Circle of fifths

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In music theory, the circle of fifths (sometimes also cycle of fifths) organizes the twelve pitch classes of the chromatic scale in a cycle of ascending perfect fifths. Since the cycle ascends in the opposite direction by perfect fourths, it is sometimes also called the circle of fourths. Starting on a C, the sequence is: C, G, D, A, E, B/C♭, F♯/G♭, C♯/D♭, A♭, E♭, B♭, F, and C. This order places the most closely related key signatures adjacent to one another. Ascending by twelve justly tuned perfect fifths with a frequency ratio of 3:2 does not return exactly to the starting pitch class, but instead overshoots it by a small interval known as the Pythagorean comma. This leads to tuning issues when transposing or modulating, and tuning systems were developed to address these issues. By changing (tempering) the 3:2 ratio, these systems produce a sequence of perfect fifths that returns to the starting pitch class. Such tuning systems include historical well temperaments, and 12-tone equal temperament...

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