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 In music theory, an interval is a difference in pitch (music), pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and v ...

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

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 versi ...

s 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

semitone A semitone, also called a minor second, 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 ...

s, while the

diminished fifth Diminished may refer to: *Diminution In Western culture, 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 embel ...

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 Minor may refer to: Common meanings * Minor (law), a person not under the age of certain legal activities. * Academic minor, a secondary field of study in undergraduate education Mathematics * Minor (graph theory), a relation of one graph to an ...

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 (proof theory) * Extension (predicate logic), the set of tuples of values t ...

. 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 * ''Inversion'' (artwork), a 2005 temporary sculpture in Houston, Texas * Inversion (music), a term with various meanings in music theory and musical set theory * ''Inversions'' (novel) by Iain M. Bank ...

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 "Twinkle, Twinkle, Little Star" is an 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 Nursery'', a c ...

"; 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 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, unple ...

. 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 determined by choosing a sequence of fifthsBruce Benward and Marilyn Nadine Saker (2003). ''Music: In Theory and Practice'', seventh editi ...

, one of the twelve fifths (the

wolf fifth In music theory, the wolf fifth (sometimes also called Procrustean fifth, or imperfect fifth) is a particularly dissonant musical interval spanning seven semitones. Strictly, the term refers to an interval produced by a specific tuning syst ...

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

enharmonic In music, two written notes have enharmonic equivalence if they produce the same pitch but are notated differently. Similarly, written intervals, chords, or key signatures are considered enharmonic if they represent identical pitches that ar ...

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 In music theory, 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'' because it ...

(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 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 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 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 Key, Keys, The Key or The Keys may refer to: Common uses * Key (cryptography), a piece of information needed to encode or decode a message * Key (instrument), a component of a musical instrument * Key (lock), a device used to operate a lock * ...

. 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 music, there are two common meanings for tuning: * #Tuning practice, Tuning practice, the act of tuning an instrument or voice. * #Tuning systems, Tuning systems, the various systems of Pitch (music), pitches used to tune an instrument, and ...

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

triad Triad or triade may refer to: * a group of three Humanities * Trichotomy (philosophy), often called triads * Triad (sociology), a group of three people as a unit of study * Triad (relationship), or ''ménage à trois'' Music * Triad (music ...

s, 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 sounds. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness, unple ...

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 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 Igor Fyodorovich Stravinsky ( – 6 April 1971) was a Russian composer and conductor with French citizenship (from 1934) and American citizenship (from 1945). He is widely considered one of the most important and influential composers of ...

'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 The piccolo trumpet is the smallest member of the trumpet family, pitched one octave higher than the standard B trumpet. Most piccolo trumpets are built to play in either B or A, using a separate leadpipe for each key. The tubing in the B picco ...

, and one

horn Horn may refer to: Common uses * Horn (acoustic), a tapered sound guide ** Horn antenna ** Horn loudspeaker ** Vehicle horn ** Train horn *Horn (anatomy), a pointed, bony projection on the head of various animals * Horn (instrument), a family ...

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 introd ...

'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 ''Messe de Nostre Dame'' (''Mass of Our Lady'') is a polyphonic mass composed before 1365 by French poet and composer Guillaume de Machaut (c. 1300–1377). Widely regarded as one of the masterpieces of medieval music and of all religious music, ...

'', 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 A Requiem (Latin: ''rest'') or Requiem Mass, also known as Mass for the dead () or Mass of the dead (), is a Mass of the Catholic Church offered for the repose of the souls of the deceased, using a particular form of the Roman Missal. It is ...

'', and the first movement of

Bruckner Joseph Anton Bruckner (; ; 4 September 182411 October 1896) was an Austrian composer and organist best known for his symphonies and sacred music, which includes Masses, Te Deum and motets. The symphonies are considered emblematic of the final ...

'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 Punk rock (also known as simply punk) is a rock music genre that emerged in the mid-1970s. Rooted in 1950s rock and roll and 1960s garage rock, punk bands rejected the corporate nature of mainstream 1970s rock music. They typically produced sh ...

, 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 Andean music is a group of styles of music from the Andes region in South America. Original chants and melodies come from the general area inhabited by Quechua people, Quechuas (originally from Peru, Bolivia, Ecuador, Chile), Aymara people, Aymar ...

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 and Bolivia 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 technique to ...

''. The same melody is being led by

parallel fifths In music, consecutive fifths or parallel fifths are progressions in which the interval of a perfect fifth is followed by a ''different'' perfect fifth between the same two musical parts (or voices): for example, from C to D in one part alon ...

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

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

cadence In Classical music, Western musical theory, a cadence () is the end of a Phrase (music), phrase in which the melody or harmony creates a sense of full or partial resolution (music), resolution, especially in music of the 16th century onwards.Don ...

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 temperaments are musical temperaments; that is, a variety of tuning systems constructed, similarly to Pythagorean tuning, as a sequence of equal fifths, both rising and descending, scaled to remain within the same octave. But rather tha ...

tuning. The

circle of fifths In music theory, the circle of fifths (sometimes also cycle of fifths) is a way of organizing pitches as a sequence of perfect fifths. Starting on a C, and using the standard system of tuning for Western music (12-tone equal temperament), the se ...

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 farther apart. Depe ...

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

Alternative definitions

Other qualities

Pitch ratio

Use in harmony

Bare fifth, open fifth, or empty fifth

Use in tuning and tonal systems

See also

References