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A jump from the lowest semitone to the highest semitone in one octave doubles the frequency (for example, the fifth A is 440 Hz and the sixth A is 880 Hz). The frequency of a pitch is derived by multiplying (ascending) or dividing (descending) the frequency of the previous pitch by the twelfth root of two (approximately 1.059463).
For example, a just perfect fifth (for example C to G) is 3:2 (Play ⓘ), 1.5, and may be approximated by an equal tempered perfect fifth (Play ⓘ) which is 2 7/12 (about 1.498). If the A above middle C is 440 Hz , the perfect fifth above it would be E , at (440*1.5=) 660 Hz, while the equal tempered E5 is 659.255 Hz.
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".
A combination of letters and numbers—as in scientific pitch notation, where notes are labelled upwards from C 0, the 16 Hz C; Numbers that represent the frequency in hertz (Hz), the number of cycles per second; For example, one might refer to the A above middle C as a′, A 4, or 440 Hz.
Scientific pitch, also known as philosophical pitch, Sauveur pitch or Verdi tuning, is an absolute concert pitch standard which is based on middle C (C 4) being set to 256 Hz rather than ~ 261.63 Hz, [a] making it ~ 31.77 cents lower than the common A440 pitch standard.
A440 (also known as Stuttgart pitch [1]) is the musical pitch corresponding to an audio frequency of 440 Hz, which serves as a tuning standard for the musical note of A above middle C, or A 4 in scientific pitch notation. It is standardized by the International Organization for Standardization as ISO 16.
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The quantity log 2 ( f / 440 Hz ) is the number of octaves above the 440 Hz concert A, or A 4, or a ′ . Multiplying it by 12 gives the number of semitones above 440 Hz (the value is negative if the frequency f is lower in pitch than 440 Hz).