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An octave is the interval between one musical pitch and another with double or half its frequency. For example, if one note has a frequency of 440 Hz, the note one octave above is at 880 Hz, and the note one octave below is at 220 Hz. The ratio of frequencies of two notes an octave apart is therefore 2:1.
For example, C 4 is one note above B 3, and A 5 is one note above G 5. The octave number is tied to the alphabetic character used to describe the pitch, with the division between note letters ‘B’ and ‘C’, thus: "B 3" and all of its possible variants (B, B ♭, B, B ♯, B) would properly be designated as being in octave "3".
Octave clef Treble and bass clefs can be modified by octave numbers. An "8" below the clef (as in the diagram) indicates that pitches will sound an octave lower than they would with the unmodified clef. A "15" below indicates a two-octave shift. These numbers may also be used above the clef to indicate pitches one or two octaves higher.
Although Boethius is the first author known to use this nomenclature in the literature, Ptolemy wrote of the two-octave range five centuries before, calling it the perfect system or complete system – as opposed to other, smaller-range note systems that did not contain all possible species of octave (i.e., the seven octaves starting from A, B ...
Today the most widespread are cipher notations ("not angka" in the broadest sense) in which the pitches are represented with some subset of the numbers 1 to 7, with 1 corresponding to either highest note of a particular octave, as in Sundanese gamelan, or lowest, as in the kepatihan notation of Javanese gamelan.
Sometimes written with “8v” below the treble, to represent the octave (8 tones in a major scale). Tenor C is an organ builder's term for small C or C 3 (130.813 Hz), the note one octave below middle C. In older stoplists it usually means that a rank was not yet full compass, omitting the bottom octave, until that octave was added later on.
Pitch classes can be notated in this way by assigning the number 0 to some note and assigning consecutive integers to consecutive semitones; so if 0 is C natural, 1 is C ♯, 2 is D ♮ and so on up to 11, which is B ♮. The C above this is not 12, but 0 again (12 − 12 = 0). Thus arithmetic modulo 12 is used to represent octave equivalence.
The numbered musical notation (simplified Chinese: 简谱; traditional Chinese: 簡譜; pinyin: jiǎnpǔ; lit. 'simplified notation', not to be confused with the integer notation) is a cipher notation system used in mainland China, Taiwan, Hong Kong, and to some extent in Japan, Indonesia (in a slightly different format called "not angka"), Malaysia, Australia, Ireland, the United Kingdom ...