In music, an octave or perfect octave is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon, referred to as the "basic miracle of music", the use of, "common in most musical systems"; the interval between the first and second harmonics of the harmonic series is an octave. In music notation, notes separated by an octave have the same letter name and are of the same pitch class. To emphasize that it is one of the perfect intervals, the octave is designated P8. Other interval qualities are possible, though rare; the octave above or below an indicated note is sometimes abbreviated 8a or 8va, 8va bassa, or 8 for the octave in the direction indicated by placing this mark above or below the staff. For example, if one note has a frequency of 440 Hz, the note one octave above is at 880 Hz, the note one octave below is at 220 Hz; the ratio of frequencies of two notes an octave apart is therefore 2:1. Further octaves of a note occur at 2 n times the frequency of that note, such as 2, 4, 8, 16, etc. and the reciprocal of that series.

For example, 55 Hz and 440 Hz are one and two octaves away from 110 Hz because they are ​ 1⁄2 and 4 times the frequency, respectively. The number of octaves between two frequencies is given by the formula: Number of octaves = log 2 ⁡ Most musical scales are written so that they begin and end on notes that are an octave apart. For example, the C major scale is written C D E F G A B C, the initial and final C's being an octave apart; because of octave equivalence, notes in a chord that are one or more octaves apart are said to be doubled in the chord. The word is used to describe melodies played in parallel in more than multiple octaves. While octaves refer to the perfect octave, the interval of an octave in music theory encompasses chromatic alterations within the pitch class, meaning that G♮ to G♯ is an Augmented octave, G♮ to G♭ is a diminished octave; the use of such intervals is rare, as there is a preferable enharmonically-equivalent notation available, but these categories of octaves must be acknowledged in any full understanding of the role and meaning of octaves more in music.

Octaves are identified with various naming systems. Among the most common are the scientific, organ pipe, MIDI, MIDI note systems. In scientific pitch notation, a specific octave is indicated by a numerical subscript number after note name. In this notation, middle C is C4, because of the note's position as the fourth C key on a standard 88-key piano keyboard, while the C an octave higher is C5; the notation 8a or 8va is sometimes seen in sheet music, meaning "play this an octave higher than written". 8a or 8va stands for the Italian word for octave. Sometimes 8va is used to tell the musician to play a passage an octave lower, though the similar notation 8vb is used. 15ma means "play two octaves higher than written" and 15mb means "play two octaves lower than written." The abbreviations col 8, coll' 8, c. 8va stand for coll'ottava, meaning "play the notes in the passage together with the notes in the notated octaves". Any of these directions can be cancelled with the word loco, but a dashed line or bracket indicates the extent of the music affected.

After the unison, the octave is the simplest interval in music. The human ear tends to hear both notes as being "the same", due to related harmonics. Notes separated by an octave "ring" together; the interval is so natural to humans that when men and women are asked to sing in unison, they sing in octave. For this reason, notes an octave apart are given the same note name in the Western system of music notation—the name of a note an octave above A is A; this is called octave equivalence, the assumption that pitches one or more octaves apart are musically equivalent in many ways, leading to the convention "that scales are uniquely defined by specifying the intervals within an octave". The conceptualization of pitch as having two dimensions, pitch height and pitch class, inherently include octave circularity, thus all C♯s, or all 1s, in any octave are part of the same pitch class. Octave equivalence is a part of most "advanced musical cultures", but is far from universal in "primitive" and early music.

The languages in which the oldest extant written documents on tuning are written and Akkadian, have no known word for "octave". However, it is believed that a set of cuneiform tablets that collectively describe the tuning of a nine-stringed instrument, believed to be a Babylonian lyre, describe tunings for seven of the strings, with indications

Brian Afanador

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