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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).
The easiest intervals to identify and tune are those where the note frequencies have a simple whole-number ratio (e.g. octave with a 2:1 ratio, perfect fifth with 3:2, etc.) because the harmonics of these intervals coincide and beat when they are out of tune. (For a perfect fifth, the 3rd harmonic of the lower note coincides with the 2nd ...
The purpose of this adjustment is to move the 12 notes within a smaller range of frequency, namely within the interval between the base note D and the D above it (a note with twice its frequency). This interval is typically called the basic octave (on a piano keyboard, an octave has only 12 keys).
Notes in it include a prime symbol below the note's letter. Names of subsequent lower octaves are preceded with "sub". Notes in each include an additional prime symbol below the note's letter. The octave starting at middle C is called the "small" octave. Notes in it are written as lower case letters, so middle C itself is written c in Helmholtz ...
MIDI note number Other names Audio C −1: C͵͵͵ or ͵͵͵C or CCCC: Octocontra: 8.176 Hz 0: Quadruple Low C (64 ft. organ pipes) C 0: C͵͵ or ͵͵C or CCC: Subcontra: 16.352 Hz 12: Triple Low C (32 ft. organ pipes), Octobass C: C 1: C͵ or ͵C or CC: Contra: 32.703 Hz 24
For standard A440 pitch equal temperament, the system begins at a frequency of 16.35160 Hz, which is assigned the value C 0. The octave 0 of the scientific pitch notation is traditionally called the sub-contra octave , and the tone marked C 0 in SPN is written as ,,C or C,, or CCC in traditional systems, such as Helmholtz notation .
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.
The lower note is a constant A (440 Hz in either scale), the upper note is a C ♯ in the equal-tempered scale for the first 1", and a C ♯ in the just intonation scale for the last 1". Phase differences make it easier to detect the transition than in the previous sample.