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In music theory, the circle of fifths (sometimes also cycle of fifths) is a way of organizing pitches as a sequence of perfect fifths. Starting on a C, and using the standard system of tuning for Western music (12-tone equal temperament), the sequence is: C, G, D, A, E, B, F ♯ /G ♭, C ♯ /D ♭, G ♯ /A ♭, D ♯ /E ♭, A ♯ /B ♭, F ...
The circle of fifths in 12-tone equal temperament drawn within the chromatic circle as a star dodecagon [1] For any positive integer N, one can represent all of the equal-tempered pitch classes of N-tone equal temperament by the cyclic group of order N, or equivalently, the residue classes modulo twelve, Z/NZ.
Twelve-tone equal temperament (12 TET) is obtained by making all semitones the same size, with each equal to one-twelfth of an octave; i.e. with ratios 12 √ 2 : 1. Relative to Pythagorean tuning , it narrows the perfect fifths by about 2 cents or 1 / 12 th of a Pythagorean comma to give a frequency ratio of 2 7 / 12 : 1 {\displaystyle ...
This phenomenon gives rise to infinite shades of key-colors, which are lost in the modern standard version: 12-tone equal temperament (12-TET). Unlike meantone temperament, which alters the fifth to "temper out" the syntonic comma, 12-TET tempers out the Pythagorean comma, thus creating a cycle of fifths that repeats itself exactly after 12 steps.
12-tone Pythagorean temperament is based on a sequence of perfect fifths, each tuned in the ratio 3:2, the next simplest ratio after 2:1 (the octave). Starting from D for example (D-based tuning), six other notes are produced by moving six times a ratio 3:2 up, and the remaining ones by moving the same ratio down:
This is a list of the fundamental frequencies in hertz (cycles per second) of the keys of a modern 88-key standard or 108-key extended piano in twelve-tone equal temperament, with the 49th key, the fifth A (called A 4), tuned to 440 Hz (referred to as A440). [1] [2] Every octave is made of twelve steps called semitones.
In order to close the circle of fifths in 12 note scales, twelve fifths must average out to 700 cents [b] Each of the first eleven fifths (starting with the fifth below the tonic, the subdominant: F in the key of C, when each black key is tuned to a meantone sharp / no flats) has a value of 700 − ε cents, where ε is some small number of ...
By definition, in quarter-comma meantone 1 so-called "perfect" fifth (P5 in the table) has a size of approximately 696.6 cents ( 700 − ε cents, where ε ≈ 3.422 cents); since the average size of the 12 fifths must equal exactly 700 cents (as in equal temperament), the other one must have a size of 700 + 11 ε cents, which is about 737.6 ...