Circle of fifths

In music theory, the circle of fifths is a way of organizing the 12 chromatic pitches as a sequence of perfect fifths. (This is strictly true in the standard 12-tone equal temperament system — using a different system requires one interval of diminished sixth to be treated as a fifth). If C is chosen as a starting point, the sequence is: C, G, D, A, E, B (=C), F (=G), C (=D), A, E, B, F. Continuing the pattern from F returns the sequence to its starting point of C. This order places the most closely related key signatures adjacent to one another. It is usually illustrated in the form of a circle. The circle of fifths organizes pitches in a sequence of perfect fifths, generally shown as a circle with the pitches (and their corresponding keys) in a clockwise progression. Musicians and composers often use the circle of fifths to describe the musical relationships between pitches. Its design is helpful in composing and harmonizing melodies, building chords, and modulating to different keys within a composition. Using the system of just intonation, a perfect fifth consists of two pitches with a frequency ratio of 3:2, but generating twelve successive perfect fifths in this way does not result in a return to the pitch class of the starting note. To adjust for this, instruments are generally tuned with the equal temperament system. Twelve equal-temperament fifths lead to a note exactly seven octaves above the initial tone—this results in a perfect fifth that is equivalent to seven equal-temperament semitones. The top of the circle shows the key of C Major, with no sharps or flats. Proceeding clockwise, the pitches ascend by fifths. The key signatures associated with those pitches also change: the key of G has one sharp, the key of D has 2 sharps, and so on. Similarly, proceeding counterclockwise from the top of the circle, the notes change by descending fifths and the key signatures change accordingly: the key of F has one flat, the key of B has 2 flats, and so on. Some keys (at the bottom of the circle) can be notated either in sharps or in flats.