Octave

In music, an octave—also known as the eighth or perfect octave—is the interval between two pitches in which one has double or half the frequency of the other. It is one of the most fundamental structures in musical systems around the world and is commonly described as the “basic miracle of music” because of its natural basis in the harmonic series. The interval between the first and second harmonics forms an octave, and in Western notation notes separated by one or more octaves share the same note name and belong to the same pitch class. The perfect octave is written as P8, though augmented (A8) and diminished (d8) octaves also exist within chromatic theory.

Explanation and Definition

An octave is defined by a frequency ratio of 2:1. If a pitch vibrates at 440 Hz, the pitch one octave above vibrates at 880 Hz, while the pitch an octave below vibrates at 220 Hz. Consequently, octaves occur at intervals of 2n2^n2n times the basic frequency for upward motion, and their reciprocals for downward motion.
The number of octaves separating two frequencies can be calculated using:
Number of octaves=log⁡2(f2f1)\text{Number of octaves} = \log_{2}\left(\frac{f_{2}}{f_{1}}\right)Number of octaves=log2​(f1​f2​​)
The universality of the octave results from its alignment with natural harmonic patterns. Because of this, most musical scales begin and end an octave apart; for example, a C major scale begins on C and ends on the next C above.

Music Theory

Octave equivalence is a widely observed principle: notes separated by one or more octaves are regarded as versions of the same pitch. This principle means that chords containing notes in different octaves are described as doublings, and that melodic lines may be performed in parallel octaves while retaining their identity.
While the perfect octave is the most common form, theoretical music recognises variants:

• Augmented octave (A8): 13 semitones
• Diminished octave (d8): 11 semitones

These are conceptually octaves because they span the same pitch class boundary, although in practice musicians often use enharmonic alternatives such as the major seventh or minor ninth.
The idea of pitch incorporates two components:

• Pitch height: the absolute frequency
• Pitch class: the cyclical position within the octave

Thus, all Cs—whatever their register—belong to the same pitch class. This two-dimensional understanding of pitch underlies the circularity of octave perception.

Notation

Various systems exist to identify octaves precisely:

• Scientific pitch notation uses numeric subscripts, e.g. C₄ for middle C.
• Helmholtz notation uses letter and comma/prime symbols.
• Organ pipe notation, MIDI numbers and other systems offer further classifications.

In printed music, octaves are frequently indicated with shorthand instructions such as:

• 8va (ottava alta): play an octave higher
• 8vb (ottava bassa or sotto): play an octave lower
• 15ma (quindicesima): two octaves higher
• 15mb (quindicesima bassa): two octaves lower

These instructions may be bounded by dashed lines, brackets or cancelled with the term loco. Notations such as coll’ottava indicate that a line should be played together with its octave.

Equivalence and Perception

After unison, the octave is the simplest interval in music. The close alignment of their harmonic spectra causes the human ear to perceive octave-separated notes as strongly related, often to the extent of sounding “the same”. Untrained singers frequently default to singing in octaves rather than in exact unison, especially between male and female voices.
Octave perception, while widespread, is not universal across all cultures or historical contexts. The earliest known written tuning systems—from Sumerian and Akkadian cuneiform—contain no explicit term for the octave, although indirect references to octave relationships appear in tuning descriptions for a nine-string Babylonian lyre.
Modern research suggests octave perception has biological foundations. Studies indicate that monkeys display octave equivalence and that neurons in the auditory thalamus respond in an octave-related pattern. Evidence of octave perception has also been observed in human infants, rats and trained musicians, whereas certain birds, older children and non-musicians may not demonstrate the same degree of octave recognition.

Role in Musical Practice

Octave equivalence supports many core features of Western music, including scale construction, key signatures and transposition. It enables musical patterns to be identified and transposed seamlessly across registers and underpins the structure of instruments such as pianos, organs and guitars, which are designed around repeating octave cycles.
In harmony, doubled octaves help reinforce tonal centres and blend timbres, while in melody, octave displacement is used for expressive variation or clarity. The concept also allows for register-specific notation, facilitating the performance of music across wide pitch ranges without excessive ledger lines.