Octave
Interval of 12 semitones.
What it means
The octave comprises twelve semitones and eight scale degrees. Its frequency ratio is 2:1 — the simplest ratio after the unison. Its two notes merge so strongly that they are perceived as the same note in a different register; this is why they carry the same name, and why the whole tone system repeats itself at octave distances.
Musical use
This equating is the foundation of everything further. Scales and chords are described within one octave, vocal ranges are measured in octaves, clefs and octave signs serve to represent different octave registers conveniently. The designation of notes with capital letters, lower-case letters, and strokes likewise follows this order.
In part-writing theory, the octave counts as a perfect consonance, with the corresponding consequences: parallel octaves are forbidden, because two voices led in parallel cease to be two voices. In orchestration, by contrast, octave doubling is a common and effective means of giving a line carrying power and colour.
Acoustically it is notable that octaves on pianos are often tuned slightly stretched, because the partials of real strings do not lie exactly at integer ratios. On paper the octave is the purest interval; in practice it too has its subtleties.
The octave is, after the unison, the simplest frequency ratio, 2:1. Two notes at octave distance are perceived as so similar that they carry the same name in almost all musical cultures; one speaks of octave identity. In part-writing theory, parallel octaves between independent voices are forbidden, but as a deliberate doubling for tonal reinforcement they are common, for instance in the orchestra or in piano writing. A leap of an octave seems striking and occurs right at the beginning in many well-known melodies.
Performance practice
When tuning, check octaves first — deviations are most clearly audible there, because the merging is disturbed. With octave doublings, match embouchure or attack, length, and vibrato, so that one colour arises instead of two lines. And use the octave when singing as a secure reference point from which other intervals can be derived.