circle of fifths

circle of fifths, in music theory, visual representation of the organization of the 12 major and 12 minor musical keys and the relationships between them. The circle of fifths is so named because of its circular shape and because each key is a perfect fifth from the next. The circle includes two layers: the outer layer represents the major keys, and the inner layer represents the relative minor keys. The circle also identifies the key signature (the group of sharp or flat signs at the beginning of the staff) for each of the major and minor keys.

Organization

Starting at the top of the circle and moving clockwise, the major and relative minor keys are organized as follows:

• C major–A minor (no sharps or flats)
• G major–E minor (one sharp)
• D major–B minor (two sharps)
• A major–F♯ minor (three sharps)
• E major–C♯ minor (four sharps)
• B major/C♭ major–G♯ minor/A♭ minor (five sharps/seven flats)
• F♯ major/G♭ major–D♯ minor/E♭ minor (six sharps/six flats)
• C♯ major/D♭ major–A♯ minor/B♭ minor (seven sharps/five flats)
• A♭ major–F minor (four flats)
• E♭ major–C minor (three flats)
• B♭ major–G minor (two flats)
• F major–D minor (one flat)

History

The origin of the circle of fifths is often anachronistically credited to Pythagoras. In the 6th century bce Pythagoras discovered that changing the length of a string on an instrument could change the string’s pitch; he further found that dividing the length of a string in half forms an octave. However, there are no concrete records indicating that he developed the circle’s concept. In 1677 the first circle of fifths diagram appeared in Grammatika, a treatise on composition written by Kyiv-born composer and music theorist Nikolay Diletsky that was oriented toward teaching audiences how to write Western-style pieces. A revised version of the circle of fifths, and the one known today, was published in 1728 by German Baroque composer and music theorist Johann David Heinichen.

Significance

Identifying key signatures is one of the primary uses of the circle of fifths. Indeed, key signatures can be identified quickly, since the number of sharps increases with each step clockwise around the circle and the number of flats increases with each counterclockwise step. For example, a person who knows that G major has one sharp can easily determine that D major has two sharps. Likewise, a person who knows that F major has one flat can quickly determine that B♭ major has two flats. Key signatures help musicians understand which chords may be encountered while playing a song.

Additionally, the circle of fifths facilitates the development of smooth transitions when changing keys within a song. This is because the representation provides a quick reference for the selection of keys and closely related keys that produce desirable sounds. For example, if a piece is in the key of C major, a key change to G or F major would maintain musical continuity.

Progressions

The circle of fifths is also a valuable tool for understanding which sequences of chords work well together to create interesting chord progressions based on related keys. For example, a common chord progression used in many popular songs is I-IV-V (the root, the fourth, and the fifth of the key). In the key of C major the I-IV-V chord progression is C major, F major, and G major, and in the key of F major it is F major, B♭ major, and C major. Chord progressions based on the circle of fifths are used in a wide variety of music genres.