music theory Music theory is the study of the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory". The first is the "rudiments", that are needed to understand music notation (ke ...

, 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 distinct from Western folk music or popular music traditions. It is sometimes distinguished as Western classical music, as the term "classical music" also ...

from

Western culture Leonardo da Vinci's ''Vitruvian Man''. Based on the correlations of ideal Body proportions">human proportions with geometry described by the ancient Roman architect Vitruvius in Book III of his treatise ''De architectura''. image:Plato Pio-Cle ...

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

note Note, notes, or NOTE may refer to: Music and entertainment * Musical note, a pitched sound (or a symbol for a sound) in music * ''Notes'' (album), a 1987 album by Paul Bley and Paul Motian * ''Notes'', a common (yet unofficial) shortened version ...

s in a

diatonic scale In music theory, a diatonic scale is any heptatonic 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 either two or three whole steps, ...

. The perfect fifth (often abbreviated P5) spans seven

semitone A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent no ...

s, while the

diminished fifth Diminished may refer to: *Diminution In Western music and music theory, diminution (from Medieval Latin ''diminutio'', alteration of Latin ''deminutio'', decrease) has four distinct meanings. Diminution may be a form of embellishment in which ...

spans six and the

augmented fifth In classical music from Western culture, 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 ...

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. Examples are and pronounced with the lips; and pronounced with the front of the tongue; and pronounced wit ...

, or stable, than any other interval except the

unison In music, unison is two or more musical parts that sound either the same pitch or pitches separated by intervals of one or more octaves, usually at the same time. ''Rhythmic unison'' is another term for homorhythm. Definition Unison or per ...

and the

octave In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...

. It occurs above the

root In vascular plants, the roots are the 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 below the sur ...

of all

major Major (commandant in certain jurisdictions) is a military rank of commissioned officer status, with corresponding ranks existing in many military forces throughout the world. When used unhyphenated and in conjunction with no other indicators ...

and

minor Minor may refer to: * Minor (law), a person under the age of certain legal activities. ** A person who has not reached the age of majority * Academic minor, a secondary field of study in undergraduate education Music theory *Minor chord ** Barb ...

chords (triads) and their

extensions Extension, extend or extended may refer to: Mathematics Logic or set theory * Axiom of extensionality * Extensible cardinal * Extension (model theory) * Extension (predicate logic), the set of tuples of values that satisfy the predicate * E ...

. Until the late 19th century, it was often referred to by one of its Greek names, ''diapente''. Its

inversion Inversion or inversions may refer to: Arts * , a French gay magazine (1924/1925) * ''Inversion'' (artwork), a 2005 temporary sculpture in Houston, Texas * Inversion (music), a term with various meanings in music theory and musical set theory * ...

is the

perfect fourth A fourth is a 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 interval from C to ...

. The octave of the fifth is the twelfth. A perfect fifth is at the start of "

Twinkle, Twinkle, Little Star "Twinkle, Twinkle, Little Star" is a popular English lullaby. The lyrics are from an early-19th-century English poem written by Jane Taylor, "The Star". The poem, which is in couplet form, was first published in 1806 in '' Rhymes for the Nurser ...

"; the pitch of the first "twinkle" is the root note and 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 In music, consonance and dissonance are categorizations of simultaneous or successive sounds. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness, unpl ...

. When an instrument with only twelve notes to an octave (such as the piano) is tuned using

Pythagorean tuning Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2.Bruce Benward and Marilyn Nadine Saker (2003). ''Music: In Theory and Practice'', seventh edition, 2 vols. (Boston: Mc ...

, one of the twelve fifths (the

wolf fifth In music theory, the wolf fifth (sometimes also called Procrustean fifth, or imperfect fifth) Paul, Oscar (1885). A manual of harmony for use in music-schools and seminaries and for self-instruction', p.165. Theodore Baker, trans. G. Schirmer. ...

) sounds severely discordant and can hardly be qualified as "perfect", if this term is interpreted as "highly consonant". However, when using correct

enharmonic In modern musical notation and tuning, an enharmonic equivalent is a note, interval, or key signature that is equivalent to some other note, interval, or key signature but "spelled", or named differently. The enharmonic spelling of a written n ...

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 produced by narrowing a minor sixth by a chromatic semitone.Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.54. . Specific example of an d6 not ...

(for instance G–E). Perfect intervals are also defined as those natural intervals whose inversions are also perfect, 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 Just or JUST may refer to: __NOTOC__ People * Just (surname) * Just (given name) Arts and entertainment * ''Just'', a 1998 album by Dave Lindholm * "Just" (song), a song by Radiohead * "Just", a song from the album ''Lost and Found'' by Mudvayne ...

'', 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 tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, wh ...

. 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 In music from Western culture, a sixth is a musical interval encompassing six note letter names or staff positions (see Interval number for more details), and the major sixth is one of two commonly occurring sixths. It is qualified as ''major ...

(5:3).

Other qualities

In addition to perfect, there are two other kinds, or qualities, of fifths: the

, which is one

chromatic semitone In modern Western tonal music theory an augmented unison or augmented prime is the interval between two notes on the same staff position, or denoted by the same note letter, whose alterations cause them, in ordinary equal temperament, to be one ...

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 musical interval composed of three adjacent 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 decomposed into the three a ...

(or augmented fourth), and the

minor sixth In Western classical music, 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 ''mi ...

, respectively.

Pitch ratio

The justly tuned pitch ratio of a perfect fifth is 3:2 (also known, in early music theory, as a ''

hemiola In music, hemiola (also hemiolia) is the ratio 3:2. The equivalent Latin term is sesquialtera. In rhythm, ''hemiola'' refers to three beats of equal value in the time normally occupied by two beats. In pitch, ''hemiola'' refers to the interval of ...

''), 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 known as a ''fiddle'', is a wooden chordophone (string instrument) in the violin family. Most violins have a hollow wooden body. It is the smallest and thus highest-pitched instrument (soprano) in the family in regular ...

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 The piano is a stringed keyboard instrument in which the strings are struck by wooden hammers that are coated with a softer material (modern hammers are covered with dense wool felt; some early pianos used leather). It is played using a keyboa ...

normally use an

equal-tempered An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, w ...

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 o ...

explored

musical tuning In music, there are two common meanings for tuning: * Tuning practice, the act of tuning an instrument or voice. * Tuning systems, the various systems of pitches used to tune an instrument, and their theoretical bases. Tuning practice Tun ...

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) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability. The Helmholtz Association, ...

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

. 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 An overtone is any resonant frequency above the fundamental frequency of a sound. (An overtone may or may not be a harmonic) In other words, overtones are all pitches higher than the lowest pitch within an individual sound; the fundamental i ...

, it is not unusual to omit the fifth of a chord (especially in root position). The perfect fifth is also present in

seventh chords A seventh chord is a chord consisting of a triad plus a note forming an interval of a seventh above the chord's root. When not otherwise specified, a "seventh chord" usually means a dominant seventh chord: a major triad together with a minor ...

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 In music, consonance and dissonance are categorizations of simultaneous or successive Sound, sounds. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness ...

intervals of these chords, as in the

major seventh chord In music, a major seventh chord is a seventh chord in which the third is a major third above the root and the seventh is a major seventh above the root. The major seventh chord, sometimes also called a ''Delta chord'', can be written as maj7, M7, , ...

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 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 advocate of the ''Ne ...

. This harmony also appears in

Stravinsky Igor Fyodorovich Stravinsky (6 April 1971) was a Russian composer, pianist and conductor, later of French (from 1934) and American (from 1945) citizenship. He is widely considered one of the most important and influential 20th-century clas ...

's ''

The Rite of Spring ''The Rite of Spring''. Full name: ''The Rite of Spring: Pictures from Pagan Russia in Two Parts'' (french: Le Sacre du printemps: tableaux de la Russie païenne en deux parties) (french: Le Sacre du printemps, link=no) is a ballet and orchestral ...

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

trumpet The trumpet is a brass instrument commonly used in classical and jazz ensembles. The trumpet group ranges from the piccolo trumpet—with the highest register in the brass family—to the bass trumpet, pitched one octave below the standard ...

s, a piccolo trumpet, and one

horn Horn most often refers to: *Horn (acoustic), a conical or bell shaped aperture used to guide sound ** Horn (instrument), collective name for tube-shaped wind musical instruments *Horn (anatomy), a pointed, bony projection on the head of various ...

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 Pérotin () was a composer associated with the Notre Dame school of polyphony in Paris and the broader musical style of high medieval music. He is credited with developing the polyphonic practices of his predecessor Léonin, with the introdu ...

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

Mozart Wolfgang Amadeus Mozart (27 January 17565 December 1791), baptised as Joannes Chrysostomus Wolfgangus Theophilus Mozart, was a prolific and influential composer of the Classical period (music), Classical period. Despite his short life, his ra ...

's ''

Requiem A Requiem or Requiem Mass, also known as Mass for the dead ( la, Missa pro defunctis) or Mass of the dead ( la, Missa defunctorum), is a Mass of the Catholic Church offered for the repose of the soul or souls of one or more deceased persons, ...

'', and the first movement of

Bruckner Josef Anton Bruckner (; 4 September 182411 October 1896) was an Austrian composer, organist, and music theorist best known for his symphonies, masses, Te Deum and motets. The first are considered emblematic of the final stage of Austro-Germ ...

'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 and secular music of Western Europe during the Middle Ages, from approximately the 6th to 15th centuries. It is the first and longest major era of Western classical music and followed by the Renaissance ...

sacred harp Sacred Harp singing is a tradition of sacred choral music that originated in New England and was later perpetuated and carried on in the American South. The name is derived from ''The Sacred Harp'', a ubiquitous and historically important tune ...

singing, and throughout

rock music Rock music is a broad genre of popular music that originated as " rock and roll" in the United States in the late 1940s and early 1950s, developing into a range of different styles in the mid-1960s and later, particularly in the United States an ...

. In

hard rock Hard rock or heavy rock is a loosely defined subgenre of rock music typified by aggressive vocals and distorted electric guitars. Hard rock began in the mid-1960s with the garage, psychedelic and blues rock movements. Some of the earliest hard ...

metal A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typicall ...

, and punk music, overdriven or distorted

electric guitar An electric guitar is a guitar that requires external amplification in order to be heard at typical performance volumes, unlike a standard acoustic guitar (however combinations of the two - a semi-acoustic guitar and an electric acoustic gui ...

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 fifth chord) is a colloquial name for a chord in guitar music, especially electric guitar, that consists of the root note and the fifth, as well as possibly octaves of those notes. Power chords are commonly played on am ...

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 Kantu or k'antu is an ancient style of music and circle dance which is widespread since incaic or even preincaic epoch on the Peruvian and Bolivian highlands. Modern versions of this style still use the Quechua or Aymara language and the siku ...

'' and ''

sikuri Sikuri is a musical style from Peru the kind of huayño, consisting of siku players and drum accompaniment. There are usually around twenty siku players. As each siku cannot play all the notes of a scale, the siku players use an interlocking tec ...

''. 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 New Line Theatre in St. Louis, Missouri, is an alternative musical theatre company producing challenging, adult, politically and socially relevant works of musical theatre. The company was created in 1991 and produces world premieres such as ''Lo ...

'', accessed December 28, 2012 Empty fifths are also sometimes used to give a

cadence In Western musical theory, a cadence (Latin ''cadentia'', "a falling") is the end of a phrase in which the melody or harmony creates a sense of full or partial resolution, especially in music of the 16th century onwards.Don Michael Randel (1999) ...

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

. A slightly narrowed perfect fifth is likewise the basis for

meantone Meantone temperament is a musical temperament, that is a tuning system, obtained by narrowing the fifths so that their ratio is slightly less than 3:2 (making them ''narrower'' than a perfect fifth), in order to push the thirds closer to pure. Me ...

tuning. The

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 ...

is a model of

pitch space In music theory, pitch spaces model relationships between pitches. These models typically use distance to model the degree of relatedness, with closely related pitches placed near one another, and less closely related pitches placed farther apa ...

for the

chromatic scale The chromatic scale (or twelve-tone scale) is a set of twelve pitches (more completely, pitch classes) used in tonal music, with notes separated by the interval of a semitone. Chromatic instruments, such as the piano, are made to produce the ...

(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