octaves

An octave is the interval between two musical pitches where the higher pitch has exactly twice the frequency of the lower one. In Western music, notes separated by an octave share the same letter name and belong to the same pitch class, for example C4 and C5. Octave equivalence means that pitches an octave apart are perceived as the same note in a different register.

The defining property of an octave is the 2:1 frequency ratio. In the harmonic series, octaves align with successive doublings of frequency, contributing to their strong consonance. Because pitch perception is roughly logarithmic, octaves give a sense of repeated structure across the tonal range.

In practice, Western tuning commonly uses twelve-tone equal temperament, which divides each octave into 12 equal semitones. After ascending or descending 12 semitones, you return to the same note name in the next octave. Other tuning systems, such as just intonation or meantone, use different approximations to the octave, while the fundamental 2:1 ratio remains.

Historically, the concept of the octave dates to ancient Greece, and the term octave comes from the Latin octavus, meaning eighth. Octaves organize scales, keys, and instrument layouts, and they facilitate transposition and modulation. In notation, scientists and musicians often refer to middle C as C4 in scientific pitch notation to indicate its position within a standard octave framework.