Why a note and its double sound like the same note
Ask men and women to sing a tune together in unison and they usually end up an octave apart without noticing. The octave, a jump to exactly twice the frequency, sounds so much like sameness that Western notation gives both notes one name. Monkeys and rats seem to hear it too.
An octave joins two pitches whose frequencies stand in the ratio 2 to 1. If one note vibrates 440 times a second, the note an octave up vibrates 880 times and the one below 220. Stack more octaves and the frequency keeps doubling or halving, so counting octaves between two tones means taking a base-two logarithm of their ratio. The name comes from the Latin for eighth, because a standard scale such as C major runs through eight note names, starting and ending on C.
Why the ear treats the pair as twins has to do with harmonics. The gap between the first and second harmonic of any vibrating string or air column is itself an octave, so the overtones of the two notes line up closely and ring together. After the unison it is the simplest interval there is. Musicians call this octave equivalence, and it lets theorists describe pitch in two ways at once: height, the absolute frequency, and class, the position within the octave, so that every C belongs to the same family however high or low.
Sheet music has shorthand for it. The marking 8va over a passage means play it an octave higher, a version below the staff sends it an octave lower, and 15ma asks for two octaves up. The word loco cancels the instruction. Middle C is called C4 because it is the fourth C on an 88-key piano.
The idea is widespread but not universal. Sumerian and Akkadian, the languages of the oldest surviving writing on tuning, have no known word for octave, though Babylonian tablets on tuning a nine-stringed instrument seem to set two strings an octave from others. Monkeys show octave equivalence, possibly via an octave map of neurons in the auditory thalamus, and so do rats and human infants. Starlings, children aged 4 to 9 and non-musicians did not show it in studies.
Source: Octave
