music theory Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory": The first is the "Elements of music, ...

, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so. In

classical music Classical music generally refers to the art music of the Western world, considered to be #Relationship to other music traditions, distinct from Western folk music or popular music traditions. It is sometimes distinguished as Western classical mu ...

from

Western culture Western culture, also known as Western civilization, European civilization, Occidental culture, Western society, or simply the West, refers to the Cultural heritage, internally diverse culture of the Western world. The term "Western" encompas ...

, a fifth is the interval from the first to the last of the first five consecutive notes in a

diatonic scale In music theory a diatonic scale is a heptatonic scale, heptatonic (seven-note) scale that includes five whole steps (whole tones) and two half steps (semitones) in each octave, in which the two half steps are separated from each other by eith ...

. The perfect fifth (often abbreviated P5) spans seven semitones, while the diminished fifth spans six and the

augmented fifth In Western classical music, an augmented fifth () is an interval produced by widening a perfect fifth by a chromatic semitone.Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.54. . For instance, the interval from C to G i ...

spans eight semitones. For example, the interval from C to G is a perfect fifth, as the note G lies seven semitones above C. The perfect fifth may be derived from the harmonic series as the interval between the second and third harmonics. In a diatonic scale, the dominant note is a perfect fifth above the tonic note. The perfect fifth is more

consonant In articulatory phonetics, a consonant is a speech sound that is articulated with complete or partial closure of the vocal tract, except for the h sound, which is pronounced without any stricture in the vocal tract. Examples are and pronou ...

, or stable, than any other interval except the

unison Unison (stylised as UNISON) is a Great Britain, British trade union. Along with Unite the Union, Unite, Unison is one of the two largest trade unions in the United Kingdom, with over 1.2 million members who work predominantly in public servic ...

and the

octave In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referr ...

. It occurs above the

root In vascular plants, the roots are the plant organ, organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often bel ...

of all

major Major most commonly refers to: * Major (rank), a military rank * Academic major, an academic discipline to which an undergraduate student formally commits * People named Major, including given names, surnames, nicknames * Major and minor in musi ...

and minor chords (triads) and their extensions. Until the late 19th century, it was often referred to by one of its Greek names, ''diapente''. Its inversion is the

perfect fourth A fourth is a interval (music), musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth () is the fourth spanning five semitones (half steps, or half tones). For example, the ascending int ...

. The octave of the fifth is the twelfth. A perfect fifth is at the start of " Twinkle, Twinkle, Little Star"; the pitch of the first "twinkle" is the root note and the pitch of the second "twinkle" is a perfect fifth above it.

Alternative definitions

The term ''perfect'' identifies the perfect fifth as belonging to the group of ''perfect intervals'' (including the

, and

), so called because of their simple pitch relationships and their high degree of consonance. When an instrument with only twelve notes to an octave (such as the piano) is tuned using Pythagorean tuning, one of the twelve fifths (the wolf fifth) sounds severely discordant and can hardly be qualified as "perfect", if this term is interpreted as "highly consonant". However, when using correct enharmonic spelling, the wolf fifth in Pythagorean tuning or meantone temperament is actually not a perfect fifth but a

diminished sixth In classical music from Western culture, a diminished sixth () is an Interval (music), interval produced by Diminution, narrowing a minor sixth by a chromatic semitone.Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.54. . Sp ...

(for instance G–E). Perfect intervals are also defined as those natural intervals whose inversions are also natural, where natural, as opposed to altered, designates those intervals between a base note and another note in the major diatonic scale starting at that base note (for example, the intervals from C to C, D, E, F, G, A, B, C, with no sharps or flats); this definition leads to the perfect intervals being only the

, fourth, fifth, and

, without appealing to degrees of consonance. The term ''perfect'' has also been used as a synonym of '' just'', to distinguish intervals tuned to ratios of small integers from those that are "tempered" or "imperfect" in various other tuning systems, such as

equal temperament An equal temperament is a musical temperament or Musical tuning#Tuning systems, tuning system that approximates Just intonation, just intervals by dividing an octave (or other interval) into steps such that the ratio of the frequency, frequencie ...

. The perfect unison has a pitch ratio 1:1, the perfect octave 2:1, the perfect fourth 4:3, and the perfect fifth 3:2. Within this definition, other intervals may also be called perfect, for example a perfect third (5:4) or a perfect major sixth (5:3).

Other qualities

In addition to perfect, there are two other kinds, or qualities, of fifths: the diminished fifth, which is one chromatic semitone smaller, and the

, which is one chromatic semitone larger. In terms of semitones, these are equivalent to the

tritone In music theory, the tritone is defined as a interval (music), musical interval spanning three adjacent Major second, whole tones (six semitones). For instance, the interval from F up to the B above it (in short, F–B) is a tritone as it can be ...

(or augmented fourth), and the

minor sixth In music theory, a minor sixth is a musical interval encompassing six staff positions (see Interval number for more details), and is one of two commonly occurring sixths (the other one being the major sixth). It is qualified as ''minor'' bec ...

, respectively.

Pitch ratio

The justly tuned pitch ratio of a perfect fifth is 3:2 (also known, in early music theory, as a '' hemiola''), meaning that the upper note makes three vibrations in the same amount of time that the lower note makes two. The just perfect fifth can be heard when a

violin The violin, sometimes referred to as a fiddle, is a wooden chordophone, and is the smallest, and thus highest-pitched instrument (soprano) in regular use in the violin family. Smaller violin-type instruments exist, including the violino picc ...

is tuned: if adjacent strings are adjusted to the exact ratio of 3:2, the result is a smooth and consonant sound, and the violin sounds in tune. Keyboard instruments such as the

piano A piano is a keyboard instrument that produces sound when its keys are depressed, activating an Action (music), action mechanism where hammers strike String (music), strings. Modern pianos have a row of 88 black and white keys, tuned to a c ...

normally use an equal-tempered version of the perfect fifth, enabling the instrument to play in all keys. In 12-tone equal temperament, the frequencies of the tempered perfect fifth are in the ratio

(\sqrt 2^7

or approximately 1.498307. An equally tempered perfect fifth, defined as 700 cents, is about two cents narrower than a just perfect fifth, which is approximately 701.955 cents.

Kepler Johannes Kepler (27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws of p ...

explored musical tuning in terms of integer ratios, and defined a "lower imperfect fifth" as a 40:27 pitch ratio, and a "greater imperfect fifth" as a 243:160 pitch ratio. His lower perfect fifth ratio of 1.48148 (680 cents) is much more "imperfect" than the equal temperament tuning (700 cents) of 1.4983 (relative to the ideal 1.50).

Hermann von Helmholtz Hermann Ludwig Ferdinand von Helmholtz (; ; 31 August 1821 – 8 September 1894; "von" since 1883) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability. The ...

uses the ratio 301:200 (708 cents) as an example of an imperfect fifth; he contrasts the ratio of a fifth in equal temperament (700 cents) with a "perfect fifth" (3:2), and discusses the audibility of the beats that result from such an "imperfect" tuning.

Use in harmony

W. E. Heathcote describes the octave as representing the prime unity within the triad, a higher unity produced from the successive process: "first Octave, then Fifth, then Third, which is the union of the two former". Hermann von Helmholtz argues that some intervals, namely the perfect fourth, fifth, and octave, "are found in all the musical scales known", though the editor of the English translation of his book notes the fourth and fifth may be interchangeable or indeterminate. The perfect fifth is a basic element in the construction of major and minor triads, and their extensions. Because these chords occur frequently in much music, the perfect fifth occurs just as often. However, since many instruments contain a perfect fifth as an overtone, it is not unusual to omit the fifth of a chord (especially in root position). The perfect fifth is also present in seventh chords as well as "tall tertian" harmonies (harmonies consisting of more than four tones stacked in thirds above the root). The presence of a perfect fifth can in fact soften the dissonant intervals of these chords, as in the major seventh chord in which the dissonance of a major seventh is softened by the presence of two perfect fifths. Chords can also be built by stacking fifths, yielding quintal harmonies. Such harmonies are present in more modern music, such as the music of

Paul Hindemith Paul Hindemith ( ; ; 16 November 189528 December 1963) was a German and American composer, music theorist, teacher, violist and conductor. He founded the Amar Quartet in 1921, touring extensively in Europe. As a composer, he became a major advo ...

. This harmony also appears in Stravinsky's ''

The Rite of Spring ''The Rite of Spring'' () is a ballet and orchestral concert work by the Russian composer Igor Stravinsky. It was written for the 1913 Paris season of Sergei Diaghilev's Ballets Russes company; the original choreography was by Vaslav Nijinsky ...

'' in the "Dance of the Adolescents" where four C

trumpet The trumpet is a brass instrument commonly used in classical and jazz musical ensemble, ensembles. The trumpet group ranges from the piccolo trumpet—with the highest Register (music), register in the brass family—to the bass trumpet, pitche ...

s, a piccolo trumpet, and one horn play a five-tone B-flat quintal chord.

Bare fifth, open fifth, or empty fifth

A bare fifth, open fifth or empty fifth is a chord containing only a perfect fifth with no third. The closing chords of Pérotin's '' Viderunt omnes'' and ''Sederunt Principes'',

Guillaume de Machaut Guillaume de Machaut (, ; also Machau and Machault; – April 1377) was a French composer and poet who was the central figure of the style in late medieval music. His dominance of the genre is such that modern musicologists use his death to ...

's '' Messe de Nostre Dame'', the

Kyrie ', a transliteration of Greek , vocative case of ('' Kyrios''), is a common name of an important prayer of Christian liturgy, also called the ( ; ). In the Bible The prayer, , "Lord, have mercy" derives from a Biblical phrase. Greek , ...

Mozart Wolfgang Amadeus Mozart (27 January 1756 – 5 December 1791) was a prolific and influential composer of the Classical period (music), Classical period. Despite his short life, his rapid pace of composition and proficiency from an early age ...

's '' Requiem'', and the first movement of Bruckner's '' Ninth Symphony'' are all examples of pieces ending on an open fifth. These chords are common in

Medieval music Medieval music encompasses the sacred music, sacred and secular music of Western Europe during the Middle Ages, from approximately the 6th to 15th centuries. It is the Dates of classical music eras, first and longest major era of Western class ...

sacred harp Sacred Harp singing is a tradition of sacred choral music which developed in New England and perpetuated in the American South. The name is derived from ''The Sacred Harp'', a historically important shape notes, shape-note tunebook printed in ...

singing, and throughout

rock music Rock is a Music genre, genre of popular music that originated in the United States as "rock and roll" in the late 1940s and early 1950s, developing into a range of styles from the mid-1960s, primarily in the United States and the United Kingdo ...

. In

hard rock Hard rock or heavy rock is a heavier subgenre of rock music typified by aggressive vocals and Distortion (music), distorted electric guitars. Hard rock began in the mid-1960s with the Garage rock, garage, Psychedelic rock, psychedelic and blues ...

metal A metal () is a material that, when polished or fractured, shows a lustrous appearance, and conducts electrical resistivity and conductivity, electricity and thermal conductivity, heat relatively well. These properties are all associated wit ...

, and punk music, overdriven or distorted

electric guitar An electric guitar is a guitar that requires external electric Guitar amplifier, sound amplification in order to be heard at typical performance volumes, unlike a standard acoustic guitar. It uses one or more pickup (music technology), pickups ...

can make thirds sound muddy while the bare fifths remain crisp. In addition, fast chord-based passages are made easier to play by combining the four most common guitar hand shapes into one. Rock musicians refer to them as ''

power chord A power chord , also called a fifth chord, is a colloquial name for a chord on guitar, especially on electric guitar, that consists of the root note and the fifth, as well as possibly octaves of those notes. Power chords are commonly pla ...

s''. Power chords often include octave doubling (i.e., their bass note is doubled one octave higher, e.g. F3–C4–F4). An ''empty fifth'' is sometimes used in

traditional music Folk music is a music genre that includes traditional folk music and the contemporary genre that evolved from the former during the 20th-century folk revival. Some types of folk music may be called world music. Traditional folk music has b ...

, e.g., in Asian music and in some Andean music genres of pre-Columbian origin, such as '' k'antu'' and '' sikuri''. The same melody is being led by parallel fifths and octaves during all the piece. Western composers may use the interval to give a passage an exotic flavor.Scott Miller,
Inside ''The King and I''
, '' New Line Theatre'', accessed December 28, 2012 Empty fifths are also sometimes used to give a cadence an ambiguous quality, as the bare fifth does not indicate a major or minor tonality.

Use in tuning and tonal systems

The just perfect fifth, together with the

, forms the basis of Pythagorean tuning. A slightly narrowed perfect fifth is likewise the basis for meantone tuning. The circle of fifths is a model of pitch space for the chromatic scale (chromatic circle), which considers nearness as the number of perfect fifths required to get from one note to another, rather than chromatic adjacency.

References

{{DEFAULTSORT:Perfect Fifth Fifths (music) Perfect intervals 3-limit tuning and intervals