hit by hammer
1/4000 of a second: hits upper limit of motion
2/4000 of a second: crosses center…

