In music theory, 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 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. 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 f ...

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 wi ...

, 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. 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 su ...

of all major and minor 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 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 octave), 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, 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 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 octave, 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. 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 adj ...

(or augmented fourth), and the minor sixth, 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 regu ...

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 keybo ...

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 o ...

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

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 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 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 ' ...

. This harmony also appears in Stravinsky's ''

The Rite of Spring , image = Roerich Rite of Spring.jpg , image_size = 350px , caption = Concept design for act 1, part of Nicholas Roerich's designs for Diaghilev's 1913 production of ' , composer = Igor Stravinsky , based_on ...

'' 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 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 intro ...

's '' Viderunt omnes'' and ''Sederunt Principes'', Guillaume de Machaut'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 f ...

in Mozart's '' Requiem'', 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-Germa ...

's '' Ninth Symphony'' are all examples of pieces ending on an open fifth. These chords are common in Medieval music,

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,

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 gu ...

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 ...

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 ...

, e.g., in Asian music and in some Andean music genres of pre-Columbian origin, such as '' k'antu'' 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'', 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 (199 ...

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 octave, forms the basis of Pythagorean tuning. 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 of ...

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 th ...

(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