oktáv

An oktáv (octave) is the musical interval between one pitch and another with exactly twice its frequency. In Western music theory, an octave is perceived as a natural equivalence class: pitches separated by an octave are considered the same note name in different registers, such as middle C and the C an octave higher.

Etymology and concept: the term derives from Latin octavus meaning "eighth." The octave spans eight diatonic steps in a heptatonic scale, but its defining property is the 2:1 frequency ratio rather than the number of steps. In practical terms, the note names repeat at the octave, and melodies and harmonies often move freely within and across octaves while retaining recognizability.

Tuning and temperaments: in an idealized simple ratio, the octave is exactly 2:1. In most modern music, equal temperament divides the octave into twelve equal semitones, so each semitone has a frequency ratio of the twelfth root of two. Other tuning systems, such as just intonation or Pythagorean tuning, realize the octave as 2:1 as well but differ in how the internal steps within the octave are tuned relative to each other.

Usage and examples: octaves are foundational for melody, harmony, and instrument design. Instruments with repeating pitch ranges—pianos, guitars, flutes—are organized into registers that span one or more octaves. The same note name (for example, C) appears in each octave, with higher octaves generally sounding brighter and louder in many acoustic contexts.

Microtonal and historical notes: some non-Western musical traditions and modern microtonal systems explore tunings where octaves may be subdivided differently or where octave equivalence is treated variably.

See also: interval, scale, octave equivalence, tuning.

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