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.

Structure and use[edit]

Diatonic key signatures[edit]

Each of the twelve pitches can serve as the tonic of a major or minor key, and each of these keys will have a diatonic scale associated with it. The circle diagram shows the number of sharps or flats in each key signature, with the major key indicated by a capital letter and the minor key indicated by a lower-case letter. Major and minor keys that have the same key signature are referred to as relative major and relative minor of one another.

Modulation and chord progression[edit]

Tonal music often modulates to a new tonal center whose key signature differs from the original by only one flat or sharp. These closely-related keys are a fifth apart from each other and are therefore adjacent in the circle of fifths. Chord progressions also often move between chords whose roots are related by perfect fifth, making the circle of fifths useful in illustrating the "harmonic distance" between chords.

The circle of fifths is used to organize and describe the harmonic or tonal function of chords.^[2] Chords can progress in a pattern of ascending perfect fourths (alternately viewed as descending perfect fifths) in "functional succession". This can be shown "...by the circle of fifths (in which, therefore, scale degree II is closer to the dominant than scale degree IV)".^[3] In this view the tonic or tonal center is considered the end point of a chord progression derived from the circle of fifths.

"Fly Me to the Moon"

Bart Howard

Approach chord

Sonata form

Well temperament

Circle of fifths text table

Pitch constellation

Multiplicative group of integers modulo n

Multiplication (music)

Circle of thirds

Barnett, Gregory (2002). "Tonal Organization in Seventeenth-century Music Theory.". In Thomas Christensen (ed.). The Cambridge History of Western Music Theory. Cambridge: Cambridge University Press. pp. 407–455.

(2012). The Jazz Standards: A Guide to the Repertoire. Oxford University Press. ISBN 9780199769155.

Gioia, Ted

(1965). Harmony in Western Music. New York: W. W. Norton.

Goldman, Richard Franko

Jensen, Claudia R. (Summer 1992). "A Theoretical Work of Late Seventeenth-Century Muscovy: Nikolai Diletskii's "Grammatika" and the Earliest Circle of Fifths". . 45 (2): 305–331. doi:10.2307/831450. JSTOR 831450.

Journal of the American Musicological Society

Lester, Joel (1989). Between Modes and Keys: German theory 1592–1802. Stuyvesant: Pendragon Press.

McCartin, Brian J. (November 1998). . The College Mathematics Journal. 29 (5): 354–370. doi:10.1080/07468342.1998.11973971. JSTOR 2687250. Archived from the original on 2008-05-17. Retrieved 2008-07-29.

"Prelude to Musical Geometry"

(1990). Music and Discourse: Toward a Semiology of Music, translated by Carolyn Abbate. Princeton, New Jersey: Princeton University Press. ISBN 0-691-02714-5. (Originally published in French, as Musicologie générale et sémiologie. Paris: C. Bourgois, 1987. ISBN 2-267-00500-X).

Nattiez, Jean-Jacques

(2010). The Oxford History of Western Music: Music in the Seventeenth and Eighteenth Centuries. Oxford University Press.

Taruskin, Richard

(1903). Cours de composition musicale. Paris: A. Durand et fils.

D'Indy, Vincent

Lester, Joel. . 1990.

Between Modes and Keys: German Theory, 1592–1802

Miller, Michael. . [Indianapolis, IN]: Alpha, 2005. ISBN 1-59257-437-8.

The Complete Idiot's Guide to Music Theory, 2nd ed

Purwins, Hendrik (2005)."". Ph.D. thesis. Berlin: Technische Universität Berlin.

Profiles of Pitch Classes: Circularity of Relative Pitch and Key—Experiments, Models, Computational Music Analysis, and Perspectives

Purwins, Hendrik, Benjamin Blankertz, and Klaus Obermayer (2007). "". in: Computing in Musicology 15 ("Tonal Theory for the Digital Age"): 73–98.