# Octave

Perfect octave
Inverse unison
Name
Other names -
Abbreviation P8
Size
Semitones 12
Interval class 0
Just interval 2:1
Cents
Equal temperament 1200
Just intonation 1200

The octave is the span or intervallic space between one tone and another, the latter having twice or half as many vibrations per second. The octave has been and remains a principal tonal foundation in both western and non-western music. This foundation is due to the strength and consistency of the interval between its first and last tones. Many composers have clearly favored the use of the octave since the first and last tones of its interval fit so well together that the listener appears to hear the two tones as one.

## Octave

The frequent use of the octave is a part of most music, though there are those ethnomusicologists who say that it is far from universal in formative and early music (e.g., Nettl, 1956; Sachs & Kunst, 1962). Yet the strong resemblances between the two analogous tones that are an octave apart explain why the octave was noticed in many musical cultures and at a time when music was rapidly developing. In the later Middle Ages, the Gregorian chant or plainsong of the Christian Church was followed by polyphonic music in the form called organum, which added a second voice to a single melody. The second voice was usually a fourth or fifth apart; however, when these two voices were duplicated an octave apart creating four voices, the richness of the organum created a full and complete harmonic sound, giving greater richness to the religious offerings. Another example is in the indigenous music of India, in which the octave span is composed of quarter tones. Octave relationships appear very frequently in the tones of the instruments, i.e. the tabla and baya (drums) in juxtaposition to the singer(s). Octaves were used to bring stability and grandeur to Indian classical and folk compositions. In addition, many musical cultures used the overtone in their instrumentation and vocalisms to create octaves for a more complex sound. An overtone is a higher partial note heard over the main tone which is created by a voice or musical instrument. Overtones were favored in various folk songs to add fullness and dexterity to the melodic line.

Technically, an octave (sometimes abbreviated 8ve or 8va) is the interval between one musical note and another with half or double the frequency or vibrations per second. For example, if one note is pitched at 400 Hz, the note an octave above it is at 800 Hz, and the note an octave below is at 200 Hz. The ratio of frequencies of two notes an octave apart is therefore two to one. Further octaves of a note occur at $2^n$ times the frequency of that note (where n is an integer), such as 2, 4, 8, 16, etc. and the reciprocal of that series. Moreover, 50 Hz and 400 Hz are one and two octaves away from 100 Hz because they are $1/2$ ($1/2^1$) and 4 ($2^2$) times the frequency, respectively, however 300 Hz is not a whole number octave above 100 Hz, despite being a harmonic of 100 Hz.

The octave is the second simplest interval in music (after the unison). Since the human ear tends to hear both notes as being essentially "the same," notes played an octave apart are given the same note name in the Western system of music notation—for example, the name of a note an octave above A is also A. This is called octave equivalency, and is closely related to the concept of harmonics. This is similar to enharmonic equivalency, and less so transpositional equivalency and, less still, inversional equivalency, the latter two of which are generally used only in musical set theory or atonal theory. Thus all C#s, or all 1s (if C=0), in any octave are part of the same pitch class. As well as being used to describe the relationship between two notes, the word is also used when speaking of a range of notes that fall between a pair an octave apart. In the diatonic scale, this is eight notes if one counts both ends, hence the name "octave," from Italian for eight. In the chromatic scale, this is 13 notes counting both ends, although traditionally, one speaks of 12 notes of the chromatic scale, not counting both ends. In most Western music, the octave is divided into 12 semitones (see musical tuning). These semitones are usually equally spaced out in a method known as equal temperament. Other scales may have a different number of notes covering the range of an octave, but the "octave" is still used. In a scale which uses microtones usually occurring in non-western music, there would be a number of notes, for example 17, 22, or any other number of notes, between the two octave tones depending on the instrumental capabilities and the compositional sliding or "bending of the tones." Yet the octave would be intact and used as a musical guidepost.

 Diatonic intervals edit Perfect : unison (0) | fourth (5) | fifth (7) | octave (12) Major : second (2) | third (4) | sixth (9)| seventh (11) Minor : second (1) | third (3)| sixth (8)| seventh (10) Augmented/Diminished : tritone (6) semitones are given in brackets

The notation 8va is sometimes seen in sheet music, meaning "play this an octave higher than written." 8va stands for ottava, the Italian word for octave. Sometimes 8va will also be used to indicate when a passage is to be played an octave lower, although the similar notation 8vb (ottava bassa) is more common. Similarly, 15ma means "play two octaves higher than written." Coll'ottava means to play the passage in octaves. Any of these directions can be cancelled with the word loco, but often a dashed line or bracket indicates the extent of the music affected.

For music-theoretical purposes (not on sheet music), octave can be abbreviated as P8.

From Gregorian chants through the magnificent symphonies of the classical masters to the iridescent sounds of jazz and New Age music, the octave has been and will continually rule as one of the most important intervals in theory and composition.

## Sources

• Burns, Edward M. "Intervals, Scales, and Tuning," The Psychology of Music second edition. Deutsch, Diana, ed. San Diego: Academic Press, 1999. ISBN 0122135644.
• Sachs, C. and Kunst, J. The wellsprings of music. ed. Kunst, J. The Hague: Marinus Nijhoff, 1962.